High-Resolution Strain Measurement for Biomechanical ...downloads.hindawi.com/journals/mpe/2019/2402606.pdf · ResearchArticle High-Resolution Strain Measurement for Biomechanical

Research ArticleHigh-Resolution Strain Measurement forBiomechanical Parameters Assessment in Native andDecellularized Porcine Vessels

JuanMelchor 123 JuanM Soto 4 Elena Loacutepez-Ruiz 235

Javier Suarez 1 Gema Jimeacutenez 2367 Cristina Antich67

Macarena Peraacuten 25 Juan A Marchal 2367 and Guillermo Rus 123

1Department of Structural Mechanics University of Granada Granada 18071 Spain2Instituto de Investigacion Biosanitaria (ibsGRANADA) Spain3Excellence Research Unit ldquoModeling Naturerdquo (MNat) University of Granada 18071 Spain4Department of Optics Faculty of Physical Sciences Complutense University of Madrid Madrid 28040 Spain5Department of Health Sciences University of Jaen Jaen Spain6Biopathology and RegenerativeMedicine Institute (IBIMER) Centre for Biomedical Research University of Granada Granada Spain7Department of Human Anatomy and Embryology Faculty of Medicine University of Granada Granada Spain

Correspondence should be addressed to Juan Melchor jmelchorugres

Received 19 December 2018 Revised 12 February 2019 Accepted 27 February 2019 Published 9 April 2019

Academic Editor Gregory Chagnon

Copyright copy 2019 Juan Melchor et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Decellularized vascular scaffolds are promising materials for vessel replacements However despite the natural origin ofdecellularized vessels issues such as biomechanical incompatibility immunogenicity risks and the hazards of thrombus formationstill need to be addressed In this study we assess the mechanical properties of two groups of porcine carotid blood vessels (i)native arteries and (ii) decellularized arteries The biomechanical properties of both groups (n = 10 sample size of each group) aredetermined by conducting uniaxial and circumferential tensile tests by using an ad hoc and lab-made device comprising a peristalticpump that controls the load applied to the sampleThis load is regularly incremented (8 grams per cycle with a pause of 20 secondsafter each step) while keeping the vessels continuously hydrated The strain is measured by an image cross-correlation techniqueapplied on a high-resolution videoThemechanical testing analyses of the arteries revealed significant differences in burst pressurebetween the native (134508plusmn9658 mbar) and decellularized (106779plusmn11213 mbar) groups Moreover decellularized samples showa significantly lower maximum load at failure (1578plusmn079 N) in comparison with native vessels (1942plusmn080 N) Finally the averageultimate circumferential tensile also changes between native (371plusmn037 MPa) and decellularized (293plusmn018 MPa) groups Thistechnique is able to measure the strain in the regime of large displacements and enables high-resolution image of the local strainsthus providing a valuable tool for characterizing several biomechanical parameters of the vessels also applicable to other soft tissuepresenting hyperelastic behaviours

1 Introduction

Arterial graft remains the primary therapy for patientswith advanced cardiovascular disease The ongoing need forarterial conduits is due to the poor clinical efficacy of existingsynthetic grafts in small diameter artery applications around(sim 5 mm) [1 2] Besides many patients with pathologicalarterial walls need an efficient replacement based on tissue

engineering procedures [3ndash5] In particular tissue engineer-ing has been successfully applied to fabrication of printed-based matrices for developing useful implants [6 7]

The arterial graft typically involves a decellularizationprocedure depending on the geometrical shape and thebiomechanical properties of the required tissue [8] More-over the process of acquiring native arteries and theirdecellularization requires a difficult methodology not always

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 2402606 14 pageshttpsdoiorg10115520192402606

2 Mathematical Problems in Engineering

put into practice in an optimum manner In this study weexplore the possibility of obtaining porcine decellularizatedarteries by applying an enzymatic digestion and detergentextraction procedure [1 9 10] This process is able to provideimplants to patients similarly to those made of syntheticmaterials once the demanded biomechanical resistance isknown Some authors have also studied the fabrication of ahybrid tissue vascular graft by applying polymerized coatingson the outside of different aortic or carotid decellularizedvessels which significantly enhances their biomechanicalbehaviour [2 11]

Theoutstanding role of assessing the biomechanical prop-erties of biological specimens (in this case different arteries)justifies the application of the mechanics of continuousmedia formalism Particularly it has been used to describethe results from several mechanical tensile tests aiming atretrieving the stiffness and elasticity of the samples Typicallythe mechanical characterization of the blood vessels hasbeen obtained without taking into account the resolutionof the displacements in axial or circumferential tests [12ndash14] The error introduced by an inaccurate distance mea-surement is translated into significant misleading variationsof the mechanical parameters In this regard we proposean image cross-correlation algorithm to improve the straintracking experienced by the sample during the stress teststhereby providing a high-resolution characterization of theirmechanical parameters The researchers that may introducethese mechanical concepts in the field of tissue engineeringor clinical practice need this accurate characterization of themechanical properties [15ndash17]

Soft tissues (such as blood vessels) understood as hyper-elastic materials when subjected to uniaxial loads are char-acterized by relevant shape changes as well as a stronglynonlinear response Hyperelastic materials experience a greatstrain when a load is applied Nevertheless once the load isremoved they return to a position very close to the initial oneOn the other hand when cyclical loads are applied to thesematerials a considerable dissipation in the energy is exhibitedas a response to the stress The realization of this workhas been based on the functions of the deformation energysuitable for soft tissues study developed by Holzapfel Ogdenand Vito [18ndash21] In this way a semianalytical description ofconstitutive equations for soft tissues is explored and then ithas been applied to develop a new technique for measuringthe strain in mechanical tensile tests

The remainder of the paper is organized as follows Sec-tion 2 briefly describes themechanical behaviour of the arteryalong with the derivation of its stress tensor Next Section 3is devoted to the strain tensor Then Section 4 includesthe experimental setup the preparation of the biologicalsamples and the details of the statistical analysis performedin the experiment Later Section 5 describes the image cross-correlation algorithm proposed in this work for a bettercharacterization of the sample mechanical properties Thefollowing section includes the results from the mechanicaltests along with the histological comparisons between nativeand decellularized vessels Finally Section 7 summarizes themain conclusions of the study and paves the way for futurework

2 Biomechanical Stress Tensor onArteries Samples

The methodology applied for the mechanical characteriza-tion is based on the stress-strain curve analysis of the sampletested until failure As later explained in Section 41 thiscurve is obtained by applying a loading stress to the sampleand recording a process by a camera therefore obtaining a2D image for each load value applied to the specimen Forthis purpose Cauchy stress has been considered the mostappropriate since it corresponds to the force or load dividedby the area of the section of the sample as follows

