Investigation on Elasticity-Based Tissue Characterization of Arterial Wall

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1 Investigation on Elasticity-Based Tissue Caracterization of Arterial Wall Hideyuki Hasegawa and Hirosi Kanai Departent of Electronic Engineering, Graduate Scool of Engineering E-ail: Abstract Patological canges in arterial walls significantly influence teir ecanical properties. We ave developed a correlation-based etod, te pased tracking etod, for easureent of te regional elasticity of te arterial wall. Using tis etod, elasticity distributions of lipids, blood clots, fibrous tissue, and calcified tissue were easured by in vitro experients of excised arteries (ean ± SD: lipid 89 ± 47 kpa, blood clot 131 ± 56 kpa, fibrous tissue 1022 ± 1040 kpa, calcified tissue 2267 ± 1228 kpa). It was found tat arterial tissues can be classified into soft tissues (lipids and blood clots) and ard tissues (fibrous tissue and calcified tissue) on te basis of teir elasticity. However, tere are large overlaps between elasticity distributions of lipids and blood clots and tose of fibrous tissue and calcified tissue. Tus, it was difficult to differentiate lipids fro blood clots and fibrous tissue fro calcified tissue by setting a tresold for a single elasticity value. Terefore, we previously proposed a tissue classification etod using te elasticity distribution in eac sall region. In tis etod, te elasticity distribution of eac sall region of interest (ROI) (not a single pixel) in an elasticity iage is used to classify lipids, blood clots, fibrous tissue, and calcified tissue by calculating te likeliood function for eac tissue. In te present study, te optiu size of te ROI and tresold T o for te likeliood function were investigated to iprove te tissue classification. Te ratio of correctly classified pixels to te total nuber of classified pixels was 29.8% wen te size of a sall region was 75 μ 300 μ (a single pixel). Te ratio of correctly classified pixels becae 54.2% wen te size of a sall region was 1,500 μ 1,500 μ (100 pixels). oreover, a region wit an extreely low likeliood wit respect to all tissue coponents was defined as an unclassified region by setting tresold T o for te likeliood function to Te tissue classification of te arterial wall was iproved using te elasticity distribution of a sall region wose size was larger tan te spatial resolution (800 μ 600 μ) of ultrasound. 1. Introduction Noninvasive easureent of ecanical properties of te arterial wall, suc as elasticity, is useful for diagnosing aterosclerosis because tere are significant differences between te elastic oduli of noral arterial walls and tose affected by aterosclerosis [1][2][3]. In particular, ecanical properties of plaque are iportant because te rupture of plaque ay cause acute yocardial infarction and cerebral infarction [4][5][6]. agnetic resonance iaging (RI) and intravascular ultrasound (IVUS) are proising tecnologies for directly iaging plaque orpology [7][8]. On te oter and, te dynaic cange of artery diaeter due to te pulsation of te eart can be easured noninvasively by te previous etod wit ultrasound [9][10][11][12][13]. Soe paraeters related to artery-wall elasticity can be obtained by te easured cange in diaeter of te artery [14][15][16]. However, in te derivation of tese paraeters, te artery is assued to be a cylindrical sell wit an unifor wall tickness and, tus, te elasticity of aterosclerotic plaque cannot be evaluated. For easureent of te ecanical properties of te arterial wall, including te case wit aterosclerotic plaque, we previously developed a etod, naely, te pased tracking etod, for easuring sall vibrations in te eart wall or arterial wall wit transcutaneous ultrasound [17][18]. For soe years, we ave been easuring te displaceent and sall cange in tickness of te arterial wall caused by te eartbeat using tis etod [19][20][21][22]. In our pased tracking etod, a set of two points is assigned along an ultrasonic bea, and te cange in tickness of te layer between tese two points is estiated. Furterore, by sliding te position of te layer along te ultrasonic bea by intervals of te sapled points, te spatial distribution of canges in tickness along te ultrasonic bea can be obtained. In te estiation of te cange in tickness using a correlation estiator, te tickness of an assigned layer is larger tan te interval of te sapled points, and te layer is slid by te intervals of te sapled points. Terefore, several layers wit respective correlation estiators overlap at eac dept. Terefore, correlation estiators of layers, wic overlap at a certain dept, are copounded to obtain te cange in tickness at tat dept [23]. Altoug te angle of te ultrasonic bea was not canged in te present study, te concept of spatial copounding as been applied in previous

