16
Polyvinyl chloride as a multimodal tissue-mimicking material with tuned mechanical and medical imaging properties Weisi Li School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning 110042, China and Mechanical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109 Barry Belmont, Joan M. Greve, Adam B. Manders, Brian C. Downey, Xi Zhang, and Zhen Xu Biomedical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109 Dongming Guo School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning 110042, China Albert Shih Mechanical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109 and Biomedical Engineering Department, University of Michigan, Ann Arbor, Michigan 48109 (Received 26 July 2015; revised 2 August 2016; accepted for publication 23 August 2016; published 22 September 2016) Purpose: The mechanical and imaging properties of polyvinyl chloride (PVC) can be adjusted to meet the needs of researchers as a tissue-mimicking material. For instance, the hardness can be adjusted by changing the ratio of softener to PVC polymer, mineral oil can be added for lubrication in needle insertion, and glass beads can be added to scatter acoustic energy similar to biological tissue. Through this research, the authors sought to develop a regression model to design formulations of PVC with targeted mechanical and multimodal medical imaging properties. Methods: The design of experiment was conducted by varying three factors—(1) the ratio of softener to PVC polymer, (2) the mass fraction of mineral oil, and (3) the mass fraction of glass beads—and measuring the mechanical properties (elastic modulus, hardness, viscoelastic relaxation time constant, and needle insertion friction force) and the medical imaging properties [speed of sound, acoustic attenuation coecient, magnetic resonance imaging time constants T 1 and T 2 , and the transmittance of the visible light at wavelengths of 695 nm ( T λ695 ) and 532 nm ( T λ532 )] on twelve soft PVC samples. A regression model was built to describe the relationship between the mechanical and medical imaging properties and the values of the three composition factors of PVC. The model was validated by testing the properties of a PVC sample with a formulation distinct from the twelve samples. Results: The tested soft PVC had elastic moduli from 6 to 45 kPa, hardnesses from 5 to 50 Shore OOO-S, viscoelastic stress relaxation time constants from 114.1 to 191.9 s, friction forces of 18 gauge needle insertion from 0.005 to 0.086 N/mm, speeds of sound from 1393 to 1407 m/s, acoustic attenuation coecients from 0.38 to 0.61 (dB/cm)/MHz, T 1 relaxation times from 426.3 to 450.2 ms, T 2 relaxation times from 21.5 to 28.4 ms, T λ695 from 46.8% to 92.6%, and T λ532 from 41.1% to 86.3%. Statistically significant factors of each property were identified. The regression model relating the mechanical and medical imaging properties and their corresponding significant factors had a good fit. The validation tests showed a small discrepancy between the model predicted values and experimental data (all less than 5% except the needle insertion friction force). Conclusions: The regression model developed in this paper can be used to design soft PVC with targeted mechanical and medical imaging properties. C 2016 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4962649] Key words: tissue-mimicking materials, PVC, multimodal, elastic modulus, ultrasound, needle 1. INTRODUCTION Tissue-mimicking materials are widely used in clinical simulators and biomedical research. For clinical simulators, properties of the tissue-mimicking materials must be close to those of real tissue for surgeons, nurses, and caregivers to practice their clinical skills. 14 In medical research, tissue- mimicking materials play important roles as idealized tissue models to evaluate clinical devices, procedures, and systems, achieving more repeatable results in experiments than real tissues due to their stability, consistency, and uniform prop- erties. 57 For instance, medical imaging researchers often utilize tissue-mimicking materials to calibrate equipment and develop new imaging methods. 5 A material that can be used for two or more imaging modalities is said to be multimodal. Such materials may also have mechanical properties to make 5577 Med. Phys. 43 (10), October 2016 0094-2405/2016/43(10)/5577/16/$30.00 © 2016 Am. Assoc. Phys. Med. 5577

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Polyvinyl chloride as a multimodal tissue-mimicking materialwith tuned mechanical and medical imaging properties

Weisi LiSchool of Mechanical Engineering Dalian University of Technology Dalian Liaoning 110042 Chinaand Mechanical Engineering Department University of Michigan Ann Arbor Michigan 48109

Barry Belmont Joan M Greve Adam B Manders Brian C Downey Xi Zhangand Zhen XuBiomedical Engineering Department University of Michigan Ann Arbor Michigan 48109

Dongming GuoSchool of Mechanical Engineering Dalian University of Technology Dalian Liaoning 110042 China

Albert ShihMechanical Engineering Department University of Michigan Ann Arbor Michigan 48109and Biomedical Engineering Department University of Michigan Ann Arbor Michigan 48109

(Received 26 July 2015 revised 2 August 2016 accepted for publication 23 August 2016published 22 September 2016)

Purpose The mechanical and imaging properties of polyvinyl chloride (PVC) can be adjusted tomeet the needs of researchers as a tissue-mimicking material For instance the hardness can beadjusted by changing the ratio of softener to PVC polymer mineral oil can be added for lubrication inneedle insertion and glass beads can be added to scatter acoustic energy similar to biological tissueThrough this research the authors sought to develop a regression model to design formulations ofPVC with targeted mechanical and multimodal medical imaging propertiesMethods The design of experiment was conducted by varying three factorsmdash(1) the ratio ofsoftener to PVC polymer (2) the mass fraction of mineral oil and (3) the mass fraction of glassbeadsmdashand measuring the mechanical properties (elastic modulus hardness viscoelastic relaxationtime constant and needle insertion friction force) and the medical imaging properties [speed ofsound acoustic attenuation coefficient magnetic resonance imaging time constants T1 and T2 andthe transmittance of the visible light at wavelengths of 695 nm (Tλ695) and 532 nm (Tλ532)] on twelvesoft PVC samples A regression model was built to describe the relationship between the mechanicaland medical imaging properties and the values of the three composition factors of PVC The modelwas validated by testing the properties of a PVC sample with a formulation distinct from the twelvesamplesResults The tested soft PVC had elastic moduli from 6 to 45 kPa hardnesses from 5 to 50 ShoreOOO-S viscoelastic stress relaxation time constants from 1141 to 1919 s friction forces of 18 gaugeneedle insertion from 0005 to 0086 Nmm speeds of sound from 1393 to 1407 ms acousticattenuation coefficients from 038 to 061 (dBcm)MHz T1 relaxation times from 4263 to 4502 msT2 relaxation times from 215 to 284 ms Tλ695 from 468 to 926 and Tλ532 from 411 to 863Statistically significant factors of each property were identified The regression model relating themechanical and medical imaging properties and their corresponding significant factors had a good fitThe validation tests showed a small discrepancy between the model predicted values and experimentaldata (all less than 5 except the needle insertion friction force)Conclusions The regression model developed in this paper can be used to design soft PVC withtargeted mechanical and medical imaging properties C 2016 American Association of Physicists inMedicine [httpdxdoiorg10111814962649]

Key words tissue-mimicking materials PVC multimodal elastic modulus ultrasound needle

1 INTRODUCTION

Tissue-mimicking materials are widely used in clinicalsimulators and biomedical research For clinical simulatorsproperties of the tissue-mimicking materials must be closeto those of real tissue for surgeons nurses and caregiversto practice their clinical skills1ndash4 In medical research tissue-mimicking materials play important roles as idealized tissue

models to evaluate clinical devices procedures and systemsachieving more repeatable results in experiments than realtissues due to their stability consistency and uniform prop-erties5ndash7 For instance medical imaging researchers oftenutilize tissue-mimicking materials to calibrate equipment anddevelop new imaging methods5 A material that can be usedfor two or more imaging modalities is said to be multimodalSuch materials may also have mechanical properties to make

5577 Med Phys 43 (10) October 2016 0094-2405201643(10)557716$3000 copy 2016 Am Assoc Phys Med 5577

5578 Li et al Polyvinyl chloride as a tissue-mimicking material 5578

clinical simulators behave analogously to real tissue whilemaking imaging techniques more repeatable89 The goal ofthis research was to study the mechanical and medical imagingproperties of a multimodal tissue-mimicking material namelypolyvinyl chloride (PVC)

Common mechanical properties of tissue-mimicking mate-rials include elasticity viscoelasticity and friction forceduring needle insertion Elasticity as quantified by an elasticmodulus is one of the most basic mechanical properties oftissue-mimicking materials greatly affecting the haptics ofsimulators10 force during needle insertion11 and imagingquality in elastography12 It should be noted however thatmost tissue-mimicking soft materials are viscoelastic and thishas a great effect on deformation13ndash15 The friction forcefurther affects the haptic feel of a material during needle-basedprocedures1116

To be of the most use tissue-mimicking materials shouldalso target properties of soft tissues in one or more medicalimaging modalities to make possible multifaceted valida-tion17 In ultrasound imaging technology development tissue-mimicking materials are usually created with similar acousticproperties (ie speed of sound acoustic attenuation andacoustic impedance) to those of the soft tissues of interest5ndash8

Examples of ultrasound phantoms include agar based wall-lessvessel phantoms for Doppler flow measurements18 mixed agarand gelatin phantoms for elasticity imaging19 and anthro-pomorphic phantoms made from multiple tissue-mimickingmaterials for medical training20 For magnetic resonanceimaging (MRI) phantoms tissue-mimicking materials musthave physiologically relevant relaxation times denoted T1 andT2 as the rate at which the longitudinal and the transversemagnetization vectors recover and decay respectively21 Theoptical clarity of a tissue-mimicking material is also oftendesirable for medical imaging research as transparency canfacilitate observation of internal structures of a phantomespecially appealing for flow phantoms that might utilizeparticle image velocimetry (PIV) a nonintrusive technique tomeasure mean and instantaneous fluid velocities by recordingthe change in position of seeded particles22

Multimodal tissue-mimicking materials are valuable formedical imaging research because they can be used todevelop and validate techniques across imaging modalitiesDemonstrating the initial feasibility of such research Hungret al16 made a multimodal prostate phantom using PVC forimage guided biopsy procedures The phantom had clearlydistinguishable morphology visible via ultrasound MRI andcomputed tomography (CT) Chmarra et al17 developed anagarose based liver phantom to get images from ultrasoundimaging MRI and CT modalities similar to those of patientsChen et al9 created a polyvinyl alcohol (PVA) brain phantomthat could be used to validate the results of ultrasound MRIand CT imaging

Table I summarizes results of prior research on somemechanical and medical imaging properties of nine commontissue-mimicking materials [agar agarose gelatin gellangum PVA PVC room-temperature vulcanizing (RTV) poly-merized siloxanes (silicone) polydimethylsiloxane (PDMS)and polyurethane (PU)] and five types of tissues from human

and animals (liver brain fat muscle and prostate) Agaragarose gelatin and gellan gum are biopolymers materialsthat contain a high mass fraction of water (gt80) makingthem similar in many respects to soft biological tissues23

However due to the evaporation of water and bacterialgrowth biopolymers are not stable for long-term storageand use24 PVA RTV silicone PDMS PVC and PU arecommon chemically synthesized polymers Compared tobiopolymers these tissue-mimicking materials are more stableand durable1125 though the lack of water in most chemicallysynthesized polymers makes them less similar to the realtissue particularly in needle insertion procedures16

Of these materials PVC has many advantages includinghigh optical transparency and a hardness that is close toreal tissue Compared to biopolymers PVC has the benefitof the ability to resist bacterial attack and moisture lossAs compared to the other listed chemically synthesizedpolymers PVC is easier to manufacture than PVA and hasdistinct acoustic advantages over silicone and PDMS forultrasound imaging2627 The speed of sound of PVC about1400 ms162528 is closer to that of generic human soft tissue1500ndash1600 ms29ndash32 than silicone (only about 1000 ms)2633 orPU (about 1800 ms)3435 PVC also has a hardness and elasticmodulus closer to soft tissues than PU and PDMS which is animportant factor to make the simulator have a tactile feelingsimilar to real tissue In addition the curing time of PVCis shorter than many RTV silicones These advantages makePVC promising for clinical simulator production

Properties of soft PVCmdashmade by combining a PVCpolymer solution and a softenermdashcan be tailored to mimicdifferent soft tissues by adjusting the ratio of the softener topolymer16 Similar to other chemically synthesized polymerscured PVC does not have internal fluid components causingthe friction force during needle insertion to feel unlike thatof the same procedure in soft tissues16 To more closelyalign the properties of PVC with those of soft tissues inthis regard a lubricating agent can be added into a PVCsample to simulate the interstitial fluids of tissue Wang et al11

utilized mineral oil as a lubricating agent in RTV siliconetissue-mimicking materials and conducted needle insertiontests With the addition of mineral oil the hardness elasticmodulus and needle insertion friction force of RTV siliconechanged The friction force decreased as the ratio of mineraloil in RTV silicone increased11 In this study mineral oil wasadded to soft PVC primarily to act as a lubricant to decreasethe needle insertion friction force We also noted that duringmany needle based procedures ultrasound imaging is usedto monitor needle insertion path PVC without any sort ofadditive looks very different from soft tissue under ultrasoundexamination because of its lack of specular reflectors Glassbeads were added to PVC to act as a scattering agent toenhance this scattering effect making PVC appear moretissue-like under ultrasound examination The change of thecomposition of PVC also affected other imaging propertiessuch as optical clarity and the relaxation time constants ofMRI This paper presents the design and fabrication of softPVC materials and evaluates their mechanical and medicalimaging properties

Medical Physics Vol 43 No 10 October 2016

5579 Li et al Polyvinyl chloride as a tissue-mimicking material 5579

T I Properties of the tissue-mimicking materials and tissues

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

Biopolymers

Agar

52ndash499 (Ref 36)

mdash

1546ndash1554(Ref 39)

032ndash053(Ref 39)

1090ndash1150[05ndash15 T] (Ref 41)

42ndash50 [05ndash15 T](Ref 41) 80 (380ndash1000

nm) (Ref 43)30ndash2300 (Ref 37) 1564ndash1671(Ref 40)

069ndash083(Ref 40)

380ndash2909 (100MHz) (Ref 42)

247ndash143 (100 MHz)(Ref 42)

5ndash118 (Ref 38)

Agarose2ndash50 (Ref 44)

mdash158828plusmn1572

(Ref 46)128plusmn0045

(Ref 46)

1300ndash2600 [035 T](Ref 48)

20ndash130 [035 T](Ref 48)

40 (660 nm50 C) (Ref 50)

15ndash1580(Ref 45)

1500ndash1630(Ref 47)

1000ndash2743 [14 T](Ref 49)

23ndash278 [14 T](Ref 49)

Gelatin10ndash70 (Ref 8) 0025ndash0036 [1 mm]

(Ref 52)

1518ndash1535(Ref 8)

035ndash05 (Ref 8) 369ndash498 (60 MHz)(Ref 8)

28ndash63 (60 MHz)(Ref 8)

98 (350ndash800 nm)(Ref 54)

