ELASTICITY-BASED TISSUE CHARACTERIZATION OF
ARTERIAL WALL
HIDEYUKI HASEGAWA1)2), KENTARO TSUZUKI2), MASATAKA ICHIKI3),
FUMIAKI TEZUKA4), HIROSHI KANAI2)1)

1) Graduate School of Biomedical Engineering, Tohoku University,
6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
2) Graduate School of Engineering, Tohoku University,
6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
3) Sendai Hospital of East Railway Company,
1-5 Itsutsubashi, Aoba-ku, Sendai 980-8508, Japan1-4) Sendai Medical Center, 2-8-8 Miyagino, Miyagino-ku, Sendai 983-8520, Japan
Pathological changes in arterial walls significantly influence their mechanical properties.
We have developed a correlation-based method, the phased-tracking method, formeasurement of the regional elasticity of the arterial wall. Using this method, elasticity
distributions of lipids, blood clots, fibrous tissue, and calcified tissue were measured byin 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 foundthat arterial tissues can be classified into soft tissues (lipids and blood clots) and hardtissues (fibrous tissue and calcified tissue) on the basis of their elasticity. However, there
are large overlaps between elasticity distributions of lipids and blood clots and those offibrous tissue and calcified tissue. Thus, it was difficult to differentiate lipids from bloodclots and fibrous tissue from calcified tissue when a threshold for a single elasticity value
was set. Therefore, we developed and optimized a tissue classification method using theelasticity distribution in each small region. In this method, the elasticity distribution ofeach small region of interest (ROI) (not a single pixel) in an elasticity image is used toclassify lipids, blood clots, fibrous tissue, and calcified tissue by calculating the
likelihood function for each tissue. 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), but became 54.2% when the size of a small region was 1,500 μm ×1,500 μm (100 pixels).

1. Introduction
Noninvasive measurement of elasticity of the arterial wall is useful for
diagnosis of atherosclerosis because there are significant differences between

12

the elasticity of a normal arterial wall and that of an arterial wall affected byatherosclerosis [1]. In particular, mechanical properties of atherosclerotic plaqueare important because plaque rupture may cause acute myocardial infarction andcerebral infarction [2-4]. Magnetic resonance imaging (MRI) and intravascularultrasound (IVUS) are promising technologies for directly imaging plaquemorphology [5,6]. On the other hand, the dynamic change of artery diameter
due to the pulsation of the heart can be measured noninvasively by conventional
methods with ultrasound [7-10]. Some parameters related to artery-wallelasticity can be obtained by the measured change in diameter of the artery [1113]. However, in the derivation of these parameters, the artery is assumed to bea cylindrical shell with an uniform wall thickness and, thus, the elasticity ofatherosclerotic plaque cannot be evaluated.
For measurement of the mechanical properties of the arterial wall, including
the case with atherosclerotic plaque, we previously developed a method, namely,
the phased-tracking method, for measuring small vibrations in the heart wall orarterial wall with transcutaneous ultrasound [14]. For a number of years, wehave been measuring the displacement and small change in thickness of thearterial wall caused by the heartbeat using this method for elasticity imaging[15-17]. Elasticity images of the human carotid artery have been obtained by themeasured distribution of changes in thickness, and the potential fortranscutaneous tissue characterization has been shown by classifying theelasticity images using elasticity reference data obtained by in vitro experiments[16,18,19].
We have already measured the elasticity distributions for lipids, blood clots,
fibrous tissue (mixture of the smooth muscle and collagen), and calcified tissue.
In these previous studies, it was found that 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
from blood clots and fibrous tissue from calcified tissue. We thus proposed atissue classification method using the elasticity distribution in a small region[20]. In this method, the elasticity distribution of each small ROI (not a single
pixel) in an elasticity image was used to classify lipids, blood clots, fibrous
tissue, and calcified tissue. The precision of tissue classification was improved
using the elasticity distribution in each small region.
However, the accuracy of this method in relation to the size of an ROI has
not yet been thoroughly investigated. In the present study, to determine theoptimum size of an ROI, the accuracy of tissue classification (including
calcified tissue) was quantitatively investigated in relation to the size of the ROI.