2 studies to agnitudes of ecoes, wic are obtained by scanning eac point in te ROI wit ultrasonic beas aving different bea angles, to iprove B-ode iages [24]. Elasticity iages of te uan carotid artery ave been obtained by te easured displaceent distribution, and te potential for transcutaneous tissue caracterization as been sown by classifying te elasticity iages using te elasticity reference data obtained by in vitro experients [25][22][26]. We ave already easured te elasticity distributions for lipids, blood clots, fibrous tissue (ixture of te soot uscle and collage, and calcified tissue. In tese previous studies, it was found tat arterial tissues can be classified into soft tissues (lipids, blood clots) and ard tissues (fibrous tissue, calcified tissue) on te basis of teir elasticity. However, it was difficult to differentiate lipids fro blood clots and fibrous tissue fro calcified tissue. Terefore, we proposed a tissue classification etod using te elasticity distribution in a sall region [27]. In tis etod, te elasticity distribution of eac sall ROI (not a single pixel) in an elasticity iage was used in classification of lipids, blood clots, fibrous tissue, and calcified tissue. Precision of tissue classification was iproved using te elasticity distribution in eac sall region. However, te accuracy of tis etod in relation to te size of an ROI as not yet been torougly investigated, and te etod as not been applied to te differentiation of fibrous tissue fro calcified tissue. In te present study, to deterine te optiu size of an ROI, te accuracy of tissue classification (including calcified tissue) was quantitatively investigated in relation to te size of te ROI by evaluating te ratio of te nuber of correctly classified pixels to te total nuber of classified pixels. In addition, in te proposed classification etod, te likeliood function of eac sall ROI is obtained for eac tissue coponent (lipids, blood clots, fibrous tissue, and calcified tissue), and te region is classified into a tissue coponent tat sows te axiu likeliood. However, an ROI is classified into one of te four tissue coponents even wen te axiu likeliood is low. In te present study, suc a region is defined as an unclassified region by setting a tresold for te likeliood. Fro tese investigations, tissue classification was uc iproved in coparison wit tat in te previous study [28]. 2. aterials and etods 2.1. Experiental setup and speciens Figure 1 sows a sceatic diagra of te easureent syste. Te cange in pressure inside te artery was realized by circulating a fluid using a flow pup. Te fluid inside te artery and tat circulating in te flow pup were separated by a rubber ebrane to prevent te flow pup fro being containated, and only te cange in internal pressure propagated to te inside of te artery. Te cange in internal pressure was easured by a pressure transducer (odel 110-4, Caino, San Diego, CA, USA). In ultrasonic easureent, excised arteries were easured wit a conventional 7.5 Hz linear-type ultrasonic probe (SSH-140A, Tosiba, Japa. Te quadrature deodulated signals of RF ecoes were acquired at 10 Hz at a frae rate of 200 Hz. In tis study, te elasticity of te arterial wall is defined as te tissue strain calibrated by te average stress of te entire wall tickness, naely, circuferential elastic odulus E θ [23] (See appendix.). Te strain distribution is obtained by applying te pased tracking etod to te easured deodulated signals [21][23] (See appendix.). Fig.1. Sceatic diagra of te easureent syste. In tis study, eigt iliac and ten feoral arteries wic ad been surgically excised fro eigteen patients wit arteriosclerosis obliterans were easured in vitro. Tese arteries ad been excised at te tie of bypass grafting surgery. During te ultrasonic easureent, a needle was attaced to te external surface of te artery for identification of te easured section so tat a patological iage of te sae section could be obtained after te ultrasonic easureent. Tis study was approved by te Etics Coittee on Clinical Investigation, Graduate Scool of Engineering, Tooku University, and was perfored in accordance wit te policy of te Declaration of Helsinki; all subjects gave infored consent Tissue classification using te likeliood function In tis study, eac pixel in an elasticity iage is classified into one of 5 categories of lipids, blood clots, fibrous tissue, calcified tissue, and unknown using te likeliood function {L i } (i=1: lipid, 2: blood clot, 3: fibrous tissue, 4: calcified tissue) of te elasticity distribution in te sall region around te pixel. To obtain te likeliood function {L i }, te elasticity distribution of te i-t tissue is translated into te noral distribution to describe te probability distribution by te ean and te standard deviation as described below [27]. Fro in vitro experients, te elasticity distribution of eac tissue i is obtained as illustrated in Fig. 2(a). Te elasticity distribution of te i-t tissue consists of J i data points wit te respective elastic oduli. Using all data of J i points (J 1 : 228, J 2 : 179, J 3 : 19,121, J 4 : 1,101) wit te respective elastic oduli, te ascending sequence is constructed for tissue i as sown in Fig. 2(b). In tis sequence, te j-t datu (j=1, 2,..., J i )