367ndash1115(Ref 51)

1535ndash1558(Ref 15)

029ndash107(Ref 15)

500ndash900 (10 MHz)(Ref 53)

50ndash180 (10 MHz)(Ref 53)

GellanGum

471ndash174(Ref 23)

002 [127 mm](Ref 56)

1548ndash1584(Ref 23)

064ndash088(Ref 23) mdash mdash mdash

015ndash148(Ref 55)

00075 [127 mm](Ref 57)

1579ndash1647(Ref 58)

059ndash065(Ref 58)

Chemically synthesized polymers

PVA

25ndash615 (Ref 14)

mdash

1420ndash1464(Ref 12)

04ndash4 (dBcm)(Ref 12)

470ndash810 [15 T](Ref 61)

40ndash90 [15 T](Ref 61)

95 (380ndash700 nm)(Ref 62)

22ndash150 (Ref 12) 1520ndash1540(Ref 59)

0075ndash028(Ref 59)

718ndash1034 [15 T](Ref 59)

108ndash175 [15 T](Ref 59)

40 (550 nm)(Ref 63)

1535ndash1559(Ref 60)

05ndash12 (Ref 60)

PVC 3ndash200 (Ref 16)0036 [046 mm]

(Ref 64)

1360ndash1400(Ref 16)

014ndash116(Ref 28) mdash mdash mdash

1400ndash1470(Ref 28)

057plusmn101(dBcm) (Ref 25)

1400plusmn20(Ref 25)

RTVsilicone

18ndash122 (Ref 65) 00175ndash01 [101 mm](Ref 11)

959ndash1113(Ref 33)

0ndash25 (Ref 33) 423ndash757 [3 T](Ref 66)

13ndash57 [3 T] (Ref 66)mdash

95ndash96 (Ref 13) 1069 (Ref 26) 143 (Ref 26) 410ndash765 [14 T](Ref 67)

50ndash165 [14 T](Ref 67)

PU5ndash636 MPa

(Ref 68) 1ndash4 [3 mm] (Ref 70)1773ndash1994(Ref 35)

122ndash154(Ref 71)

306plusmn15 [15 T](Ref 71)

30plusmn1 [15 T](Ref 71)

90 (320ndash700 nm)(Ref 74)

10ndash100 MPa(Ref 69)

1750ndash1905(Ref 34)

03ndash10 (Ref 72) 285ndash300 [15 T](Ref 73)

38ndash41 [15 T](Ref 73)

92 (320ndash800 nm)(Ref 75)

PDMS145ndash2485(Ref 76)

mdash1076ndash1119(Ref 27)

327ndash64 (Ref 27) 716 [15 T] (Ref 77) 68 [15 T] (Ref 77)85 (290ndash1100nm) (Ref 78)

96 (400ndash700 nm)(Ref 79)

Tissue

Liver094

(bovine ex vivo)(Ref 80)

0025 [147 mm](hog ex vivo)

(Ref 82)

1584ndash1607(human ex vivo)

(Ref 84)

08ndash15(human ex vivo)

(Ref 84)

443 [035 T](human in vivo)

(Ref 86)

51 [035 T](human in vivo)

(Ref 86)

mdash

Medical Physics Vol 43 No 10 October 2016

5580 Li et al Polyvinyl chloride as a tissue-mimicking material 5580

T I (Continued)

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

059ndash173(human ex vivo)

(Ref 81)

0012 [127 mm](bovine ex vivo)

(Ref 83)

1577(bovine ex vivo)

(Ref 85)

1ndash175(bovine ex vivo)

(Ref 85)

812 [3 T](mouse ex vivo)

(Ref 87)

42 [3 T](mouse ex vivo)

(Ref 87)

Brain058

(human ex vivo)(Ref 88)

000043 [0235 mm](rat in vivo)

(Ref 89)

1561ndash1565(human in vivo)

(Ref 31)

058ndash08(human ex vivo)

(Ref 32)

1300 [15 T](human in vivo)

(Ref 90)

75 [15 T](human in vivo)

(Ref 90)

mdash

104(human in vivo)

(Ref 31)

1820 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

99 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

Fat25

(human in vivo)(Ref 91)

mdash1476

(human ex vivo)(Ref 92)

06ndash52(human ex vivo)

(Ref 32)

266 [035 T](human in vivo)

(Ref 86)

57 [035 T](human in vivo)

(Ref 86)

mdash

1430ndash1480(human ex vivo)

(Ref 93)

246 [035 T](human in vivo)

(Ref 94)

545 [035 T](human in vivo)

(Ref 94)

Muscle15

(bovine ex vivo)(Ref 80)

015 [16 mm](pig ex vivo)

(Ref 96)

1555ndash1616(bovine ex vivo)

(Ref 30)

103(bovine ex vivo)

(Ref 30)

514 [035 T](human in vivo)

(Ref 94)

32 [035 T](human in vivo)

(Ref 94)

mdash

128(human in vivo)

(Ref 95)

Prostate11ndash25

(human ex vivo)(Ref 97)

018(insertion force)

[127 mm](human in vivo)

(Ref 99)

1614(human ex vivo)

(Ref 29)

018(human ex vivo)

(Ref 29)

1022 [15 T](human in vivo)

(Ref 100)

86 [15 T](human in vivo)

(Ref 100)

mdash

13ndash56(human ex vivo)

(Ref 98)

2 MATERIALS AND METHODS

In this study a general full factorial design of experiment(DOE) was created to study the effects of the ratio of softener toPVC polymer mass fraction of mineral oil and mass fractionof glass beads on mechanical and medical imaging propertiesof soft PVC Factorial analysis was utilized to identify thestatistical significance of three factors and a regression modelwas developed to find the quantitative relationship betweenPVC properties and three factors A regression model wasused to find values of three factors of the PVC as an exampleto achieve targeted mechanical and medical imaging propertiesand validate the results experimentally

2A Design of experiment

Three factors the mass ratio of softener to PVC polymersolution (RSP) the mass fraction of the mineral oil (wo)and the mass fraction of glass beads (wg) were identified inthe general full factorial DOE101 The RSP greatly affectedboth the mechanical and medical imaging properties of PVCThree levels of RSP (0 05 and 1) were examined for this

experiment PVC samples with RSP in this range had similarhardness to that of soft tissue The other two factors beingrelatively unknown (wo and wg) were tested at two levels Thehighest wo at which the mineral oil did not leak after curingwas found to be 5 This was the high value assigned towo If the mass fraction of glass beads wg was larger than1 the glass beads would precipitate during PVC curingTwo levels of the wg were chosen to be 0 and 1 InTable II twelve combinations of factors and their levels of theDOE in this study are shown The statistical analysis softwareMinitabreg (Minitab Inc State College PA USA) was usedto do factorial analysis and build regression model

T II Values of each factor at different levels for the DOE

Level

Factor Low Middle High

RSP 0 05 1wo 0 mdash 5wg 0 mdash 1

Medical Physics Vol 43 No 10 October 2016

5581 Li et al Polyvinyl chloride as a tissue-mimicking material 5581

2B Soft PVC fabrication

Soft PVC was made by mixing PVC polymer solutionand a softener in this case phthalate ester (both from M-FManufacturing Ft Worth TX USA) In this study mineraloil (WS Dodge Oil Maywood CA USA) and sphericalglass beads (50 microm average diameter) (Comco Burbank CAUSA) were added and mixed uniformly based on the DOERoom temperature mixture (initially white and opaque) ofthe PVC polymer solution the plastic softener and additives(mineral oil andor glass beads) was heated by a heat plateto 150 C with a magnetic bar stirring the liquid25 Increasingthe temperature beyond 120 C the PVC monomers start tocross-link to polymers and the solution becomes transparentreaching optimal cross-linking at 150 C After the mixtureturned transparent it was moved to a vacuum chamber toremove bubbles Once vacuumed the liquid mixture waspoured into molds and cooled to room temperature Threetypes of PVC samples as shown in Fig 1 were made The50 mm long PVC samples [445 mm in diameter Fig 1(a)]were used for needle insertion experiments The 20 mm longPVC samples [445 mm in diameter Fig 1(b)] were used forthe indentation hardness elastic modulus acoustic propertiesand the MRI time constants The samples with 10times10 mm2

and a length of 40 mm [Fig 1(c)] were made for visible lighttransmittance testing The top surface of the sample was aconcave meniscus as seen in Fig 1(a) due to the surfacetension during cooling

2C Compression test for elasticmodulus measurement

The method to measure the elastic modulus of PVCwas through compression testing a common method toobtain stressndashstrain relationships16102 Figure 2 shows thePVC sample on an acrylic plate before compression byan aluminum plate mounted to the linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) The samplewas compressed 9 mm (045 maximum engineering strain)at a speed of 05 mms The force exerted on the samplewas measured by a piezoelectric dynamometer (Model 9273Kistler Winterthur Switzerland) The engineering stress vsengineering strain curve indicated a nonlinear behavior of thematerial at large strains with a larger elastic modulus appearing

F 1 Samples of soft PVC (a) 445 mm in diameter and 50 mm in length(b) 445 mm in diameter and 20 mm in length and (c) 10times10 mm2 and40 mm in length

F 2 Experimental setup of the elastic modulus measurement

at higher strains The linear regime (below 015) was usedto calculate the elastic modulus of the PVC sample usingMATLABreg (Mathworks Natick MA USA) with the leastsquares method The average elastic modulus of three samplesof each composition was used to represent the PVC material

2D Shore hardness measurement

A Type OOO-S Shore durometer (Instron Norwood MAUSA) with a sphere surface indenter (1067 mm in radius)was used to measure the hardness of the soft PVC as shownin Fig 3 Since the PVC is soft and the sample size issmall the deformation of the sample under the compression

F 3 Experimental setup for measuring hardness of the soft PVC

Medical Physics Vol 43 No 10 October 2016

5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5578 Li et al Polyvinyl chloride as a tissue-mimicking material 5578

clinical simulators behave analogously to real tissue whilemaking imaging techniques more repeatable89 The goal ofthis research was to study the mechanical and medical imagingproperties of a multimodal tissue-mimicking material namelypolyvinyl chloride (PVC)

Common mechanical properties of tissue-mimicking mate-rials include elasticity viscoelasticity and friction forceduring needle insertion Elasticity as quantified by an elasticmodulus is one of the most basic mechanical properties oftissue-mimicking materials greatly affecting the haptics ofsimulators10 force during needle insertion11 and imagingquality in elastography12 It should be noted however thatmost tissue-mimicking soft materials are viscoelastic and thishas a great effect on deformation13ndash15 The friction forcefurther affects the haptic feel of a material during needle-basedprocedures1116

To be of the most use tissue-mimicking materials shouldalso target properties of soft tissues in one or more medicalimaging modalities to make possible multifaceted valida-tion17 In ultrasound imaging technology development tissue-mimicking materials are usually created with similar acousticproperties (ie speed of sound acoustic attenuation andacoustic impedance) to those of the soft tissues of interest5ndash8

Examples of ultrasound phantoms include agar based wall-lessvessel phantoms for Doppler flow measurements18 mixed agarand gelatin phantoms for elasticity imaging19 and anthro-pomorphic phantoms made from multiple tissue-mimickingmaterials for medical training20 For magnetic resonanceimaging (MRI) phantoms tissue-mimicking materials musthave physiologically relevant relaxation times denoted T1 andT2 as the rate at which the longitudinal and the transversemagnetization vectors recover and decay respectively21 Theoptical clarity of a tissue-mimicking material is also oftendesirable for medical imaging research as transparency canfacilitate observation of internal structures of a phantomespecially appealing for flow phantoms that might utilizeparticle image velocimetry (PIV) a nonintrusive technique tomeasure mean and instantaneous fluid velocities by recordingthe change in position of seeded particles22

Multimodal tissue-mimicking materials are valuable formedical imaging research because they can be used todevelop and validate techniques across imaging modalitiesDemonstrating the initial feasibility of such research Hungret al16 made a multimodal prostate phantom using PVC forimage guided biopsy procedures The phantom had clearlydistinguishable morphology visible via ultrasound MRI andcomputed tomography (CT) Chmarra et al17 developed anagarose based liver phantom to get images from ultrasoundimaging MRI and CT modalities similar to those of patientsChen et al9 created a polyvinyl alcohol (PVA) brain phantomthat could be used to validate the results of ultrasound MRIand CT imaging

Table I summarizes results of prior research on somemechanical and medical imaging properties of nine commontissue-mimicking materials [agar agarose gelatin gellangum PVA PVC room-temperature vulcanizing (RTV) poly-merized siloxanes (silicone) polydimethylsiloxane (PDMS)and polyurethane (PU)] and five types of tissues from human

and animals (liver brain fat muscle and prostate) Agaragarose gelatin and gellan gum are biopolymers materialsthat contain a high mass fraction of water (gt80) makingthem similar in many respects to soft biological tissues23

However due to the evaporation of water and bacterialgrowth biopolymers are not stable for long-term storageand use24 PVA RTV silicone PDMS PVC and PU arecommon chemically synthesized polymers Compared tobiopolymers these tissue-mimicking materials are more stableand durable1125 though the lack of water in most chemicallysynthesized polymers makes them less similar to the realtissue particularly in needle insertion procedures16

Of these materials PVC has many advantages includinghigh optical transparency and a hardness that is close toreal tissue Compared to biopolymers PVC has the benefitof the ability to resist bacterial attack and moisture lossAs compared to the other listed chemically synthesizedpolymers PVC is easier to manufacture than PVA and hasdistinct acoustic advantages over silicone and PDMS forultrasound imaging2627 The speed of sound of PVC about1400 ms162528 is closer to that of generic human soft tissue1500ndash1600 ms29ndash32 than silicone (only about 1000 ms)2633 orPU (about 1800 ms)3435 PVC also has a hardness and elasticmodulus closer to soft tissues than PU and PDMS which is animportant factor to make the simulator have a tactile feelingsimilar to real tissue In addition the curing time of PVCis shorter than many RTV silicones These advantages makePVC promising for clinical simulator production

Properties of soft PVCmdashmade by combining a PVCpolymer solution and a softenermdashcan be tailored to mimicdifferent soft tissues by adjusting the ratio of the softener topolymer16 Similar to other chemically synthesized polymerscured PVC does not have internal fluid components causingthe friction force during needle insertion to feel unlike thatof the same procedure in soft tissues16 To more closelyalign the properties of PVC with those of soft tissues inthis regard a lubricating agent can be added into a PVCsample to simulate the interstitial fluids of tissue Wang et al11

utilized mineral oil as a lubricating agent in RTV siliconetissue-mimicking materials and conducted needle insertiontests With the addition of mineral oil the hardness elasticmodulus and needle insertion friction force of RTV siliconechanged The friction force decreased as the ratio of mineraloil in RTV silicone increased11 In this study mineral oil wasadded to soft PVC primarily to act as a lubricant to decreasethe needle insertion friction force We also noted that duringmany needle based procedures ultrasound imaging is usedto monitor needle insertion path PVC without any sort ofadditive looks very different from soft tissue under ultrasoundexamination because of its lack of specular reflectors Glassbeads were added to PVC to act as a scattering agent toenhance this scattering effect making PVC appear moretissue-like under ultrasound examination The change of thecomposition of PVC also affected other imaging propertiessuch as optical clarity and the relaxation time constants ofMRI This paper presents the design and fabrication of softPVC materials and evaluates their mechanical and medicalimaging properties