120590 = NA (1)

where 120590 is known as Cauchy stress N is the applied force(in our experiments it corresponds to the load applied to theblood vessel in each measurement) and A is the area of thesample section Consequently 120590 is calculated by taken intoconsideration the geometry of the sample

In particular the porcine vessels exhibit the strain-stresscurve displayed in Figure 1 In this representation two differ-ent behaviour phases can occur depending on the amount ofstrain experimented by the sample as explained in [22 23]Firstly for low values of the strain a linear region exists inwhich the elastin composition prevails in the mechanicalresponse of behaviour of the artery which is the collagencomposition By linear fitting of each region it is possible toobtain the value of Youngrsquos modulus that characterizes theelastin and collagen phases respectively Collagen Youngrsquosmodulus is much larger than its elastin counterpart thusimplying a lower stiffness of the sample in this phaseTherefore the collagen phase is chosen because in the elastinphase there are not enough significant points to approximatewith reliably Besides this elastin phase is considered whenthe sample has less rigidity and the hyperelastic model isbetter fit with collagen region

Moreover it is also important to obtain the strength ofthe material (Fm) as the maximum load to failure so that ifthe loading stress continues then the material breaks Otherrelevant parameters are the ultimate tensile strength (UTS)defined as Sr = Fm and the elongation under maximum loadas explained later Furthermore the true (or logarithmic)deformation d120576 is defined as the ratio between the increasein length (l) and the length of the sample (l) at any instant

d120576 = ll (2)

The values of engineering (d120576) and logarithmic (s) deforma-tions are related according to the following expression

s = ln(1 + l1198970 ) (3)

From the values (F l) obtained in the mechanical test oneis able to plot the uniaxial component of tensors of Cauchy(120590) and the finite strain tensors (s) as displayed in Figure 1thus obtaining its characteristic points (basically the pointin which the material suffers the mechanical failure and thepoint of the transition between elastin and collagen regions)

Mathematical Problems in Engineering 3

Colla

gen

Elastin

2

1

1

1

(ＬＬ)

Figure 1 Theoretical stress-strain relationship for an elastic swinevessel reported by Garcia Herrera [22 23] Different Youngrsquosmodulus values E1 and E2 characterize the regions in whichthe mechanical behaviour is dominated by elastin and collagencomposition of the vessel respectively These regions are separatedby a critical point of the curve of stress-strain (120576

11205901) and the collagenphase ends abruptly when the failure of the material occurs (120576r120590r)

3 Biomechanical Strain Tensor Calculation onArteries Samples

From the previous section we have derived an expression forthe Cauchy stress that depends on the strain tensor Let usnow define two Cartesian directions a and b (in our case theplane defined by ab corresponds to the XY plane since the2D image is recorded in the plane parallel to the force appliedto the specimen) The plane ab is discretized by defining a2D mesh within a region of interest (ROI denoted as x)distributed along the aforementioned directions Then boththe deformation gradient (F) and the Green-Lagrange axialdeformation (S) are obtained to estimate the deformation ofthe specimen

First the deformation gradient of the region of interest inthe direction a regarding the address b is a tensor given by

119865119886119887 = 1205971199091198861205971199090119887

(4)

where in the previous expression the superscript 0 refers tothe position at the initial instant of the experiment Fab isa Jacobian matrix or deformation gradient that acts as anoperator transforming certain initial vectors (belonging tothe environment of a point) from a reference configurationinto the corresponding vectors in a final configuration In thiscase the initial state is when any deformation is applied tothe sample whereas the ending state is measured after severalsuccessive deformations even leading to the failure of thematerial

For the computational calculation (4)must be discretizedbut this procedure is nontrivial Since we move in a 2D plane

one can define the four components in which Lagrangiannotation is applied as

11986511989611(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (5)

11986511989612(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990902(i + 1 j) minus 1199090

2(i + 1 j) (6)

11986511989621(i j) asymp 119909119896

2(i j) minus 119909119896

2(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (7)

11986511989622(i j) asymp 119909119896

2(i j) minus 119909119896

2(i + 1 j)

11990902(i j) minus 1199090

2(i + 1 j) (8)

with i and j being the original coordinates representing therecorded ROI of the specimen (therefore it is an immobilereference) and the superscript k denotes the video frame ofthe sequence of the experiment (k = 0 is the initial frame)since the stress 120590 is evaluated for each load increment in thetensile test On the other hand subscripts 1 and 2 denoterespectively the X and Y Cartesian directions to which thedeformation of the analyzed ROI points Note that in thisformulation the initial position of the specimen (superscript0) has been defined as reference These expressions justifythe need for the application of an interpolation betweenframes k to facilitate the convergence Note also that if thedenominator reaches an extremely low value then the valueof F would be too large To avoid this the amount of loadapplied between consecutive video frames must be appropri-ate for linearly fitting the strain (and the deformation tensorcomponents) Once the deformation gradient is computedthen Green-Lagrange strain can be derived as

120576 = 12 (119865119865

119879 minus 119868) (9)

in which I denotes the identity matrix and T superscriptis the transposed matrix Physically the strain 120576 representsthe quadratic difference between the lengths of deformedand nondeformed state that is to say this tensor measuresthe difference between the squares of differential surfaceelements in both cases

By considering that our interest lies in the deformation inthe direction in which the load is applied to the sample then(9) is simplified to

e = l1198970 = l minus 1198970

1198970 (10)

where e is the elongation atmaximum load For the particularcase of a vessel sample let us assume that it has a thin wallnamely its thickness is lower than one tenth of its length(see [24])This approximation allows for the treatment of thewall as a surface and is subsequently using the Laplace-Youngequation to estimate the circumferential stress created by an


internal pressure (burst pressure) in a thin-walled cylindricalpressure vessel as shown below

Tc = 119875119903119905 997888rarr

119875 = 2tTcr

(11)

where Tc = 119873119860 is the circumferential stress P is thepressure r is the radius and t is the sample thickness Notethat double the thickness has been considered in (11) dueto the form of adjusting the sample (ring) to the clamps asfurther explained in Section 62

4 Materials and Methods

41 Mechanical Testing The theory of large strains has beenapplied for studying carotid vessels of swines as hyperelasticmaterials in order to test their tensile strength and elongationat fracture The samples have been grouped into two groupsnative and decellularized arteries further referred to asNA and DA respectively The main objective of this studyis evaluating the impact of the arteries decellularizationprocedure on their mechanical properties In particular thisanalysis requires the following

