Investigation on Elasticity-Based Tissue
Characterization of Arterial Wall
Hideyuki Hasegawa and Hiroshi Kanai
Department of Electronic Engineering, Graduate School of Engineering
E-mail: hasegawa@us.ecei.tohoku.ac.jp, hkanai@ecei.tohoku.ac.jp

Abstract

1. Introduction

Pathological changes in arterial walls significantly
influence their mechanical properties. We havedeveloped a correlation-based method, the phased
tracking method, for measurement of the regionalelasticity of the arterial wall. Using this method,elasticity distributions of lipids, blood clots, fibrous
tissue, and calcified tissue were measured by in vitro
experiments of excised arteries (mean ± SD: lipid 89 ±47 kPa, blood clot 131 ± 56 kPa, fibrous tissue 1022 ±
1040 kPa, calcified tissue 2267 ± 1228 kPa). It was
found that arterial tissues can be classified into soft
tissues (lipids and blood clots) and hard tissues (fibrous
tissue and calcified tissue) on the basis of theirelasticity. However, there are large overlaps between
elasticity distributions of lipids and blood clots andthose of fibrous tissue and calcified tissue. Thus, it wasdifficult to differentiate lipids from blood clots andfibrous tissue from calcified tissue by setting athreshold for a single elasticity value. Therefore, we
previously proposed a tissue classification method
using the elasticity distribution in each small region. In
this method, the elasticity distribution of each small
region of interest (ROI) (not a single pixel) in anelasticity image is used to classify lipids, blood clots,
fibrous tissue, and calcified tissue by calculating the
likelihood function for each tissue. In the present study,
the optimum size of the ROI and threshold To for the
likelihood function were investigated to improve thetissue classification. The ratio of correctly classified
pixels to the total number of classified pixels was
29.8% when the size of a small region was 75 μm ×
300 μm (a single pixel). The ratio of correctlyclassified pixels became 54.2% when the size of asmall region was 1,500 μm × 1,500 μm (100 pixels).
Moreover, a region with an extremely low likelihood
with respect to all tissue components was defined as an
unclassified region by setting threshold To for the
likelihood function to 0.16. The tissue classification of
the arterial wall was improved using the elasticity
distribution of a small region whose size was larger
than the spatial resolution (800 μm × 600 μm) of
ultrasound.

Noninvasive measurement of mechanical propertiesof the arterial wall, such as elasticity, is useful for
diagnosing atherosclerosis because there are significant
differences between the elastic moduli of normal
arterial walls and those affected by atherosclerosis[1][2][3]. In particular, mechanical properties of plaqueare important because the rupture of plaque may cause
acute myocardial infarction and cerebral infarction[4][5][6]. Magnetic resonance imaging (MRI) andintravascular ultrasound (IVUS) are promisingtechnologies for directly imaging plaque morphology[7][8]. On the other hand, the dynamic change of arterydiameter due to the pulsation of the heart can bemeasured noninvasively by the previous method withultrasound [9][10][11][12][13]. Some parameters
related to artery-wall elasticity can be obtained by themeasured change in diameter of the artery [14][15][16].
However, in the derivation of these parameters, theartery is assumed to be a cylindrical shell with an
uniform wall thickness and, thus, the elasticity ofatherosclerotic plaque cannot be evaluated.
For measurement of the mechanical properties of thearterial wall, including the case with atherosclerotic
plaque, we previously developed a method, namely, thephased tracking method, for measuring small
vibrations in the heart wall or arterial wall withtranscutaneous ultrasound [17][18]. For some years, wehave been measuring the displacement and smallchange in thickness of the arterial wall caused by theheartbeat using this method [19][20][21][22]. In ourphased tracking method, a set of two points is assigned
along an ultrasonic beam, and the change in thicknessof the layer between these two points is estimated.
Furthermore, by sliding the position of the layer along
the ultrasonic beam by intervals of the sampled points,
the spatial distribution of changes in thickness along
the ultrasonic beam can be obtained.
In the estimation of the change in thickness using acorrelation estimator, the thickness of an assigned layer
is larger than the interval of the sampled points, and thelayer is slid by the intervals of the sampled points.
Therefore, several layers with respective correlation
estimators overlap at each depth. Therefore, correlation
estimators of layers, which overlap at a certain depth,
are compounded to obtain the change in thickness atthat depth [23]. Although the angle of the ultrasonicbeam was not changed in the present study, the conceptof spatial compounding has been applied in previous

