TISSUE ELASTICITY RECONSTRUCTION BASED ON ULTRASONIC STRAIN MEASUREMENTS

0-7803-3615-1/96/$5.00 0 1996 IEEE 1996 IEEE ULTRASONICS SYMPOSIUM - 1113

Again substituting ( 4 ) into (1) results in a closed set of roupled differential equations with respect t o p

To solvr the static equilibrium equation, we can use the fir1it.r elenlent met,hod and the domain is devided into a finite numher of e1ement.s. Within each element thc shear nlodulus as we-ll as t.he displacement field he- tween the element’s nodes ar? expressed by appropriate polynomials. The system of ( 5 ) and (6) ran he numer- ically solved along with the boundary conditions.

B. Mensurements of Duplacernent and Straan

local displacement hvtween two RF envelope images The spatio-temporal derivative method detects the

returned from the tissue[4]. Let the envelope int.ensit,y at the point ( ~ , y ) in the B-scan image be denoted hy f l ( s . y ) and f z ( s , y). respectively. When the image f l ( s ,y ) i s displaced hy U < in the x-direction and by uy i n t.he y-direction and the amplitude at the point (z.y) is assumed to vary hy a factor of l-k, we can write

fz(1,y) = (1 - r:! ’ f l ( I - uz.y -Uy). (7)

This amplitude variation may come from the move-

nlent (uz, u y ) a5 well as the amplitude variation, k, are u e n t of the random scatterers in the tissue. If displace-

small. By t,aking Taylor expansion of (7) and neglert- ing higher order terms. we obtain

( f 2 - f l ) + I I X f ? + u y f v + k f l = 0 (8 )

where fz is afl(s, y)/B.r. f y is afl(s, y)/ay. In order to estimatr the 2-D displacement, ( u z , uy), and the anr- plitndr variation, k. at t h r location ( x , y)% we take thr least, squares estimation of (8). Here we assunle that ut.. u y . and I; arr nmrly roust,ant within slnall t,arget regiou. G. around the location (I. y). Thus, we define

J = / l ;(f t + u,:f2 + Uyfy + kf1)”2dy. (9)

Minimizing .l gives us the least squares estimate of ( u z , u y , k ) a t the location (x, y).

C. Computation of Components of Strain Tensor

herr ran meawrr tht, 2-D displacement field ( u = , u y ) The spatio-temporal derivative method proposed

het,ween two B-scan images. Since the second ranked strain tensor can b? computed as t.he spatial derivative of the displacement distribution, t,he strain image often

Image s i teof Bo,“d

Acrylic

Ultrasonic Absorption Material

Fig. 1. Schematic of in vivo experimmt.. The phantom consisting of a kind of gelatiu and a piece of pork w-as com- pressed by 1.5mm to the right, hy moving the tranceducrr which was usrd to image the displacement field.

exhibits significant artifads. The displarement, image is filtered with a simple 2-D moving average filter prior to strain romputat,ion.

111. RESVLTS .AND DISCUSSIONS

A . I n vitro Experiment An in vitro experiment, has heen performed to d m -

onstrate the usefullness of the spatio-temporal deriva- tivr method 1.0 measure t,issue displacement. The ex- perimental setup is shown in Fig. 1. ThP tissne-equiv- alent phantom is composrd of a kind of gelatin and a pierr of pork. The transducer waq displaced to th r right hy 1.5111nl in order to rompress thr phantom. Measurement,s were p~rfornwd using a cornnlerrially availahle ult,rasound scanner. wirh a ~ . ~ M H L focused phased array. Two RF rnvelope B-sran images of re-

itized and transfered to the computer to estimate the gion of interest before and after compression were dig-

local tissue displarement and st,rain.

as well as the measured displacement images. The im- Fig. Z(a)-(c) show the B-scan image of the phant,onl

age of phantom is displayed over 77mmx9Gmm. For quantitative evaluation, displacenlent distribution al. ong a line iudicat.ed in the images are shown in Fig.

derivative method in displacement estimate, G of (9) 2 j r ) and ( f ) . The target size of the spatio-temporal

wa~i approxinlately Gmrnx61mn. The spatial resolution to obtain a reasonable acruracy in ultrasonic displace- ment will depend on various imaging paramenters such

1114 - 1996 IEEE ULTRASONICS SYMPOSIUM

as ultrasonir frequency. target, size. single to noise rat,io of digitized image, and so on. I t should be noted t,hat the local displacement less than 0.2mm can be detected

show tlw romponmt,s o f strain tensor and Fig. 2(gj(k) with the target, size of GmmxGmm. Fig. 2(d)(h)(i)

the line indicated in Fig. 2(a). The strain E,, has the ( I ) depict. the profiles of respective strain fields along

0.06 in th r region of pork. Fig. Z( j ) and Fig. 2(m) give value of 0.01-0.02 in t,hr region of gelatin and 0.04-

the reconstructed distrihntion of relative shear modu- lus and its profile along the line indicated in Fig. 2(a). Thr relative shear modulus in t,he region of pork ha5 t h r d u t . of 0.4. which means t,hat pork is more soft than gelatin.