(1) Stress rupture testing of each type of artery by cal-culating the maximum tensile load required for thefracture

(2) Computing the modulus of elasticity NA and DAvessels

(3) Extracting the hydrostatic pressure from arteriesunder circumferential tension

(4) Analyzing the relationship between the mechanicalproperties and histological analyses of vessels

To carry out these goals the strain-stress curve of eachsample needs to be measured With this purpose the tensile-compression press included in Figure 2 has been arranged forthe mechanical test of the samples In particular it includesthe bars that support the entire setup a water container toapply a load to the vessel and another bucket filled withwater acting as a counterweight The press as indicated inFigures 2 and 3(a) consists of two clamps fabricated in epoxyresin for favoring the fastening of the arteries The vesselsample remains fixed by means of PLA-printed holders (seeFigure 3(b)) that prevent the artery from torsion and otherundesired movement

A peristaltic pump (controlled by an Arduino microcon-troller) is used to increase the load gradually at 8 gramsincrements while keeping the vessels continuously hydratedAfter each load step a pause of 20 seconds has been set inorder to stabilize the system and avoid undesired rheologicalphenomena or oscillations that may hinder the tracking Itis worth pointing out that such a small load increment hasbeen chosen because when the motion between consecutiveframes is excessively large a nonlinear regime of movementmay occur

Then the deformation has been measured by recording ahigh-resolution video and obtaining the displacements fromthe recorded images as previously reported [2 25 26] Inparticular we apply a cross-correlation image algorithm thatis described thoroughly in Section 5 for strain measurementThis video is triggered at the beginning of pumping andcustom image capture software is used to record at a rateof 1 frame per load increment until the sample breakdownA conventional camera (IPEVO Ziggi-HD High DefinitionUSB CDVU-04IP model 5 Mpix 1280times720 resolution) hasbeen used to acquire the image sequence in the parallel planewith respect to the surface in which the deformation tensor ismeasured Finally it is worth underlining that the preparationof the experiment is essential and includes some basic steps

(i) By engraving the vessel with a speckle or randomdot pattern the monitorization of the strain of dif-ferent regions of the sample is facilitated Taking intoaccount the fact that the strain is measured by usinga cross-correlation technique (as explained in Sec-tion 5) if more details are added to the vessel then thisalgorithm works better as more characteristic pointscan be followed with the tracking procedure Theanalysis of an image sequence based on correlationworks better if some details of the sample changesduring the experiment as this operation highlightsthe morphological differences that have occurred Asthe surface of the sample is flat and without anystriking feature the staining is mandatory if a reliablestrain assessment is needed In this case acrylic blackpaint has been used to apply the pattern over thesample and then the sample is dried out a fewminutes

(ii) A uniform background and illumination throughoutthe entire experiment help to maintain an optimumcontrast in the recorded image

(iii) The arteries must be kept continuously hydrated tomaintain their mechanical properties for instanceby spraying them with PBS during the mechanicaltestThanks to the waterproof capability of the acrylicpaint once the artery is stained the pattern is notremoved with the PBS thus providing an enduringmarking of the sample

(iv) All the blood vessels are cut with the same mold (seeFigure 3(c)) for tailoring them and maintain similardimensions thus controlling the area of theminimumsection where each one break

42 Tissue Harvest and Preparation Porcine carotid arter-ies are obtained from a slaughterhouse and transportedto the laboratory stored in cold PBS with 1 peni-cillinstreptomycin Immediately after arrival carotid arteriesare cleaned to remove the excess of connective and adventitialtissues Next the carotid arteries are rinsed in sterile PBSand cut into segments of 3-5 cm in length and 3-4 mm indiameter Finally they were immediately frozen in PBS at-80∘C for later use it has been previously shown that thefreeze-and-defrost process does not significantly affect arterymechanics [26ndash28] At the time of testing specimens were


CounterweightWeight (controlled load increment)

Lamp

Press systemwith holders

(a)

Snapshot each load increment

Loadcontainer Water

tankArduino

UNO boardPC

Counterweight

Balljoint

Vessel

Peristalticpump

(b) (c)

Figure 2 (a) Press setup comprising clips and fasteners for holding the sample attached to several weights and counterweights for controllingthe applied load The data are sent to a computer and processed with MATLAB (b) Schematic representation of the whole measurementsystemThe artery suffers an increasing load and the process is registered by a camera (c) Placement of the sample into the clamps to undertakethe uniaxial tensile experiment

thawed in a 37∘C water bath and tested within 1 h of thawing[29]

43 Decellularization Process The decellularization processof carotid tissue samples is performed as previously described[2] using enzymatic digestion and detergent extractionCarotid arteries were immersed in deionized water for 24h at 4∘C followed by treatment with 005 Trypsin with002 EDTA (Sigma Aldrich St Louis MO USA) for 1 hat 37∘C After a short rinse in PBS to remove trypsin excess

the samples are treated with a solution of 2 Triton X-100and 08 ammonium hydroxide (Sigma) in deionized waterfor 72 h at 4∘C This solution has been changed every 24 hAfter the decellularization samples werewashed in deionizedwater three times for 24 h each to remove chemical residuesAll these steps of the preparation are carried out undercontinuous shaking except trypsin incubation

44 Histological and Immunofluorescence Analyses Sampleswere fixed in 4 paraformaldehyde embedded in paraffin in


(a)

(b)

(c)

Figure 3 (a) Close-up view of the camera attached to the press setup for performing the tracking of themotion (b)Vessel sample placed in thepress during a test Note that a random speckle pattern has been impressed over it to ease the strain tracking with the image cross-correlationalgorithm (c) Mold printed in 3D with polylactic acid (PLA) to maintain the dimensions of the samples

an automatic tissue processor (TP1020 Leica Germany) cutinto 5 mm sections and stained with Hematoxylin and Eosin(HampE) and Massonrsquos Trichrome as previously reported [30]Images are acquired with an inverted microscope (NikonH550s USA)

45 Scanning Electron Microscopy (SEM) Arteries arewashed twice with 01 M cacodylate buffer (Sigma) andfixed with 25 (wv) glutaraldehyde in 01 M cacodylatebuffer (pH 74 Poly-sciences Warrington PA) for 4 h at 4∘CThereafter samples are rinsed several times with sodiumcacodylate buffer After fixation samples are postfixed with1 wv osmium tetroxide for 1 h RT dehydrated stepwisewith ethanol (50 70 90 and 100 15 min each) criticalpoint dried in CO2 and gold coated by sputtering Finallythe images are examined by using a FEI Quanta 400 scanningelectron microscope (Oregon USA)