studies to magnitudes of echoes, which are obtained byscanning each point in the ROI with ultrasonic beams
having different beam angles, to improve B-mode
images [24].
Elasticity images of the human carotid artery havebeen obtained by the measured displacement
distribution, and the potential for transcutaneous tissue
characterization has been shown by classifying theelasticity images using the elasticity reference dataobtained by in vitro experiments [25][22][26].
We have already measured the elasticity
distributions for lipids, blood clots, fibrous tissue(mixture of the smooth muscle and collagen), andcalcified tissue. In these previous studies, it was foundthat arterial tissues can be classified into soft tissues(lipids, blood clots) and hard tissues (fibrous tissue,
calcified tissue) on the basis of their elasticity.
However, it was difficult to differentiate lipids fromblood clots and fibrous tissue from calcified tissue.
Therefore, we proposed a tissue classification method
using the elasticity distribution in a small region [27].
In this method, the elasticity distribution of each small
ROI (not a single pixel) in an elasticity image was usedin classification of lipids, blood clots, fibrous tissue,and calcified tissue. Precision of tissue classification
was improved using the elasticity distribution in eachsmall region.
However, the accuracy of this method in relation to
the size of an ROI has not yet been thoroughly
investigated, and the method has not been applied tothe differentiation of fibrous tissue from calcified tissue.
In the present study, to determine the optimum size ofan ROI, the accuracy of tissue classification (including
calcified tissue) was quantitatively investigated inrelation to the size of the ROI by evaluating the ratio of
the number of correctly classified pixels to the total
number of classified pixels. In addition, in the
proposed classification method, the likelihood functionof each small ROI is obtained for each tissue
component (lipids, blood clots, fibrous tissue, andcalcified tissue), and the region is classified into atissue component that shows the maximum likelihood.
However, an ROI is classified into one of the four
tissue components even when the maximum likelihood
is low. In the present study, such a region is defined as
an unclassified region by setting a threshold for the
likelihood. From these investigations, tissueclassification was much improved in comparison withthat in the previous study [28].

2. Materials and Methods
2.1. Experimental setup and specimens
Figure 1 shows a schematic diagram of themeasurement system. The change in pressure inside theartery was realized by circulating a fluid using a flow
pump. The fluid inside the artery and that circulating in
the flow pump were separated by a rubber membrane
to prevent the flow pump from being contaminated,and only the change in internal pressure propagated tothe inside of the artery. The change in internal pressure

was measured by a pressure transducer (Model 110-4,
Camino, San Diego, CA, USA).
In ultrasonic measurement, excised arteries were
measured with a conventional 7.5 MHz linear-typeultrasonic probe (SSH-140A, Toshiba, Japan). The
quadrature demodulated signals of RF echoes wereacquired at 10 MHz at a frame rate of 200 Hz. In thisstudy, the elasticity of the arterial wall is defined as thetissue strain calibrated by the average stress of theentire wall thickness, namely, circumferential elastic
modulus Eθh [23] (See appendix.). The strain
distribution is obtained by applying the phased
tracking method to the measured demodulated signals[21][23] (See appendix.).

Fig.1. Schematic diagram of the measurement system.
In this study, eight iliac and ten femoral arteries
which had been surgically excised from eighteenpatients with arteriosclerosis obliterans were measured
in vitro. These arteries had been excised at the time of
bypass grafting surgery. During the ultrasonicmeasurement, a needle was attached to the externalsurface of the artery for identification of the measured
section so that a pathological image of the same section
could be obtained after the ultrasonic measurement.
This study was approved by the Ethics Committee on
Clinical Investigation, Graduate School of Engineering,Tohoku University, and was performed in accordancewith the policy of the Declaration of Helsinki; allsubjects gave informed consent.

2.2. Tissue classification using the likelihood
functionIn this study, each pixel in an elasticity image isclassified into one of 5 categories of lipids, blood clots,
fibrous tissue, calcified tissue, and unknown using the
likelihood function {Li} (i=1: lipid, 2: blood clot, 3:
fibrous tissue, 4: calcified tissue) of the elasticity
distribution in the small region around the pixel. To
obtain the likelihood function {Li}, the elasticity
distribution of the i-th tissue is translated into thenormal distribution to describe the probability
distribution by the mean and the standard deviation as
described below [27].
From in vitro experiments, the elasticity distributionof each tissue i is obtained as illustrated in Fig. 2(a).
The elasticity distribution of the i-th tissue consists of
Ji data points with the respective elastic moduli. Using
all data of Ji points (J1: 228, J2: 179, J3: 19,121, J4:
1,101) with the respective elastic moduli, the ascending
sequence is constructed for tissue i as shown in Fig.
2(b). In this sequence, the j-th datum (j=1, 2, . . ., Ji)

has the corresponding elastic modulus Ej (Ej≤Ej+1),
where j is termed the elasticity number. The probability
distribution of each tissue was obtained by allocating
all the data of Ji points of each tissue i to boxes of thenormal distribution. The box numbers, {Bi}, of thenormal distribution are determined so that the numberof data in the box at each end is only one. As shown in
Fig. 2(c), the number of data, Di,h (h=1, 2, . . ., Bi),
included in box Bi is determined so as to follow the
profile of the normal distribution. Thus, the (Ji/2)-thdatum is included in the box with the highest
probability. By allocating all the data of Ji points ofeach tissue to boxes of the corresponding normal
distribution, the mean elasticity Ēi,h of the data includedin each box is obtained.