Medical Physics Vol 43 No 10 October 2016

5579 Li et al Polyvinyl chloride as a tissue-mimicking material 5579

T I Properties of the tissue-mimicking materials and tissues

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

Biopolymers

Agar

52ndash499 (Ref 36)

mdash

1546ndash1554(Ref 39)

032ndash053(Ref 39)

1090ndash1150[05ndash15 T] (Ref 41)

42ndash50 [05ndash15 T](Ref 41) 80 (380ndash1000

nm) (Ref 43)30ndash2300 (Ref 37) 1564ndash1671(Ref 40)

069ndash083(Ref 40)

380ndash2909 (100MHz) (Ref 42)

247ndash143 (100 MHz)(Ref 42)

5ndash118 (Ref 38)

Agarose2ndash50 (Ref 44)

mdash158828plusmn1572

(Ref 46)128plusmn0045

(Ref 46)

1300ndash2600 [035 T](Ref 48)

20ndash130 [035 T](Ref 48)

40 (660 nm50 C) (Ref 50)

15ndash1580(Ref 45)

1500ndash1630(Ref 47)

1000ndash2743 [14 T](Ref 49)

23ndash278 [14 T](Ref 49)

Gelatin10ndash70 (Ref 8) 0025ndash0036 [1 mm]

(Ref 52)

1518ndash1535(Ref 8)

035ndash05 (Ref 8) 369ndash498 (60 MHz)(Ref 8)

28ndash63 (60 MHz)(Ref 8)

98 (350ndash800 nm)(Ref 54)

367ndash1115(Ref 51)

1535ndash1558(Ref 15)

029ndash107(Ref 15)

500ndash900 (10 MHz)(Ref 53)

50ndash180 (10 MHz)(Ref 53)

GellanGum

471ndash174(Ref 23)

002 [127 mm](Ref 56)

1548ndash1584(Ref 23)

064ndash088(Ref 23) mdash mdash mdash

015ndash148(Ref 55)

00075 [127 mm](Ref 57)

1579ndash1647(Ref 58)

059ndash065(Ref 58)

Chemically synthesized polymers

PVA

25ndash615 (Ref 14)

mdash

1420ndash1464(Ref 12)

04ndash4 (dBcm)(Ref 12)

470ndash810 [15 T](Ref 61)

40ndash90 [15 T](Ref 61)

95 (380ndash700 nm)(Ref 62)

22ndash150 (Ref 12) 1520ndash1540(Ref 59)

0075ndash028(Ref 59)

718ndash1034 [15 T](Ref 59)

108ndash175 [15 T](Ref 59)

40 (550 nm)(Ref 63)

1535ndash1559(Ref 60)

05ndash12 (Ref 60)

PVC 3ndash200 (Ref 16)0036 [046 mm]

(Ref 64)

1360ndash1400(Ref 16)

014ndash116(Ref 28) mdash mdash mdash

1400ndash1470(Ref 28)

057plusmn101(dBcm) (Ref 25)

1400plusmn20(Ref 25)

RTVsilicone

18ndash122 (Ref 65) 00175ndash01 [101 mm](Ref 11)

959ndash1113(Ref 33)

0ndash25 (Ref 33) 423ndash757 [3 T](Ref 66)

13ndash57 [3 T] (Ref 66)mdash

95ndash96 (Ref 13) 1069 (Ref 26) 143 (Ref 26) 410ndash765 [14 T](Ref 67)

50ndash165 [14 T](Ref 67)

PU5ndash636 MPa

(Ref 68) 1ndash4 [3 mm] (Ref 70)1773ndash1994(Ref 35)

122ndash154(Ref 71)

306plusmn15 [15 T](Ref 71)

30plusmn1 [15 T](Ref 71)

90 (320ndash700 nm)(Ref 74)

10ndash100 MPa(Ref 69)

1750ndash1905(Ref 34)

03ndash10 (Ref 72) 285ndash300 [15 T](Ref 73)

38ndash41 [15 T](Ref 73)

92 (320ndash800 nm)(Ref 75)

PDMS145ndash2485(Ref 76)

mdash1076ndash1119(Ref 27)

327ndash64 (Ref 27) 716 [15 T] (Ref 77) 68 [15 T] (Ref 77)85 (290ndash1100nm) (Ref 78)

96 (400ndash700 nm)(Ref 79)

Tissue

Liver094

(bovine ex vivo)(Ref 80)

0025 [147 mm](hog ex vivo)

(Ref 82)

1584ndash1607(human ex vivo)

(Ref 84)

08ndash15(human ex vivo)

(Ref 84)

443 [035 T](human in vivo)

(Ref 86)

51 [035 T](human in vivo)

(Ref 86)

mdash

Medical Physics Vol 43 No 10 October 2016

5580 Li et al Polyvinyl chloride as a tissue-mimicking material 5580

T I (Continued)

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

059ndash173(human ex vivo)

(Ref 81)

0012 [127 mm](bovine ex vivo)

(Ref 83)

1577(bovine ex vivo)

(Ref 85)

1ndash175(bovine ex vivo)

(Ref 85)

812 [3 T](mouse ex vivo)

(Ref 87)

42 [3 T](mouse ex vivo)

(Ref 87)

Brain058

(human ex vivo)(Ref 88)

000043 [0235 mm](rat in vivo)

(Ref 89)

1561ndash1565(human in vivo)

(Ref 31)

058ndash08(human ex vivo)

(Ref 32)

1300 [15 T](human in vivo)

(Ref 90)

75 [15 T](human in vivo)

(Ref 90)

mdash

104(human in vivo)

(Ref 31)

1820 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

99 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

Fat25

(human in vivo)(Ref 91)

mdash1476

(human ex vivo)(Ref 92)

06ndash52(human ex vivo)

(Ref 32)

266 [035 T](human in vivo)

(Ref 86)

57 [035 T](human in vivo)

(Ref 86)

mdash

1430ndash1480(human ex vivo)

(Ref 93)

246 [035 T](human in vivo)

(Ref 94)

545 [035 T](human in vivo)

(Ref 94)

Muscle15

(bovine ex vivo)(Ref 80)

015 [16 mm](pig ex vivo)

(Ref 96)

1555ndash1616(bovine ex vivo)

(Ref 30)

103(bovine ex vivo)

(Ref 30)

514 [035 T](human in vivo)

(Ref 94)

32 [035 T](human in vivo)

(Ref 94)

mdash

128(human in vivo)

(Ref 95)

Prostate11ndash25

(human ex vivo)(Ref 97)

018(insertion force)

[127 mm](human in vivo)

(Ref 99)

1614(human ex vivo)

(Ref 29)

018(human ex vivo)

(Ref 29)

1022 [15 T](human in vivo)

(Ref 100)

86 [15 T](human in vivo)

(Ref 100)

mdash

13ndash56(human ex vivo)

(Ref 98)

2 MATERIALS AND METHODS

In this study a general full factorial design of experiment(DOE) was created to study the effects of the ratio of softener toPVC polymer mass fraction of mineral oil and mass fractionof glass beads on mechanical and medical imaging propertiesof soft PVC Factorial analysis was utilized to identify thestatistical significance of three factors and a regression modelwas developed to find the quantitative relationship betweenPVC properties and three factors A regression model wasused to find values of three factors of the PVC as an exampleto achieve targeted mechanical and medical imaging propertiesand validate the results experimentally

2A Design of experiment

Three factors the mass ratio of softener to PVC polymersolution (RSP) the mass fraction of the mineral oil (wo)and the mass fraction of glass beads (wg) were identified inthe general full factorial DOE101 The RSP greatly affectedboth the mechanical and medical imaging properties of PVCThree levels of RSP (0 05 and 1) were examined for this

experiment PVC samples with RSP in this range had similarhardness to that of soft tissue The other two factors beingrelatively unknown (wo and wg) were tested at two levels Thehighest wo at which the mineral oil did not leak after curingwas found to be 5 This was the high value assigned towo If the mass fraction of glass beads wg was larger than1 the glass beads would precipitate during PVC curingTwo levels of the wg were chosen to be 0 and 1 InTable II twelve combinations of factors and their levels of theDOE in this study are shown The statistical analysis softwareMinitabreg (Minitab Inc State College PA USA) was usedto do factorial analysis and build regression model

T II Values of each factor at different levels for the DOE

Level

Factor Low Middle High

RSP 0 05 1wo 0 mdash 5wg 0 mdash 1

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5581 Li et al Polyvinyl chloride as a tissue-mimicking material 5581

2B Soft PVC fabrication

Soft PVC was made by mixing PVC polymer solutionand a softener in this case phthalate ester (both from M-FManufacturing Ft Worth TX USA) In this study mineraloil (WS Dodge Oil Maywood CA USA) and sphericalglass beads (50 microm average diameter) (Comco Burbank CAUSA) were added and mixed uniformly based on the DOERoom temperature mixture (initially white and opaque) ofthe PVC polymer solution the plastic softener and additives(mineral oil andor glass beads) was heated by a heat plateto 150 C with a magnetic bar stirring the liquid25 Increasingthe temperature beyond 120 C the PVC monomers start tocross-link to polymers and the solution becomes transparentreaching optimal cross-linking at 150 C After the mixtureturned transparent it was moved to a vacuum chamber toremove bubbles Once vacuumed the liquid mixture waspoured into molds and cooled to room temperature Threetypes of PVC samples as shown in Fig 1 were made The50 mm long PVC samples [445 mm in diameter Fig 1(a)]were used for needle insertion experiments The 20 mm longPVC samples [445 mm in diameter Fig 1(b)] were used forthe indentation hardness elastic modulus acoustic propertiesand the MRI time constants The samples with 10times10 mm2

and a length of 40 mm [Fig 1(c)] were made for visible lighttransmittance testing The top surface of the sample was aconcave meniscus as seen in Fig 1(a) due to the surfacetension during cooling

2C Compression test for elasticmodulus measurement

The method to measure the elastic modulus of PVCwas through compression testing a common method toobtain stressndashstrain relationships16102 Figure 2 shows thePVC sample on an acrylic plate before compression byan aluminum plate mounted to the linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) The samplewas compressed 9 mm (045 maximum engineering strain)at a speed of 05 mms The force exerted on the samplewas measured by a piezoelectric dynamometer (Model 9273Kistler Winterthur Switzerland) The engineering stress vsengineering strain curve indicated a nonlinear behavior of thematerial at large strains with a larger elastic modulus appearing

F 1 Samples of soft PVC (a) 445 mm in diameter and 50 mm in length(b) 445 mm in diameter and 20 mm in length and (c) 10times10 mm2 and40 mm in length

F 2 Experimental setup of the elastic modulus measurement

at higher strains The linear regime (below 015) was usedto calculate the elastic modulus of the PVC sample usingMATLABreg (Mathworks Natick MA USA) with the leastsquares method The average elastic modulus of three samplesof each composition was used to represent the PVC material

2D Shore hardness measurement

A Type OOO-S Shore durometer (Instron Norwood MAUSA) with a sphere surface indenter (1067 mm in radius)was used to measure the hardness of the soft PVC as shownin Fig 3 Since the PVC is soft and the sample size issmall the deformation of the sample under the compression

F 3 Experimental setup for measuring hardness of the soft PVC

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5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

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5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

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5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

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5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5579 Li et al Polyvinyl chloride as a tissue-mimicking material 5579

T I Properties of the tissue-mimicking materials and tissues

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

Biopolymers

Agar

52ndash499 (Ref 36)

mdash

1546ndash1554(Ref 39)

032ndash053(Ref 39)

1090ndash1150[05ndash15 T] (Ref 41)

42ndash50 [05ndash15 T](Ref 41) 80 (380ndash1000

nm) (Ref 43)30ndash2300 (Ref 37) 1564ndash1671(Ref 40)

069ndash083(Ref 40)

380ndash2909 (100MHz) (Ref 42)

247ndash143 (100 MHz)(Ref 42)

5ndash118 (Ref 38)

Agarose2ndash50 (Ref 44)

mdash158828plusmn1572

(Ref 46)128plusmn0045

(Ref 46)

1300ndash2600 [035 T](Ref 48)

20ndash130 [035 T](Ref 48)

40 (660 nm50 C) (Ref 50)

15ndash1580(Ref 45)

1500ndash1630(Ref 47)

1000ndash2743 [14 T](Ref 49)

23ndash278 [14 T](Ref 49)

Gelatin10ndash70 (Ref 8) 0025ndash0036 [1 mm]

(Ref 52)

1518ndash1535(Ref 8)

035ndash05 (Ref 8) 369ndash498 (60 MHz)(Ref 8)

28ndash63 (60 MHz)(Ref 8)

98 (350ndash800 nm)(Ref 54)

367ndash1115(Ref 51)

1535ndash1558(Ref 15)

029ndash107(Ref 15)

500ndash900 (10 MHz)(Ref 53)

50ndash180 (10 MHz)(Ref 53)

GellanGum

471ndash174(Ref 23)

002 [127 mm](Ref 56)

1548ndash1584(Ref 23)

064ndash088(Ref 23) mdash mdash mdash

015ndash148(Ref 55)

00075 [127 mm](Ref 57)

1579ndash1647(Ref 58)

059ndash065(Ref 58)

Chemically synthesized polymers

PVA

25ndash615 (Ref 14)

mdash

1420ndash1464(Ref 12)

04ndash4 (dBcm)(Ref 12)

470ndash810 [15 T](Ref 61)

40ndash90 [15 T](Ref 61)

95 (380ndash700 nm)(Ref 62)

22ndash150 (Ref 12) 1520ndash1540(Ref 59)

0075ndash028(Ref 59)

718ndash1034 [15 T](Ref 59)

108ndash175 [15 T](Ref 59)

40 (550 nm)(Ref 63)

1535ndash1559(Ref 60)

05ndash12 (Ref 60)

PVC 3ndash200 (Ref 16)0036 [046 mm]

(Ref 64)

1360ndash1400(Ref 16)

014ndash116(Ref 28) mdash mdash mdash

1400ndash1470(Ref 28)

057plusmn101(dBcm) (Ref 25)

1400plusmn20(Ref 25)

RTVsilicone

18ndash122 (Ref 65) 00175ndash01 [101 mm](Ref 11)