46 Statistical Analysis Each experiment has been con-ducted with 10 samples Results are presented as mean plusmnstandard deviation (SD) A Studentrsquos t-test is used to testthe significance level between specific cases The results areconsidered significantly different at p-values p lt 005(lowast) andp lt 001(lowastlowast)

5 Image Cross-Correlation Algorithm forStrain Tracking

Traditionally obtaining precise strain measurements duringuniaxial tensile testing can be performed by clamping astrain gauge to the sample Nevertheless here we aim atobtaining a contactless strain measurement whereby weneed laser extensometers or a recording of digital imagesseries and then applying a digital image correlation softwaresee [31 32] The most conventional correlation algorithmsmonitor the positions of two parallel markers during theexperiment (for instance comparing an intensity profilealong the tensile direction) and hence the strain of thesample can be calculated According to previous works [32]one of the main difficulties for strain assessment based oncorrelation occurs when the deformed area of the sample islarge to hinder the matching of consecutive images In thisregard our protocol of measurement is robust thanks to thespeckle engraving of the sample

As previously explained in Section 41 and sketched inFigure 2(b) a press system has been designed for conductingdifferent mechanical test over the vessel samples Note that itis important to choose an appropriate distance for recordingso that the failure of the sample occurs far from the edges ofthe image and at the same time make the most of the camerafield of view Moreover for obtaining a good calibration for


for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ

Figure 4 Flowchart summarizing the algorithm of cross-correlation for finding the strain from an image sequence

the measurement of the strains the pixel size of the cameraand its resolutionmust be taken into account or alternativelyan object of known dimensions can be included in therecorded field of view In this way it is possible to correlatethe measurement in pixels registered by the camera and thereal distances After the acquisition of this image sequencea tracking algorithm based on image cross-correlation isapplied sequentially between each consecutive pair of framesof the sequence This algorithm also summarized in theflowchart from the Figure 4 follows these steps

(1) We start with a sequence of N input images thatcontains a recording of all the experiment If they are

inRGBcolor (as in our case) they are firstly convertedto grayscale

(2) A ROI or mask is defined in the first frame of thesequence so that all the images outside this mask areignored Typically this ROI is the middle area of thevessel in order to circumvent unwanted border effectsFor this ROI the movement is approximated by apiecewise linear function

(3) A discretization is applied to transform the ROI intoan array of discrete blocks so that the number of char-acteristic points is reduced The tracking algorithm isapplied to each of these blocks instead of applying it


pixel by pixel for alleviating its computational costNote that the number of blocks should be optimizedby taking into account both the camera resolution andthe amount of strain experienced by the sample Forinstance if the block-size is extremely small then theROI will contain too many blocks thus producing anincrease in computation time Moreover these tinyblocks are more prone to noise problems Converselythe discretization with a small number of large blocksis expected to hinder the most subtle movementsFurthermore the largest the strain is experienced bythe sample themore the blocks are needed tomonitorthe process while minimizing in the measured dis-tances Consequently there is a trade-off between thecomputational cost and the precision of the trackingalgorithm In this case a rectangular discretizationmesh has been chosen with blocks of 8 pixels in widthby 16 pixels in height

(4) Between each pair of consecutive frames hereinafterreferred to as A (the first image) and B (the secondone) the motion of each block of the discretized ROIis measured by finding the peak of cross-correlationbetweenAandBWe compute themaximumof imagecross-correlation (xcorr) to obtain themotion (strain)that have occurred within every discretization blockof the block between A and B One can obtain the 2Dstrain as follows

120576 (xk1 xk2) = max [xcorr (imagek imagek+1)] (12)

In this way the bestmatching between the two imagesis found It is important to highlight that as theimages are bidimensional (2D) the correlation is alsoevaluated in the 2D plane It is worth remarking thatthe speckle pattern impressed in the artery helps outwith tracking as it enhances the number of featuresto be trailed unless an undesired torsion movementoccurs Nevertheless the two clamps that hold thesample edges prevent this torsion from happening

(5) Taking into consideration the fact that throughoutour experiments only uniaxial tests (eg along x1axis) have been performed then the strain in thatdirection prevails over the torsion movement (alongx2 axis) Consequently by averaging the 2Dmotion ofall the blocks one obtains the mean strain suffered bythe sample under test for the k-image of the sequencedenoted as

120576k = mean [120576 (xk1 xk2)] (13)

(6) Now we proceed with the following pair of images ofthe sequence The initial ROI is updated for takinginto account themeanmovement (120576k) experienced bythe sample in the previous pair of frames The steps((3)-(5)) are repeated until reaching the end of therecorded sequence

ROI

Holder

Tensile direction

Vessel

Figure 5 Example of vessel attached to two holders that secureit during the uniaxial tensile experiment thus avoiding undesiredtorsion movement The region of interest (ROI) has been delimitedby a dashed yellow line

(7) We compute the global strain along all the experimentby adding all the strain between consecutive images

120576 =119873minus1

sum119870=1

120576k (14)

Thanks to this image correlation algorithm differentmechan-ical tests have been conducted and monitored namelyuniaxial test (explained in Section 61) and circumferentialtensile stress test (Section 62)

6 Results and Discussion

61 Uniaxial Testing For uniaxial testing the sample isplaced as shown in Figure 5 and stretched with the exper-imental setup from Figure 2 From this framework it ispossible to obtain a 2D strain but the movement along thedirection in which the load is applied has a prevailing effect(as demonstrated in the experiment sequences displayed inFigures 6 and 7) Consequently only this direction is consid-ered for the analysis In this way the strain-stress curve of thesamples is obtained (see an example for two arteries one ofeach group in Figure 8(a)) Next Youngrsquos modulus has beenextracted as the slope of its linear region (see Figure 8(b))Werecall that this linear region is associated with the collagencontent of the sample In particular from Figure 8(a) theexpected value for Youngrsquos modulus is 431plusmn025 MPa forthe decellularized sample and 311plusmn015 MPa for the nativeone After computing this stress-strain curve for n = 10samples in each category we obtain the results includedin Figure 8(b) 498plusmn067 MPa for the decellularized versus353plusmn056 MPa for the native specimens These values are ingood agreement with the usual blood vessels range of Youngrsquosmodulus [10 13 26] The value of Youngrsquo modulus slightlychanges when a conventional correlation algorithm based onthe tracking of two parallel markers is used These markersare placed in both edges of the vessel along the direction in