3

In addition, in the proposed classification method, an ROI is classified into oneof the four tissue components, i.e. lipids, blood clots, fibrous tissue, andcalcified tissue, 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, tissue classification was much improvedin comparison with that in the previous study [21,22].
2. Materials and Methods
2.1. Experimental setup and specimens
Change in the pressure inside an excised artery was realized by circulating a
fluid using a flow pump. The fluid inside the artery and that circulating in theflow pump were separated by a rubber membrane to prevent the flow pumpfrom being contaminated, and only the change in internal pressure propagated tothe inside of the artery. The change in internal pressure was measured by apressure transducer (Model 110-4, Camino, San Diego, CA, USA).
In the acquisition of ultrasonic echoes, excised arteries (eight iliac and ten
femoral) were measured with a conventional 7.5 MHz linear-type ultrasonicprobe (SSH-140A, Toshiba, Japan). The quadrature demodulated signals of RF
echoes were acquired at 10 MHz at a frame rate of 200 Hz. The elasticity of thearterial wall was defined as the tissue strain calibrated by the average stress ofthe entire wall thickness, namely, the circumferential elastic modulus Eθh [17].
The strain distribution was obtained by applying the phased-tracking method tothe measured demodulated signals [17]. During the ultrasonic measurement, aneedle was attached to the external surface of the artery for identification of themeasured section so that a pathological image of the same section could beobtained after the ultrasonic measurement.
2.2. Tissue classification using the likelihood function
Each pixel in an elasticity image was classified into one of 5 categories,
namely, 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 was translated into the normal distribution to describe the probability
distribution by the mean and the standard deviation as described below [20].
From in vitro experiments, the elasticity distribution of each tissue i was
obtained as illustrated in Fig. 1(a). The elasticity distribution of the i-th tissue

4

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. 1(b). In thissequence, the j-th datum ( j = 1, 2, . . ., Ji) has the corresponding elastic modulus
Ej (Ej ≤ Ej+1), where j was termed the elasticity number. The probability
distribution of each tissue was obtained by allocating all the data of Ji points ofeach tissue i to boxes of the normal distribution. The box numbers, {Bi}, of thenormal distribution are determined so that the number of data in the box at eachend is only one. As shown in Fig. 1(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)-th datum is included in the box with the highest
probability. By allocating all the data of Ji points of each tissue to boxes of thecorresponding normal distribution, the mean elasticity Ēi,h of the data includedin each box was obtained.
ROIs were assigned to an elasticity image which was obtained by ultrasonicmeasurement. The likelihood function Li(m,n) is defined as the joint probability
that all the elasticity values in ROI Rm,n (center of ROI: n-th sampled point along
the m-th beam) simultaneously belong in the i-th category as follows:
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 thatelasticity value Ek,l in the k-th row and l-th column in an 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 geometric mean for compensation of the effect of thesize of an ROI. The pixel at the center of an ROI is classified into the classwhich has the maximum likelihood.
In this classification, there may be a region which has an extremely smallvalue for the maximum likelihood. Such regions are classified as unclassified
regions by setting threshold To to the maximum likelihood. Thus, the category
C(Rm,n), to which 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(otherwise ) .
 unknown

(2.2)

5

Figure 1. (a) Original elasticity distribution of the tissue. (b) Ascending sequence of the elastic
modulus in an elasticity distribution. (c) Normal distribution whose number of boxes depends on thenumber of data points of (a).