3 as te corresponding elastic odulus E j (E j E j+1 ), were j is tered te elasticity nuber. Te probability distribution of eac tissue was obtained by allocating all te data of J i points of eac tissue i to boxes of te noral distribution. Te box nubers, {B i }, of te noral distribution are deterined so tat te nuber of data in te box at eac end is only one. As sown in Fig. 2(c), te nuber of data, D i, (=1, 2,..., B i ), included in box B i is deterined so as to follow te profile of te noral distribution. Tus, te (J i /2)-t datu is included in te box wit te igest probability. By allocating all te data of J i points of eac tissue to boxes of te corresponding noral distribution, te ean elasticity Ē i, of te data included in eac box is obtained. ROI. Te pixel at te center of an ROI is classified into te class wic as te axiu likeliood. In tis classification, tere ay be a region wic as an extreely sall value for te axiu likeliood. Suc regions are classified into te unclassified region by setting tresold T o to te axiu likeliood. Tus, te category C(R,n ), to wic an ROI R,n belongs, is expressed as follows: arg ax Li (, 1 i 4 C( R, = ( if ax Li (, To ). 1 i 4 unknown ( oterwise). (2.2) Fig.3. Illustration of region of interest (ROI). Fig.2. (a) Original elasticity distribution of te tissue. (b) Ascending sequence of elastic odulus in an elasticity distribution. (c) Noral distribution wose nuber of boxes depends on te nuber of data points of (a). As sown in Fig. 3, an ROI was assigned to an elasticity iage wic was obtained by ultrasonic easureent. Te likeliood function L i (, is defined as a joint probability tat all te elasticity values in ROI R,n (center of ROI: n-t sapled point along -t bea) siultaneously belong in te i-t category as follows: Li (, = pi ( E ( k, l) R, n 1 N0 k, l ), (i=1, 2, 3, 4) (2.1) were p i (E k,l ) is te probability density wic sows te probability tat elasticity value E k,l in te k-t row and l-t colun in te ROI belongs to te i-t tissue category, and N 0 denotes te nuber of pixels in an ROI R,n. Te ultiplier 1/N 0 sows te geoetric ean for copensation of te effect of te size of an Figure 4 sows exaples of tissue classification iages wic were anually estiated by referring to te patological iages of iliac arteries (A) and (B). By coparing te patology-based classification iages sown in Fig. 4 wit te tissue classification iages obtained by te proposed etod, te recognition rate R r (S ROI ) for all tissues in te arterial wall was defined by te ratio of te nuber of correctly classified pixels to te nuber N of all pixels in te iage as follows: N i i R ( S ) = 100 [%], (2.3) r ROI N were N i is te nuber of correctly classified pixels of tissue i and S ROI is te size of an ROI. Recognition rate R r (S ROI ) was used to deterine te optiu size of an ROI. For an ROI wit a very low likeliood for all classes (i = 1, 2, 3, 4), te pixel wic is located at te center of te ROI sould be defined as an unclassified pixel by tresolding. For deterination of te optiu tresold for te likeliood function, te false recognition rate F r (S ROI ) for all tissues in te arterial wall was defined by te ratio of te nuber of isclassified pixels except for te pixels classified as unclassified pixels to te nuber N of all pixels as follows: F i i Fr ( S ROI ) = 100 [%], N (2.4) were F i is te nuber of isclassified pixels of tissue i except for te pixels classified as unclassified pixels. Altoug te unclassified pixels are included in te denoinator of eqs. (2.3) and (2.4), tat is, te nuber of all pixels N, tey are not included in te nuber of correctly classified pixels N i nor tat of isclassified pixels F i. Terefore, te su of te recognition rate

4 R r (S ROI ) and te false recognition rate F r (S ROI ) does not becoe 100%. Fig.4. Tissue classification iages obtained by referring to patological iages. (a) Iliac artery (A). (b) Iliac artery (B). 3. In Vitro Experiental Results 3.1. easureent of elasticity distribution of eac tissue Figure 5(a) sows a B-ode iage of one of te feoral arteries. Te strong ecoes fro outside te posterior wall correspond to a needle. For te posterior wall, te iages of te axiu cange in tickness during te cardiac cycle were easured as sown in Fig. 5(b). Figure 6(a) sows te elasticity iage of te feoral artery obtained fro te axiu cange in internal pressure and tat in tickness obtained by te pased tracking etod sown in Fig. 5(b). By referring to te patological iage of te sae section sown in Fig. 6(b), fibrous tissue in te intia-edia region was identified. Te corresponding region, naely, te region surrounded by te green line in Fig. 6(a), was ten assigned to te elasticity iage. Figure 6(c) sows te elasticity distribution of fibrous tissues extracted fro te region surrounded by te green line in Fig. 6(a). By applying te sae procedure to te oter arteries, te elasticity distribution of eac tissue in te arterial wall was obtained. Figure 7 sows te elasticity distribution of eac tissue, tat is, te frequency of te elasticity values wic belong to te range defined by te position and widt of eac vertical bar. Te widt of a vertical bar was set at 50 kpa. eans and standard deviations are 89 ± 47 (lipids), 131 ± 56 (blood clots), 1,022 ± 1,040 (fibrous tissue), and 2,267 ± 1,228 kpa (calcified tissue). Altoug siilarities were found in te elasticity distributions of lipids and blood clots and in tose of fibrous and calcified tissues, differences in te elasticity distributions of tese tissues were found. Fig.5. (a) B-ode iage of a feoral artery. (b) Iage of te axiu cange in tickness during te cardiac cycle. Fig.6. (a) Elasticity iage of te arterial wall. (b) Patological iage of te corresponding section. (c) Elasticity distribution in te region between te two green lines in (a).

