Ultrasound in Med. & Biol., Vol. 34, No. 4, pp. 573–585, 2008
Copyright © 2008 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved
0301-5629/08/$–see front matterdoi:10.1016/j.ultrasmedbio.2007.10.005● Original Contribution
OPTIMAL REGION-OF-INTEREST SETTINGS FOR TISSUE
CHARACTERIZATION BASED ON ULTRASONIC ELASTICITY IMAGINGKENTARO TSUZUKI,* HIDEYUKI HASEGAWA,* MASATAKA ICHIKI,†
FUMIAKI TEZUKA,‡ and HIROSHI KANAI**Graduate School of Engineering, Tohoku University, Sendai, Japan; †Sendai Hospital of East Railway Company,
Sendai, Japan; and ‡Sendai Medical Center, Sendai, Japan(Received 11 May 2007, revised 28 September 2007, in final form 11 October 2007)

Abstract—Pathologic changes in arterial walls significantly influence their mechanical properties. We havedeveloped a correlation-based method, the phased tracking method, for measurement of the regional elasticity 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 ⴞ SD: lipids, 89 ⴞ 47 kPa; blood clots, 131 ⴞ
56 kPa; fibrous tissue, 1022 ⴞ 1040 kPa; calcified tissue, 2267 ⴞ 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 thebasis of their elasticity. However, there are large overlaps between elasticity distributions of lipids and blood clots
and those of fibrous tissue and calcified tissue. Thus, it was difficult to differentiate lipids from blood clots andfibrous tissue from calcified tissue by setting a threshold for a single elasticity value. Therefore, we previously
proposed a tissue classification method using the elasticity distribution in each small region. In this method, theelasticity distribution of each 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.
In the present study, the optimum size of the ROI and threshold To for the likelihood function were investigatedto improve the tissue 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 ␮m ⴛ 300 ␮m (a single pixel). The ratio of correctly classified
pixels became 35.1% when the size of a small region was 1,500 ␮m ⴛ 1,500 ␮m (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 0.21. 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 ␮m ⴛ 600␮m) of ultrasound. In this study, the arteries used in construction of the elasticity databases were classified into
each tissue using the constructed elasticity databases. Other arteries, which are not used for constructing theelasticity databases, should be classified in future work to thoroughly show the effectiveness of the proposed
method. (E-mail: hkanai@ecei.tohoku.ac.jp) © 2008 World Federation for Ultrasound in Medicine & Biology.
Key Words: Atherosclerosis, Phased tracking method, Elasticity distribution, Tissue classification.

INTRODUCTION

tion or cerebral infarction (Falk et al. 1995; Davies 1996;
Golledge et al. 2000). Magnetic resonance imaging(MRI) and intravascular ultrasound (IVUS) are promising technologies for directly imaging plaque morphology(McConnell et al. 1999; Potkin et al. 1990). On the other
hand, the dynamic change of artery diameter because of
the pulsation of the heart can be measured noninvasively
by ultrasound (Hoeks et al. 1985, 1993; Länne et al.
1992; Brands et al. 1996; Meinders et al. 2001). Someparameters related to artery-wall elasticity can be obtained by the measured change in diameter of the artery(Bergel 1961; Peterson et al. 1960; Hayashi et al. 1980).
However, in the derivation of these parameters, the artery is assumed to be a cylindrical shell with a uniform

Noninvasive measurement of mechanical properties of
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 (Lee et al. 1991;
Loree et al. 1994; Simons et al. 1999). In particular,
mechanical properties of plaque are important because
the rupture of plaque may cause acute myocardial infarcAddress correspondence to: Hiroshi Kanai, Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Aramaki-aza-Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japan.
E-mail: hkanai@ecei.tohoku.ac.jp573

