Investigation on Elasticity-Based Tissue
Characterization of Arterial Wall
Hideyuki Hasegawa1,2 and Hiroshi Kanai2,1
1 Graduate School of Biomedical Engineering,
2 Graduate School of Engineering
E-mail: hasegawa@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). In
this classification, a region with an extremely low
likelihood with respect to all tissue components was
defined as an unclassified region by setting thresholdTo for the likelihood function. The optimal threshold
was determined from the standard deviation in themeasurements of radial strains evaluated by basic
experiments using a phantom. The tissue classificationof 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 [22][25][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][29].

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 [25]. The strain distribution is obtained byapplying the phased tracking method to the measured
demodulated signals [21][23].

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.

⎛⎞
Li (m, n) = ⎜ ∏ pi ( E k ,l ) ⎟⎜ ( k ,l )∈R
⎟
m,n
⎝
⎠

1 N0

,
(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
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:

Figure 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 ( S RO I ) = 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.

3. In Vitro Experiments for Construction of“Elasticity Library”
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 a cycle of the flow pump were measured asshown 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.

these databases, each pixel in an elasticity image wasclassified as a certain tissue component.
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 ( = 20
pixels) in the radial direction and 1,500 μm ( = 5pixels) in the longitudinal direction. Moreover, theregion with low likelihood for all tissue components iscolored gray. The threshold To for the maximum of thelikelihood functions {Li} was set at 0.21. As shown in
Fig. 9(d), the region with the maximum likelihood
which is higher than threshold To is accurately
classified as the corresponding tissue identified byreferring to the pathological image.

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

4. Determination of the Optimal Size of a
Region of Interest
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 showing the elastic modulus is nonlinear. Using

Fig. 5. (a) B-mode image of a femoral artery. (b) Imageof the maximum change in thickness during the cardiac
cycle.
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. In Fig. 11, the horizontal axis shows the width
W = S ROI of an ROI in the longitudinal direction.
An ROI consists of a single pixel when the width, W,
in Fig. 11 is 0.3 mm. Only in this specific case, 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 and the recognition rate
Rr (SROI) in arteries which are composed of a single
type of tissue, such as fibrous tissue. In such case, therecognition rate Rr (SROI) is monotonically improved byincreasing the size of an ROI because an elasticity
image is uniformly classified as the corresponding
tissue using a large ROI, which results from theworsening spatial resolution in tissue classification.
Figure 11(a) shows the relationship between width Wof an ROI and the recognition rate Rr (SROI) in arteries
composed of different types of tissues. For this case,tissue classification using some pixels in an ROI is
superior to that using a single pixel. However, theimprovement of tissue classification by theenlargement 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 an 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.

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).

Fig. 8. Probability density for each tissue. (a) Lipids.
(b) Blood clots. (c) Fibrous tissue. (d) Calcified tissue.

5. Determination of the Optimal Threshold
5.1 Basic experiments using a phantom forevaluation of variance in measurement ofradial strain

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).

A homogeneous cylindrical phantom (internal
radius: ri = 4 mm, external radius: ro = 5 mm, elastic
modulus: E = 750 kPa) made from silicone rubber
containing 5% carbon powder by weight was measured
with a 7.5 MHz linear ultrasonic probe. The scan plane
was parallel to the longitudinal direction of thephantom, and the directions of all ultrasonic beams
coincided with the radial direction of the phantom. Thechange in internal pressure, which was applied using aflow pump, was measured by a pressure sensor. The
sampling frequency of the quadrature demodulated
signal and the frame rate were 10 MHz and 200 Hz,
respectively. The theoretical value of radial strainΔεr (r) at each radial position r is obtained by [30]Δε r (r ) = −3 ri 2 ro2 Δp 1,
2 ro2 − ri 2 E r 2(5.1)

where Δp is the pressure increment. The radial strain
measured by the phased tracking method wascompared with the theoretical value Δεr (r).

over every pressure increment. The regression line wasdetermined as follows:

Fig. 9. For the iliac artery (A). (a) Pathological imageof an 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).

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).