By comparing the pathology-based classification images with the tissueclassification images obtained by the proposed method, the recognition rate
Rr(SROI) for all tissues in the arterial wall was defined as the ratio of the numberof correctly classified pixels to the number N of all pixels in the image asfollows:
Rr ( SROI ) = N × 100 [%],
i

N

i

(2.3)

where Ni is the number of correctly classified pixels of tissue i and SROI is thesize 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), thepixel which is located at the center of the ROI should be defined as an
unclassified pixel by thresholding. For determination of the optimum threshold6

for the likelihood function, the false recognition rate Fr(SROI) for all tissues in
the arterial wall was defined as 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:
Fr ( S ROI ) = F × 100 [%],
i

i

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 number of all pixels N, they
are not included in the number of correctly classified pixels Ni nor that of
misclassified pixels Fi. Therefore, the sum of the recognition rate Rr(SROI) andthe false recognition rate Fr(SROI) does not become 100%.
3. In Vitro Experimental Results
3.1. Measurement of elasticity distribution of each tissue
Figure 2 shows the elasticity distribution of each tissue, that is, thefrequency of the elasticity values which belong to the range defined by the
position and width 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 the elasticity distributions of lipids andblood clots and in those of fibrous and calcified tissues, differences in theelasticity distributions of these tissues were also found.

7
Figure 2. Elasticity distribution of each tissue. (a) Lipids (N = 288), (b) blood clots (N = 178), (c)fibrous tissue (N = 19,120), and (d) calcified tissue (N = 1,101).

3.2. Results of classification
Figures 3(c) and 3(d) show an example of tissue classification results
obtained by the proposed method for an iliac artery. The regions classified as
lipids, blood clots, fibrous tissue, and calcified tissue were stained yellow, red,
blue, and purple, respectively. Figure 3(c) graphically shows the tissueclassification image obtained with an ROI size of 1 × 1 pixel. Although arterial
tissues were roughly classified as soft tissues (lipids and blood clots) and hardtissues (fibrous tissue and calcified tissue), the classified tissue distributions arescattered, and the misclassified regions are prominent. Alternatively, Fig. 3(d)shows the result of classification with an ROI size of 1,500 μm ( = 20 pixels) in
the radial direction and 1,500 μm ( = 5 pixels) in the longitudinal direction.
Moreover, the region with low likelihood for all tissue components is coloredgray. The threshold To for the maximum of the likelihood functions {Li} was set
at 0.21. As shown in Fig. 3(d), the region with the maximum likelihood which ishigher than threshold To is accurately classified as the corresponding tissue
identified by referring to the pathological image.
Figure 4 shows the relationship between the size SROI of an ROI and therecognition rate Rr(SROI). The ROI size SROI was changed with its square shape
being maintained. The horizontal axis shows the width W = (SROI)-1/2 of an ROI
in the longitudinal direction. An ROI consists of a single pixel when width W in
Fig. 4 is 0.3 mm. Only in this specific case is an ROI not square (75 μm × 300
μm).
Figure 4(b) shows the relationship between width W = (SROI)-1/2 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 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 intissue classification. Figure 4(a) shows the relationship between width W of an
ROI and the recognition rate Rr(SROI) in arteries composed of different types oftissues. For this case, tissue classification using a certain number of pixels in an
ROI is superior to that using a single pixel. However, the improvement of tissueclassification by the enlargement of an ROI is limited because the classification
using a large ROI provides a uniform tissue classification image, whereas thearterial wall is composed of different kinds of tissues. Therefore, there should be8an optimum size of an ROI. As shown in Fig. 4(a), the recognition rates
became maximum in most arteries when the size of an ROI was 1,500 μm ×1,500 μm.

Figure 3. Example of tissue classification. (a) Pathological image of an arterial wall subjected toelastica-Masson staining. (b) Elasticity image. (c) Tissue classification image (ROI size: 1 × 1 pixel).
(d) Tissue classification image (ROI size: 5 × 20 pixels).

In this study, the optimum threshold To was determined by considering theratio (CMR(To)) of the number of correctly classified pixels (the numerator of9eq. (2.3)) to the number of misclassified pixels (the numerator of eq. (2.4)) for
all arteries composed of different types of tissues, which was evaluated asfollows:
CMR(To ) =

N
F
i

i ,allii ,all,(3.1)

where Ni,all and Fi,all are the sum of correctly classified pixels of tissue i and thatof misclassified pixels of tissue i, respectively, for all arteries composed ofdifferent types of tissues. Figure 5 shows the relationship between threshold To
for the likelihood function and the average CMR(To) of all arteries composed ofdifferent types of tissues. As shown in Fig. 5, the CMR(To) reached the
maximum when the threshold To was 0.21.

