Japanese Journal of Applied Physics
Vol. 45, No. 5B, 2006, pp. 4732–4735#2006 The Japan Society of Applied Physics

Tissue Classiﬁcation of Arterial Wall Based on Elasticity Image
Jun I NAGAKI, Hideyuki H ASEGAWA, Hiroshi K ANAI, Masataka I CHIKI1 and Fumiaki TEZUKA2
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan1
Sendai Hospital of East Railway Company, Sendai 983-8508, Japan
2
Sendai Medical Center, Sendai 980-8520, Japan(Received November 30, 2005; accepted March 8, 2006; published online May 25, 2006)

The phased tracking method was developed for measuring the minute change in thickness during one cardiac cycle and theelasticity of the arterial wall. By comparing elasticity images measured by the phased tracking method with the corresponding
pathological images, the elasticity distribution for each tissue in the arterial wall was determined. We have already measured
the elasticity distributions for lipids, ﬁbrous tissues (mixture of smooth-muscle and collagen ﬁber), blood clots and calciﬁed
tissues. From these previous studies, 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 their elasticity. However, it was diﬃcult to diﬀerentiate
lipids from blood clots and also ﬁbrous tissue from calciﬁed tissue. In this study, we investigated how to improve the tissueclassiﬁcation of the arterial wall using statistical properties of the elasticity distribution of each tissue.
[DOI: 10.1143/JJAP.45.4732]
KEYWORDS: tissue classification, elasticity image, elasticity distribution, likelihood function, atherosclerosis

1.

Introduction

The rupture of atherosclerotic plaques is probably themost important factor underlying the sudden outbreak ofacute coronary syndrome.1) Circulatory diseases such like
cerebral infarction and myocardial infarction are terminal
symptoms of atherosclerosis. Therefore, the direct characterization of the composition and vulnerability of atherosclerotic plaque may oﬀer insight into the mechanism of plaqueregression and progression.2,3) The elasticity of the arterial
wall is largely aﬀected by changes in the composition of thewall due to the development of atherosclerosis.4) Therefore,
the measurement of elasticity has potential for the tissue
characterization of the arterial wall. For the assessment ofelasticity, we have developed a method using transcutaneous
ultrasound for measuring minute changes in the thickness of
the arterial wall during a heart cycle5–13) and the elasticity
distribution of each tissue in the arterial wall.14) However,
the elasticity distribution of lipids is close to that of bloodclots. Moreover, the elasticity distributions of ﬁbrous tissue
and calciﬁed tissue largely overlapped each other. Suchsimilarities are bottlenecks in the classiﬁcation of tissues
based on elasticity distribution.
In this study, a method of classifying tissue in the arterial
wall based on statistical properties of the elasticity distribution is proposed. The proposed method improves tissueclassiﬁcation in comparison with that using only the meanelasticity.
2.

Methods

2.1 Tissue classiﬁcation based on Mahalanobis distanceFor comparison with the proposed method, each pixel inan elasticity image was classiﬁed into a tissue using thesquared Mahalanobis distance di2 to the elasticity distributionof each tissue i (i ¼ 1: lipid, 2: blood clot, 3: ﬁbrous tissue,
4: calciﬁed tissue). In an elasticity image, there are M
ultrasonic beams and Nm pixels along m-th beam ðm ¼
1;
P.M. . ; MÞ. Therefore, in an elasticity image, there are
m¼1 Nm pixels (intervals: 75 mm in the depth directionE-mail address: kanai@ecei.tohoku.ac.jp