(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g

Figure 6 Four different frames from a recording of a uniaxial tensile test in a decellularized vessel with an increasing load The sample isstretched in the direction marked with red arrows and the strain tracking is enhanced thanks to the speckle pattern applied to the sample

(a)

(b)

Figure 7 Two different frames showing the typical output of the tracking algorithm for uniaxial tensile test over an artery Green dotsrepresent the center of each block in the discretized ROI and the green line represents the movement in regard to the first frame of therecorded sequenceThe reader is further referred to the video Visualization 1 in Supplementary Materials to see the whole tracking sequence


Decellularized (DA)Native (NA)Fitting Collagen DAFitting Collagen NA

05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)

Mean Youngs modulus (MPa)

NA0

1

2

3

4

5

6

DA

(b)

Figure 8 (a) Experimental stress-strain relationship for elastic swine vessels along with the linear fitting of the curve along the collagenregion (b) Young modulus for each group of vessels (represented as mean+-SD (lowastlowast) p lt 001)

which the load is applied With this procedure one reaches avalue of 447plusmn082 MPa for decellularized and 346 plusmn075 fornative vessels respectively The underestimation of Youngrsquosmodulus is probably due to the deformation experienced bythe sample hence obstructing the tracking of the strain Theartery warped not only along the longitudinal direction asexpected in a uniaxial test but also in the traverse directionMoreover by averaging several 2D blocks of the sampleinstead of only using 1D intensity profile correlation-basedmatching we obtain a more accurate measurement as thesmall undesired and unavoidable torsion of the sample alongthe traverse direction has also been taken into accountThe deformation maps have been also analyzed for nativeand decellularized arteries at several elongation ratios (seeFigure 9) An initial cross-section of 20 mm times 5 mm has beenconsidered for all the vessels

Indeed there exist relevant changes (p-values of p lt 001in Studentrsquos T- test) between both groups Therefore it couldbe interpreted as the procedure of decellularization has aremarkable impact on elasticity

62 Ring Testing Ultimate tensile strength maximum loadand burst pressure has been determined for ring sectionsof arteries (n = 10 samples in each group) in order to testthe circumferential stress The ring sections are preparedas explained in Section 42 and mounted on custom-madeholders Each sample is tested by applying an increasingload until failure The diameter width thickness and lengthof each sample used for the calculations aforementioned inSection 2 are measured with a high-precision slide caliperThe sample displacement is determined by the image cor-relation algorithm and in this case the speckle pattern is

engraved in the transversewall of the ringWemust underlinethat the mean radius of the ring samples has been used forcalculations because it represents the distance to the neutralaxis or centroid

The burst pressure of the samples is calculated fromtheir maximum load to failure We recall that twice thesample thickness has been considered as defined in (11)The ring is arranged wrapping the two clamps and isstretched along a certain direction in which there is a doublelayer of vessel thus the effective thickness is twice thatof the ring The radial stress is calculated and convertedto millibars by considering the load the mean radius andthe circumferential UTS [9 24 33] In comparison withthe uniaxial test the circumferential mechanical proper-ties are significantly different due to different disposal ofvessel fibers along longitudinal and circumferential direc-tions

The mechanical testing revealed significant differencesbetween NA and DA rings As summarized in Figure 10there exist relevant dissimilarities between the mean burstpressure of the native arteries (134508plusmn9658 mbar) andthe decellularized group (106779plusmn11213 mbar) Furthermorethere also exist differences regarding the maximum load thateach type of artery can stand the native stands 1942plusmn080N whereas the decellularized is able to withstand a lowervalue (1578plusmn079 N) Finally the circumferential UTS isalso different with an expected value of 371plusmn037 [MPa]within the native group while in the decellularized this valuedecreases (293plusmn018 [MPa])

63 Histological Characterization of Native and DecellularizedArteries As explained in Section 42 the samples are first


d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20

(b) Decellularized arteries

Figure 9 Deformation maps for a native (a) and decellularized (b) vessel evaluated at different elongation ratios An initial rectangularcross-section of 20 mm times 5 mm has been considered in all cases The rectangular grid accounts for the discretization mesh applied for thetracking algorithm

NA0

5

10

15

20

25

DA

lowastlowast

(a) Maximum load (N)

0

05

1

15

2

25

3

35

4

45

NA DA

lowast

(b) Ultimate tensile strength (MPa)

0

500

1000

1500

NA DA

lowast

(c) Mean burst pressure (mbar)

Figure 10 Comparison between the mechanical parameters of native (NA) and decellularized (DA) arteries in the circumferential stress testincluding the load (a) ultimate tensile strength (b) and hydrostatic burst pressure (c) from annular portions (rings) of samples All the resultsare represented as mean+-SD (lowast) p lt 005 and (lowastlowast) p lt 001)


(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)

Figure 11 Characterization of porcine carotid arterial tissue before and after decellularization (ab) Macroscopic images of decellularizedleft common porcine carotid artery (artery length sim 50 mm inner diameter sim 4 mm) Histology of porcine arteries (c e) native arteries and(d f) decellularized arteries (c) HampE staining of native arteries (d) HampE staining of decellularized arteries showing complete removal ofvascular cells (e) Massonrsquos Trichrome staining of native arteries (f) Massonrsquos Trichrome staining of decellularized artery showing collagensfibers and no cells (20x magnification) SEM micrographs of the luminal surface (g) native arteries and (h) decellularized arteries scale barindicates 20 120583m and 50 120583m respectively

prepared and cut (see Figures 11(a) and 11(b)) Then his-tological analyses and scanning electron microscopy (SEM)are performed on artery samples to demonstrate the efficacyof the decellularization process in native carotid arteriesComplete removal of vascular cells is confirmed by HampE andMassonrsquos Trichrome staining after the decellularization pro-cedure (Figures 11(d) and 11(f)) when compared with nativearteries (Figures 11(c) and 11(e)) Native arteries showed

high density of cells embedded in collagen fibers (stainedturquoise) (Figure 11(e)) while no cells were detected in thedecellularized arteries (Figures 11(d) and 11(f)) In additionthe characteristic concentric layers of elastin (stained pink)and collagen fibers of native arteries remained intact at decel-lularized arteries showing the same circumferential orienta-tion and a well preserved ECM (Figures 11(d) and 11(f)) SEManalyses were used to further confirm the removal of the cells


at the luminal surface and demonstrated that decellularizedarteries retain the basic extracellular microstructure (Figures11(g) and 11(h))