ROI. The pixel at the center of an ROI is classified into
the class which has the maximum likelihood.
In this classification, there may be a region which
has an extremely small value for the maximum
likelihood. Such regions are classified into theunclassified region by setting threshold To to the
maximum likelihood. Thus, the category C(Rm,n), towhich an ROI Rm,n belongs, is expressed as follows:⎧ arg max Li ( m, n)
1≤ i ≤ 4⎪⎪(if max Li (m, n) ≥ To ) .
C ( Rm , n ) = ⎨1≤ i ≤ 4⎪⎪⎩ unknown(otherwise ) .

(2.2)

Fig.3. Illustration of region of interest (ROI).

Fig.2. (a) Original elasticity distribution of the tissue.
(b) Ascending sequence of elastic modulus in anelasticity distribution. (c) Normal distribution whose
number of boxes depends on the number of data pointsof (a).
As shown in Fig. 3, an ROI was assigned to anelasticity image which was obtained by ultrasonicmeasurement. The likelihood function Li(m,n) is
defined as a joint probability that all the elasticity
values in ROI Rm,n (center of ROI: n-th sampled point
along m-th beam) simultaneously belong in the i-th
category as follows:
1N
⎛
⎞
⎜
⎟
Li (m, n) = ∏ pi ( E k ,l )⎜ ( k ,l )∈R⎟⎝⎠ ,(i=1, 2, 3, 4)(2.1)
where pi(Ek,l) is the probability density which shows
the probability that elasticity value Ek,l in the k-th row
and l-th column in the ROI belongs to the i-th tissue
category, and N0 denotes the number of pixels in an
ROI Rm,n. The multiplier 1/N0 shows the geometricmean for compensation of the effect of the size of an
0m,nFigure 4 shows examples of tissue classification
images which were manually estimated by referring to
the pathological images of iliac arteries (A) and (B).
By comparing the pathology-based classification
images shown in Fig. 4 with the tissue classification
images obtained by the proposed method, therecognition rate Rr(SROI) for all tissues in the arterial
wall was defined by the ratio of the number ofcorrectly classified pixels to the number N of all pixels
in the image as follows:
∑ Ni
(2.3)
Rr ( SROI ) = i × 100 [%],
N
where Ni is the number of correctly classified pixels oftissue i and SROI is the size of an ROI. Recognition rate
Rr(SROI) was used to determine the optimum size of an
ROI.
For an ROI with a very low likelihood for all classes(i = 1, 2, 3, 4), the pixel which is located at the centerof the ROI should be defined as an unclassified pixelby thresholding. For determination of the optimum
threshold for the likelihood function, the false
recognition rate Fr(SROI) for all tissues in the arterial
wall was defined by the ratio of the number of
misclassified pixels except for the pixels classified as
unclassified pixels to the number N of all pixels as
follows:∑ Fi
Fr ( S ROI ) = i × 100 [%],
N
(2.4)
where Fi is the number of misclassified pixels of tissue
i except for the pixels classified as unclassified pixels.
Although the unclassified pixels are included in the
denominator of eqs. (2.3) and (2.4), that is, the numberof all pixels N, they are not included in the number ofcorrectly classified pixels Ni nor that of misclassified
pixels Fi. Therefore, the sum of the recognition rate

Rr(SROI) and the false recognition rate Fr(SROI) does not
become 100%.

Fig.4. Tissue classification images obtained byreferring to pathological images. (a) Iliac artery (A).
(b) Iliac artery (B).

3. In Vitro Experimental Results
3.1. Measurement of elasticity distribution ofeach tissue
Figure 5(a) shows a B-mode image of one of thefemoral arteries. The strong echoes from outside theposterior wall correspond to a needle. For the posteriorwall, the images of the maximum change in thickness
during the cardiac cycle were measured as shown in
Fig. 5(b).
Figure 6(a) shows the elasticity image of the femoral
artery obtained from the maximum change in internalpressure and that in thickness obtained by the phased
tracking method shown in Fig. 5(b). By referring to thepathological image of the same section shown in Fig.
6(b), fibrous tissue in the intima-media region was
identified. The corresponding region, namely, theregion surrounded by the green line in Fig. 6(a), wasthen assigned to the elasticity image. Figure 6(c) showsthe elasticity distribution of fibrous tissues extracted
from the region surrounded by the green line in Fig.
6(a). By applying the same procedure to the otherarteries, the elasticity distribution of each tissue in thearterial wall was obtained.
Figure 7 shows the elasticity distribution of eachtissue, that is, the frequency of the elasticity values
which belong to the range defined by the position andwidth of each vertical bar. The width of a vertical bar
was set at 50 kPa. Means 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). Although similarities were found in theelasticity distributions of lipids and blood clots and in
those of fibrous and calcified tissues, differences in theelasticity distributions of these tissues were found.