959ndash1113(Ref 33)

0ndash25 (Ref 33) 423ndash757 [3 T](Ref 66)

13ndash57 [3 T] (Ref 66)mdash

95ndash96 (Ref 13) 1069 (Ref 26) 143 (Ref 26) 410ndash765 [14 T](Ref 67)

50ndash165 [14 T](Ref 67)

PU5ndash636 MPa

(Ref 68) 1ndash4 [3 mm] (Ref 70)1773ndash1994(Ref 35)

122ndash154(Ref 71)

306plusmn15 [15 T](Ref 71)

30plusmn1 [15 T](Ref 71)

90 (320ndash700 nm)(Ref 74)

10ndash100 MPa(Ref 69)

1750ndash1905(Ref 34)

03ndash10 (Ref 72) 285ndash300 [15 T](Ref 73)

38ndash41 [15 T](Ref 73)

92 (320ndash800 nm)(Ref 75)

PDMS145ndash2485(Ref 76)

mdash1076ndash1119(Ref 27)

327ndash64 (Ref 27) 716 [15 T] (Ref 77) 68 [15 T] (Ref 77)85 (290ndash1100nm) (Ref 78)

96 (400ndash700 nm)(Ref 79)

Tissue

Liver094

(bovine ex vivo)(Ref 80)

0025 [147 mm](hog ex vivo)

(Ref 82)

1584ndash1607(human ex vivo)

(Ref 84)

08ndash15(human ex vivo)

(Ref 84)

443 [035 T](human in vivo)

(Ref 86)

51 [035 T](human in vivo)

(Ref 86)

mdash

Medical Physics Vol 43 No 10 October 2016

5580 Li et al Polyvinyl chloride as a tissue-mimicking material 5580

T I (Continued)

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

059ndash173(human ex vivo)

(Ref 81)

0012 [127 mm](bovine ex vivo)

(Ref 83)

1577(bovine ex vivo)

(Ref 85)

1ndash175(bovine ex vivo)

(Ref 85)

812 [3 T](mouse ex vivo)

(Ref 87)

42 [3 T](mouse ex vivo)

(Ref 87)

Brain058

(human ex vivo)(Ref 88)

000043 [0235 mm](rat in vivo)

(Ref 89)

1561ndash1565(human in vivo)

(Ref 31)

058ndash08(human ex vivo)

(Ref 32)

1300 [15 T](human in vivo)

(Ref 90)

75 [15 T](human in vivo)

(Ref 90)

mdash

104(human in vivo)

(Ref 31)

1820 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

99 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

Fat25

(human in vivo)(Ref 91)

mdash1476

(human ex vivo)(Ref 92)

06ndash52(human ex vivo)

(Ref 32)

266 [035 T](human in vivo)

(Ref 86)

57 [035 T](human in vivo)

(Ref 86)

mdash

1430ndash1480(human ex vivo)

(Ref 93)

246 [035 T](human in vivo)

(Ref 94)

545 [035 T](human in vivo)

(Ref 94)

Muscle15

(bovine ex vivo)(Ref 80)

015 [16 mm](pig ex vivo)

(Ref 96)

1555ndash1616(bovine ex vivo)

(Ref 30)

103(bovine ex vivo)

(Ref 30)

514 [035 T](human in vivo)

(Ref 94)

32 [035 T](human in vivo)

(Ref 94)

mdash

128(human in vivo)

(Ref 95)

Prostate11ndash25

(human ex vivo)(Ref 97)

018(insertion force)

[127 mm](human in vivo)

(Ref 99)

1614(human ex vivo)

(Ref 29)

018(human ex vivo)

(Ref 29)

1022 [15 T](human in vivo)

(Ref 100)

86 [15 T](human in vivo)

(Ref 100)

mdash

13ndash56(human ex vivo)

(Ref 98)

2 MATERIALS AND METHODS

In this study a general full factorial design of experiment(DOE) was created to study the effects of the ratio of softener toPVC polymer mass fraction of mineral oil and mass fractionof glass beads on mechanical and medical imaging propertiesof soft PVC Factorial analysis was utilized to identify thestatistical significance of three factors and a regression modelwas developed to find the quantitative relationship betweenPVC properties and three factors A regression model wasused to find values of three factors of the PVC as an exampleto achieve targeted mechanical and medical imaging propertiesand validate the results experimentally

2A Design of experiment

Three factors the mass ratio of softener to PVC polymersolution (RSP) the mass fraction of the mineral oil (wo)and the mass fraction of glass beads (wg) were identified inthe general full factorial DOE101 The RSP greatly affectedboth the mechanical and medical imaging properties of PVCThree levels of RSP (0 05 and 1) were examined for this

experiment PVC samples with RSP in this range had similarhardness to that of soft tissue The other two factors beingrelatively unknown (wo and wg) were tested at two levels Thehighest wo at which the mineral oil did not leak after curingwas found to be 5 This was the high value assigned towo If the mass fraction of glass beads wg was larger than1 the glass beads would precipitate during PVC curingTwo levels of the wg were chosen to be 0 and 1 InTable II twelve combinations of factors and their levels of theDOE in this study are shown The statistical analysis softwareMinitabreg (Minitab Inc State College PA USA) was usedto do factorial analysis and build regression model

T II Values of each factor at different levels for the DOE

Level

Factor Low Middle High

RSP 0 05 1wo 0 mdash 5wg 0 mdash 1

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5581 Li et al Polyvinyl chloride as a tissue-mimicking material 5581

2B Soft PVC fabrication

Soft PVC was made by mixing PVC polymer solutionand a softener in this case phthalate ester (both from M-FManufacturing Ft Worth TX USA) In this study mineraloil (WS Dodge Oil Maywood CA USA) and sphericalglass beads (50 microm average diameter) (Comco Burbank CAUSA) were added and mixed uniformly based on the DOERoom temperature mixture (initially white and opaque) ofthe PVC polymer solution the plastic softener and additives(mineral oil andor glass beads) was heated by a heat plateto 150 C with a magnetic bar stirring the liquid25 Increasingthe temperature beyond 120 C the PVC monomers start tocross-link to polymers and the solution becomes transparentreaching optimal cross-linking at 150 C After the mixtureturned transparent it was moved to a vacuum chamber toremove bubbles Once vacuumed the liquid mixture waspoured into molds and cooled to room temperature Threetypes of PVC samples as shown in Fig 1 were made The50 mm long PVC samples [445 mm in diameter Fig 1(a)]were used for needle insertion experiments The 20 mm longPVC samples [445 mm in diameter Fig 1(b)] were used forthe indentation hardness elastic modulus acoustic propertiesand the MRI time constants The samples with 10times10 mm2

and a length of 40 mm [Fig 1(c)] were made for visible lighttransmittance testing The top surface of the sample was aconcave meniscus as seen in Fig 1(a) due to the surfacetension during cooling

2C Compression test for elasticmodulus measurement

The method to measure the elastic modulus of PVCwas through compression testing a common method toobtain stressndashstrain relationships16102 Figure 2 shows thePVC sample on an acrylic plate before compression byan aluminum plate mounted to the linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) The samplewas compressed 9 mm (045 maximum engineering strain)at a speed of 05 mms The force exerted on the samplewas measured by a piezoelectric dynamometer (Model 9273Kistler Winterthur Switzerland) The engineering stress vsengineering strain curve indicated a nonlinear behavior of thematerial at large strains with a larger elastic modulus appearing

F 1 Samples of soft PVC (a) 445 mm in diameter and 50 mm in length(b) 445 mm in diameter and 20 mm in length and (c) 10times10 mm2 and40 mm in length

F 2 Experimental setup of the elastic modulus measurement

at higher strains The linear regime (below 015) was usedto calculate the elastic modulus of the PVC sample usingMATLABreg (Mathworks Natick MA USA) with the leastsquares method The average elastic modulus of three samplesof each composition was used to represent the PVC material

2D Shore hardness measurement

A Type OOO-S Shore durometer (Instron Norwood MAUSA) with a sphere surface indenter (1067 mm in radius)was used to measure the hardness of the soft PVC as shownin Fig 3 Since the PVC is soft and the sample size issmall the deformation of the sample under the compression

F 3 Experimental setup for measuring hardness of the soft PVC

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5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5580 Li et al Polyvinyl chloride as a tissue-mimicking material 5580

T I (Continued)

Elastic modulusE (kPa)

Needle insertion frictionforce f (Nmm) [needle

diameter]Speed of sound

c (ms)

Acousticattenuation α

[(dBcm)MHz]

T1 (ms) [fieldstrength] (Larmor

frequency)

T2 (ms) [fieldstrength] (Larmor

frequency)Visible lighttransmittance

059ndash173(human ex vivo)

(Ref 81)

0012 [127 mm](bovine ex vivo)

(Ref 83)

1577(bovine ex vivo)

(Ref 85)

1ndash175(bovine ex vivo)

(Ref 85)

812 [3 T](mouse ex vivo)

(Ref 87)

42 [3 T](mouse ex vivo)

(Ref 87)

Brain058

(human ex vivo)(Ref 88)

000043 [0235 mm](rat in vivo)

(Ref 89)

1561ndash1565(human in vivo)

(Ref 31)

058ndash08(human ex vivo)

(Ref 32)

1300 [15 T](human in vivo)

(Ref 90)

75 [15 T](human in vivo)

(Ref 90)

mdash

104(human in vivo)

(Ref 31)

1820 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

99 [3 T](gray matter)

(mouse ex vivo)(Ref 87)

Fat25

(human in vivo)(Ref 91)

mdash1476

(human ex vivo)(Ref 92)

06ndash52(human ex vivo)

(Ref 32)

266 [035 T](human in vivo)

(Ref 86)

57 [035 T](human in vivo)

(Ref 86)

mdash

1430ndash1480(human ex vivo)

(Ref 93)

246 [035 T](human in vivo)

(Ref 94)

545 [035 T](human in vivo)

(Ref 94)

Muscle15

(bovine ex vivo)(Ref 80)

015 [16 mm](pig ex vivo)

(Ref 96)

1555ndash1616(bovine ex vivo)

(Ref 30)

103(bovine ex vivo)

(Ref 30)

514 [035 T](human in vivo)

(Ref 94)

32 [035 T](human in vivo)

(Ref 94)

mdash

128(human in vivo)

(Ref 95)

Prostate11ndash25

(human ex vivo)(Ref 97)

018(insertion force)

[127 mm](human in vivo)

(Ref 99)

1614(human ex vivo)

(Ref 29)

018(human ex vivo)

(Ref 29)

1022 [15 T](human in vivo)

(Ref 100)

86 [15 T](human in vivo)

(Ref 100)

mdash

13ndash56(human ex vivo)

(Ref 98)

2 MATERIALS AND METHODS

In this study a general full factorial design of experiment(DOE) was created to study the effects of the ratio of softener toPVC polymer mass fraction of mineral oil and mass fractionof glass beads on mechanical and medical imaging propertiesof soft PVC Factorial analysis was utilized to identify thestatistical significance of three factors and a regression modelwas developed to find the quantitative relationship betweenPVC properties and three factors A regression model wasused to find values of three factors of the PVC as an exampleto achieve targeted mechanical and medical imaging propertiesand validate the results experimentally

2A Design of experiment

Three factors the mass ratio of softener to PVC polymersolution (RSP) the mass fraction of the mineral oil (wo)and the mass fraction of glass beads (wg) were identified inthe general full factorial DOE101 The RSP greatly affectedboth the mechanical and medical imaging properties of PVCThree levels of RSP (0 05 and 1) were examined for this

experiment PVC samples with RSP in this range had similarhardness to that of soft tissue The other two factors beingrelatively unknown (wo and wg) were tested at two levels Thehighest wo at which the mineral oil did not leak after curingwas found to be 5 This was the high value assigned towo If the mass fraction of glass beads wg was larger than1 the glass beads would precipitate during PVC curingTwo levels of the wg were chosen to be 0 and 1 InTable II twelve combinations of factors and their levels of theDOE in this study are shown The statistical analysis softwareMinitabreg (Minitab Inc State College PA USA) was usedto do factorial analysis and build regression model

T II Values of each factor at different levels for the DOE

Level

Factor Low Middle High

RSP 0 05 1wo 0 mdash 5wg 0 mdash 1

Medical Physics Vol 43 No 10 October 2016

5581 Li et al Polyvinyl chloride as a tissue-mimicking material 5581

2B Soft PVC fabrication

Soft PVC was made by mixing PVC polymer solutionand a softener in this case phthalate ester (both from M-FManufacturing Ft Worth TX USA) In this study mineraloil (WS Dodge Oil Maywood CA USA) and sphericalglass beads (50 microm average diameter) (Comco Burbank CAUSA) were added and mixed uniformly based on the DOERoom temperature mixture (initially white and opaque) ofthe PVC polymer solution the plastic softener and additives(mineral oil andor glass beads) was heated by a heat plateto 150 C with a magnetic bar stirring the liquid25 Increasingthe temperature beyond 120 C the PVC monomers start tocross-link to polymers and the solution becomes transparentreaching optimal cross-linking at 150 C After the mixtureturned transparent it was moved to a vacuum chamber toremove bubbles Once vacuumed the liquid mixture waspoured into molds and cooled to room temperature Threetypes of PVC samples as shown in Fig 1 were made The50 mm long PVC samples [445 mm in diameter Fig 1(a)]were used for needle insertion experiments The 20 mm longPVC samples [445 mm in diameter Fig 1(b)] were used forthe indentation hardness elastic modulus acoustic propertiesand the MRI time constants The samples with 10times10 mm2

and a length of 40 mm [Fig 1(c)] were made for visible lighttransmittance testing The top surface of the sample was aconcave meniscus as seen in Fig 1(a) due to the surfacetension during cooling

2C Compression test for elasticmodulus measurement

The method to measure the elastic modulus of PVCwas through compression testing a common method toobtain stressndashstrain relationships16102 Figure 2 shows thePVC sample on an acrylic plate before compression byan aluminum plate mounted to the linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) The samplewas compressed 9 mm (045 maximum engineering strain)at a speed of 05 mms The force exerted on the samplewas measured by a piezoelectric dynamometer (Model 9273Kistler Winterthur Switzerland) The engineering stress vsengineering strain curve indicated a nonlinear behavior of thematerial at large strains with a larger elastic modulus appearing

F 1 Samples of soft PVC (a) 445 mm in diameter and 50 mm in length(b) 445 mm in diameter and 20 mm in length and (c) 10times10 mm2 and40 mm in length

F 2 Experimental setup of the elastic modulus measurement

at higher strains The linear regime (below 015) was usedto calculate the elastic modulus of the PVC sample usingMATLABreg (Mathworks Natick MA USA) with the leastsquares method The average elastic modulus of three samplesof each composition was used to represent the PVC material