5 functions {L i } was set at As sown in Fig. 9(d), te region wit te axiu likeliood wic is iger tan tresold T o is accurately classified as te corresponding tissue identified by referring to te patological iage. Fig.7. Elasticity distribution of eac tissue. (a) Lipids (N = 288). (b) Blood clots (N = 178). (c) Fibrous tissue (N = 19,120). (d) Calcified tissue (N = 1,101) Results of classification Figure 8 sows te probability density of eac tissue obtained by te axis transforation of te elasticity distribution. As sown in tese figures, te orizontal axis of te elastic odulus is nonlinear. Using tese databases, eac pixel in an elasticity iage was classified as a certain tissue coponent. Fig.8. Probability density for eac tissue. (a) Lipids. (b) Blood clots. (c) Fibrous tissue. (d) Calcified tissue. Figures 9(c) and 9(d) sow te tissue classification results obtained by te proposed etod for te iliac artery (A). Te regions classified as lipids, blood clots, fibrous tissue, and calcified tissue were stained yellow, red, blue, and purple, respectively. Figure 9(c) grapically sows te tissue classification iage obtained wit an ROI size of 1 1 pixel. Altoug arterial tissues were rougly classified into soft tissues (lipids and blood clots) and ard tissues (fibrous tissue and calcified tissue), te classified tissue distributions are scattered, and te isclassified regions are outstanding. Alternatively, Fig. 9(d) sows te result of classification wit an ROI size of 1,500 μ (=20 pixels) in te radial direction and 1,500 μ (=5 pixels) in te longitudinal direction. oreover, te region wit low likeliood for all tissue coponents is colored gray. Te tresold T o for te axiu of te likeliood Fig.9. For te iliac artery (A). (a) Patological iage of an arterial wall subjected to elastica-asson staining. (b) Elasticity iage. (c) Tissue classification iage (ROI size: 1 1 pixel). (d) Tissue classification iage (ROI size: 5 20 pixels). For anoter specien (iliac artery (B)), calcified tissue in te fibrous tissue was identified as sown in Fig. 10(e). As in Fig. 8, tissue classification was iproved using te elasticity distribution of eac ROI (not a single pixel). In te case of Fig. 10, tere was no region wit low likeliood for any of te tissue coponents. Figure 11 sows te relationsip between te size S ROI of an ROI and te recognition rate R r (S ROI ). Te ROI size S ROI was canged wit its sape being kept square, and in Fig. 11, te orizontal axis sows te widt W = S of an ROI in te longitudinal ROI direction. An ROI consists of a single pixel wen te widt, W, in Fig. 11 is 0.3. Only in tis specific case, is an ROI not square (75 μ 300 μ). Figure

6 11(b) sows te relationsip between widt W = S ROI of an ROI in te longitudinal direction and te recognition rate R r (S ROI ) in arteries wic are coposed of a single type of tissue, suc as fibrous tissue. In suc case, te recognition rate R r (S ROI ) is onotonically iproved by increasing te size of an ROI because an elasticity iage is uniforly classified as te corresponding tissue using a large ROI, wic results fro te worsening spatial resolution in tissue classification. Figure 11(a) sows te relationsip between widt W of an ROI and te recognition rate R r (S ROI ) in arteries coposed of different types of tissues. For tis case, tissue classification using soe pixels in an ROI is superior to tat using a single pixel. However, te iproveent of tissue classification by te enlargeent of an ROI is liited because te classification using a large ROI provides a unifor tissue classification iage wereas te arterial wall is coposed of different kinds of tissues. Terefore, tere sould be an optiu size of ROI. As sown in Fig. 11(a), te recognition rates becae axiu in ost arteries wen te size of an ROI was 1,500 μ 1,500 μ. Figures 12 and 13 sow te relationsips between te tresold T o for te likeliood function and te recognition rate R r (S ROI ) and