Fig.5. (a) B-mode image of a femoral artery. (b) Imageof the maximum change in thickness during the cardiac
cycle.

Fig.6. (a) Elasticity image of the arterial wall. (b)Pathological image of the corresponding section. (c)Elasticity distribution in the region between the twogreen lines in (a).

functions {Li} was set at 0.21. As shown in Fig. 9(d),the region with the maximum likelihood which ishigher than threshold To is accurately classified as thecorresponding tissue identified by referring to thepathological image.

Fig.7. Elasticity distribution of each tissue. (a) Lipids(N = 288). (b) Blood clots (N = 178). (c) Fibrous tissue(N = 19,120). (d) Calcified tissue (N = 1,101).

3.2. Results of classification
Figure 8 shows the probability density of each tissue
obtained by the axis transformation of the elasticity
distribution. As shown in these figures, the horizontal
axis of the elastic modulus is nonlinear. Using these
databases, each pixel in an elasticity image wasclassified as a certain tissue component.

Fig.8. Probability density for each tissue. (a) Lipids. (b)Blood clots. (c) Fibrous tissue. (d) Calcified tissue.
Figures 9(c) and 9(d) show the tissue classification
results obtained by the proposed method for the iliac
artery (A). The regions classified as lipids, blood clots,
fibrous tissue, and calcified tissue were stained yellow,
red, blue, and purple, respectively. Figure 9(c)graphically shows the tissue classification image
obtained with an ROI size of 1 × 1 pixel. Althougharterial tissues were roughly classified into soft tissues(lipids and blood clots) and hard tissues (fibrous tissue
and calcified tissue), the classified tissue distributions
are scattered, and the misclassified regions areoutstanding. Alternatively, Fig. 9(d) shows the result ofclassification with an ROI size of 1,500 μm (=20pixels) in the radial direction and 1,500 μm (=5 pixels)
in the longitudinal direction. Moreover, the region withlow likelihood for all tissue components is colored gray.
The threshold To for the maximum of the likelihood

Fig.9. For the iliac artery (A). (a) Pathological image ofan arterial wall subjected to elastica-Masson staining.
(b) Elasticity image. (c) Tissue classification image(ROI size: 1 × 1 pixel). (d) Tissue classification image(ROI size: 5 × 20 pixels).
For another specimen (iliac artery (B)), calcified
tissue in the fibrous tissue was identified as shown in
Fig. 10(e). As in Fig. 8, tissue classification was
improved using the elasticity distribution of each ROI(not a single pixel). In the case of Fig. 10, there was noregion with low likelihood for any of the tissue
components.
Figure 11 shows the relationship between the size
SROI of an ROI and the recognition rate Rr(SROI). The
ROI size SROI was changed with its shape being kept
square, and in Fig. 11, the horizontal axis shows thewidth W = S ROI of an ROI in the longitudinal
direction. An ROI consists of a single pixel when thewidth, W, in Fig. 11 is 0.3 mm. Only in this specificcase, is an ROI not square (75 μm × 300 μm). Figure11(b) shows the relationship between width
W = S ROI of an ROI in the longitudinal direction andthe recognition rate Rr(SROI) in arteries which arecomposed of a single type of tissue, such as fibrous
tissue. In such case, the recognition rate Rr(SROI) is
monotonically improved by increasing the size of an
ROI because an elasticity image is uniformly classified
as the corresponding tissue using a large ROI, which
results from the worsening spatial resolution in tissueclassification. Figure 11(a) shows the relationshipbetween width W of an ROI and the recognition rate
Rr(SROI) in arteries composed of different types oftissues. For this case, tissue classification using somepixels in an ROI is superior to that using a single pixel.
However, the improvement of tissue classification by
the enlargement of an ROI is limited because theclassification using a large ROI provides a uniform
tissue classification image whereas the arterial wall iscomposed of different kinds of tissues. Therefore, there
should be an optimum size of ROI. As shown in Fig.
11(a), the recognition rates became maximum in mostarteries when the size of an ROI was 1,500 μm × 1,500μm.
Figures 12 and 13 show the relationships between
the threshold To for the likelihood function and therecognition rate Rr(SROI) and between To and the false
recognition rate Fr(SROI), respectively, for arteries
composed of different types of tissues. As shown in
Figs. 12 and 13, the false recognition rate Fr(SROI)
begins to be reduced at a lower threshold incomparison with the recognition rate because the pixels
with lower likelihood are more likely to be
misclassified. However, the correctly classified pixels
are also classified as unclassified pixels when thethreshold To is too high. Therefore, threshold To should
be determined by considering both Rr(SROI) andFr(SROI). In this study, the ratio (CMR(To)) of thenumber of correctly classified pixels (the numerator ofeq. (2.3)) to the number of misclassified pixels (thenumerator of eq. (2.4)) for all arteries composed ofdifferent types of tissues was evaluated as follows:∑ N i,all ,CMR(To ) = i∑i Fi ,all
(3.1)
where Ni,all and Fi,all are the sum of correctly classified
pixels of tissue i and that of misclassified pixels oftissue i, respectively, for all arteries composed ofdifferent types of tissues. Figure 14 shows therelationship between threshold To for likelihood
function and CMR(To) averaged by all arteries
composed of different types of tissues. As shown in Fig.
14, the CMR(To) reached the maximum when thethreshold To was 0.21.