2D Shore hardness measurement

A Type OOO-S Shore durometer (Instron Norwood MAUSA) with a sphere surface indenter (1067 mm in radius)was used to measure the hardness of the soft PVC as shownin Fig 3 Since the PVC is soft and the sample size issmall the deformation of the sample under the compression

F 3 Experimental setup for measuring hardness of the soft PVC

Medical Physics Vol 43 No 10 October 2016

5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5581 Li et al Polyvinyl chloride as a tissue-mimicking material 5581

2B Soft PVC fabrication

Soft PVC was made by mixing PVC polymer solutionand a softener in this case phthalate ester (both from M-FManufacturing Ft Worth TX USA) In this study mineraloil (WS Dodge Oil Maywood CA USA) and sphericalglass beads (50 microm average diameter) (Comco Burbank CAUSA) were added and mixed uniformly based on the DOERoom temperature mixture (initially white and opaque) ofthe PVC polymer solution the plastic softener and additives(mineral oil andor glass beads) was heated by a heat plateto 150 C with a magnetic bar stirring the liquid25 Increasingthe temperature beyond 120 C the PVC monomers start tocross-link to polymers and the solution becomes transparentreaching optimal cross-linking at 150 C After the mixtureturned transparent it was moved to a vacuum chamber toremove bubbles Once vacuumed the liquid mixture waspoured into molds and cooled to room temperature Threetypes of PVC samples as shown in Fig 1 were made The50 mm long PVC samples [445 mm in diameter Fig 1(a)]were used for needle insertion experiments The 20 mm longPVC samples [445 mm in diameter Fig 1(b)] were used forthe indentation hardness elastic modulus acoustic propertiesand the MRI time constants The samples with 10times10 mm2

and a length of 40 mm [Fig 1(c)] were made for visible lighttransmittance testing The top surface of the sample was aconcave meniscus as seen in Fig 1(a) due to the surfacetension during cooling

2C Compression test for elasticmodulus measurement

The method to measure the elastic modulus of PVCwas through compression testing a common method toobtain stressndashstrain relationships16102 Figure 2 shows thePVC sample on an acrylic plate before compression byan aluminum plate mounted to the linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) The samplewas compressed 9 mm (045 maximum engineering strain)at a speed of 05 mms The force exerted on the samplewas measured by a piezoelectric dynamometer (Model 9273Kistler Winterthur Switzerland) The engineering stress vsengineering strain curve indicated a nonlinear behavior of thematerial at large strains with a larger elastic modulus appearing

F 1 Samples of soft PVC (a) 445 mm in diameter and 50 mm in length(b) 445 mm in diameter and 20 mm in length and (c) 10times10 mm2 and40 mm in length

F 2 Experimental setup of the elastic modulus measurement

at higher strains The linear regime (below 015) was usedto calculate the elastic modulus of the PVC sample usingMATLABreg (Mathworks Natick MA USA) with the leastsquares method The average elastic modulus of three samplesof each composition was used to represent the PVC material

2D Shore hardness measurement

A Type OOO-S Shore durometer (Instron Norwood MAUSA) with a sphere surface indenter (1067 mm in radius)was used to measure the hardness of the soft PVC as shownin Fig 3 Since the PVC is soft and the sample size issmall the deformation of the sample under the compression

F 3 Experimental setup for measuring hardness of the soft PVC

Medical Physics Vol 43 No 10 October 2016

5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5582 Li et al Polyvinyl chloride as a tissue-mimicking material 5582

of the durometer was large and would be difficult to ensurefull contact between the durometer plate and the samplein manual tests To overcome this problem the durometerwas mounted to a computer-controlled linear actuator (ModelHLD60 Moog Animatics Milpitas CA USA) to controlits movement and position After the indenter contacted thesample surface the actuator drove the durometer down 5 mmuntil the durometer plate (see Fig 3) touched the samplesurface and the reading on the dial denoted as H was takenas the Shore OOO-S hardness of this PVC sample Three PVCsamples (20 mm in length) were measured for each of the 12groups of PVC

The indentation test results were used to calculate theelastic modulus of the sample as the indentation force canbe obtained based on the American Society for Testing andMaterials (ASTM) Standard D2240-05 (Ref 103)

F = 001756H+0167 (1)

where H is the durometer reading and F is the indentationforce The indentation depth h of the indenter can be calculatedwith H 103

h= 0005(1minus H

100

) (2)

Based on the model of Briscoe et al104 the elastic modulusE of the PVC sample can be calculated with the indentationforce F indentation depth h Poissonrsquos ratio ν and the radiusof the indenter spherical surface R

E =31minus ν2F

4radic

Rh32 (3)

The Poissonrsquos ratio of soft PVC was assumed to be 049 viathe results of Naylor105 The R of the indenter is 107 mm Theelastic modulus calculated from the hardness was comparedto that measured by the compression test with the differenceratio (EtestminusEcal)Etest

2E Viscoelastic relaxation timeconstant measurement

Soft PVC is a viscoelastic material16 If a constant strainwas applied to a sample the stress would relax over time106 Tocharacterize PVCrsquos viscoelastic properties the experimentalsetup used for the compression test of Sec 2D was modifiedsuch that the sample was compressed with a strain of 015 ata rate of 167 mms and then this strain was kept constant for300 s The force on the sample during this time was measuredby the dynamometer used in elastic modulus testing and theobtained stressndashtime curves were used to estimate the stressrelaxation time constants of the material The MATLABregcurve fitting toolbox was used to fit the stress relaxation curveswith the nonlinear least square method

2F Needle insertion friction force measurement

Needle insertion experiments were used to assess the fric-tion forces between the PVC and a needle The experimentalsetup for needle insertion (Fig 4) was designed to insert an

F 4 Experimental setup of the needle insertion tests

18 gauge (101 mm diameter) stainless steel solid trocar with10 bevel angle three-plane diamond tip into the PVC Fora solid needle insertion procedure when the needle tip wasinside the sample the axial force was the sum of cutting forceat the tip and the friction force on the surface of the needlerod After the needle tip punched out of the sample only thefriction force remained on the needle Similar to the methodused by Wang et al11 after the needle reached the farthestposition in each insertion it was retracted and advanced threetimes to test the friction force exclusively in cyclic insertion

To facilitate this measurement a needle was fixed to acustom designed needle holder that was mounted to a stackof linear stages in parallel Two linear stages (Model 200criSiskiyou Instrument Grants Pass OR USA) were used todrive the needle into the PVC sample with the same speedin the same directionmdashthe combination of the two stagesin parallel allowed the distance over which the needle wasmoved to be longer (insertion speed of 07 mms and aninsertion distance of 70 mm) Another linear stage (Model100cri Siskiyou Instrument Grants Pass OR USA) wasused to adjust the position of the needle A piezoelectricdynamometer (Model 9256 Kistler Winterthur Switzerland)was used to measure the force during the needle insertion Acylindrical PVC sample (445 mm in diameter and 50 mm in

F 5 Picture of the experimental setup for acoustic propertiesrsquomeasurement

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5583 Li et al Polyvinyl chloride as a tissue-mimicking material 5583

F 6 The stressndashstrain curve of the PVC material with RSP of 1 wo of0 and wg of 0

length) was secured by a holder to top of the dynamometer Foreach sample the insertion procedure was repeated six timesalong a concentric circle of the cylinder by rotating the sample60 between each run

2G Acoustic propertiesrsquo measurements

The speed of sound and acoustic attenuation coefficient ofthe PVC samples were measured using the method describedby Xu and Kaufman107 A PVC sample was placed ina degassed water tank between an unfocused ultrasoundtransducer (35 MHz 13 mm aperture Aerotech LaboratoriesLewistown PA USA) and a hydrophone (HNR-0500 ONDACorporation Sunnyvale CA USA) To ensure that theacoustic path length through the sample was equal to thethickness of the sample the hydrophone was aligned at a pointperpendicular to the center of the transducer surface and theplane of the sample was oriented parallel to the transducer sur-face (see Fig 5) The thickness of each sample was measuredwith a caliper The unfocused transducer generated and sentacoustic pulses through the samples that were then receivedby the hydrophone The received acoustic signal was capturedand displayed using an oscilloscope (1 GHz LC574ALLeCroy Chestnut Ridge NY USA) To measure the acousticproperties acoustic pulses were first generated and measuredwithout a sample between the transducer and the hydrophone

F 7 The elastic modulus of 12 PVC samples obtained from the compres-sion test (red line representing the elastic modulus estimated based on theShore hardness)

F 8 The hardness of 12 PVC samples measured by durometer

giving a baseline reading of the time delay and amplitude ofthe acoustic signal in water Once a baseline was establisheda sample was placed between the transducer and the receiverWith the sample in between the delay of the received signalwas altered and the amplitude was reduced Knowing the delayof the received signals with and without the sample in the paththe speed of sound in the PVC material could be calculated by

c=δ

t1minus t0cwminusδcw

(4)

where c is the speed of sound in the sample δ is the thicknessof the sample cw is the speed of sound in water t0 is thetime delay without the sample and t1 is the time delay withthe sample Taking the ratio of the signal amplitude with andwithout the sample in the path allowed us to calculate theattenuation coefficient with

α =minus20 logA1

A0δ f (5)

where α is the acoustic attenuation coefficient A1 is thereceived signal amplitude with the sample in the path A0 isthe signal amplitude without the sample δ is the thicknessof the sample in centimeter and f is the frequency ofthe ultrasound wave (35 MHz for this study) To test thescattering effect of the glass beads ultrasound images of thePVC samples with and without glass beads were recordedwith a handheld ultrasound probe (Vascular Access 99-5930 Interson Medical Instruments Pleasanton CA USA)connected to a computer via universal serial bus (USB)

F 9 The sample data of viscoelasticity measurement fitted with five-parameter generalized Maxwell model

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

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2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5584 Li et al Polyvinyl chloride as a tissue-mimicking material 5584

F 10 The values of relaxation time constants τ for 12 PVC samples

2H Optical clarity characterization

In optics and spectroscopy transmittance is the fraction ofincident light (electromagnetic radiation) at a specified wave-length that passes through a sample108 In this study transmit-tance was chosen to represent the transparency of the PVCmaterial The samples were placed into 45 ml poly(methylmethacrylate) (PMMA) cuvettes (dispolab Kartell) withdeionized water Samples were chosen with minimal surfacevariations to lessen the effects of surface properties on themeasurements A spectrophotometer (Biomate 3S ThermoScientific Waltham MA USA) was used to measure thetransmittance of visible light (380ndash750 nm in 1 nm increments)through each of the twelve types of samples A qualitativeassessment of the optical clarity of PVC was also made byplacing a sample over a checkerboard pattern and observingits clarity

2I MRI time constant T1 and T2 measurements

The order of the samples was chosen randomly for imagingand personnel acquiring and analyzing the MRI data wereblinded to the contents of the samples All MRIs wereperformed at 70 T using a Direct Drive Console (AgilentTechnologies Santa Clara CA USA) and a 72 mm inner-diameter transmit-receive radiofrequency (RF) volume coil(Rapid Biomedical Rimpar Germany) Prior to imaging thesamples were fitted into a plastic ring to fix the sample andwrapped in a parafilm in order to avoid contamination of theequipment The wrapped samples were taped onto a plastictray within the RF coil to further minimize motion Following

F 11 An example of needle force of the six insertions into the PVC withRSP of 05 wo of 0 and wg of 1

scout imaging to confirm proper placement of samples a spin-echo sequence was used to acquire data using a 64times64 matrixzero-filled to 128times128 For calculations of T1 the spin-echosequence included a preparatory inversion pulse (180) andthe inversion time (TI) was arrayed with values relevantto approximate T1 values for these samples [field of view= 60times60 mm2 slice thickness= 2 mm 1 slice repetition time= 2550 ms echo time (TE)= 15 ms inversion time TI = 50400 1100 and 2500 ms number of excitations (NEX) = 1and acquisition time sim 11 min] For calculations of T2 thespin-echo sequence included an array of TE values relevant toT2 fitting for these samples (field of view = 60times60 mm2 slicethickness= 2 mm 1 slice repetition time= 2550 ms TE= 112825 455 6275 and 80 ms NEX= 1 and acquisition timesim 13 min) Prior to data acquisition on all samples a subsetwas used to determine the appropriate TIs and TEs Althoughthe Larmor frequency of the samples differs from water basedsubstances using the automatic prescan settings in preparationfor acquiring images the MRI system automatically detectedand assigned the appropriate frequency to use for imagingthese samples Due to the dependence of T1 on temperature109

ambient temperature near to the sample was measured using afiber optic temperature probe (SA Instruments Stony BrookNY USA)

Images were analyzed using MRVision (Winchester MAUSA) to produce a T1 and T2 map for each sample Respectiveimage sets were fitted to the equation for T1 mapping

SI=M01minus (1+a)eTIT1

(6)

F 12 Schematics to illustrate the difference in the insertion and retraction procedures (a) before needle insertion (b) needle insertion (Region III V and VIIin Fig 11) and (c) needle retraction (Regions II IV and VI in Fig 11)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5585 Li et al Polyvinyl chloride as a tissue-mimicking material 5585

F 13 Friction force per length f in needle insertion of 12 PVC samples

and for T2 mapping

SI=M0eminusTET2 (7)

where SI is the signal intensity of a given image M0 is the finalor initial signal intensity (for T1 and T2 mapping respectively)and a is the adjusting coefficient for potential incomplete T1relaxation due to repetition time used The T1 mapping methodprovided through MRVision uses a nonlinear least squaresfit to the set of inversion recovery weighted images withfitting parameters of M0 T1 and a and input parameters beingthe TI values Initial guesses for the fitting parameters areautomatically estimated for each pixel using the final signallevel for M0 an estimation of T1 from the approximate nullpoint and a = 1 [which would make the argument (1+a)= 2or complete T1 relaxation] The T2 mapping method providedthrough MRVision uses a linear regression analysis on the setof T2 weighted images with fitting parameters M0 and T2 foreach pixel and input parameters being the TE values Fromthe resultant maps the mean values and standard deviationsof T1 a and T2 were measured using a region of interestlocated approximately at the center of the sample trying toavoid potential artifacts at the interface between the sampleand plastic ring or air bubbles within the sample

3 RESULTS AND DISCUSSION3A Elastic modulus

A representative engineering stress vs engineering straincurve of a PVC sample is shown in Fig 6 In the beginning