wall thickness and, thus, the elasticity of atherosclerotic
plaque cannot be evaluated.
For measurement of the mechanical properties of
the arterial wall, including cases with atherosclerotic
plaque, intravascular elasticity imaging, namely IVUS
elastography, was introduced by de Korte et al. (1997)
and Céspedes et al. (2000). Although an elasticity distribution of coronary atherosclerotic plaque has been measured with IVUS (de Korte et al. 1997; Céspedes et al.
2000), a transcutaneous approach has not been investigated. For noninvasive vascular elasticity imaging, wedeveloped a method, namely the phased tracking
method, for measuring small vibrations in the heart wallor arterial wall with transcutaneous ultrasound (Kanai etal. 1996, 1997). For some years, we have been measuring
the displacement and small change in thickness (strain)of the arterial wall caused by the heartbeat using thismethod (Hasegawa et al. 1997, 2002; Kanai et al. 1999,
2003). Various studies on noninvasive strain imaging of
the arterial wall have also been recently reported by othergroups (Maurice et al. 2004; Kim et al. 2004; Ribbers etal. 2007).
In our phased tracking method, a set of two points
is assigned along an ultrasonic beam, and the change inthickness of 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, arecompounded to obtain the change in thickness at that
depth (Hasegawa and Kanai 2006). Although the angleof the ultrasonic beam was not changed in the present
study, the concept of spatial compounding has been
applied in previous studies to magnitudes of echoes,
which are obtained by scanning each point in the ROI
with ultrasonic beams having different beam angles, toimprove B-mode images (Jespersen 1998).
Elasticity images of the human carotid artery havebeen obtained by the measured displacement distribu-

tion, and the potential for transcutaneous tissue characterization has been shown by classifying the elasticity
images using the elasticity reference data obtained byin-vitro experiments (Hasegawa et al. 2004; Kanai et al.
2003; Inagaki et al. 2005).
We have already measured the elasticity distributions for lipids, blood clots, fibrous tissue (mixture of thesmooth muscle and collagen) and calcified tissue (Hasegawa et al. 2006; Inagaki et al. 2005). In these previous
studies, it was found that arterial tissues can be classified
as soft tissues (lipids, blood clots) and hard tissues (fibrous tissue, calcified tissue) on the basis of their elasticity. However, differentiation of lipids from blood clots
and fibrous tissue from calcified tissue was difficult.
Therefore, we proposed a tissue classification method
using the elasticity distribution in a small region (Inagaki
et al. 2006). In this method, the elasticity distribution ofeach small ROI (not a single pixel) in an elasticity image
was used for the classification of lipids, blood clots,
fibrous tissue and calcified tissue. Precision of tissueclassification 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 investi-

6

(a)
4

2

0

0

2

4
6
elastic modulus [MPa]8(b)elasticity

low

high

. . .
1 2 3 4 5 6

. . .

Ji

elasticity number
40

(c)

80

30

60

20

40

10

20

0
0.06

...

...
0.37
2.62
mean of elasticity [MPa]

...

1

...

...
100
box number: h

...

200

number of data: Di,hFig. 1. Schematic diagram of the measurement system.

Volume 34, Number 4, 2008

frequency [%]Ultrasound in Medicine and Biology

probability density: p(E i,h )574

0Fig. 2. (a) Original elasticity distribution of the tissue. (b)Ascending sequence of elastic modulus in an elasticity distribution. (c) Normal distribution whose number of boxes depends on the number of data points of (a).

Optimal ROI settings for tissue characterization ● K. TSUZUKI et al.

575

m
k

elasticity image

n
l

3 mm

ROI R m,mFig. 3. Illustration of region of interest (ROI).

gated, and the method has not been applied to the differentiation of fibrous tissue from calcified tissue. In thepresent study, to determine the optimum size of an ROI,
the accuracy of tissue classification (including calcified
tissue) was quantitatively investigated in relation to thesize of the ROI by evaluating the ratio of the number ofcorrectly classified pixels to the total number of classified pixels. In addition, in the proposed classification
method, the likelihood function of each small ROI is
obtained for each tissue component (lipids, blood clots,
fibrous tissue and calcified tissue), and the region isclassified into a tissue component that shows the maximum likelihood. However, an ROI is classified into oneof the four tissue components even when the maximum
likelihood is low. In the present study, such a region isdefined as an unclassified region by setting a thresholdfor the likelihood. By the procedures used in the present

study, tissue classification was much improved in comparison with that in the previous study.
MATERIALS AND METHODS
Experimental setup and specimens
Figure 1 shows a schematic diagram of the measurement system. The change in pressure inside the artery 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 toprevent the flow pump from being contaminated, andonly the change in internal pressure propagated to the

10 mmmeasured region

(a)

lumen

(a)
needlelipids(b)iliac artery (A)blood clots
fibroustissuecalcifiedtissueunclassified(b)iliac artery (B)Fig. 4. Tissue classification images obtained by referring topathologic images. (a) Iliac artery (A). (b) Iliac artery (B).