Fig.10. For the iliac artery (B). (a) Pathological imageof another arterial wall subjected to hematoxylin-eosin
staining. (b) Pathological image of the arterial wall
subjected to elastica-Masson staining. (c) Elasticity
image. (d) Tissue classification image (ROI size: 1 × 1
pixel). (e) Tissue classification image (ROI size: 5 ×
20 pixels).

4. Discussion
In Figs. 8 and 9, it can be seen that the tissueclassification was improved using the elasticity
distribution in each ROI (not a single pixel). When thesize of an ROI is smaller than the spatial resolution ΔS
of ultrasound (including the case of a single pixel), theelasticity distribution in the ROI becomes narrow as
illustrated in Fig. 15(b) by the purple curve because theelasticity values within the space of the resolution ofultrasound ΔS have some degree of similarity. Under
such a condition, even in the case that the ROI is
perfectly composed of tissue A as shown in Fig. 15(a),there is a possibility that the ROI for tissue A and thatfor tissue B will become similar, as shown in Fig. 15(b),because the elasticity distribution in the ROI is narrow
and the elasticity distributions of tissue A and tissue B
overlap. By enlarging the size of an ROI so that it islarger than the space of the resolution of ultrasound ΔS,
the number of independent elasticity values increases,
and the elasticity distribution in the ROI tends tobecome similar to that of tissue A because the ROI is
composed of tissue A. This is an advantage of the
proposed method with an ROI whose size is larger than
the resolution of ultrasound ΔS. Figure 13 shows anexample of this case. Figures 16(a), 16(b), 16(c) and17(d) show a tissue classification image, an enlarged
view of an ROI, and elasticity distributions of ROIs
with sizes of 600 μm × 600 μm and 1,500 μm × 1,500
μm, respectively. In Fig. 16(c), the elasticity
distribution of the smaller ROI (purple line) is narrowand located in the overlapping region of the elasticity
distributions of lipids and blood clots, the orange andred dashed lines showing the elasticity distributions oflipids and blood clots, respectively. Therefore, tissueclassification is very difficult. On the other hand, in Fig.
16(d), the elasticity distribution is broadened andbecomes similar to that of a blood clot, and the ROI
can be correctly classified as a blood clot.

Fig.13. Relationship between threshold To forlikelihood function and the false recognition rate
Fr(SROI) in arteries composed of several types of tissues.

Fig.14. Relationship between threshold To forlikelihood function and the ratio of the number ofcorrectly classified pixels to the number of
misclassified pixels in all arteries which are composedof several types of tissues.

Fig.11. Relationship between width W of an ROI in thelongitudinal direction and the recognition rate Rr(SROI).
(a) Arteries composed of several types of tissues. (b)Arteries composed of a single tissue. Each line shows
the recognition rate Rr(SROI) of the corresponding artery.

Fig.12. Relationship between threshold To forlikelihood function and the recognition rate Rr(SROI) in
arteries composed of several types of tissues.

Fig.15. (a) ROI Rm,n (1,500 μm × 1,500 μm) and spatial
resolution of ultrasound in only tissue A. (b) Elasticity
distribution of ROI Rm,n when ROI size is smaller than
the resolution of ultrasound. (c) Elasticity distribution
of ROI Rm,n when ROI size is 1,500 μm × 1,500 μm.
As described above, the proposed method reduces
the misclassification at the expense of the spatial
resolution in tissue classification. As illustrated in Fig.
17, in actual cases, an ROI is not composed of only one
tissue component. When the content of tissue A in an
ROI is much larger than that of tissue B, the ROI isclassified as tissue A even if the pixel, which is in thecenter of the ROI, is composed of tissue B and thesmall clusters of tissue B in the ROI are not identified.
When the contents of tissues A and B are similar, as
illustrated in Fig. 18, the elasticity distribution of the
ROI exists in the overlapping region even when the

ROI is broadened. Figure 19 shows an example of thiscase, and tissue classification is found to be difficult
even by the use of the proposed method because theelasticity distribution in the ROI is located in theoverlapping region for each ROI size.