between T o and te false recognition rate F r (S ROI ), respectively, for arteries coposed of different types of tissues. As sown in Figs. 12 and 13, te false recognition rate F r (S ROI ) begins to be reduced at a lower tresold in coparison wit te recognition rate because te pixels wit lower likeliood are ore likely to be isclassified. However, te correctly classified pixels are also classified as unclassified pixels wen te tresold T o is too ig. Terefore, tresold T o sould be deterined by considering bot R r (S ROI ) and F r (S ROI ). In tis study, te ratio (CR(T o )) of te nuber of correctly classified pixels (te nuerator of eq. (2.3)) to te nuber of isclassified pixels (te nuerator of eq. (2.4)) for all arteries coposed of different types of tissues was evaluated as follows: N i i,all CR( To ) =, F i i,all (3.1) were N i,all and F i,all are te su of correctly classified pixels of tissue i and tat of isclassified pixels of tissue i, respectively, for all arteries coposed of different types of tissues. Figure 14 sows te relationsip between tresold T o for likeliood function and CR(T o ) averaged by all arteries coposed of different types of tissues. As sown in Fig. 14, te CR(T o ) reaced te axiu wen te tresold T o was Fig.10. For te iliac artery (B). (a) Patological iage of anoter arterial wall subjected to eatoxylin-eosin staining. (b) Patological iage of te arterial wall subjected to elastica-asson staining. (c) Elasticity iage. (d) Tissue classification iage (ROI size: 1 1 pixel). (e) Tissue classification iage (ROI size: 5 20 pixels). 4. Discussion In Figs. 8 and 9, it can be seen tat te tissue classification was iproved using te elasticity distribution in eac ROI (not a single pixel). Wen te size of an ROI is saller tan te spatial resolution ΔS of ultrasound (including te case of a single pixel), te elasticity distribution in te ROI becoes narrow as illustrated in Fig. 15(b) by te purple curve because te elasticity values witin te space of te resolution of ultrasound ΔS ave soe degree of siilarity. Under suc a condition, even in te case tat te ROI is perfectly coposed of tissue A as sown in Fig. 15(a), tere is a possibility tat te ROI for tissue A and tat for tissue B will becoe siilar, as sown in Fig. 15(b), because te elasticity distribution in te ROI is narrow and te elasticity distributions of tissue A and tissue B overlap. By enlarging te size of an ROI so tat it is larger tan te space of te resolution of ultrasound ΔS, te nuber of independent elasticity values increases, and te elasticity distribution in te ROI tends to

7 becoe siilar to tat of tissue A because te ROI is coposed of tissue A. Tis is an advantage of te proposed etod wit an ROI wose size is larger tan te resolution of ultrasound ΔS. Figure 13 sows an exaple of tis case. Figures 16(a), 16(b), 16(c) and 17(d) sow a tissue classification iage, an enlarged view of an ROI, and elasticity distributions of ROIs wit sizes of 600 μ 600 μ and 1,500 μ 1,500 μ, respectively. In Fig. 16(c), te elasticity distribution of te saller ROI (purple line) is narrow and located in te overlapping region of te elasticity distributions of lipids and blood clots, te orange and red dased lines sowing te elasticity distributions of lipids and blood clots, respectively. Terefore, tissue classification is very difficult. On te oter and, in Fig. 16(d), te elasticity distribution is broadened and becoes siilar to tat of a blood clot, and te ROI can be correctly classified as a blood clot. Fig.13. Relationsip between tresold T o for likeliood function and te false recognition rate F r (S ROI ) in arteries coposed of several types of tissues. Fig.14. Relationsip between tresold T o for likeliood function and te ratio of te nuber of correctly classified pixels to te nuber of isclassified pixels in all arteries wic are coposed of several types of tissues. Fig.11. Relationsip between widt W