and 300 mm in the arterial axial direction) with respective
elastic moduli, Em;n ðm ¼ 1; . . . ; M; n ¼ 1; . . . ; Nm Þ.12) The
squared Mahalanobis distance between each pixel in anelasticity image and the elasticity distribution of each tissue
is obtained as follows:Em;n  i 2
di2 ¼
;
i
ði ¼ 1; 2; 3; 4; m ¼ 1; . . . ; M; n ¼ 1; . . . ; Nm Þ ð2:1Þ
where i and i are the mean and standard deviation of theelasticity distribution of class i. The means and standard
deviations (SD) of the elasticity distributions of respective
tissues were determined to be 81  40 kPa for lipids,
95  56 kPa for blood clots, 1:0  0:63 MPa for ﬁbrous
tissue and 2:0  1:2 MPa for calciﬁed tissue (mean  SD).
Each pixel in the elasticity image is classiﬁed into class i
which has the shortest Mahalanobis distance.
2.2 Tissue classiﬁcation based on likelihood function
In this study, an elasticity image is classiﬁed using the
likelihood function Li (i ¼ 1: lipid, 2: blood clot, 3: ﬁbrous
tissue, 4: calciﬁed tissue) of the elasticity distributions. To
obtain the likelihood function of the elasticity distribution ofeach tissue, the elasticity distribution is translated using thenormal distribution to obtain the probability distribution.
From in vitro experiments, the elasticity distribution ofeach tissue, i, is obtained as illustrated in Fig. 1(a).14) The
elasticity distribution of each tissue consists of Ji data points
with respective elastic moduli (i ¼ 1: lipid, 2: blood clot, 3:
ﬁbrous tissue, 4: calciﬁed tissue). Using all data of Ji points(J1 : 425, J2 : 301, J3 : 5979, J4 : 579) with respective elastic
moduli, the ascending sequence is made for each tissue, i,
as shown in Fig. 1(b). In this sequence, the j-th datum( j ¼ 1; . . . ; Ji ) has the corresponding elastic modulus E j(E j  E jþ1 ) where j is named the elasticity number. It isclear in Fig. 1(a) that the mean elastic modulus of the
distribution is largely diﬀerent from the elastic modulus ofthe (Ji =2)-th datum at the center of the ascending sequence.
One of reasons for this is considered as follows: To obtain
the elastic modulus, the change in the thickness (radialstrain) of the arterial wall due to a heartbeat is measured

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J. INAGAKI et al.

10

0.1

0.2
0.3
elasticity [MPa]elasticity

low
1 2 3456

40

0.4

high

. . .
. . .
elasticity number

(b)

Ji
0.4
(c)

60

0.3

40

0.2

20

0.1
1

2

3

4 5
6 7
box number: h

8

9

0

0.4

(b–1)

30

blood clot
_ 56kPa
95 +(N=301)

20
10

0
0.5
1
elastic modulus [MPa]42probability

0

21 28 44 83 133192 245
elastic modulus [kPa]
(c–1)

1
0

0.4

1
2
3
4
elastic modulus [MPa]

(c–2)

0.3
0.2
0.1

frequency [%]00.09 0.30 0.71 1.6
3.0
0.19 0.45 1.1
2.2
elastic modulus [MPa]
4

(d–1)

calcified tissue_ 1.2 MPa
2.0 +(N=579)

3
2
1
0

0.4
probablity

using ultrasound. The measured change in thickness isexpressed by the sum of the actual change in thickness hand noise e of the measurement system, and the elastic
modulus is proportional to the reciprocal 1=ðh þ eÞ of themeasured change in thickness.13) Therefore, the variance ofthe estimated elastic moduli increases with decreasing actualchange in thickness (increasing elastic modulus) in comparison with the case of increasing change in thickness(decreasing elastic modulus). As a result, the elasticity
distribution is broadened at a high elastic modulus. Thus, as
shown in Fig. 1(c), the normal distribution is assumed withrespect to the elasticity number j so that the probability
around the center of the ascending sequence made becomesmaximum.
The probability distribution of each tissue was obtainedby allocating all the data of Ji points of each tissue i to boxesof the normal distribution. The number of boxes, fBi g, of thenormal distributions is determined so that the number of datain the box for a box number, which is located at threefold thestandard deviation of the box number from the mean
(mean  3  SD), becomes one. As shown in Fig. 1(c), thenumber of data, Di;h ðh ¼ 1; . . . ; Bi Þ, included in each box isdetermined by following the line of the normal distribution.
Then, the (Ji =2)-th datum is included in the box with thehighest probability.
By allocating all the data of Ji points of each tissue toboxes of the corresponding normal distribution, the meanelasticity Ei;h of the data included in each box is obtained.
Figures 2(a-1), 2(b-1), 2(c-1), and 2(d-1) show the elasticity
distributions for lipids, blood clots, ﬁbrous tissue, and