Figure 4. Relationship between width W of an ROI in the longitudinal 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.

Figure 5. Relationship between threshold To for the likelihood function and the ratio of the numberof correctly classified pixels to the number of misclassified pixels in all arteries composed of several
types of tissues.

4. Conclusions
In this study, tissue classification based on the likelihood function with theconfigured appropriate ROI size (not a single pixel) and a lower limit oflikelihood were investigated. Using the elasticity distribution of an ROI, the10differentiation of lipids from blood clots and that of fibrous tissue from
calcified tissue were improved.
References
1. R. T. Lee, A. J. Grodzinsky, E. H. Frank, R. D. Kamm and F. J. Schoen,
Circulation 83, 1764 (1991).
2. E. Falk, P. K. Shah and V. Fuster, Circulation 92, 657 (1995).
3. M. J. Davies, Circulation 94, 2013 (1996).
4. J. Golledge, R. M. Greenhalgh and A. H. Davies, Stroke 31, 774 (2000).
5. M. V. McConnell, M. Aikawa, S. E. Maier, P. Ganz, P. Libby and R. T. Lee,
Arterioscler. Thromb. Vasc. Biol. 19, 1956 (1999).
6. B. N. Potkin, A. L. Bartorelli, J. M. Gessert, R. F. Neville, Y. Almagor, W.
C. Roberts and M. B. Leon, Circulation 81, 1575 (1990).
7. A. P. G. Hoeks, C. J. Ruissen, P. Hick and R. S. Reneman, Ultrasound Med.
Biol. 11, 51 (1985).
8. A. P. G. Hoeks, X. Di, P. J. Brands and R. S. Reneman, Ultrasound Med.
Biol. 19, 727 (1993).
9. T. Länne, H. Stale, H. Bengtsson, D. Gustafsson, D. Bergqvist, B. Sonesson,
H. Lecerof and P. Dahl, Ultrasound Med. Biol. 18, 451 (1992).
10. P. J. Brands, A. P. G. Hoeks, M. C. Rutten and R. S. Reneman, UltrasoundMed. Biol. 22, 895 (1996).
11. D. H. Bergel, J. Physiol. 156, 445 (1961).
12. L. H. Peterson, R. E. Jensen and J. Parnel, Circ. Res. 8, 622 (1960).
13. K. Hayashi, H. Handa, S. Nagasawa, A. Okamura and K. Moritake, J.
Biomech. 13, 175 (1980).
14. H. Kanai, M. Sato, Y. Koiwa and N. Chubachi, IEEE Trans. Ultrason.
Ferroelect. Freq. Contr. 43, 791 (1996).
15. H. Hasegawa, H. Kanai, Y. Koiwa and N. Chubachi, Electron. Lett. 33, 340(1997).
16. H. Kanai, H. Hasegawa, M. Ichiki, F. Tezuka and Y. Koiwa, Circulation
107, 3018 (2003).
17. H. Hasegawa and H. Kanai, IEEE Trans. Ultrason. Ferroelect. Freq. Contr.
53, 2050 (2006).
18. H. Hasegawa, H. Kanai, N. Hoshimiya and Y. Koiwa, J. Med. Ultrason. 31,
81 (2004).
19. J. Inagaki, H. Hasegawa, H. Kanai, M. Ichiki and F. Tezuka, Jpn. J. Appl.
Phys. 44, 4593 (2005).
20. J. Inagaki, H. Hasegawa, H. Kanai, M. Ichiki and F. Tezuka, Jpn. J. Appl.
Phys. 45, 4732 (2006).
21. K. Tsuzuki, H. Hasegawa, H. Kanai, M. Ichiki and F. Tezuka, UltrasoundMed. Biol. 34, 573 (2008).

11

22. K. Tsuzuki, H. Hasegawa, H. Kanai, M. Ichiki and F. Tezuka, Jpn. J.
Appl. Phys. 47, 4180 (2008).