F 14 Speeds of sound c of 12 PVC samples

F 15 Acoustic attenuation coefficients α of 12 PVC samples

the stress increased with the strain linearly and after the strainexceeded approximately 015 the stress began to increasewith stain nonlinearly To get the elastic modulus E in thelinear elastic region of the material the measured stress datawith strain below 015 were used Figure 7 shows the elasticmodulus of 12 PVC samples measured through compressiontest The error bars (in black) represent the standard deviationof the value of the three samples for each PVC materialAll values were seen to be below 50 kPa E decreased withincreasing RSP The elastic moduli of PVC with RSP valuesof 0 were about five times larger than those with an RSP of1 (all below 10 kPa) The PVC samples with mineral oil hada smaller E than those without mineral oil The glass beadstended to slightly lower E of the PVC Consulting the list oftissue properties seen in Table I our PVC samples were foundto be within the range of in vivo human muscle and ex vivohuman prostate

3B Shore hardness

The Shore OOO-S hardness H of the PVC with differentcompositions is shown in Fig 8 The error bars represent thestandard deviation of the value of three samples for each PVCmaterial These PVC samples were very soft with H typicallybelow 50 PVC samples with RSP values of 0 were observedto have hardness of five times greater than those with RSP

values of 1 The addition of mineral oil also lowered H by10ndash40

The elastic modulus can also be estimated based on theShore hardness [Eqs (1)ndash(3)] Red lines in Fig 7 representthe elastic moduli calculated based on the durometer Shorehardness indentation test For harder PVC samples (RSP = 0)the E estimated based on H was about 7 greater than thatmeasured via the compression test This trend was reversedwhen the PVC material was softer (RSP = 05 and 1) Ingeneral the durometer indentation test which is easier toperform than the compression test can be utilized to predictthe E for the PVC samples with less than 30 error

3C Viscoelastic relaxation time constant

The viscoelastic stress relaxation time constant of thePVC sample was investigated by fitting the experimentallymeasured stressndashtime curve with a five-parameter generalized

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5586 Li et al Polyvinyl chloride as a tissue-mimicking material 5586

F 16 Ultrasound pictures of PVC samples with and without glass beads(a) RSP = 0 wo = 0 and wg = 0 and (b) RSP = 0 wo = 0 and wg = 1

Maxwell model to obtain the viscoelastic relaxation timeconstants110 The equation to describe the stress relaxationbehavior in five-parameter generalized Maxwell model is

σ =σ0+σ1eminustτ1+σ2eminustτ2 (8)

where σ0 is the stable stress σ1 and σ2 are the stress constantsand τ1 and τ2 are the relaxation time constants for two Maxwellbranches In the data fitting the σ0 was appointed with thevalue of the stress at 300 s to avoid the fitted stable σ deviatingtoo far from the measured value This generalized Maxwellmodel can fit the stress relaxation curve accurately (R2= 099)as shown in Fig 9

Among five parameters of this model the relaxation timeconstants τ1 and τ2 are parameters of the viscous property Toestablish a regression model of the relaxation time constantthe larger of τ1 and τ2 was chosen to represent the principlerelaxation time constant τ of the stress relaxation behaviorThe τ as shown in Fig 10 is increased with RSP Withthe same RSP the addition of mineral oil decreased the τ Theerror bars represent the standard deviation of the value of thethree samples for each PVC material

3D Friction force in needle insertion

An example of the needle insertion force along the axialdirection for six insertions to the PVC sample (RSP of 05

wo of 0 and wg of 1) is shown in Fig 11 This needleinsertion force profile was similar to that of silicone11 Sevenregions (marked as Regions IndashVII) were identified in the forceprofile In Region I the needle was inserted into the sample andpunched out There were four phases (marked as Phases IndashIV)in Region I In Phase I the insertion force increased with timeas the needle tip indented and deformed the soft sample untilit reached the small peak value (of 015 N in the case shownin Fig 11) In Phase II the insertion force dropped slightlyafter the needle tip cut into the PVC surface In Phase IIIthe insertion force increased due to the increase in the contactarea and friction force between the needle and the PVC duringthe needle insertion until reaching the large peak value (of113 N in this case) To this point the needle insertion forceis the summation of the cutting force and the friction force InPhase IV the insertion force dropped and remained relativelyunchanged because the needle tip had punched out of the PVCsample The contact surface area and friction force (about105 N) between the needle and PVC sample remained thesame in this phase

In Regions IIndashVII the needle was retracted and insertedthree times In Regions II IV and VI the needle was retractedby 20 mm with the tip still outside the sample The forcein these regions (about 087 N) was the friction force in thedirection opposite to that in Region I This force (087 N)was lower than that of Region I (105 N) due to the concavemeniscus surface of the PVC phantom [as shown in Fig 12(a)]As shown in Fig 12(b) the sample was more constrained inthe advancing procedure than that in the retraction as shownin Fig 12(c) Therefore higher friction force on the needlesurface was observed in Regions I (Phase IV) III V andVII The friction force remained almost unchanged in therepeated needle insertions or retractions It showed that thePVC samples were durable and could resist repeated needleinsertions

The average force of Phase IV in Region I was used torepresent the friction force of the needle insertion The frictionforce per unit length denoted as f was used as a parameterto compare the difference of the needle insertion property ofthe 12 PVC samples (as shown in Fig 13) The error barsin Fig 13 represent the standard deviation of the value of

F 17 Visible light transmittance in each PVC sample in the wavelength range from 380 to 750 nm

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5587 Li et al Polyvinyl chloride as a tissue-mimicking material 5587

F 18 Transmittance of PVC samples at different wavelength of two lasers (a) 532 nm and (b) 695 nm

the three samples for each PVC material PVC samples withwo = 5 had about 50 lower f than those with wo = 0The f of the PVC samples in this study was in the range of0005ndash0086 Nmm which was similar to that of silicone with20ndash40 mineral oil11 According to Table I the f of thePVC samples was close to that of ex vivo animal liver

3E Acoustic properties of the PVC samples

The speeds of sound c of the PVC samples are shownin Fig 14 The error bars represent the standard deviationof the values of the three samples for each PVC materialThe c decreased with the increase of RSP The PVC sampleswith glass beads tended to have a slightly higher c than thosewithout glass beads (except PVC sample with RSP = 0 wo

= 5 and wg = 1) As seen in Table I most tissues in humanand animals have speeds of sound around 1500ndash1600 ms dueto their water content The speeds of sound in PVC samplesof this paper were between 1390 and 1410 ms which has agap with that of the normal tissue

The acoustic attenuation coefficients α of the PVCsamples are shown in Fig 15 The error bars represent thestandard deviation of the value of the three samples for eachPVC material The α decreased with the increasing RSP Theaddition of glass beads raised α except in the PVC sample withRSP = 05 wo = 5 and wg = 1 The difference betweensamples with and without glass beads was large in sampleswith RSP = 1 According to Table I α of PVC samples areslightly smaller than those of human brain and fat

The addition of glass beads enhanced the acoustic scat-tering of the PVC samples for ultrasound imaging Withoutglass beads ultrasound images of PVC samples appear darkas seen in Fig 16(a) With glass beads the ultrasound imagegenerated speckles [see Fig 16(b)] similar to those seen inhuman tissue ultrasound images

3F Optical clarity of the PVC samples

The visible light transmittance of each PVC sample isshown in Fig 17 The PVC samples with glass beads had20ndash73 lower visible light transmittance than those withoutglass beads However the value of RSP also influencedthe transmittance tending to increase transmittance with a

larger RSP Figure 17 shows pictures of the clearest and theopaquest PVC samples atop a checkerboard background Thetransparency of the other PVC samples was between these twoextremes

To make the results more immediately practical valuesof transmittance for the PVC samples for two common laserwavelengths are shown in Fig 18 In this way researcherscould quantitatively design PVC material with desired opticaltransmittance given a desired wavelength of observationThese wavelengths are 532 nm [typically seen in NG-YAGlasers widely used in PIV (Ref 111)] and 695 nm (seenin ruby lasers112) These two wavelengths are marked inFig 17 The transmittance at these two targeted wavelengths532 and 695 nm is defined as Tλ695 and Tλ532 respectivelyThe transmittance of the samples increased with RSP exceptfor the samples with oil but without glass beads becausethe softener can cross-link with the PVC polymer and makethe sample more transparent The sample with RSP = 05wo = 5 and wg = 0 had smaller transmittance than that of thesample with RSP = 0 wo = 5 and wg = 0 It was attributedto the effect of oil on the cross-linking of the PVC polymersin the samples with RSP = 05 When the RSP was largerthe effect of the oil was negligible and the transmittance waslarger Figure 18 shows that the addition of glass beads loweredthe transmittance by 20ndash73 In the samples with RSP = 0the drop of transmittance by the glass beads was larger thanthose of the sample with softener It was because the softenercould increase the transparency of the sample and weakenthe negative effect of the glass beads on the transmittance

F 19 Representative T1 and T2 images with resulting time constant maps(TI = inversion time and TE= echo time)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5588 Li et al Polyvinyl chloride as a tissue-mimicking material 5588

F 20 MRI time constants of 12 PVC samples (a) T1 and (b) T2

The significance of the three factors on Tλ695 and Tλ532 wasanalyzed in Sec 4

3G MRI time constants T1 and T2 of PVC samples

A representative image set a typical region of interestand T1 or T2 maps of the sample with RSP = 1 wo = 0and wg = 1 are shown in Fig 19 Summary data (meanplusmn standard deviation) of T1 and T2 values of the PVC samplesare shown in Figs 20(a) and 20(b) The error bars representthe standard deviation of the value of the three samples foreach PVC material Ambient temperature near to the samplefluctuated minimally across all acquisitions (166plusmn 04 C)T1 values varied about 9 across all samples (mean 438 msrange 421ndash461 ms) with the mean of the fitting parameteraccounting for potential incomplete relaxation (a) being087plusmn004 T2 values varied about 37 (mean 25 ms range21ndash29 ms) At the same high field strength (7 T) as that inthis paper the T2 of fat was about 31ndash40 ms (Ref 113) the T1of the white matter was 1220 ms (Ref 114) and the T1 and T2of lymph nodes are 994 and 32 ms (Ref 115) The T1 and T2 ofthe PVC samples are all lower than real tissue RSP had thegreatest effect on T1 and T2 Both the time constants increasedwith increasing RSP Mineral oil had no clear effect on T1 orT2 while the addition of glass beads tended to slightly lowerT2

Although this work was performed at a higher field strength(70 T) than that which is approved for typical clinical use itwas the same field strength at which novel research is currentlyperformed in humans113ndash115 Due to the unknowns related

to the anatomy or physiology of interest along with thoseassociated with a newer field strength this type of research athigher field strength was thought to benefit the most from theuse of tissue-mimicking materials and phantoms to validateMRI techniques including but not limited to pulse sequenceand RF design The only notable difference here was that thiswork was performed on a small bore system

For T1 measurements the parameter (a) calculated fromfitting suggested that we did not use a repetition time longenough to allow for complete relaxation of spins (a = 087 vs1) This would result in a slight underestimation of T1However the comparisons of sample content with respectto T1 and T2 time constants made here were performed withdata acquired with imaging conditions being nearly constantincluding temperature which has a known influence on T1109

4 REGRESSION MODEL OF THE MECHANICALAND IMAGING PROPERTIES OF PVC4A Factorial analysis

The factorial analysis results of the main effects and two-way interactions of three factors (RSP wo and wg) onthe elastic modulus (E) hardness (H) viscoelastic stressrelaxation time constant (τ) needle insertion friction force( f ) speed of sound (c) acoustic attenuation (α) MRI timeconstants (T1 and T2) transmittance at 695 nm (Tλ695) and532 nm (Tλ532) are summarized in Table III Significant factorsand interactions (p le 005) are marked with a superscript (a)The RSP had statistically significant effect on all properties of

T III The factorial analysis of the three factors on PVC mechanical and imaging properties

p value

FactorElastic

modulus E

HardnessH

Stress relaxationtime constant τ

Frictionforce f

Speed ofSound c

Attenuationα

MRI RelaxationTime T1

MRI RelaxationTime T2

TransmittanceTλ695

TransmittanceTλ532

RSP lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a lt0001a 0074 0076wo lt0001a lt0001a 0021a lt0001a 0480 0380 0106 0236 0217 0118wg 0007a 0098 0933 0396 0120 0146 0053 lt0001a 0008a 0011a

RSP wo 0007a 0060 0666 lt0001a 0816 0662 0081 0456 0435 0470RSP wg 0046a 0008a 0754 0757 0509 0117 0739 0584 0132 0142wo wg 0309 0696 0948 lt0001a 0367 0774 0280 0834 0712 0566

aStatistically significant p le 005

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5589 Li et al Polyvinyl chloride as a tissue-mimicking material 5589

T IV The regression equations of E H τ f c α T1 T2 Tλ695 and Tλ532

Regression equation R2 Applicable range

E (kPa)= 455minus78RSPminus757wominus218wg +636RSPwo+216RSPwg +396R2SP 099 6ndash45

H = 509minus636RSPminus656wominus133RSPwg +215R2SP 099 6ndash51

τ (s)= 1253+587RSPminus214wo 083 1141ndash1919f (Nmm)= 008minus013RSPminus069w0+074RSPwominus718wowg +0062R2

SP 097 0005ndash0086c (ms)= 1407minus217RSP+839R2

SP 084 1393ndash1407α (dBcmMHz)= 061minus05RSP+027R2

SP 072 038ndash061T1 (ms)= 430+200RSPminus393wg 067 4263ndash4502T2 (ms)= 223+613RSPminus819wg 097 215ndash284Tλ695 ()= 765+161RSPminus2970wg 088 468ndash926Tλ532 ()= 687+176RSPminus2760wg 083 411ndash863

the PVC except Tλ695 and Tλ532 wo had statistically significanteffect on E H τ and f and wg had statistically significanteffect on E H T2 Tλ695 and Tλ532 The interaction of RSP

and wo (denoted as RSP wo in Table III) had statisticallysignificant effect on E and f The interaction of RSP and wg

was statistically significant to E and H The interaction of wo

and wg only had statistically significant effect on f Based onthe factorial analysis results in Table III regression equationsof all properties tested in this paper were developed using theMinitabregwith the corresponding statically significant factorsand interactions Since the p value of wg (0053) to T1 is veryclose to 005 wg was added to the regression equation ofT1 Although RSP is a little larger than 005 for Tλ695 andTλ532 we found that RSP greatly affected the transparency ofPVC samples Therefore RSP was added to the regressionequations for Tλ695 and Tλ532

4B Regression model

The regression equations and their R2 values based on ourexperiments are listed in Table IV The statistically significantfactors and interactions were included in the regressionequations The R2

SP term was added to improve accuracyof the regression model For example the regression equationof H included the statistically significant factors RSP and wothe interaction RSP wg and the R2

SP The ranges of the inputparameters were 0 lt RSP le 1 0 lt wo le 5 and 0 lt wg le 1

and the output parameter ranges in the regression model arelisted in Table IV

5 APPLICATION OF REGRESSION MODELTO DESIGN THE PVC WITH TARGETEDMECHANICAL PROPERTIESAND THE EXPERIMENTAL VALIDATION

The mechanical properties of the PVC samples have largeranges and close to those of tissues according to Table IHowever the medical imaging properties have a small rangeand a discrepancy with real tissue Therefore the regressionmodels of the mechanical properties can be used to design thematerial while those of medical imaging properties could stillbe used to forecast the properties of PVC samples with theRSP wo and wg in the ranges of this study