Fig.16. (a) Tissue classification image obtained byreferring to pathological images. (b) Close-up of ROI.
(c) Elasticity distribution (ROI size: 600 μm × 600 μm).
(d) Elasticity distribution (ROI size: 1,500 μm × 1,500μm).

likelihood were investigated. Using the elasticity
distribution in an ROI, the differentiation of lipids fromblood clots and that of fibrous tissue from calcified
tissue were improved.

Fig.18. (a) ROI Rm,n (1,500 μm × 1,500 μm) and spatial
resolution of ultrasound in tissue A and tissue B (tissue
A ≈ tissue B). (b) Elasticity distribution of ROI Rm,nwhen ROI size is smaller than the resolution ofultrasound. (c) Elasticity distribution of ROI Rm,n when
ROI size is 1,500 μm × 1,500 μm.

Fig.17. (a) ROI Rm,n (1,500 μm × 1,500 μm) and spatial
resolution of ultrasound in tissue A and tissue B.
Tissue B is distributed as small clusters. (b) Elasticity
distribution of ROI Rm,n when ROI size is smaller than
the resolution of ultrasound. (c) Elasticity distribution
of ROI Rm,n when ROI size is 1,500 μm × 1,500 μm.

Fig.19. (a) Tissue classification image obtained byreferring to pathological images. (b) Close-up of ROI.
(c) Elasticity distribution (ROI size: 600 μm × 600 μm).
(d) Elasticity distribution (ROI size: 1,500 μm × 1,500μm).

In this study, each of 33,938 pixels of the elasticity
images of the 18 arteries from which the elasticity
distribution of each tissue was obtained was classified
to show the possibility of using the proposed method
for noninvasive classification of the tissue compositionin the arterial wall based on ultrasound elasticity
imaging. However, different arteries not used forconstructing the elasticity databases should beclassified in future work to thoroughly show theeffectiveness of the proposed method.

References

4. Conclusion
In this study, tissue classification based on thelikelihood function with the configured appropriate
ROI size (not a single pixel) and a lower limit of[1] Lee RT, Grodzinsky AJ, Frank EH, Kamm RD and

Schoen FJ. Structure-dependent dynamic mechanicalbehavior of fibrous caps from human atherosclerotic
plaques. Circulation 83, 1764–1770, 1991.
[2] Loree HM, Grodzinsky AJ, Park SY, Gibson LJ
and Lee RT. Static circumferential tangential modulusof human atherosclerotic tissue. J Biomech 27, 195–
204, 1994.
[3] Simons PCG, Algra A, Bots ML, Grobbee DE andvan der Graaf Y. Common carotid intima-media
thickness and arterial stiffness. Circulation 100, 951–
957, 1999.
[4] Falk E, Shah PK and Fuster V. Coronary plaquedisruption. Circulation 92, 657–671, 1995.

[5] Davies MJ. Stability and instability: Two faces of[21] Kanai H, Koiwa Y and Zhang J. Real-timecoronary atherosclerosis. Circulation 94, 2013–2020,
1996.
[6] Golledge J, Greenhalgh RM and Davies AH. The
symptomatic carotid plaque. Stroke 31, 774–781, 2000.
[7] McConnell MV, Aikawa M, Maier SE, Ganz P,
Libby P and Lee RT. MRI of rabbit atherosclerosis in
response to dietary cholesterol lowering. Arterioscler
Thromb and Vasc Biol 19, 1956–1959, 1999.
[8] Potkin BN, Bartorelli AL, Gessert JM, Neville RF,
Almagor Y, Roberts WC and Leon MB. Coronary
artery imaging with intravascular high-frequency
ultrasound. Circulation 81, 1575-1585, 1990.
[9] Hoeks APG, Ruissen CJ, Hick P and Reneman RS.
Transcutaneous detection of relative changes in arterydiameter. Ultrasound Med Biol 11, 51–59, 1985.
[10] Hoeks APG, Di X, Brands PJ and Reneman RS.
Comparison of the performance of the RF crosscorrelation and Doppler autocorrelation technique toestimate the mean velocity of simulated ultrasoundsignals. Ultrasound Med Biol 19, 727–740, 1993.
[11] Länne T, Stale H, Bengtsson H, Gustafsson D,
Bergqvist D, Sonesson B, Lecerof H and Dahl P.
Noninvasive measurement of diameter changes in the
distal abdominal aorta in man. Ultrasound Med Biol 18,
451–457, 1992.
[12] Brands PJ, Hoeks APG, Rutten MC and Reneman
RS. A noninvasive method to estimate arterial
impedance by means of assessment of local diameterchange and the local centerline blood flow velocity
using ultrasound. Ultrasound Med Biol 22, 895–905,
1996.
[13] Meinders JM, Brands PJ, Willigers JM, Kornet L
and Hoeks APG. Assessment of the spatialhomogeneity of artery dimension parameters with highframe rate 2-D B-mode. Ultrasound Med Biol 27, 785–
794, 2001.
[14] Bergel DH. The static elastic properties of thearterial wall. J Physiol 156, 445–457, 1961.
[15] Peterson LH, Jensen RE and Parnel J. Mechanicalproperties of arteries in vivo. Circ Res 8, 622–639,
1960.
[16] Hayashi K, Handa H, Nagasawa S, Okamura A
and Moritake K. Stiffness and elastic behavior ofhuman intracranial and extracranial arteries. J Biomech
13, 175–184, 1980.
[17] Kanai H, Sato M, Koiwa Y and Chubachi N.
Transcutaneous measurement and spectrum analysis ofheart wall vibrations. IEEE Trans Ultrason FerroelectFreq Contr 43, 791–810, 1996.
[18] Kanai H, Hasegawa H, Chubachi N, Koiwa Y and
Tanaka M. Noninvasive evaluation of local myocardial
thickening and its color-coded imaging. IEEE TransUltrason Ferroelect Freq Contr 44, 752–768, 1997.
[19] Hasegawa H, Kanai H, Koiwa Y and Chubachi N.
Noninvasive evaluation of Poisson’s ratio of arterial
wall using ultrasound. Electron Lett 33, 340–342, 1997.
[20] Hasegawa H, Kanai H and Koiwa Y. Modified
phased tracking method for measurement of change inthickness of arterial wall. Jpn J Appl Phys 41, 3563–
3571, 2002.