0.2

fibrous tissue_ 0.63 MPa
1.0 +(N=5979)

30Fig. 1. Illustration of allocation of elasticities of elasticity distribution toboxes of normal distribution. (a) Original elasticity distribution of thetissue. (b) Ascending sequence of elastic modulus of elasticity distribution. (c) Normal distribution whose number of boxes correspond to thatof (a).

(b–2)

0.3

0.1

0

frequency [%]800frequency [%]

0

0.4
60
(a–2)
(a–1)
50
0.3
lipid
40
_ 40 kPa81+
0.230(N=425)
20
0.1
10
0
0 0
12 22 50 83 131183
0.5
1elastic modulus [MPa] elastic modulus [kPa]probability

20

0

number of data: Di,hfrequency [%]30

probability: p( Ei,h)frequency [%](a)probability

40

0

1

2
3
4
5
elastic modulus [MPa]

6

(d–2)

0.3
0.2
0.1
0

0.53 0.73 1.2 2.1 4.0
elastic modulus [MPa]4.8

Fig. 2. Elasticity distribution and probability distribution of each tissue.
(a) Lipid, (b) blood clot, (c) ﬁbrous tissue, and (d) calciﬁed tissue.

calciﬁed tissue, respectively, and Figs. 2(a-2), 2(b-2), 2(c-2),
and 2(d-2) show the respective probability distributions,pi ðEi;h Þ, whose horizontal axis was labeled by the meanelasticity Ei;h of the corresponding box Bi;h .
When the elastic modulus Em;n measured at the depth n4733

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J. INAGAKI et al.

along the m-th ultrasonic beam is closest to the meanelasticity Ei;h of the box Bi;h , the probability p0 i ðEm;n Þ withrespect to the elastic modulus Em;n was determined to bepi ðEi;h Þ.
For each pixel with the corresponding elastic modulus
Em;n , the region of interest (ROI) Rm;n of 450 mm in thedepth direction and 450 mm in the arterial axis direction is
assigned. Thus, there are up to 36 elastic moduli in the ROI.
Using the probability distribution p0 i ðEm;n Þ, the log likelihood function ln Li for the i-th class is obtained withrespect to elasticities in Rm;n as
X
ln Li ¼
ln p0 i ðEk;l Þ: ði ¼ 1; 2; 3; 4Þð2:2Þ

(a) classification image
L
3 mm

BC
F
C

(b−1) lipid
3 mmðk;lÞ2Rm;nHowever, the size of an ROI varies at the edge of anelasticity image. Therefore, we employ the log likelihood
function normalized by the number of elasticities in an ROI.
Thus, all pixels in an elasticity image are classiﬁed into theclass that has the highest likelihood.
3.

(b−2) blood clot
3 mm

Results

3.1 Tissue classiﬁcation based on Mahalanobis distance
Figures 3(a) and 3(b) show the elasticity image of thearterial wall and the corresponding pathological image,respectively. The regions of lipids, blood clots and ﬁbrous
tissue were identiﬁed by referring to the pathological image.
The regions of lipids, blood clots and ﬁbrous tissue weresuperimposed in Fig. 3(b) by yellow, red and blue dashed(b−3) fibrous tissue
3 mm(a) elasticity image

4 MPa
elastic modulus

likelihood

2
1.5
1
0.5
0

3 mm

Max

(b−4) calcified tissue
3 mm

Min

(b) pathological image
3 mm

L

3 mm
Fig. 4. (a) Tissue classiﬁcation image using likelihood function of eachtissue (L: lipid, BC: blood clot, F: ﬁbrous tissue, and C: calciﬁed tissue).
(b) Likelihood image of each tissue.