Figures 12(a)-12(d) show the strain distribution
along the radial direction of the phantom obtained by
the phased tracking method for cases of pressure
increments Δp = 40, 50, 60, and 70 mmHg,
respectively. Plots and vertical bars show means andstandard deviations for 60 ultrasonic beams. The
difference between the mean and the theoretical value
is lower than the standard deviation, and mean value
follows the theoretical profile.
Figure 13 shows the relationship between the mean
μs and the standard deviation σs normalized by themean value. The plots and the straight line show all themeasured results in Fig. 12 and the regression line,
respectively. A positive correlation was found between
the mean μs and the normalized standard deviation σs
because the standard deviation was almost constantσ s = 7.1 ⋅ μ s + 0.40.

(5.2)

The threshold To,i (Rm,n) for likelihood function Li (m,n) of tissue i of each ROI Rm,n is determined using theexperimental results with the phantom. Using eq. (5.2),
the normalized standard deviation σs(Rm,n) in themeasurement of the radial strain in Rm,n was given
approximately by:σ s ( Rm, n ) = 7.1 ⋅ μ ( Rm, n ) + 0.40,
μ ( Rm , n ) =1∑ ε max (k , l ),N 0 ( k ,l )∈Rm , n

(5.3)
(5.4)

where εmax(k, l) and μ are the maximum radial strain
during one cardiac cycle in the k-th row and l-th column

and the average of the maximum radial strain in Rm,n,respectively.

Thus, the mean Eˆ R

of the measured elasticity values
m,n{Eˆ k ,l } is gisven by(5.7)

Eˆ Rm , n = ERm , n + bRm , n ,where E R
Rm;n

m,n

and bRm,n are the true mean elasticity in

and

the

bias

error

bRm , n = E( k ,l )∈Rm , n [ΔEk ,l ],respectively. By substituting eq. (5.7), eq. (5.5) is
modified as follows:σ 02 ( Rm, n ) =E( k , l )∈Rm , n

+2

[(

)]

2
⎡⎛
[Ek ,l ]⎞⎟ ⎤⎥ + ( k ,l )E∈Rm , n ek ,l − eRm, n 2⎢⎜ Ek ,l − ( k ,l )E
R
∈
m
,
n
⎠ ⎦
⎣⎝

E

( k , l )∈Rm , n[E ⋅ e ] + 2b
k ,l

k ,l

Rm , nE( k , l )∈Rm , n

[e ],
k ,l

(5.8)
where e Rm,n

is assumed to be zero because {ek,l} israndom error. Variance (σe(Rm,n))2 of the measurement
error{ek,l}
inRm,nisexpressedbywhere σs(Rm,n) is(σ e ( Rm ,n )) 2 = (σ s ( Rm ,n ) ⋅ Eˆ R ) 2 ,m ,ndetermined by eq. (5.3). By defining the variance due tothe elastic inhomogeneity of tissue in Rm,n by σ ( Rm,n ) 2
eq. (5.8) is expressed as follows:2

Fig. 11. Relationship between width W of an ROI in
the longitudinal direction and the recognition rate
Rr (SROI). (a) Arteries composed of several types oftissues. (b) Arteries composed of a single tissue. Eachline shows the recognition rate Rr (SROI) of thecorresponding artery.

σ 02 ( Rm, n ) = (σ ( Rm, n )) 2 + ⎛⎜ σ s ( Rm, n ) ⋅ Eˆ k ,l ⎞⎟ + 2⎝⎠

E( k , l )∈R m , n[E ⋅ e ],
k ,l

k ,l

(5.9)
where there is no correlation between the inhomogeneityof Ek,l and {ek,l} in Rm,n. Therefore, variance (σ(Rm,n))2
without error of eq. (5.9) is given by {σ s ( Rm ,n ) Eˆ R }2m ,nFigure 14 shows an illustration for determining thethreshold To,i (Rm,n) for the likelihood function Li (m, n)of tissue i. Let us consider the elasticity distribution in an
ROI. Variance σ 02 ( Rm,n ) of the measured elasticity Eˆ k ,lin the k-th row and l-th column in Rm,n is expressed asfollows:

subtracted from the variance σ 02 of the measured
elasticity values {Eˆ k ,l } in Rm,n as follows:{σ 2 ( Rm, n ) = σ 02 ( Rm, n ) − σ s ( Rm, n ) ⋅ Eˆ R

}.
2

m, n

(5.10)(5.5)