measurements of local myocardium motion and arterial
wall thickening. IEEE Trans Ultrason Ferroelec Freq
Contr 46, 1229–1241, 1999.
[22] Kanai H, Hasegawa H, Ichiki M, Tezuka F and
Koiwa Y. Elasticity imaging of atheroma withtranscutaneous ultrasound -preliminary study-.
Circulation 107, 3018–3021, 2003.
[23] Hasegawa H and Kanai H. Modification of thephased tracking method for reduction of artifacts inestimated artery wall deformation. IEEE TransUltrason Ferroelect Freq Contr 53, 2050-2064, 2006.
[24] Jespersen SK, Wilhjelm JE and Sillesen H. Multiangle compound imaging. Ultrason Imag 20, 81–102,
1998.
[25] Hasegawa H, Kanai H, Hoshimiya N and Koiwa Y.
Evaluating the regional elastic modulus of a cylindricalshell with nonuniform wall thickness. J Med Ultrason
31, 81–90, 2004.
[26] Inagaki J, Hasegawa H, Kanai H, Ichiki M and
Tezuka F. Construction of reference data for tissue
characterization of arterial wall based on elasticity
images. Jpn J Appl Phys 44, 4593–4597, 2005.
[27] Inagaki J, Hasegawa H, Kanai H, Ichiki M and
Tezuka F. Tissue classification of arterial wall based onelasticity image. Jpn J Appl Phys 45, 4732–4735, 2006.
[28] Tsuzuki K, Hasegawa H, Kanai H, Ichiki M and
Tezuka F.Optimal region of interest settings for tissue
characterization based on ultrasonic elasticity imaging.
Ultrasound Med Biol (in press).

Appendix: Strain Estimation by the Phased
Tracking Method with Correlation Estimator
Compounding [17][23]
By referring to a cross-sectional image of an artery,
initial positions x1(1) and x’1(1) of two points aremanually assigned in the first frame as shown in Fig.
20 (x’1(1)-x1(1)=ML·Δx; Δx: spacing of sampled points
in the depth direction). Instantaneous positions x1(n)and x’1(n) of these assigned points in the n-th frame arethen tracked by the phased tracking method [17].
The change in thickness between two reflectors at
depths x1(n) and x1(n) is then obtained as follows: Thephases θ1(n) and θ’1(n) of echoes from these two
reflectors depend on x1(n) and x’1(n). Therefore, thephase difference θh(n)=θ’1(n)-θ1(n) depends on the
distance h(n)=x’1(n)-x1(n) (thickness of the layer)
between two reflectors as follows [20][23]:h(n) = x1' (n) − x1 (n)(A-1)
c= 0 {θ1' (n) − θ1 (n)}4π f 0c= 0 ⋅ θ h (n),4π f 0where c0 and f0 are the speed of sound and center
frequency of ultrasound, respectively. Thus, the rate
vh(n) of the change in thickness of the layer between
two reflectors is expressed as follows:h(n + 1) − h( n)Tc0{θ h (n + 1) − θ h (n)}=4π f 0Tv h ( n) =