3 mm

−50

0
change in thickness [µm]50Fig. 5. (a) B-mode image of a femoral artery. (b) Image of the
maximum change in thickness during a cycle of flow pump.

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Ultrasound in Medicine and Biology

(a)

3 mm

0

2
1
elastic modulus [MPa]

3

4

(b)

3 mm

12

frequency [%]

(c)
8

4

0
0

2

4

6

8

elastic modulus [MPa]Fig. 6. (a) Elasticity image of the arterial wall. (b) Pathologic
image of the corresponding section. (c) Elasticity distribution in
the region surrounded by the green line in (a).

Volume 34, Number 4, 2008

inside of the artery. The change in internal pressure wasmeasured 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-type ultrasonic probe (SSH-140A, Toshiba, Japan). The quadrature demodulated signals of radiofrequency (RF) echoes
were acquired at 10 MHz at a frame rate of 200 Hz. In
this study, the elasticity of the arterial wall is defined as
the tissue strain calibrated by the average stress of theentire wall thickness, namely, circumferential elastic
modulus E␪h (Hasegawa et al. 2004; see appendix.). The
strain distribution is obtained by applying the phased
tracking method to the measured demodulated signals(Kanai 1999; Hasegawa and Kanai 2006; see appendix.).
In this study, eight iliac and 10 femoral arteries that
had been surgically excised from 18 patients with arteriosclerosis obliterans were measured in vitro. These
arteries had been excised at the time of bypass grafting
surgery. During the ultrasonic measurement, a needle
was attached to the external surface of the artery for
identification of the measured section so that a pathologic 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 accordance with the policy of the Declarationof Helsinki; all subjects gave informed consent.

Tissue classification using the likelihood function
In this study, each pixel in an elasticity image wasclassified into one of five categories—lipids, blood clots,
fibrous tissue, calcified tissue and unknown— using the
likelihood function {Li} (i ⫽ 1: lipids, 2: blood clots, 3:fibrous tissue, 4: calcified tissue) of the elasticity distribution in the small region around the pixel. To obtain thelikelihood function {Li}, the elasticity distribution of thei-th tissue was translated into the normal distribution todescribe the probability distribution by the mean and thestandard deviation as described later (Inagaki et al.
2006).
From in-vitro experiments, the elasticity distribution of each tissue i was obtained as illustrated in Fig.
2(a). The elasticity distribution of the i-th tissue consistsof 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 was constructed for tissue i as shown in a Fig.
2(b). In this sequence, the j-th datum (j ⫽ 1, 2,. . ., Ji) has
the corresponding elastic modulus Ej (Ej ⱕ Ej⫹1), where
j is termed the elasticity number. The probability distribution of each tissue was obtained by allocating all theOptimal ROI settings for tissue characterization ● K. TSUZUKI et al.

60

6
(c)

40

frequency [%]frequency [%]

(a)

20

0

0

0.2

0.4
0.6
elastic modulus [MPa]

0.8

4

2

0

1

(b)

0

2

4
6
elastic modulus [MPa]

20

10

8

(d)

4

frequency [%]30
frequency [%]

577

3
2
1

0

0

0.2

0.4
0.6
elastic modulus [MPa]

0.8

0

1

0

2

4
6
elastic modulus [MPa]8Fig. 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).

data of Ji points of each tissue i to boxes of the normal
distribution. The box numbers, {Bi}, of the normal distribution were determined so that the number of data inthe box at each end was only one. As shown in Fig. 2(c),the number of data, Di,h (h ⫽ 1, 2, . . ., Bi), included inbox Bi was determined so as to follow the profile of thenormal distribution. Thus, the (Ji/2)-th datum was included in the box with the highest probability. By allo-

cating all the data of Ji points of each tissue to boxes of
the corresponding normal distribution, the mean elasticity E៮ i,h of the data included in each box was obtained.
As shown in Fig. 3, an ROI was assigned to anelasticity image obtained by ultrasonic measurement.
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)

40

40

30

20

10

0

(c)
probability density [%]probability density [%]

(a)

24

34

30

20

10

0
0.06

40 56 76 108 149 205 232
elastic modulus [kPa]

0.17

0.37
1.07
2.62
elastic modulus [MPa]

40

40

(d)
probability density [%]probability density [%]

(b)
30

20

10

0

5.98

39

47

78
128 177 244
elastic modulus [kPa]