of an ROI in te longitudinal direction and te recognition rate R r (S ROI ). (a) Arteries coposed of several types of tissues. (b) Arteries coposed of a single tissue. Eac line sows te recognition rate R r (S ROI ) of te corresponding artery. Fig.12. Relationsip between tresold T o for likeliood function and te recognition rate R r (S ROI ) in arteries coposed of several types of tissues. Fig.15. (a) ROI R,n (1,500 μ 1,500 μ) and spatial resolution of ultrasound in only tissue A. (b) Elasticity distribution of ROI R,n wen ROI size is saller tan te resolution of ultrasound. (c) Elasticity distribution of ROI R,n wen ROI size is 1,500 μ 1,500 μ. As described above, te proposed etod reduces te isclassification at te expense of te spatial resolution in tissue classification. As illustrated in Fig. 17, in actual cases, an ROI is not coposed of only one tissue coponent. Wen te content of tissue A in an ROI is uc larger tan tat of tissue B, te ROI is classified as tissue A even if te pixel, wic is in te center of te ROI, is coposed of tissue B and te sall clusters of tissue B in te ROI are not identified. Wen te contents of tissues A and B are siilar, as illustrated in Fig. 18, te elasticity distribution of te ROI exists in te overlapping region even wen te

8 ROI is broadened. Figure 19 sows an exaple of tis case, and tissue classification is found to be difficult even by te use of te proposed etod because te elasticity distribution in te ROI is located in te overlapping region for eac ROI size. likeliood were investigated. Using te elasticity distribution in an ROI, te differentiation of lipids fro blood clots and tat of fibrous tissue fro calcified tissue were iproved. Fig.16. (a) Tissue classification iage obtained by referring to patological iages. (b) Close-up of ROI. (c) Elasticity distribution (ROI size: 600 μ 600 μ). (d) Elasticity distribution (ROI size: 1,500 μ 1,500 μ). Fig.18. (a) ROI R,n (1,500 μ 1,500 μ) and spatial resolution of ultrasound in tissue A and tissue B (tissue A tissue B). (b) Elasticity distribution of ROI R,n wen ROI size is saller tan te resolution of ultrasound. (c) Elasticity distribution of ROI R,n wen ROI size is 1,500 μ 1,500 μ. Fig.17. (a) ROI R,n (1,500 μ 1,500 μ) and spatial resolution of ultrasound in tissue A and tissue B. Tissue B is distributed as sall clusters. (b) Elasticity distribution of ROI R,n wen ROI size is saller tan te resolution of ultrasound. (c) Elasticity distribution of ROI R,n wen ROI size is 1,500 μ 1,500 μ. In tis study, eac of 33,938 pixels of te elasticity iages of te 18 arteries fro wic te elasticity distribution of eac tissue was obtained was classified to sow te possibility of using te proposed etod for noninvasive classification of te tissue coposition in te arterial wall based on ultrasound elasticity iaging. However, different arteries not used for constructing te elasticity databases sould be classified in future work to torougly sow te effectiveness of te proposed etod. 4. Conclusion In tis study, tissue classification based on te likeliood function wit te configured appropriate ROI size (not a single pixel) and a lower liit of Fig.19. (a) Tissue classification iage obtained by referring to patological iages. (b) Close-up of ROI. (c) Elasticity distribution (ROI size: 600 μ 600 μ). (d) Elasticity distribution (ROI size: 1,500 μ 1,500 μ). References [1] Lee RT, Grodzinsky AJ, Frank EH, Ka RD and Scoen FJ. Structure-dependent dynaic ecanical beavior of fibrous caps fro uan aterosclerotic plaques. Circulation 83, , [2] Loree H, Grodzinsky AJ, Park SY, Gibson LJ and Lee RT. Static circuferential tangential odulus of uan aterosclerotic tissue. J Bioec 27, , [3] Sions PCG, Algra A, Bots L, Grobbee DE and van der Graaf Y. Coon carotid intia-edia tickness and arterial stiffness. Circulation 100, , [4] Falk E, Sa PK and Fuster V. Coronary plaque disruption. Circulation 92, , 1995.