Based on this relation, by setting the acceptanceregion [from –aσi (Rm,n) to aσi (Rm,n)] of the probability
density N ( μ i , σ i2 ( Rm,n )) for each tissue i, the thresholdwhere E( k ,l )∈R [⋅] shows the averaging for the data

To,i (Rm,n) for the likelihood function Li (m, n) of tissue iin Rm,n was determined by the probability of the
distribution N ( μ i , σ 02,i ( Rm,n )) with the error at the distanceσ ( Rm, n ) =20E( k , l )∈R m , n[Eˆ ]− ⎛⎜⎝ Eˆ
2
k ,l

2

Rm , n

⎞⎟ ,
⎠

m, n

included in the ROI Rm,n, and Eˆ R

is the average of them,nmeasured elasticity values {Eˆ k ,l } in Rm,n. By assumingthat the true elasticity values {Ek,l} are not constant in
Rm,n due to the elasticity inhomogeneity of tissue evenwhen there is no measurement error, the measured
elasticity {Eˆ k ,l } is described by the sum of true elasticity{Ek,l} and the error {ΔEk,l} (sum of random error {ek,l}and bias error bRm,n) as follows:Eˆ k , l = Ek ,l + ΔEk , l ,(k , l ) ∈ Rm , n .

(5.6)

from mean μi as shown in Fig. 15. Therefore, thethreshold To,i (Rm,n) for the likelihood function Li (m, n)of tissue i is given by{

To ,i ( Rm , n ) =

}

2
⎡⎛
2 ⎞ ⎤
⎢ ⎜ a σ 02 ( Rm , n ) − σ s ( Rm , n ) Eˆ Rm , n ⎟ ⎥
⎟ ⎥
⎢⎜
1
⎠ ,
exp ⎢ ⎝⎥2σ
22π σ 0,i
0
,
i
⎥
⎢
⎥
⎢
⎦
⎣

(5.11)

where σ0,i is the variance of measured elasticity
distribution for tissue i.
Figures 16(c)-16(g) show the tissue classification
images for an excised human iliac artery (A). The
regions classified as lipids, blood clots, fibrous tissue,and calcified tissue are color-coded yellow, red, blue,
and purple, respectively. Figure 16(c) shows theclassification image obtained with an ROI size of 5 × 20
pixels (1,500 × 1,500 μm2) without thresholding.
Although the pixels were roughly classified into thecorrect tissues, the pixels which have low likelihood
Li (m, n) were also classified. Figures 16(d)-16(g) show
the classification images obtained with thresholds
To,i (Rm,n) determined at four different area ratios of w =99, 95, 90, and 85%, respectively. In Figs. 16(d)-16(g), a
region whose likelihood is less than the thresholdTo,i (Rm,n) for all tissue components is colored gray. As
shown in Figs. 16(d)-16(g), similarities among theclassification images seem to be qualitatively highespecially for those at an area ratio w less than or equal
to 95%. It can be expected from the result shown in Fig.
17 that improvement in the recognition rate Rr (w) bydecreasing area ratio w slightly diminish at area ratio w
less than 95%. For these results, the misclassification
was reduced using the threshold To,i (Rm,n) determinedfrom the area ratio of the acceptance region less than orequal to 95%.

Fig. 13. Relationship between mean μs and standard
deviation σs normalized by mean μs of the measured
strains of the phantom.

図 14. Illustration of a method for determining thresholdTo,i (Rm,n) to likelihood function Li (m, n).

Fig. 12. Estimated strains of the phantom, plotted as afunction of the distance from the lumen. (a) Δp = 40mmHg. (b) Δp = 50 mmHg. (c) Δp = 60 mmHg. (d) Δp =70 mmHg.

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 oflikelihood 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.

図 15. Example of determination of threshold To,i (Rm,n)to likelihood function Li (m, n).

Fig. 16. Results of tissue classification for iliac artery (A). (a) Pathological image. (b) Elasticity image. Tissueclassification images obtained with (c) no thresholding, (d) To,i (Rm,n) at w=99%, (e) To,i (Rm,n) at w=95%, (f)To,i (Rm,n) at w=90%, and (g) To,i (Rm,n) at w=85%.
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Fig. 17. Recognition rate Rr (w) plotted as a function of
acceptance region w.