7 Conclusions

In order to provide quality criteria for natural and bio-engineered arteries different traction mechanical tests havebeen carried out for two types of blood vessels native anddecellularizedThemechanical properties have been analyzedwhich are the UTS Youngrsquos modulus maximum load atfailure and burst pressure To assess these parameters severalintermediate physical measurements of the vessel sampleshave been measured such as radial stress radius thicknesswidth and lengthThe stress-strain curves are also computedbased on an image cross-correlation algorithm developed in-house combined with a laboratory-prototyped tensile testingmachine designed for this purpose

Strain at failure is seen to increase after decellularizationdue to cell removal and increased collagen fiber mobilityalong with the uncrimping of collagen fibers After decellu-larization the collagenmatrix remains but other cellular pro-teins are removedTherefore the amount of collagen tends toincrease as a percentage of dry weight after decellularizationThen the increase in stiffness in terms of elastic modulusin the decellularized arteries may be due to the decrease inthe cell layer leaving only a hardening collagen layer (shownin Figure 11) Note that the results are interesting for futureexperiments or biomedical applications in which differentcoatings are tested to reinforce the strength of the arteries

Several studies have shown structural alterations thatcould be related to changes inmechanical propertiesThoughthe intention of most decellularization procedures is toeffectively remove all the cells and nuclear components whileminimize disruption to the ECM the removal of cells canlead to changes to native ECM structure [29] Moreoverdepending on the decellularization method some studieshave demonstrated alterations of the ECM structure andthus in the mechanical properties being SDS and Triton X-100 based protocols more suitable for maintaining the majorstructure of the elastin and collagen network in the ECM[34]

In summary this technique is able to measure the strainin the regime of large displacements and enables high-resolution image of the local strains Thus it provides a valu-able tool for characterizing several biomechanical parametersof the vessels (Youngrsquos modulus stress-strain curve etc) andalso other hyperelastic materials through uniaxial (or biaxial)tension test Finally it is worth pointing out that with imagecross-correlation algorithm it is possible to obtain a two-dimensional strain map from which the heterogeneity andseveral components of the strain tensor can be reconstructedfrom a single measurement In this way it provides a 2Dtracking of the mechanical properties variations hence adeeper insight of the stress test is obtained

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was supported by the Ministry of Edu-cation [DPI2014-51870-R DPI2017-85359-R UNGR15-CE-3664 and PI1600339] Junta de Andalucıa [PIN-0030-2017 PIN-0379 CTS-6568 and PI-0107-2017 Projects] andUniversity of Granada [PP2017-PIP2019] Ministerio deEconomıa y Competitividad is also acknowledged for fund-ing the project [TEC2014-57394-P] and MNat Scientific Unitof Excellence (UCEPP201703)

Supplementary Materials

Visualization 1 tracking algorithm for uniaxial tensile testuntil failure applied in an artery Green dots representthe center of each block in the discretized ROI and thegreen line represents the movement apropos of the firstframe of the recorded sequence A pause of 20 seconds hasbeen set between the acquisitions of consecutive frames(Supplementary Materials)

References

[1] C Quint Y Kondo R J Manson J H Lawson A Dardik andL E Niklason ldquoDecellularized tissue-engineered blood vesselas an arterial conduitrdquo Proceedings of the National Acadamy ofSciences of theUnited States of America vol 108 no 22 pp 9214ndash9219 2011

[2] E Lopez-Ruiz S Venkateswaran M Peran et alldquoPoly(ethylmethacrylate-co-diethylaminoethyl acrylate)coating improves endothelial re-population bio-mechanicaland anti-thrombogenic properties of decellularized carotidarteries for blood vessel replacementrdquo Scientific Reports vol 7no 1 2017

[3] A Carpentier J L Guermonprez A Deloche C Frechette andC DuBost ldquoThe aorta-to-coronary radial artery bypass graft atechnique avoiding pathological changes in graftsrdquo The Annalsof Thoracic Surgery vol 16 no 2 pp 111ndash121 1973

[4] L R Caplan ldquoLacunar infarction and small vessel diseasepathology and pathophysiologyrdquo Journal of Stroke vol 17 no1 p 2 2015

[5] F M van der Valk S L Verweij K A Zwinderman et alldquoThresholds for arterial wall inflammation quantified by 18F-FDG PET imagingrdquo JACC Cardiovascular Imaging vol 9 no10 pp 1198ndash1207 2016

[6] L Iop andG Gerosa ldquoGuided tissue regeneration in heart valvereplacement from preclinical research to first-in-human trialsrdquoBioMed Research International vol 2015 Article ID 432901 13pages 2015

[7] A Keable K Fenna H M Yuen et al ldquoDeposition of amyloid120573 in the walls of human leptomeningeal arteries in relation toperivascular drainage pathways in cerebral amyloid angiopa-thyrdquo Biochimica et Biophysica Acta (BBA) - Molecular Basis ofDisease vol 1862 no 5 pp 1037ndash1046 2016

[8] S L Dahl C Rhim Y C Song and L E Niklason ldquoMechanicalproperties and compositions of tissue engineered and native


arteriesrdquo Annals of Biomedical Engineering vol 35 no 3 pp348ndash355 2007

[9] Y Zhao S Zhang J Zhou et al ldquoThe development of a tissue-engineered artery using decellularized scaffold and autologousovine mesenchymal stem cellsrdquo Biomaterials vol 31 no 2 pp296ndash307 2010

[10] Y M Ju J S Choi A Atala J J Yoo and S J Lee ldquoBilayeredscaffold for engineering cellularized blood vesselsrdquo Biomateri-als vol 31 no 15 pp 4313ndash4321 2010

[11] W Gong D Lei S Li et al ldquoHybrid small-diameter vasculargrafts Anti-expansion effect of electrospun poly 120576-caprolactoneon heparin-coated decellularized matricesrdquo Biomaterials vol76 pp 359ndash370 2016

[12] Y-C Fung Biomechanics Springer 1990[13] J D Enderle and J D Bronzino Introduction to Biomedical

Engineering Academic Press 2012[14] F A Duck Physical Properties of Tissues A Comprehensive

Reference Book Academic Press 2013[15] A N Natali E L Carniel P G Pavan P Dario and I Izzo

ldquoHyperelastic models for the analysis of soft tissue mechanicsdefinition of constitutive parametersrdquo in Proceedings of theBiomedical Robotics and Biomechatronics BioRob 2006 pp 188ndash191 IEEE 2006

[16] E J Weinberg and M R Kaazempur-Mofrad ldquoA large-strainfinite element formulation for biological tissueswith applicationto mitral valve leaflet tissue mechanicsrdquo Journal of Biomechan-ics vol 39 no 8 pp 1557ndash1561 2006