257

30

20

10

0

0.54

1.02
1.87
4.22
elastic modulus [MPa]7.00

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

578

(a)

lipidsUltrasound in Medicine and Biology

Volume 34, Number 4, 2008

blood clots

setting threshold To to the maximum likelihood. Thus,
the category C (Rm,n), to which an ROI Rm,n belongs, isexpressed as follows:

4 MPapathologic image

2
1.5
1
0.5
0

(b)

3 mm

3 mm

elastic modulus

fibrous tissue

C(Rm,n) ⫽

blood
clots

classification image
ROI: 75 μ m 300 μm
(d)

1ⱕiⱕ4

共otherwise兲

unknown

Figure 4 shows examples of tissue classification
images that were estimated manually by referring to thepathologic images of iliac arteries (A) and (B). By comparing the pathology-based classification images shownin Fig. 4 with the tissue classification images obtained by
the proposed method, the recognition rate Rr(SROI) for all
tissues in the arterial wall was defined by the ratio of thenumber of correctly classified pixels to the number N of
all pixels in the image as follows:

lipids

3 mm

1ⱕiⱕ4

(2)

elasticity image(c)

再arg max Li(m, n) 共if max Li(m, n) ⱖ To兲

fibroustissuecalcifiedtissue3 mm

unclassified(a)calcified tissue

3 mmpathologic image (HE stain)
4 MPa

(b)
3 mm

Fig. 9. For the iliac artery (A): (a) pathologic image of anarterial wall subjected to elastica-Masson staining, (b) elasticity
image, (c) tissue classification image (ROI size: 1 ⫻ 1 pixel)and (d) tissue classification image (ROI size: 5 ⫻ 20 pixels).

fibrous tissue
pathologic image (EM stain)
(c)

3 mm

elasticity image

simultaneously belong in the i-th category as
follows:
Li(m, n) ⫽冉 兿 共 兲冊pi Ek,l, (i ⫽ 1, 2, 3, 4)

1⁄N0

(d)

lipids
3 mm
blood
clots

(1)

classification image
ROI: 75 μ m 300 μm(k,l)僆Rm,nwhere pi(Ek,l) is the probability density that shows theprobability that elasticity value Ek,l in the k-th row andl-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 geometric mean for compensation of the effect of the size of an ROI. The pixel at thecenter of an ROI is classified into the class that has the
maximum likelihood.
In this classification, there may be a region that has
an extremely small value for the maximum likelihood.
Such regions are classified into the unclassified region by

2
1.5
1
0.5
0

elastic modulus

classification image
ROI: 1,500 μ m 1,500 μ m

(e)

3 mm

fibroustissuecalcifiedtissueclassification image
ROI: 1,500 μ m 1,500 μ m

Fig. 10. For the iliac artery (B): (a) pathologic image of anotherarterial wall subjected to hematoxylin-eosin staining, (b) pathologic image of the arterial wall subjected to elastica-Masson
staining, (c) elasticity image, (d) tissue classification image(ROI size: 1 ⫻ 1 pixel) and (e) tissue classification image (ROI
size: 5 ⫻ 20 pixels).

Optimal ROI settings for tissue characterization ● K. TSUZUKI et al.
false recognition rate Fr ( SROI) [%](a)
recognition rate R r (S ROI) [%]80
artery (C)70artery (D)6050artery (E)40artery (B)30artery (A)0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7
3width W of ROI in the arterial axis direction [mm]recognition rate R r (SROI ) [%]artery (F)artery (G)artery (H)artery (I)artery (J)artery (K)

60

20

40
artery (D)200artery (E)artery (C)artery (A)artery (B)

0

0.05
0.1
0.15
0.2
0.25
threshold To for likelihood function

artery (O)0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3
width W of ROI in the arterial axis direction [mm]Fr(SROI) ⫽Fig. 11. Relationship between width W ⫽ 兹SROI 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.

Rr(SROI) ⫽兺 N ⫻ 100[%],i

0.3

for all tissues in the arterial wall was defined by the ratioof the number of misclassified pixels except for the
pixels classified as unclassified pixels to the number N of
all pixels as follows:

artery (L)artery (M)artery (N)4060Fig. 13. Relationship between threshold To for likelihood function and the false recognition rate Fr(SROI) in arteries composedof several types of tissues.