9 [5] Davies J. Stability and instability: Two faces of coronary aterosclerosis. Circulation 94, , [6] Golledge J, Greenalg R and Davies AH. Te syptoatic carotid plaque. Stroke 31, , [7] cconnell V, Aikawa, aier SE, Ganz P, Libby P and Lee RT. RI of rabbit aterosclerosis in response to dietary colesterol lowering. Arterioscler Trob and Vasc Biol 19, , [8] Potkin BN, Bartorelli AL, Gessert J, Neville RF, Alagor Y, Roberts WC and Leon B. Coronary artery iaging wit intravascular ig-frequency ultrasound. Circulation 81, , [9] Hoeks APG, Ruissen CJ, Hick P and Renean RS. Transcutaneous detection of relative canges in artery diaeter. Ultrasound ed Biol 11, 51 59, [10] Hoeks APG, Di X, Brands PJ and Renean RS. Coparison of te perforance of te RF cross correlation and Doppler autocorrelation tecnique to estiate te ean velocity of siulated ultrasound signals. Ultrasound ed Biol 19, , [11] Länne T, Stale H, Bengtsson H, Gustafsson D, Bergqvist D, Sonesson B, Lecerof H and Dal P. Noninvasive easureent of diaeter canges in te distal abdoinal aorta in an. Ultrasound ed Biol 18, , [12] Brands PJ, Hoeks APG, Rutten C and Renean RS. A noninvasive etod to estiate arterial ipedance by eans of assessent of local diaeter cange and te local centerline blood flow velocity using ultrasound. Ultrasound ed Biol 22, , [13] einders J, Brands PJ, Willigers J, Kornet L and Hoeks APG. Assessent of te spatial oogeneity of artery diension paraeters wit ig frae rate 2-D B-ode. Ultrasound ed Biol 27, , [14] Bergel DH. Te static elastic properties of te arterial wall. J Pysiol 156, , [15] Peterson LH, Jensen RE and Parnel J. ecanical properties of arteries in vivo. Circ Res 8, , [16] Hayasi K, Handa H, Nagasawa S, Okaura A and oritake K. Stiffness and elastic beavior of uan intracranial and extracranial arteries. J Bioec 13, , [17] Kanai H, Sato, Koiwa Y and Cubaci N. Transcutaneous easureent and spectru analysis of eart wall vibrations. IEEE Trans Ultrason Ferroelect Freq Contr 43, , [18] Kanai H, Hasegawa H, Cubaci N, Koiwa Y and Tanaka. Noninvasive evaluation of local yocardial tickening and its color-coded iaging. IEEE Trans Ultrason Ferroelect Freq Contr 44, , [19] Hasegawa H, Kanai H, Koiwa Y and Cubaci N. Noninvasive evaluation of Poisson s ratio of arterial wall using ultrasound. Electron Lett 33, , [20] Hasegawa H, Kanai H and Koiwa Y. odified pased tracking etod for easureent of cange in tickness of arterial wall. Jpn J Appl Pys 41, , [21] Kanai H, Koiwa Y and Zang J. Real-tie easureents of local yocardiu otion and arterial wall tickening. IEEE Trans Ultrason Ferroelec Freq Contr 46, , [22] Kanai H, Hasegawa H, Iciki, Tezuka F and Koiwa Y. Elasticity iaging of ateroa wit transcutaneous ultrasound -preliinary study-. Circulation 107, , [23] Hasegawa H and Kanai H. odification of te pased tracking etod for reduction of artifacts in estiated artery wall deforation. IEEE Trans Ultrason Ferroelect Freq Contr 53, , [24] Jespersen SK, Wiljel JE and Sillesen H. ultiangle copound iaging. Ultrason Iag 20, , [25] Hasegawa H, Kanai H, Hosiiya N and Koiwa Y. Evaluating te regional elastic odulus of a cylindrical sell wit nonunifor wall tickness. J ed Ultrason 31, 81 90, [26] Inagaki J, Hasegawa H, Kanai H, Iciki and Tezuka F. Construction of reference data for tissue caracterization of arterial wall based on elasticity iages. Jpn J Appl Pys 44, , [27] Inagaki J, Hasegawa H, Kanai H, Iciki and Tezuka F. Tissue classification of arterial wall based on elasticity iage. Jpn J Appl Pys 45, , [28] Tsuzuki K, Hasegawa H, Kanai H, Iciki and Tezuka F.Optial region of interest settings for tissue caracterization based on ultrasonic elasticity iaging. Ultrasound ed Biol (in press). Appendix: Strain Estiation by te Pased Tracking etod wit Correlation Estiator Copounding [17][23] By referring to a cross-sectional iage of an artery, initial positions x 1 (1) and x 1 (1) of two points are anually assigned in te first frae as sown in Fig. 20 (x 1 (1)-x 1 (1)= L Δx; Δx: spacing of sapled points in te dept directio. Instantaneous positions x 1 ( and x 1 ( of tese assigned points in te n-t frae are ten tracked by te pased tracking etod [17]. Te cange in tickness between two reflectors at depts x 1 ( and x 1 ( is ten obtained as follows: Te pases θ 1 ( and θ 1 ( of ecoes fro tese two reflectors depend on x 1 ( and x 1 (. Terefore, te pase difference θ (=θ 1 (-θ 1 ( depends on te distance (=x 1 (-x 1 ( (tickness of te layer) between two reflectors as follows [20][23]: ( = x1 ( x1 ( c (A-1) 0 = { θ1( θ1( } 4π f c0 = 4π f 0 0 θ (, were c 0 and f 0 are te speed of sound and center frequency of ultrasound, respectively. Tus, te rate v ( of te cange in tickness of te layer between two reflectors is expressed as follows:

10 ( n + 1) ( v ( = T c0 = 4π f T 0 { θ ( n + 1) θ ( } c0 = Δθ (, 4π f 0T were Δθ ( is te cange in θ ( during a frae interval T. Pase difference θ ( can be expressed by pase β x1 (, x1 ( ) of product β, x1 ( ) of coplex deodulated signals z * (n; x 1 () and z(n; x 1 () as follows: θ ( = θ1( θ1( = β, ), (A-3) * β, ) = z( n; ) z x1 ( ). (A-4) In tis study, correlation estiator γ (n; x) at dept x, wose pase γ x) corresponds to θ (n+1)- θ (=Δθ (, is obtained by siply calculating te correlation around te duration of te eployed ultrasonic pulse as follows: ˆ γ x (1) + i Δx) = K / 2 1 k = K / 2 β ( n + 1; x ( + k Δx, x ( + k Δx) 1 (A-2) * β x1 ( + k Δx, + k Δx), (i = 0, 1, 2,..., L ) (A-5) were te estiate in te rigt-and side of eq. (A-5) is used for correlation estiators γ (n; x) at all points between x 1 (1) and x 1 (1). To obtain te spatial distribution along eac ultrasonic bea, te correlation estiator, γ, (n; x), for te cobination of two points, x (1) and x (1), at eac dept is obtained by sliding te cobination of two points along te ultrasonic bea wile keeping te distance between te two points in te first frae constant (= L Δx) as follows: ˆ γ x (1) + ( i 1) Δx) =, x K / 2 k = K / 2 β ( n + 1; x 1 ( + k Δx, x ( + k Δx) (A-6) * β ( + k Δx, ( + k Δx), ( 1) = 1) + ( 1) Δx. (A-7) ( = 1, 2,..., T +1; i = 1, 2,..., L +1) As sown in Fig. 20, soe of te T assigned layers overlap eac oter. Terefore, tere are ultiple estiates of γ (n; x) at dept x. Te copounded correlation estiator, γ x), at dept x is ten obtained by siply averaging te overlapping correlation estiators as follows: + ( (1)) 1 o x γ = ˆ (1)) γ, k (1)), (A-8) o ( xx (1)) k = were o (x) is te nuber of overlapping layers at dept x. By copounding te correlation estiator sown by eq. (A-6), te contributions of ecoes wit low aplitudes (=low signal-to-noise ratio) to te estiation of te pase sift are suppressed. Te copounded rate, v x), of te cange in tickness at dept x is obtained based on eq. (A-2) as follows: c0 v (1)) = γ (1)). (A-9) 4π f 0T Te copounded cange in tickness, Δ x), is obtained as follows: Δ ( n + 1; (1)) = Δ (1)) + v (1)) T (A-10) Te elastic odulus, E θ,, at x (1) is obtained by te estiated cange in tickness as follows [25]: 1 r T + L + 1 Δp (A-11) E,, 2 0 T θ = + + L Δ ax L Δx were r and 0 are, respectively, te radius at x (1) and te tickness of te entire wall in te first frae, and Δp and Δ are, respectively, te pulse ax pressure and te axiu of te absolute value of te cange in tickness at x (1). Te inner radius of te -t layer r and entire wall tickness 0 can be expressed as follows: r = r0 + ( 1) Δx, (A-12) 0 = L Δx, (A-13) were r 0 is te inner radius of te innerost layer. By substituting eqs. (A-12) and (A-13) into eq. (A-11), eq. (A-11) is odified as follows: 1 r0 Δp 1 r0 Δp (A-14) Eθ, = 1 1, 2 + = Δ ax 0 Δε L Δx were Δε is te strain of te -t layer. As sown by eq. (A-14), elastic odulus E θ, is defined as te average stress (r 0 / 0 +1) Δp/2 of te entire wall tickness divided by te radial strain Δε. Fig.20. Illustration of te etod for estiation of te cange in tickness of te arterial wall ( T : total nuber of assigned cobinations, L : te nuber of sapled points between two points of an assigned cobination, T: frae interval, Δx: depts of scatterers in n-t frae, x ( and x (: -t cobination of two points in n-t frae, (: distance between two scatterers in n-t frae).