[17] J M Deneweth S G McLean and E M Arruda ldquoEvaluationof hyperelasticmodels for the non-linear and non-uniformhighstrain-rate mechanics of tibial cartilagerdquo Journal of Biomechan-ics vol 46 no 10 pp 1604ndash1610 2013

[18] G A Holzapfel T C Gasser and R W Ogden ldquoA new consti-tutive framework for arterial wall mechanics and a comparativestudy of material modelsrdquo Journal of Elasticity vol 61 no 1ndash3pp 1ndash48 2000

[19] G A Holzapfel ldquoDetermination of material models for arterialwalls from uniaxial extension tests and histological structurerdquoJournal ofTheoretical Biology vol 238 no 2 pp 290ndash302 2006

[20] G A Holzapfel and R W Ogden ldquoConstitutive modellingof arteriesrdquo Proceedings of the Royal Society A MathematicalPhysical and Engineering Sciences vol 466 no 2118 pp 1551ndash1597 2010

[21] R P Vito and S A Dixon ldquoBlood vessel constitutivemodelsmdash1995ndash2002rdquoAnnual Review of Biomedical Engineeringvol 5 no 1 pp 413ndash439 2003

[22] C M Garcıa-Herrera D J Celentano M A Cruchaga et alldquoMechanical characterisation of the human thoracic descend-ing aorta experiments and modellingrdquo Computer Methods inBiomechanics and Biomedical Engineering vol 15 no 2 pp 185ndash193 2012

[23] C M Garcıa-Herrera D J Celentano and M A CruchagaldquoBending and pressurisation test of the human aortic archexperiments modelling and simulation of a patient-specificcaserdquo Computer Methods in Biomechanics and Biomedical Engi-neering vol 16 no 8 pp 830ndash839 2013

[24] K Schmidt-Nielsen Animal Physiology Adaptation and Envi-ronment Cambridge University Press 1997

[25] VAlastrue E PenaMMartınez andMDoblare ldquoExperimen-tal study and constitutive modelling of the passive mechanicalproperties of the ovine infrarenal vena cava tissuerdquo Journal ofBiomechanics vol 41 no 14 pp 3038ndash3045 2008

[26] W Sheridan G Duffy and B Murphy ldquoMechanical characteri-zation of a customized decellularized scaffold for vascular tissueengineeringrdquo Journal of the Mechanical Behavior of BiomedicalMaterials vol 8 pp 58ndash70 2012

[27] M Chow and Y Zhang ldquoChanges in the mechanical andbiochemical properties of aortic tissue due to cold storagerdquoJournal of Surgical Research vol 171 no 2 pp 434ndash442 2011

[28] BD StemperN YoganandanMR Stineman TAGennarelliJ L Baisden and F A Pintar ldquoMechanics of fresh refrigeratedand frozen arterial tissuerdquo Journal of Surgical Research vol 139no 2 pp 236ndash242 2007

[29] C Williams J Liao E Joyce et al ldquoAltered structural andmechanical properties in decellularized rabbit carotid arteriesrdquoActa Biomaterialia vol 5 no 4 pp 993ndash1005 2009

[30] G Jimenez E Lopez-Ruiz W Kwiatkowski et al ldquoActivinABMP2 chimera AB235 drives efficient redifferentiation oflong term cultured autologous chondrocytesrdquo Scientific Reportsvol 5 Article ID 16400 2015

[31] M Jerabek Z Major and R Lang ldquoStrain determination ofpolymeric materials using digital image correlationrdquo PolymerTesting vol 29 no 3 pp 407ndash416 2010

[32] P Hung and A S Voloshin ldquoIn-plane strain measurement bydigital image correlationrdquo Journal of the Brazilian Society ofMechanical Sciences and Engineering vol 25 no 3 2003

[33] R E Shadwick ldquoMechanical design in arteriesrdquo Journal ofExperimental Biology vol 202 no 23 pp 3305ndash3313 1999

[34] Y Zou and Y Zhang ldquoMechanical evaluation of decellularizedporcine thoracic aortardquo Journal of Surgical Research vol 175 no2 pp 359ndash368 2012

Hindawiwwwhindawicom Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


put into practice in an optimum manner In this study weexplore the possibility of obtaining porcine decellularizatedarteries by applying an enzymatic digestion and detergentextraction procedure [1 9 10] This process is able to provideimplants to patients similarly to those made of syntheticmaterials once the demanded biomechanical resistance isknown Some authors have also studied the fabrication of ahybrid tissue vascular graft by applying polymerized coatingson the outside of different aortic or carotid decellularizedvessels which significantly enhances their biomechanicalbehaviour [2 11]

Theoutstanding role of assessing the biomechanical prop-erties of biological specimens (in this case different arteries)justifies the application of the mechanics of continuousmedia formalism Particularly it has been used to describethe results from several mechanical tensile tests aiming atretrieving the stiffness and elasticity of the samples Typicallythe mechanical characterization of the blood vessels hasbeen obtained without taking into account the resolutionof the displacements in axial or circumferential tests [12ndash14] The error introduced by an inaccurate distance mea-surement is translated into significant misleading variationsof the mechanical parameters In this regard we proposean image cross-correlation algorithm to improve the straintracking experienced by the sample during the stress teststhereby providing a high-resolution characterization of theirmechanical parameters The researchers that may introducethese mechanical concepts in the field of tissue engineeringor clinical practice need this accurate characterization of themechanical properties [15ndash17]

Soft tissues (such as blood vessels) understood as hyper-elastic materials when subjected to uniaxial loads are char-acterized by relevant shape changes as well as a stronglynonlinear response Hyperelastic materials experience a greatstrain when a load is applied Nevertheless once the load isremoved they return to a position very close to the initial oneOn the other hand when cyclical loads are applied to thesematerials a considerable dissipation in the energy is exhibitedas a response to the stress The realization of this workhas been based on the functions of the deformation energysuitable for soft tissues study developed by Holzapfel Ogdenand Vito [18ndash21] In this way a semianalytical description ofconstitutive equations for soft tissues is explored and then ithas been applied to develop a new technique for measuringthe strain in mechanical tensile tests

The remainder of the paper is organized as follows Sec-tion 2 briefly describes themechanical behaviour of the arteryalong with the derivation of its stress tensor Next Section 3is devoted to the strain tensor Then Section 4 includesthe experimental setup the preparation of the biologicalsamples and the details of the statistical analysis performedin the experiment Later Section 5 describes the image cross-correlation algorithm proposed in this work for a bettercharacterization of the sample mechanical properties Thefollowing section includes the results from the mechanicaltests along with the histological comparisons between nativeand decellularized vessels Finally Section 7 summarizes themain conclusions of the study and paves the way for futurework