(b)

80

579

i

(3)

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 located at the center of the ROI
should be defined as an unclassified pixel by thresholding. For determination of the optimum threshold for the
likelihood function, the false recognition rate Fr(SROI)兺 F ⫻ 100[%],
i

i

N

(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 eqns (3) and (4), that is, the number of all
pixels N, they are not included in the number of correctlyclassified 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 become100%.
IN-VITRO EXPERIMENTAL RESULTS
Measurement of elasticity distribution of each tissue
component
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

recognition rate Rr ( SROI) [%]

80

60

40
artery(C)artery(B)20artery(E)artery(A)artery(D)

0

0

0.05
0.1
0.15
0.2
0.25
threshold To for likelihood function

0.3

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

Fig. 14. Relationship between threshold To for likelihood function and the ratio of the number of correctly classified pixels to
the number of misclassified pixels in all arteries composed ofseveral types of tissues.

580

Ultrasound in Medicine and Biology
(b)

(a)

elasticity distribution
of ROI Rm,ntissue A

tissue B

elasticity(c)elasticity distribution
of ROI Rm,ntissue A
resolution of ultrasound(800 µm x 600 µm)

tissue A

tissue B

elasticity

Fig. 15. (a) ROI Rm,n (1,500 ␮m ⫻ 1,500 ␮m) and spatial
resolution of ultrasound in only tissue A. (b) Elasticity distribution of ROI Rm,n when ROI size is smaller than the resolutionof ultrasound. (c) Elasticity distribution of ROI Rm,n when ROI
size is 1,500 ␮m ⫻ 1,500 ␮m.

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 internal pressure and that in thickness obtained by the phased
tracking method shown in Fig. 5(b). By referring to thepathologic image of the same section shown in Fig. 6(b),fibrous tissue in the intima-media region was identified.
The corresponding region, namely, the region surrounded by the green line in Fig. 6(a), was then assigned
to the elasticity image. Figure 6(c) shows the elasticity

Volume 34, Number 4, 2008

distribution of fibrous tissues extracted from the region
surrounded by the green line in Fig. 6(a). By applying thesame procedure to the other arteries, the elasticity distribution of each tissue in the arterial wall was obtained.
Figure 7 shows the elasticity distribution of eachtissue, that is, the frequency of the elasticity values thatbelong to the range defined by the position and width ofeach 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
and blood clots and in those of fibrous and calcified
tissues, differences in the elasticity distributions of thesetissues were found.
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 was classified
as a certain tissue component.
Figures 9(c) and (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. Although arterial tissues were

(c)

(a)

1

lipidsfibroustissueunclassified

frequency

blood clots

lipid
blood clot
ROI

0.8
0.6
0.4
0.2
0

0

0.05

0.1 0.15 0.2 0.25 0.3
elastic modulus [MPa]

0.35

0.4

(d)
(b)

1
lipid
blood clot
ROI

frequency

0.8
0.6
0.4
0.2
0

0

0.05

0.1 0.15 0.2 0.25 0.3
elastic modulus [MPa]

0.35

0.4

Fig. 16. (a) Tissue classification image obtained by referring to pathologic images. (b) Close-up of ROI. (c) Elasticity
distribution (ROI size: 600 ␮m ⫻ 600 ␮m). (d) Elasticity distribution (ROI size: 1,500 ␮m ⫻ 1,500 ␮m).

Optimal ROI settings for tissue characterization ● K. TSUZUKI et al.
(b)(a)

elasticity distribution
of ROI R m ,ntissue A

tissue B

elasticity(c)elasticity distribution
of ROI R m ,ntissue B

tissue A

resolution of ultrasound(800 µ m x 600µ m)

tissue A

tissue B

elasticity

Fig. 17. (a) ROI Rm,n (1,500 ␮m ⫻ 1,500 ␮m) 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␮m ⫻ 1,500 ␮m.

roughly classified into soft tissues (lipids and bloodclots) and hard tissues (fibrous tissue and calcified tissue), the classified tissue distributions are scattered, andthe misclassified regions are outstanding. Alternatively,
Fig. 9(d) shows the result of classification with an ROI
size of 1,500 ␮m ( ⫽ 20 pixels) in the radial direction
and 1,500 ␮m ( ⫽ 5 pixels) in the longitudinal direction.
Moreover, the region with low likelihood for all tissue
components is colored gray. The threshold To for the
maximum of the likelihood functions {Li} was set at
0.21. As shown in Fig. 9(d), the region with the maximum likelihood that is higher than threshold To is accurately classified as the corresponding tissue identified byreferring to the pathologic image.
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 no region withlow 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 ⫽ 兹SROI 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, an
ROI is not square (75 ␮m ⫻ 300 ␮m). Figure 11(b)shows the relationship between width W ⫽ 兹SROI of an
ROI in the longitudinal direction and the recognition rate
Rr(SROI) in arteries that are composed of a single type oftissue, 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 is581