B. In, Vtwo Expe~irne7kts The spatia-temporal derivat.ivr method was applied

t,o measurr t,he in 7li7ro lord movement of liver tissue arising from primary cardiac pulsation and then the relative shear modulus was reconstructed. In this re- port, wr present results for two cases: one is for a nor- mal caw and the ot,hrr is for a rirrhosis case. Measure- ments were performed using t,he linear array transducer with 3.5MHz cenber frequency a t a rate of 15 framelser.

For a normal liver case. Fig. 3(a) shows a B-scan image of abdominal region. The heart located on the left adjacent to the liver is in a diast,ole and thereby the liver t.issue is compressed t.o the right. Fig. 3(b)

two B-scan images a t time interval of 0.066 second and shows an image of t,he displacement, U*, measured from

Fig. 3(e) represent,s a displacement profile along the horizontal linr indiratrd in Fig. 3(b) for quantitative rvaluat,ion. The lord displacement decreases rapidly away from the heart. Fig. 3 ( r ) shows the strain conlponent u)mputrd frntn the displarement, image of Fig. 3(h). Fig. 3(f j r rpresmtsastrain profile along the horizontal line iurli(.atrd ill Fig. 3(r). Fig. 3(d) shows the distribntion of thr rehive shear modulus, along with a profilr giveu in Fig. 3(g). It, can he seen t.hat, t,hr local defornlatiou is relatively large in less elastic region and this implies "soft" rhararter of the normal liver h u e . The strain varies from -0.02 to -0.01 with the mean of -0.014 in the liver tissue. Since, for the both cases in in Y ~ O r,xperiments, up, and cry were mnsidrrahly small. thrrje imagrs have not been shown.

4(a) reprrsents a B-smu image. Sinre the heart located Fig. 4 gives thr resalt,s for a rirrhosis case. Fig.

on the left is agaiu in H rlia3tolic cycle, the liver tissue is compressed to thr right,. Fig. 4(b)-4(d) show the dis- placenwnt. field. the strail1 field, and the distribut,ion of the relat,ivP shear modulna. which were computed from

serond. Fig. 4(e)-4(gj depict profiles for quantitative two conserut,ive B-scan images at time interval of 0.066

evaluation aloug the line indicated in the images. The strain varies from 0 to -0.009 wit.h the mean of -0.005 in the liver tissue. The slight decrease of the local dis- placement as well&? of t,he horizont,al component of the strain tensor implies "stiff charader of liver tissw for the case of cirrhosis. C.on~pared with the normal case. the cirrhosis case shows drcrrased mohilit,y and hard- erling of soft tissue over the liver.

IV CONCLOSIONS

We have proposed to rise the spatio-temporal deriva- t,iw of echograms for estimating t,he loral displacrment and strain inside t,issues. from which t,he relative shear modulus was reronstruct,erl hy solving the stat,ir q n i - lihrium equation. In our an, vitro experiments with a tissue-mimicking phantom. the relative shear modulus was clearly small in more soft region.

The method proposed was also applied an v i v o t o characterize the elasticity of the liver tissue. The rate of deformation caused by the primary cardiac pulsa- tion was characterized using components of t,he strain tensor, The relative shear nlodulus in a dispared liver tissue was relatively larger t.han that in a normal liver. It is suggested that increased elasbicity of living soft tissue due to tumor or fihrosis may he chararr,erized from the local movement and strain measurrd from se- quences of the conventional real-time B-sran images.

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(21 K.R.Raghavam and A.Yaglr. "Forward and invprsr proh- lrms in imaging th? rlasticit,y of soft tissw." IEEE

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(41 A.R.Skovnroda. S.Y.Enwlianov, M.A.Lubinski. A.P. Sarvazyan, and M.O'Donnel1, "Theoretical analysis and vrrifiration of ultrasound displacement and strain imaging," lEEE ' h n s . Ultrason. Ferroelmt. Frrq.

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SUP elasticity reconstruction bazed on dtrasonir dis- placement and strain images: IEEE Trans. L h a -

161 C.Sumi. A.Suznki, and K.?lakayma. "Estimation of son. Ferroelert. Freq. Contr.. 42: 747-764. 1995.

shear modulus distrihution in soft tissue from strain distrihution," IEEE Trans. B i o m d Eng.. 42: 193-

(71 F.KaUel and hI.Bert,rand, "Tissne elasticity remnst,ruc- 202, 1995.

tion nsing linear perturhation method,'' IEEE Trma. hled. h a g . , 15: 299-313. 1996.

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