(A-2)

c0
⋅ Δθ h ( n),4π f 0T
where Δθh(n) is the change in θh(n) during a frameinterval T. Phase difference θh(n) can be expressed byphase ∠β (n; x1 (n), x1' (n)) of product β (n; x1 (n), x1' (n))
of complex demodulated signals z*(n; x1(n)) and z(n;x’1(n)) as follows:(A-3)
θ h (n) = θ 1' (n) − θ 1 (n) = ∠β (n; x1 (n), x1' (n)),=(A-4)β (n; x1 (n), x1' (n)) = z (n; x1' (n)) ⋅ z * (n; x1 (n)).
In this study, correlation estimator γh(n; x) at depth x,
whose phase ∠γ h (n; x) corresponds to θh(n+1)θh(n)=Δθh(n), is obtained by simply calculating thecorrelation around the duration of the employedultrasonic pulse as follows:γˆ h (n; x1 (1) + i ⋅ Δx)=

K /2∑ β (n + 1; x (n) + k ⋅ Δx, x (n) + k ⋅ Δx)

k =− K / 2'
1

1

× β * (n; x1 (n) + k ⋅ Δx, x1' (n) + k ⋅ Δx),(A-5)(i = 0, 1, 2, ...,ML)
where the estimate in the right-hand side of eq. (A-5) isused for correlation estimators γh(n; x) at all points
between x1(1) and x’1(1).
To obtain the spatial distribution along eachultrasonic beam, the correlation estimator, γh,m(n; x),
for the combination of two points, xm(1) and x’m(1), ateach depth is obtained by sliding the combination of
two points along the ultrasonic beam while keeping the
distance between the two points in the first frame
constant (=ML·Δx) as follows:γˆh , m (n; xm (1) + (i − 1) ⋅ Δx)=

K /2∑ β (n + 1; x (n) + k ⋅ Δx, x (n) + k ⋅ Δx)

k =−K / 2

'
m

m

c0
(A-9)
⋅ ∠γ h (n; x m (1)).
4π f 0T
The compounded change in thickness, Δh (n; x) , isobtained as follows:Δh ( n + 1; x m (1)) = Δh ( n; x m (1)) + v h ( n; x m (1)) ⋅ T (A-10)v h (n; x m (1)) =The elastic modulus, Eθh,m , at xm(1) is obtained by
the estimated change in thickness as follows [25]:(A-11)
M + M L − m + 1 ⎞ Δp1⎛r⎟⎟,
Eθh,m = ⎜⎜ m + TΔh
2 ⎝ h0MT + M Lm max⎠
M L ⋅ Δxwhere rm and h0 are, respectively, the radius at xm(1)and the thickness of the entire wall in the first frame,and Δp and Δhm
are, respectively, the pulsemaxpressure and the maximum of the absolute value of thechange in thickness at xm(1).
The inner radius of the m-th layer rm and entire wall
thickness h0 can be expressed as follows:(A-12)
rm = r0 + (m − 1)Δx,(A-13)
h0 = M L ⋅ Δx,
where r0 is the inner radius of the innermost layer. By
substituting eqs. (A-12) and (A-13) into eq. (A-11), eq.
(A-11) is modified as follows:
⎞ Δp
⎞ Δp
(A-14)
1⎛ r
1⎛ r= ⎜⎜ 0 + 1⎟⎟,
Eθh,m = ⎜⎜ 0 + 1⎟⎟ΔhΔε2 ⎝ h0
2
h
m max
⎠
⎝ 0
⎠ m
M L ⋅ Δxwhere Δεm is the strain of the m-th layer. As shown byeq. (A-14), elastic modulus Eθh,m is defined as theaverage stress (r0/h0+1)·Δp/2 of the entire wall
thickness divided by the radial strain Δεm.

(A-6)× β * (n; xm (n) + k ⋅ Δx, xm' (n) + k ⋅ Δx),(A-7)
xm (1) = x1 (1) + (m − 1) ⋅ Δx.
(m = 1, 2, ...,MT+1; i = 1, 2, ...,ML+1)
As shown in Fig. 20, some of the MT assigned layers
overlap each other. Therefore, there are multiple
estimates of γh(n; x) at depth x. The compounded
correlation estimator, γ h (n; x) , at depth x is thenobtained by simply averaging the overlapping
correlation estimators as follows:
m + M ( x (1))
1
γ h (n; x m (1)) =∑ γˆh,k (n; xm (1)), (A-8)
M o ( x x (1)) k =mwhere Mo(x) is the number of overlapping layers at
depth x. By compounding the correlation estimator
shown by eq. (A-6), the contributions of echoes withlow amplitudes (=low signal-to-noise ratio) to theestimation of the phase shift are suppressed.
The compounded rate, v h (n; x) , of the change inomthickness at depth x is obtained based on eq. (A-2) as
follows:

Fig.20. Illustration of the method for estimation of thechange in thickness of the arterial wall (MT: total
number of assigned combinations, ML: the number ofsampled points between two points of an assigned
combination, T: frame interval, Δx: depths of scatterers
in n-th frame, xm(n) and x’m(n): m-th combination of
two points in n-th frame, h(n): distance between two
scatterers in n-th frame).