uniformly classified as the corresponding tissue using alarge ROI, which results from the worsening spatial
resolution in tissue classification. Figure 11(a) shows therelationship between width W of 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, the improvement of tissue classificationby the enlargement of an ROI is limited because theclassification using a large ROI provides a uniform tissueclassification image, whereas the arterial wall is composed 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 ␮m ⫻ 1,500
␮m.
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 compared with the recognition rate because the pixels with lower likelihood are
more likely to be misclassified. However, the correctlyclassified pixels are also classified as unclassified pixels
when the threshold To is too high. Therefore, threshold
To should be determined by considering both Rr(SROI)
and Fr(SROI). In this study, the ratio (CMR(To)) of thenumber of correctly classified pixels (the numerator ofeqn (3)) to the number of misclassified pixels (the numerator of eqn (4)) for all arteries composed of different
types of tissues was evaluated as follows:

(b)
(a)

elasticity distribution
of ROI R m ,ntissue A

tissue B

elasticity(c)elasticity distribution
of ROI R m ,ntissue B

tissue A

resolution of ultrasound(800 µ m x 600µ m)

tissue A

tissue B

elasticity

Fig. 18. (a) ROI Rm,n (1,500 ␮m ⫻ 1,500 ␮m) and spatial
resolution of ultrasound in tissue A and tissue B (tissue A ⯝tissue B). (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 ␮m ⫻ 1,500 ␮m.

582

Ultrasound in Medicine and Biology

Volume 34, Number 4, 2008

(c)

(a)

1
fibrous tissue
calcified tissue
ROI

fibroustissuecalcifiedtissueunclassified

frequency

0.8
0.6
0.4
0.2
0

0

0.5

1

1.5
2
2.5
3
elastic modulus [MPa]

3.5

4

(d)
(b)

1
fibrous tissue
calcified tissue
ROI

frequency

0.8
0.6
0.4
0.2
0

0

0.5

1

1.5
2
2.5
3
elastic modulus [MPa]3.5

4Fig. 19. (a) Tissue classification image obtained by referring to pathologic images. (b) Close-up of ROI. (c) Elasticity
distribution (ROI size: 600 ␮m ⫻ 600 ␮m). (d) Elasticity distribution (ROI size: 1,500 ␮m ⫻ 1,500 ␮m).

CMR(T0) ⫽兺N兺Fii, allii, all,(5)where Ni,all and Fi,all are the sum of correctly classified
pixels of tissue i and that of misclassified pixels of tissue
i, respectively, for all arteries composed of different
types of tissues. Figure 14 shows the relationship between threshold To for likelihood function and CMR(To)averaged by all arteries composed of different types oftissues. As shown in Fig. 14, the CMR(To) reached the
maximum when the threshold To was 0.21.
DISCUSSIONIn 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 the sizeof an ROI is smaller than the spatial resolution ⌬S ofultrasound (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
the elasticity values within the space of the resolutionof ultrasound ⌬S 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 isnarrow and the elasticity distributions of tissue A andtissue B overlap. By enlarging the size of an ROI sothat it is larger than the space of the resolution ofultrasound ⌬S, 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 ⌬S. Figure 13 shows anexample of this case. Figure 16(a-d) show a tissue classification image, an enlarged view of an ROI and elasticity distributions of ROIs with sizes of 600 ␮m ⫻ 600
␮m and 1,500 ␮m ⫻ 1,500 ␮m, respectively. In Fig.
16(c), the elasticity distribution of the smaller ROI (purple line) is narrow and located in the overlapping regionof the elasticity distributions of lipids and blood clots, theorange and red dashed lines showing the elasticity distributions of lipids and blood clots, respectively. Therefore, tissue classification is very difficult. On the other
hand, in Fig. 16(d), the elasticity distribution is broadened and becomes similar to that of a blood clot, and the
ROI can be correctly classified as a blood clot.
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 ismuch larger than that of tissue B, the ROI is classified as
tissue A even if the pixel, which is in the center of the
ROI, is composed of tissue B and the small clusters oftissue B in the ROI are not identified.