2 Biomechanical Stress Tensor onArteries Samples

The methodology applied for the mechanical characteriza-tion is based on the stress-strain curve analysis of the sampletested until failure As later explained in Section 41 thiscurve is obtained by applying a loading stress to the sampleand recording a process by a camera therefore obtaining a2D image for each load value applied to the specimen Forthis purpose Cauchy stress has been considered the mostappropriate since it corresponds to the force or load dividedby the area of the section of the sample as follows

120590 = NA (1)

where 120590 is known as Cauchy stress N is the applied force(in our experiments it corresponds to the load applied to theblood vessel in each measurement) and A is the area of thesample section Consequently 120590 is calculated by taken intoconsideration the geometry of the sample

In particular the porcine vessels exhibit the strain-stresscurve displayed in Figure 1 In this representation two differ-ent behaviour phases can occur depending on the amount ofstrain experimented by the sample as explained in [22 23]Firstly for low values of the strain a linear region exists inwhich the elastin composition prevails in the mechanicalresponse of behaviour of the artery which is the collagencomposition By linear fitting of each region it is possible toobtain the value of Youngrsquos modulus that characterizes theelastin and collagen phases respectively Collagen Youngrsquosmodulus is much larger than its elastin counterpart thusimplying a lower stiffness of the sample in this phaseTherefore the collagen phase is chosen because in the elastinphase there are not enough significant points to approximatewith reliably Besides this elastin phase is considered whenthe sample has less rigidity and the hyperelastic model isbetter fit with collagen region

Moreover it is also important to obtain the strength ofthe material (Fm) as the maximum load to failure so that ifthe loading stress continues then the material breaks Otherrelevant parameters are the ultimate tensile strength (UTS)defined as Sr = Fm and the elongation under maximum loadas explained later Furthermore the true (or logarithmic)deformation d120576 is defined as the ratio between the increasein length (l) and the length of the sample (l) at any instant

d120576 = ll (2)

The values of engineering (d120576) and logarithmic (s) deforma-tions are related according to the following expression

s = ln(1 + l1198970 ) (3)

From the values (F l) obtained in the mechanical test oneis able to plot the uniaxial component of tensors of Cauchy(120590) and the finite strain tensors (s) as displayed in Figure 1thus obtaining its characteristic points (basically the pointin which the material suffers the mechanical failure and thepoint of the transition between elastin and collagen regions)


Colla

gen

Elastin

2

1

1

1

(ＬＬ)






119865119886119887 = 1205971199091198861205971199090119887

(4)




11986511989611(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (5)

11986511989612(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990902(i + 1 j) minus 1199090

2(i + 1 j) (6)

11986511989621(i j) asymp 119909119896

2(i j) minus 119909119896

2(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (7)

11986511989622(i j) asymp 119909119896

2(i j) minus 119909119896

2(i + 1 j)

11990902(i j) minus 1199090

2(i + 1 j) (8)


120576 = 12 (119865119865

119879 minus 119868) (9)



e = l1198970 = l minus 1198970

1198970 (10)




Tc = 119875119903119905 997888rarr

119875 = 2tTcr

(11)


















Lamp


(a)


Loadcontainer Water

tankArduino

UNO boardPC

Counterweight

Balljoint

Vessel

Peristalticpump

(b) (c)







(a)

(b)

(c)









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









Colla

gen

Elastin

2

1

1

1

(ＬＬ)






119865119886119887 = 1205971199091198861205971199090119887

(4)




11986511989611(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (5)

11986511989612(i j) asymp 119909119896

1(i j) minus 119909119896

1(i j + 1)

11990902(i + 1 j) minus 1199090

2(i + 1 j) (6)

11986511989621(i j) asymp 119909119896

2(i j) minus 119909119896

2(i j + 1)

11990901(i j) minus 1199090

1(i j + 1) (7)

11986511989622(i j) asymp 119909119896

2(i j) minus 119909119896

2(i + 1 j)

11990902(i j) minus 1199090

2(i + 1 j) (8)


120576 = 12 (119865119865

119879 minus 119868) (9)



e = l1198970 = l minus 1198970

1198970 (10)




Tc = 119875119903119905 997888rarr

119875 = 2tTcr

(11)


















Lamp


(a)


Loadcontainer Water

tankArduino

UNO boardPC

Counterweight

Balljoint

Vessel

Peristalticpump

(b) (c)







(a)

(b)

(c)









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018










Tc = 119875119903119905 997888rarr

119875 = 2tTcr

(11)


















Lamp


(a)


Loadcontainer Water

tankArduino

UNO boardPC

Counterweight

Balljoint

Vessel

Peristalticpump

(b) (c)







(a)

(b)

(c)









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018










Lamp


(a)


Loadcontainer Water

tankArduino

UNO boardPC

Counterweight

Balljoint

Vessel

Peristalticpump

(b) (c)







(a)

(b)

(c)









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









(a)

(b)

(c)









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









for k=1(N-1)Image

cross-

correlation

alignmentA B

k k+1

k=1

ROI selection

RGB to gray

stack N images

Discretized ROI

2D movement

matrix

between

images A and B

average

k=N

YESEND

NO

k=k+

1

= Σ

Ｅ=0Ｅ

Ｅ













120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018














120576k = mean [120576 (xk1 xk2)] (13)


ROI

Holder

Tensile direction

Vessel



120576 =119873minus1

sum119870=1

120576k (14)





(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









(a) Load = 44748 g (b) Load = 180510 g

(c) Load = 260370 g (d) Load = 340235 g


(a)

(b)




05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018










05 20 150

1

2

3

4St

ress

(MPa

)

1d

(a)


NA0

1

2

3

4

5

6

DA

(b)










d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









d=025d d=075

d=120 mm

5 m

m

Ｒ10

Ｒ20

(a) Native arteries

d=025d d=075

d=1

0 302010

Δ (mm)

d=175

Ｒ10

Ｒ20



NA0

5

10

15

20

25

DA

lowastlowast


0

05

1

15

2

25

3

35

4

45

NA DA

lowast


0

500

1000

1500

NA DA

lowast




(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c)

(d) (e) (f)

20 m

(g)

50 m

(h)






7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018










7 Conclusions





Data Availability




Acknowledgments




References












































Journal of












Journal of







Volume 2018






Volume 2018











































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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High-Resolution Strain Measurement for Biomechanical ...downloads.hindawi.com/journals/mpe/2019/2402606.pdf · ResearchArticle High-Resolution Strain Measurement for Biomechanical