By specifying values for any three of the four parameters(E H τ and f ) within the range of regression modelthe composition of PVC (RSP wo and wg) could beobtained For example given E = 220 kPa τ = 1393 s and f= 00318 Nmm the regression model calculated RSP = 033wo = 25 and wg = 05 The fourth mechanical property Hand medical imaging properties (c α T1 T2 Tλ695 and Tλ532)could be obtained with the regression equations

To validate the accuracy of the regression model a PVCsample with RSP = 033 wo = 25 and wg = 05 was

T V Validation results of the PVC materials with RSP of 033 wo of 25 and wg of 05

Calculated value Experimental results Error () Max allowable error ()

E (kPa) 220 228 34 867H 306 303 098 882τ (s) 1393 1343 4 682f (Nmm) 00318 00365 148 942c (ms) 1400 1408 06 1α [(dBcm)MHz] 047 045 40 377T1 (ms) 4348 444 21 53T2 (ms) 239 24 04 243Tλ695 () 67 663 10 494Tλ503 () 607 605 03 523

Note The maximum allowable error is the ratio of the difference between maximum and minimum values normalized tothe maximum value in the applicable range of the regression equation

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

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5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5590 Li et al Polyvinyl chloride as a tissue-mimicking material 5590

fabricated and the mechanical and medical imaging propertiesof the new sample were tested with experiments and comparedto the calculated values from the regression equations Asshown in Table V except f the error of each property islower than 5 The error of f is 148 because the value of fis affected by other mechanical properties of the PVC samplesuch as E and τ The errors of other properties aggregated tomake the error of f very large This example demonstratesthe feasibility of applying the regression model to find thecomposition of RSP wo and wg and design a PVC materialwith desired mechanical properties The medical imagingproperties of PVC material could be forecasted accurately

6 CONCLUSIONS

The procedure of applying a regression model to findthe formulation of PVC (RSP wo and wg) to achievetargeted mechanical properties was demonstrated and vali-dated experimentally Based on this approach PVC phantomtissues for clinical simulators or medical research devicescould be designed with desired mechanical properties andan appropriate composition of PVC can be identified usingthe regression model The medical imaging properties of thePVC samples have narrow ranges and commonly are not closeenough to those of real tissues The regression models ofmedical imaging properties were able to predict the value ofthese properties of the PVC sample with known composition

There are several limitations of the PVC material in thisstudy The mechanical and imaging properties of the PVCphantom material will gradually change over time The long-term stability and effects of properties of the PVC phantommaterial require further study This PVC material is notsuitable to mimic the brain Since the speed of sound of thePVC samples in this paper is lower than that of normal tissueother additives which can increase the speed of sound will beadded In addition more research on the echogenicity of thephantom is also needed

ACKNOWLEDGMENTS

This research work is sponsored by the Nation ScienceFoundation (NSF) Award No CMMI 1266063 and theChinese Scholarship Council

CONFLICT OF INTEREST DISCLOSURE

The authors have no COI to report

1J Dankelman ldquoSurgical simulator design and developmentrdquo World J Surg32(2) 149ndash155 (2008)

2K J Domuracki C J Moule H Owen G Kostandoff and J L PlummerldquoLearning on a simulator does transfer to clinical practicerdquo Resuscitation80(3) 346ndash349 (2009)

3A Liu F Tendick K Cleary and C Kaufmann ldquoA survey of surgical simu-lation Applications technology and educationrdquo Presence TeleoperatorsVirtual Environ 12(6) 599ndash614 (2003)

4M Srinivasan J C Hwang D West and P M Yellowlees ldquoAssessmentof clinical skills using simulator technologiesrdquo Acad Psychiatry 30(6)505ndash515 (2006)

5M O Culjat D Goldenberg P Tewari and R S Singh ldquoA review of tissuesubstitutes for ultrasound imagingrdquo Ultrasound Med Biol 36(6) 861ndash873(2010)

6R Cao Z Huang T Varghese and G Nabi ldquoTissue mimicking materialsfor the detection of prostate cancer using shear wave elastography Avalidation studyrdquo Med Phys 40(2) 022903 (9pp) (2013)

7T Yoshida K Tanaka T Kondo K Yasukawa N Miyamoto MTaniguchi and Y Shikinami ldquoTissue-mimicking materials usingsegmented polyurethane gel and their acoustic propertiesrdquo Jpn J ApplPhys Part 1 51(7S) 07GF17 (2012)

8E L Madsen M A Hobson H Shi T Varghese and G R Frank ldquoTissue-mimicking agargelatin materials for use in heterogeneous elastographyphantomsrdquo Phys Med Biol 50(23) 5597ndash5618 (2005)

9S J-S Chen P Hellier M Marchal J-Y Gauvrit R Carpentier XMorandi and D L Collins ldquoAn anthropomorphic polyvinyl alcohol brainphantom based on Colin27 for use in multimodal imagingrdquo Med Phys39(1) 554ndash561 (2012)

10M Solanki and V Raja ldquoHaptic based augmented reality simulatorfor training clinical breast examinationrdquo in IEEE EMBS Conference onBiomedical Engineering and Sciences (IEEE Kuala Lumpur Malaysia2010) pp 265ndash269

11Y Wang B L Tai H Yu and A J Shih ldquoSilicone-based tissue-mimickingphantom for needle insertion simulationrdquo J Med Devices 8(2) 021001(2014)

12J Oudry C Bastard V Miette R Willinger and L Sandrin ldquoCopolymer-in-oil phantom materials for elastographyrdquo Ultrasound Med Biol 35(7)1185ndash1197 (2009)

13A S Kashif T F Lotz M D McGarry A J Pattison and J G ChaseldquoSilicone breast phantoms for elastographic imaging evaluationrdquo MedPhys 40(6) 063503 (11pp) (2013)

14J Fromageau J-L Gennisson C Schmitt R L Maurice R Mongrainand G Cloutier ldquoEstimation of polyvinyl alcohol cryogel mechanicalproperties with four ultrasound elastography methods and comparison withgold standard testingsrdquo IEEE Trans Ultrason Eng 54(3) 498ndash509 (2007)

15M M Nguyen S Zhou J-L Robert V Shamdasani and H Xie ldquoDevel-opment of oil-in-gelatin phantoms for viscoelasticity measurement in ultra-sound shear wave elastographyrdquo Ultrasound Med Biol 40(1) 168ndash176(2014)

16N Hungr J-A Long V Beix and J Troccaz ldquoA realistic deformable pros-tate phantom for multimodal imaging and needle-insertion proceduresrdquoMed Phys 39(4) 2031ndash2041 (2012)

17M K Chmarra R Hansen R Marvik and T Lango ldquoMultimodalphantom of liver tissuerdquo PLoS One 8(5) e64180 (2013)

18D W Rickey P A Picot D A Christopher and A Fenster ldquoA wall-less vessel phantom for doppler ultrasound studiesrdquo Ultrasound Med Biol21(9) 1163ndash1176 (1995)

19C L de Korte E I Cespedes A F W van der Steen and C T LanceeldquoIntravascular elasticity imaging using ultrasound Feasibility studies inphantomsrdquo Ultrasound Med Biol 23(5) 735ndash746 (1997)

20E L Madsen E Kelly-Fry and G R Frank ldquoAnthropomorphic phantomsfor assessing systems used in ultrasound imaging of the compressed breastrdquoUltrasound Med Biol 14(1) 183ndash201 (1988)

21I Mano H Goshima M Nambu and M Iio ldquoNew polyvinyl alcohol gelmaterial for MRI phantomsrdquo Magn Reson Med 3(6) 921ndash926 (1986)

22N J Lawson and J Wu ldquoThree-dimensional particle image velocimetryExperimental error analysis of a digital angular stereoscopic systemrdquoMeas Sci Technol 8(12) 1455ndash1464 (1997)

23R K Chen and A J Shih ldquoMulti-modality gellan gum-based tissue-mimicking phantom with targeted mechanical electrical and thermal prop-ertiesrdquo Phys Med Biol 58(16) 5511ndash5525 (2013)

24B W Pogue and M S Patterson ldquoReview of tissue simulating phantomsfor optical spectroscopy imaging and dosimetryrdquo J Biomed Opt 11(4)041102 (2006)

25G M Spirou A A Oraevsky I A Vitkin and W M Whelan ldquoOpticaland acoustic properties at 1064 nm of polyvinyl chloride-plastisol for useas a tissue phantom in biomedical optoacousticsrdquo Phys Med Biol 50(14)N141ndashN153 (2005)

26I M de Carvalho R L Q Basto A F C Infantosi M A von Kruumlger andW C A Pereira ldquoBreast ultrasound imaging phantom to mimic malignlesion characteristicsrdquo Phys Procedia 3(1) 421ndash426 (2010)

27J K Tsou J Liu A I Barakat and M F Insana ldquoRole of ultrasonic shearrate estimation errors in assessing inflammatory response and vascularriskrdquo Ultrasound Med Biol 34(6) 963ndash972 (2008)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5591 Li et al Polyvinyl chloride as a tissue-mimicking material 5591

28L Maggi G Cortela M V Kruumlger C A Negreira and W C deAlbuquerque Pereira ldquoUltrasonic attenuation and speed in phantomsmade of PVCP and evaluation of acoustic and thermal properties ofultrasonic phantoms made of polyvinyl chloride plastisol (PVCP)rdquo inProceedings of International Work-Conference on Bioinformatics andBiomedical Engineering (Springer Granada Spain 2013) pp 233ndash241

29H Tanoue Y Hagiwara K Kobayashi and Y Saijo ldquoUltrasonictissue characterization of prostate biopsy tissues by ultrasound speedmicroscoperdquo in Proceedings of Annual International Conference of theIEEE Engineering in Medicine and Biology Society EMBS (IEEE BostonMA 2011) pp 8499ndash8502

30M O Woods and C A Miles ldquoUltrasound speed and attenuation in homog-enates of bovine skeletal musclerdquo Ultrasonics 24(5) 260ndash266 (1986)

31F W Kremkau R W Barnes and C P McGraw ldquoUltrasonic attenuationand propagation speed in normal human brainrdquo J Acoust Soc Am 70(1)29ndash38 (1981)

32J C Bamber ldquoUltrasonic attenuation in fress human tissuesrdquo Ultrasonics19 187ndash188 (1981)

33D L Folds ldquoSpeed of sound and transmission loss in silicone rubbers atultrasonic frequenciesrdquo J Acoust Soc Am 56(4) 1295ndash1296 (1974)

34A Ashead and S M Lindsay ldquoBrillouin scattering from polyurethanegelsrdquo Polymer 23 1884ndash1888 (1982)

35R L Cook and D Kendrick ldquoSpeed of sound of six PRC polyurethanematerials as a function of temperaturerdquo J Acoust Soc Am 70(2) 639ndash640(1981)

36K A Ross and M G Scanlon ldquoAnalysis of the elastic modulus of agar gelby indentationrdquo J Texture Stud 30(1) 17ndash27 (1999)

37V T Nayar J D Weiland C S Nelson and A M Hodge ldquoElastic andviscoelastic characterization of agarrdquo J Mech Behav Biomed Mater 760ndash68 (2012)

38T Z Pavan E L Madsen G R Frank A Adilton O Carneiro and T JHall ldquoNonlinear elastic behavior of phantom materials for elastographyrdquoPhys Med Biol 55(9) 2679ndash2692 (2010)

39C Sun S D Pye J E Browne A Janeczko B Ellis M B ButlerV Sboros A J W Thomson M P Brewin C H Earnshaw and CM Moran ldquoThe speed of sound and attenuation of an IEC agar-basedtissue-mimicking material for high frequency ultrasound applicationsrdquoUltrasound Med Biol 38(7) 1262ndash1270 (2012)

40K Manickam R R Machireddy and S Seshadri ldquoCharacterization ofbiomechanical properties of agar based tissue mimicking phantoms forultrasound stiffness imaging techniquesrdquo J Mech Behav Biomed Mater35 132ndash143 (2014)

41R F Smith B K Rutt and D W Holdsworth ldquoAnthropomorphic ca-rotid bifurcation phantom for MRI applicationsrdquo J Magn Reson Imaging10(4) 533ndash544 (1999)

42R Mathur-De Vre R Grimee F Parmentier and J Binet ldquoThe use ofagar gel as a basic reference material for calibrating relaxation times andimaging parametersrdquo Magn Reson Med 2(2) 176ndash179 (1985)

43E Raphael C O Avellaneda B Manzolli and A Pawlicka ldquoAgar-basedfilms for application as polymer electrolytesrdquo Electrochim Acta 55(4)1455ndash1459 (2010)

44B Luo R Yang P Ying M Awad M Choti and R Taylor ldquoElasticityand echogenicity analysis of agarose phantoms mimicking liver tumorsrdquoin Proceedings of the IEEE 32nd Annual Northeast BioengineeringConference (IEEE Easton PA 2006) pp 81ndash82

45V Normand D L Lootens E Amici K P Plucknett and P Aymard ldquoNewinsight into agarose gel mechanical propertiesrdquo Biomacromolecules 1(4)730ndash738 (2000)

46S A Lopez-Haro C J Trujillo A Vera and L Leija ldquoAn agarosebased phantom embedded in an in vitro liver tissue to simulate tumorsFirst experiencerdquo in Pan American Health Care Exchanges (IEEE Rio deJaneiro Brazil 2011) pp 233ndash236

47S A Lopez-Haro I Bazan-Trujillo L Leija-Salas and A Vera-Hernandez ldquoUltrasound propagation speed measurement of mimickingsoft tissue phantoms based on agarose in the range of 25 C and 50 Crdquoin 5th International Conference on Electrical Engineering ComputingScience and Automatic Control (IEEE Mexico City Mexico 2008)pp 192ndash195

48H I Litt and A S Brody ldquoBaSO4-loaded agarose A construction materialfor multimodality imaging phantomsrdquo Acad Radiol 8(5) 377ndash383 (2001)

49M D Mitchell H L Kundel L Axel and P M Joseph ldquoAgarose asa tissue equivalent phantom material for NMR imagingrdquo Magn ResonImaging 4(3) 263ndash266 (1986)

50M Penders S Nilsson L Piculell and B Lindman ldquoClouding and diffu-sion of nonionic surfactants in agarose gels and solutionsrdquo J Phys Chem97(43) 11332ndash11338 (1993)

51X Zhang B Qiang and J Greenleaf ldquoComparison of the surface wavemethod and the indentation method for measuring the elasticity of gelatinphantoms of different concentrationsrdquo Ultrasonics 51(2) 157ndash164 (2011)