BCF(c) classification image

pathological classification

L
3 mm

BC
F

3 mm

L
BC

C

F
3 mm

BG

Fig. 3. (a) Elasticity image of arterial wall. (b) Pathological image ofarterial wall subjected to elastica-Masson staining. (c) Tissue classiﬁcation image using Mahalanobis distance (L: lipid, BC: blood clot, F:
ﬁbrous tissue, and C: calciﬁed tissue).

Fig. 5. Tissue classiﬁcation image based on pathological image (L: lipid,
BC: blood clot, F: ﬁbrous tissue, and BG: background).

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J. INAGAKI et al.

lines. Figure 3(c) shows the result of the classiﬁcation basedon the Mahalanobis distance between each pixel in anelasticity image and the elasticity distribution of each tissue.
The regions classiﬁed as lipids, blood clots, ﬁbrous tissue
and calciﬁed tissue were stained yellow, red, blue andpurple, respectively. By comparing the pathological image
and tissue classiﬁcation image, misclassiﬁed pixels weredistinct, particularly in regions of lipids and blood clots.
3.2 Tissue classiﬁcation using likelihood function
Figure 4(a) shows the result of the classiﬁcation based on
the likelihood function of each tissue. Figures 4(b-1), 4(b-2),
4(b-3), and 4(b-4) show the likelihood functions Li for lipids,
blood clots, ﬁbrous tissue and calciﬁed tissue, respectively.
The region of each tissue was indicated by dashed lines in
Figs. 4(b) and 3(b). In comparison with the result of theclassiﬁcation based on the mean elastic modulus of eachtissue shown in Fig. 3(c), misclassiﬁed regions were reduced
using the likelihood function as shown in Fig. 4(a).
Figure 5 shows the tissue classiﬁcation image obtained byanalyzing the pathological image. The pathological image
was analyzed as follows: The entire pathological image,which corresponds to the entire elasticity image, is divided
into the M sections in the arterial axial direction, and eachm-th section of the M sections is divided into Nm regions in
the arterial radial direction. Then, each region is classiﬁed
into lipids, blood clots, ﬁbrous tissue, and calciﬁed tissue
based on RGB values in each region in the pathologicalimage.14) The regions classiﬁed as lipids, blood clots, ﬁbrous
tissue, and background were stained yellow, red, blue, andgray, respectively.
Each value in Table I is the total number of pixels
classiﬁed into each tissue based on the Mahalanobis distanceof each pixel with an elastic modulus and the proposed
method. Each percentage shows the ratio of the number ofcorrectly classiﬁed pixels to the corresponding total numberof pixels. The correctness of the classiﬁcation of each pixel
was evaluated by comparing tissue classiﬁcation images
shown in Figs. 3(c) and 4(a) with that in Fig. 5 based on thepathological image. As shown in Table I, classiﬁcation was
improved using the proposed method.

Table I. Comparison of classiﬁcation results with pathological ﬁndings.
Mahalanobis distance

Proposed method

Lipid

794 (32.9%)705 (32.9%)

Blood clot

1614 (17.4%)

2472 (21.0%)

Fibrous tissue
Calciﬁed tissue2590 (64.2%)
218 (0.0%)1856 (72.8%)183 (0.0%)

4.

Conclusions

Using the likelihood function of the elasticity distributionof each tissue, the diﬀerentiation of lipids from blood clots
and that of ﬁbrous tissue from calciﬁed tissue were improvedin comparison with the classiﬁcation using only the meanelasticity of each tissue.

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