Optimal ROI settings for tissue characterization ● K. TSUZUKI et al.

583

T
1

2

frame nΔxdepth xx 1 (1)
...

...

...

...

...

...

x m (1)x M T (1)x 1 (2)

1st layerm−th layer

...

...

x M T (2)h(1)=

MT −th layer

...

...

x m (2)ML . Δ xx’1 (1)
...

...

...

x’1 (2)x’m (1)

...

...

...

...

...

x’m (2)...

...

x’M T (1)x’M T (2)Fig. 20. Illustration of the method for estimation of the change in thickness of the arterial wall (MT: total number ofassigned combinations; ML: the number of sampled points between two points of an assigned combination, T: frameinterval; ⌬x: depths of scatterers in n-th frame, xm(n) and x’m共n兲: m-th combination of two points in n-th frame; and h(n):distance between two scatterers in n-th frame).

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 this case,and tissue classification is found to be difficult even by
the use of the proposed method because the elasticity
distribution in the ROI is located in the overlapping
region for each ROI size.
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 thepossibility of using the proposed method for noninvasiveclassification of the tissue composition in the arterial wall
based on ultrasound elasticity imaging. However, different
arteries not used for constructing the elasticity databases
should be classified in future work to thoroughly show theeffectiveness of the proposed method.

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.
Acknowledgements—This work was supported in part by grants-in-aid
for scientific research from the Ministry, Education, Culture, Sports,
Science and Technology of Japan (2005 to 2007, No. 17206043; 2006
to 2007, No. 18656115).

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APPENDIX
Strain estimation by the phased tracking method with correlation
estimator compounding
By referring to a cross-sectional image of an artery, initial
positions x1(1) and x⬘1共1兲 of two points are assigned manually in the first
frame as shown in Fig. 20 共x⬘1共1兲 ⫺ x1共1兲 ⫽ M L·⌬x; ⌬x: spacing ofsampled points in the depth direction). Instantaneous positions x1(n)and x⬘1共n兲 of these assigned points in the n-th frame are then tracked by
the phased tracking method (Kanai et al. 1996).
The change in thickness between two reflectors at depths x1(n)and x⬘1共n兲 is then obtained as follows: the phases ␪1共n兲 and ␪⬘1共n兲 ofechoes from these two reflectors depend on x1(n) and x⬘1共n兲. Therefore,
the phase difference ␪h共n兲 ⫽ ␪⬘1共n兲 ⫺ ␪1共n兲 depends on the distanceh共n兲 ⫽ x⬘1共n兲 ⫺ x1共n兲 (thickness of the layer) between two reflectors as
follows (Hasegawa et al. 2002, 2006):
h(n) ⫽ x⬘1(n) ⫺ x1(n) ⫽c0c0{␪⬘ (n) ⫺ ␪1(n)} ⫽· ␪ (n), (A-1)
4␲ f 0 1
4␲ f 0 h

where c0 and f0 are the speed of sound and center frequency ofultrasound, respectively. Thus, the rate vh(n) of the change in thicknessof the layer between two reflectors is expressed as follows:
vh(n) ⫽h(n ⫹ 1) ⫺ h(n)c0c0
␪ (n ⫹ 1) ⫺ ␪h(n)其 ⫽⫽· ⌬␪h(n),T4␲ f 0T 兵 h
4␲ f 0T(A-2)

where ⌬␪h共n兲 is the change in ␪h共n兲 during a frame interval T. Phase
difference ␪h共n兲 can be expressed by phase ⬔␤共n; x1共n兲, x⬘1共n兲兲 of product ␤共n; x1共n兲, x⬘1共n兲兲 of complex demodulated signals z∗共n; x1共n兲兲 andz共n; x⬘1共n兲兲 as follows:␪h(n) ⫽ ␪⬘1(n) ⫺ ␪1(n) ⫽ ⬔ ␤共n; x1共n兲, x⬘1共n兲兲,(A-3)

␤共n; x1共n兲, x⬘1共n兲兲 ⫽ z共n; x⬘1共n兲兲 · z∗共n; x1共n兲兲

(A-4)

In this study, correlation estimator ␥h共n; x兲 at depth x, whose
phase ⬔␥h共n; x兲 corresponds to ␪h共n ⫹ 1兲 ⫺ ␪h共n兲 ⫽ ⌬␪h共n兲 is obtainedby simply calculating the correlation around the duration of the ultrasonic pulse used, as follows:Optimal ROI settings for tissue characterization ● K. TSUZUKI et al.