52R J Roesthuis Y R J van Veen A Jahya and S MisraldquoMechanics of needle-tissue interactionrdquo in IEEERSJ InternationalConference on Intelligent Robots and Systems (IEEE Stanford CA2011) pp 2557ndash2563

53J C Blechinger E L Madsen and G R Frank ldquoTissue-mimickinggelatin-agar gels for use in magnetic resonance imaging phantomsrdquo MedPhys 15(4) 629ndash636 (1988)

54S Smitha P Shajesh P Mukundan T D R Nair and K G K WarrierldquoSynthesis of biocompatible hydrophobic silica-gelatin nano-hybrid bysolndashgel processrdquo Colloids Surf B 55(1) 38ndash43 (2007)

55D F Coutinho S V Sant H Shin J T Oliveira M E Gomes NM Neves A Khademhosseini and R L Reis ldquoModified gellan gumhydrogels with tunable physical and mechanical propertiesrdquo Biomaterials31(29) 7494ndash7502 (2010)

56A Asadian M R Kermani and R V Patel ldquoA compact dynamic forcemodel for needle-tissue interactionrdquo in Annual International Conferenceof the IEEE Engineering in Medicine and Biology (IEEE Buenos AiresArgentina 2010) pp 2292ndash2295

57A Asadian R V Patel and M R Kermani ldquoCompensation for relativevelocity between needle and soft tissue for friction modeling in needleinsertionrdquo in Annual International Conference of the IEEE Engineeringin Medicine and Biology (IEEE San Diego CA 2012) pp 960ndash963

58R L King Y Liu S Maruvada B A Herman K A Wear and G RHarris ldquoDevelopment and characterization of a tissue-mimicking materialfor high-intensity focused ultrasoundrdquo IEEE Trans Ultrason Eng 58(7)1397ndash1405 (2011)

59K J M Surry H J B Austin A Fenster and T M Peters ldquoPoly(vinylalcohol) cryogel phantoms for use in ultrasound and MR imagingrdquo PhysMed Biol 49(24) 5529ndash5546 (2004)

60W Xia D Piras M Heijblom W Steenbergen T G van Leeuwen andS Manohar ldquoPoly(vinyl alcohol) gels as photoacoustic breast phantomsrevisitedrdquo J Biomed Opt 16(7) 075002 (2011)

61K C Chu and B K Rutt ldquoPolyvinyl alcohol cryogel An ideal phantommaterial for MR studies of arterial flow and elasticityrdquo Magn Reson Med37(2) 314ndash319 (1997)

62Z Wang B Huang X Qin X Zhang P Wang J Wei J Zhan XJing H Liu Z Xu H Cheng X Wang and Z Zheng ldquoGrowth of hightransmittance vertical aligned ZnO nanorod arrays with polyvinyl alcoholby hydrothermal methodrdquo Mater Lett 63(1) 130ndash132 (2009)

63M Kita Y Ogura Y Honda S H Hyon W Cha II and Y IkadaldquoEvaluation of polyvinyl alcohol hydrogel as a soft contact lens materialrdquoGraefes Arch Clin Exp Ophthalmol 228(6) 533ndash537 (1990)

64S Misra K B Reed B W Schafer K T Ramesh and A M OkamuraldquoMechanics of flexible needles robotically steered through soft tissuerdquo IntJ Rob Res 29(13) 1640ndash1660 (2010)

65M Carbone S Condino L Mattei P Forte V Ferrari and F MoscaldquoAnthropomorphic ultrasound elastography phantomsmdashCharacterizationof silicone materials to build breast elastography phantomsrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 492ndash494

66C L Cheung T Looi J Drake and P C W Kim ldquoMagnetic reso-nance imaging properties of multimodality anthropomorphic silicone rub-ber phantoms for validating surgical robots and image guided therapysystemsrdquo Proc SPIE 8316 83161X (2012)

67D C Goldstein H L Kundel M E Daube-Witherspoon L E Thibaultand E J Goldstein ldquoA silicone gel phantom suitable for multimodalityimagingrdquo Invest Radiol 22(2) 153ndash157 (1987)

68G M Bernacca B OrsquoConnor D F Williams and D J Wheatley ldquoHy-drodynamic function of polyurethane prosthetic heart valves Influences ofYoungrsquos modulus and leaflet thicknessrdquo Biomaterials 23(1) 45ndash50 (2002)

69B-S Chiou and P E Schoen ldquoEffects of crosslinking on thermal andmechanical properties of polyurethanesrdquo J Appl Polym Sci 83(1)212ndash223 (2002)

70D Fuerst D Stephan P Augat and A Schrempf ldquoFoam phantomdevelopment for artificial vertebrae used for surgical trainingrdquo in AnnualInternational Conference of the IEEE Engineering in Medicine andBiology Society (IEEE San Diego CA 2012) pp 5773ndash5776

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016

5592 Li et al Polyvinyl chloride as a tissue-mimicking material 5592

71W D DrsquoSouza E L Madsen O Unal K K Vigen G R Frank and BR Thomadsen ldquoTissue mimicking materials for a multi-imaging modalityprostate phantomrdquo Med Phys 28(4) 688ndash700 (2001)

72K Yasukawa T Kunisue K Tsuta Y Shikinami and T Kondo ldquoAnultrasound phantom with long-term stability using a new biomimic softgel materialrdquo in IEEE Ultrasonics Symposium Proceedings (IEEE NewYork City NY 2007) pp 2501ndash2502

73E L Madsen W D DrsquoSouza and G R Frank ldquoMulti-imaging modalitytissue mimicking materials for imaging phantomsrdquo US patent 6635486(November 20 2001)

74S Zhou L Wu J Sun and W Shen ldquoThe change of the properties ofacrylic-based polyurethane via addition of nano-silicardquo Prog Org Coat-ings 45(1) 33ndash42 (2002)

75M M Jalili S Moradian H Dastmalchian and A Karbasi ldquoInvestigatingthe variations in properties of 2-pack polyurethane clear coat throughseparate incorporation of hydrophilic and hydrophobic nano-silicardquo ProgOrg Coatings 59(1) 81ndash87 (2007)

76X Liang A L Oldenburg V Crecea S Kalyanam M F Insana and S ABoppart ldquoModeling and measurement of tissue elastic moduli using opticalcoherence elastographyrdquo Proc SPIE 6858 685803ndash685808 (2008)

77V P Mathews A D Elster P B Barker B L Buff J A Haller andC M Greven ldquoIntraocular silicone oil In vitro and in vivo MR and CTcharacteristicsrdquo Am J Neuroradiol 15(2) 343ndash347 (1994)

78T-K Shih C-F Chen J-R Ho and F-T Chuang ldquoFabrication of PDMS(polydimethylsiloxane) microlens and diffuser using replica moldingrdquo Mi-croelectron Eng 83(11ndash12) 2499ndash2503 (2006)

79G S Rajan G S Sur J E Mark D W Schaefer and G BeaucageldquoPreparation and characterization of some unusually transparentpoly(dimethylsiloxane) nanocompositesrdquo J Polym Sci Part B PolymPhys 41(16) 1897ndash1901 (2003)

80E J Chen J Novakofski W Kenneth Jenkins and W D OrsquoBrienldquoYoungrsquos modulus measurements of soft tissues with application to elas-ticity imagingrdquo IEEE Trans Ultrason Eng 43(1) 191ndash194 (1996)

81W C Yeh P C Li Y M Jeng H C Hsu P L Kuo M L Li P MYang and H L Po ldquoElastic modulus measurements of human liver andcorrelation with pathologyrdquo Ultrasound Med Biol 28(4) 467ndash474 (2002)

82Y Kobayashi T Sato and M G Fujie ldquoModeling of friction force basedon relative velocity between liver tissue and needle for needle insertionsimulation plates needlerdquo in Annual International Conference of the IEEEEngineering in Medicine and Biology Society (IEEE Minneapolis MN2009) pp 5274ndash5278

83A Asadian R V Patel and M R Kermani ldquoDynamics of translationalfriction in needle-tissue interaction during needle insertionrdquo Ann BiomedEng 42(1) 73ndash85 (2014)

84J C Bamber and C R Hill ldquoUltrasonic attenuation and propagation speedin mammalian tissues as a function of temperaturerdquo Ultrasound Med Biol5(2) 149ndash157 (1979)

85J C Bamber and C R Hill ldquoAcoustic properties of normal and canceroushuman liver-I Dependence on pathological conditionrdquo Ultrasound MedBiol 7(2) 121ndash133 (1981)

86R Nyman A Ericsson A Hemmingsson B Jung G Sperber and K AThuomas ldquoT1 T2 and relative proton density at 035 T for spleen liveradipose tissue and vertebral body Normal valuesrdquo Magn Reson Med 3901ndash910 (1986)

87G J Stanisz E E Odrobina J Pun M Escaravage S J Graham MJ Bronskill and R M Henkelman ldquoT1 T2 relaxation and magnetizationtransfer in tissue at 3Trdquo Magn Reson Med 54(3) 507ndash512 (2005)

88Z Taylor and K Miller ldquoReassessment of brain elasticity for analysis ofbiomechanisms of hydrocephalusrdquo J Biomech 37(8) 1263ndash1269 (2004)

89F Casanova P R Carney and M Sarntinoranont ldquoIn vivo evaluation ofneedle force and friction stress during insertion at varying insertion speedinto the brainrdquo J Neurosci Methods 237 79ndash89 (2014)

90B Fischl D H Salat A J W Van Der Kouwe N Makris F Seacutegonne B TQuinn and A M Dale ldquoSequence-independent segmentation of magneticresonance imagesrdquo NeuroImage 23(Suppl1) 69ndash84 (2004)

91J T Iivarinen R K Korhonen and J S Jurvelin ldquoExperimental andnumerical analysis of soft tissue stiffness measurement using manualindentation devicemdashSignificance of indentation geometry and soft tissuethicknessrdquo Skin Res Technol 20(3) 347ndash354 (2014)

92B A Bullen F Quaade E Olesen and S A Lund ldquoUltrasonic reflec-tions used for measuring subcutaneous fat in humansrdquo Hum Biol 37(4)375ndash384 (1965)

93R L Errabolu C M Sehgal R C Bahn and J F Greenleaf ldquoMeasure-ment of ultrasonic nonlinear parameter in excised fat tissuesrdquo UltrasoundMed Biol 14(2) 137ndash146 (1988)

94R L Ehman B O Kjos H Hricak R C Brasch and C B HigginsldquoRelative intensity of abdominal organs in MR imagesrdquo J Comput AssistTomogr 9(2) 315ndash319 (1985)

95B C W Kot Z J Zhang A W C Lee V Y F Leung and S NFu ldquoElastic modulus of muscle and tendon with shear wave ultrasoundelastography Variations with different technical settingsrdquo PLoS One 7(8)e44348 (2012)

96Y Fukushima and K Naemura ldquoEstimation of the friction force duringthe needle insertion using the disturbance observer and the recursive leastsquarerdquo ROBOMECH J 1(1) 1ndash8 (2014)

97B M Ahn J Kim L Ian K H Rha and H J Kim ldquoMechanicalproperty characterization of prostate cancer using a minimally motorizedindenter in an ex vivo indentation experimentrdquo Urology 76(4) 1007ndash1011(2010)

98X Wang J Wang Y Liu H Zong X Che W Zheng F Chen Z ZhuD Yang and X Song ldquoAlterations in mechanical properties are associatedwith prostate cancer progressionrdquo Med Oncol 31876 (2014)

99T Podder D Clark J Sherman D Fuller E Messing D RubensJ Strang R Brasacchio L Liao W-S Ng and Y Yu ldquoVivomotion and force measurement of surgical needle interventionduring prostate brachytherapyrdquo Med Phys 33(8) 2915ndash2922(2006)

100L Kjaer C Thomsen P Iversen and O Henriksen ldquoIn vivo estimation ofrelaxation processes in benign hyperplasia and carcinoma of the prostategland by magnetic resonance imagingrdquo Magn Reson Imaging 5 23ndash30(1987)

101D C Montgometry Design and Analysis of Experiments (John Wiley ampSons New Jersey 2008)

102H Mehrabian and A Samani ldquoConstrained hyperelastic parameters recon-struction of PVA (polyvinyl alcohol) phantom undergoing large deforma-tionrdquo Proc SPIE 7261 72612G (2009)

103ASTM International Standard Test Method for Rubber PropertymdashDurometer Hardness ASTM Standard D2240ndash05 (ASTM West Con-shohocken 2015)

104B J Briscoe K S Sebastian and M J Adams ldquoThe effect of indentergeometry on the elastic response to indentationrdquo J Phys D Appl Phys27(6) 1156ndash1162 (1999)

105D J Naylor ldquoStresses in nearly incompressible materials by finite elementswith application to the calculation of excess pore pressuresrdquo Int J NumerMethods Eng 8 443ndash460 (1974)

106J D Ferry Viscoelastic Properties of Polymers (Wiley New York NY1980)

107W Xu and J J Kaufman ldquoDiffraction correction methods for inser-tion ultrasound attenuation estimationrdquo IEEE Trans Biomed Eng 40(6)563ndash570 (1993)

108K Sharma Optics (Academic 2006)109R J Dickinson A S Hall A J Hind and I R Young ldquoMeasurement

of changes in tissue temperature using MR imagingrdquo J Comput AssistTomogr 10(3) 468ndash472 (1986)

110R S Lakes Viscoelastic Materials (Cambridge University Press NewYork NY 2009)

111L M Hopkins J T Kelly A S Wexler and A K Prasad ldquoParticle imagevelocimetry measurements in complex geometriesrdquo Exp Fluids 29(1)91ndash95 (2000)

112C C Dierickx M C Grossman W A Farinelli and R R AndersonldquoPermanent hair removal by normal-mode ruby laserrdquo Arch Dermatol134(7) 837ndash842 (1998)

113Y Tang S Lee M D Nelson S Richard and R A Moats ldquoAdiposesegmentation in small animals at 7T A preliminary studyrdquo BMC Genomics11(Suppl 3)S9 (2010)

114W D Rooney G Johnson X Li E R Cohen S G Kim K Ugurbil andC S Springer ldquoMagnetic field and tissue dependencies of human brainlongitudinal 1H2O relaxation in vivordquo Magn Reson Med 57(2) 308ndash318(2007)

115M A Korteweg J J M Zwanenburg P J Van Diest M A A J VanDen Bosch P R Luijten R Van Hillegersberg W P T M Mali and WB Veldhuis ldquoCharacterization of ex vivo healthy human axillary lymphnodes with high resolution 7 Tesla MRIrdquo Eur Radiol 21(2) 310ndash317(2011)

Medical Physics Vol 43 No 10 October 2016