The compounded rate, v៮ h共n; x兲 of the change in thickness at depth
x is obtained based on eqn (A-2) as follows:K⁄2␥ˆ h(n; x1(1) ⫹ i⌬x) ⫽兺 ␤(n ⫹ 1; x (n) ⫹ k · ⌬x, x (n)
⬘
1

1

585

k⫽⫺K⁄2⫹ k · ⌬x) ⫻ ␤ * (n; x1(n) ⫹ k · ⌬x, x⬘1(n) ⫹ k · ⌬x), (i ⫽ 0, 1, 2, . . . , M L)
(A-5)
where the estimate in the right-hand side of eqn (A5) is used forcorrelation estimators ␥h共n;x兲 at all points between x1(1) and x⬘1共1兲.
To obtain the spatial distribution along each ultrasonic beam, thecorrelation estimator, ␥h,m共n;x兲 for the combination of two points, xm(1)⬘and xm共1兲, at each 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 共 ⫽ M L·⌬x兲 as follows:v៮ h(n; xm(1)) ⫽c0· ⬔ ␥h(n; xm(1))
4␲ f 0T

The compounded change in thickness, ⌬h៮ 共n; x兲 is obtained asfollows:⌬h៮ (n ⫹ 1; xm(1)) ⫽ ⌬h៮ (n; xm(1)) ⫹ v៮ h(n; xm(1)) · T

The elastic modulus, E , at xm共1兲 is obtained by the estimatedchange in thickness as follows (Hasegawa et al. 2004):
E␪h,m ⫽

冉

1 rm M T ⫹ M L ⫺ m ⫹ 1⫹
2 h0
MT ⫹ ML⬘mk⫽⫺K⁄2⫹ k · ⌬x) ⫻ ␤∗(n; xm(n) ⫹ k · ⌬x, xm⬘ (n) ⫹ k · ⌬x), (A-6)
xm(1) ⫽ x1(1) ⫹ (m ⫺ 1) · ⌬x,(m ⫽ 1, 2, . . . , M T ⫹ 1;i ⫽ 1, 2, . . . , M L ⫹ 1).

(A-7)

As shown in Fig. 20, some of the MT assigned layers overlap
each other. Therefore, there are multiple estimates of ␥h共n; x兲 at depth
x. The compounded correlation estimator, ␥h共n; x兲 at depth x is thenobtained by simply averaging the overlapping correlation estimators as
follows:␥h(n; xm(1)) ⫽1
M 0(xm(1))

m⫹M 0(xm(1))

兺␥h,k(n; xm(1)),

冊ⱍ ⱍ

⌬p
,
⌬hm max(A-11)M L⌬x兺 ␤(n ⫹ 1; x (n) ⫹ k · ⌬x, x (n)m(A-10)h␪,mK⁄2

␥ˆ h,m(n; xm(1) ⫹ (i ⫺ 1) · ⌬x) ⫽

(A-9)

(A-8)

k⫽m

where Mo(x) is the number of overlapping layers at depth x. By
compounding the correlation estimator shown by eqn (A-6), the contributions of echoes with low amplitudes ( ⫽ low signal-to-noise ratio)
to the estimation of the phase shift are suppressed.

where rm and h0 are, respectively, the radius at xm(1) and the thicknessof the entire wall in the first frame, and ⌬p and |⌬hm|max are, respectively, the pulse pressure 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:rm ⫽ r0 ⫹ (m ⫺ 1)⌬x,(A-12)

h0 ⫽ M L · ⌬x,(A-13)

where r0 is the inner radius of the innermost layer. By substituting eqns
(A-12) and (A-13) into eqn (A-11), eqn (A-11) is modified as follows:E␪h,m ⫽

冉 冊ⱍ ⱍ

1 r0
⫹1
2 h0

冉 冊

⌬p
⌬p
1 r0
⫹1
,
⫽
⌬␧m
⌬hm max 2 h0

(A-14)M L⌬xwhere ⌬␧m is the strain of the m-th layer. As shown by eqn (A-14),
elastic modulus E␪h,m is defined as the average stress 共r0 ⁄ h0
⫹ 1兲·⌬p ⁄ 2 of the entire wall thickness divided by the radial strain⌬␧m.