ULTRASONIC CROSS-SECTIONAL IMAGING AND
MEASUREMENT OF MOTION AND MECHANICALPROPERTIES OF ARTERIAL WALLSHIDEYUKI HASEGAWA1), JUN INAGAKI1), TAKASHI MASHIYAMA1),
TAKANORI NUMATA1), MASATAKA ICHIKI2), FUMIAKI TEZUKA3),
HIROSHI KANAI1)
1) Graduate School of Engineering, Tohoku University,
Aoba-ku Aramaki-aza-Aoba 6-6-05, Sendai, 980-8579, Japan
2) Sendai Hospital of East Railway Company,
Aoba-ku Itsutsubashi 1-1-5, Sendai, 980-8508, Japan
3) Sendai Medical Center, Miyagino-ku Miyagino 2-8-8, Sendai, 983-8520, Japan
Ultrasound can be used for mechanical property measurements of the arterial wall in
addition to imaging of its morphology. This paper describes (1) accurate imaging of the
carotid sinus which cannot be assumed to be a straight cylindrical shell, (2) measurementof elasticity and tissue characterization of the arterial wall based on the axial motion
estimation, and (3) lateral motion estimation in the carotid artery.
Keywords: imaging of arterial morphology, beam steering, artery motion, elasticity,
atherosclerosis.

1. Introduction
Rupture of atherosclerotic plaque is probably the most important factor
underlying the sudden onset of the acute coronary syndrome [1]. Direct
characterization of the composition and vulnerability of atherosclerotic plaque,rather than measurement of the angiographic lumen [2], may offer insight into
the mechanisms of plaque regression and progression [3,4] and thereby promoteevaluation of cholesterol-lowering therapy [5,6] for reduction of cardiovascular
events.
Diagnostic ultrasound is widely used for morphology imaging of the arterial
wall. In clinical observation of the carotid artery with ultrasound, it is difficult toaccurately image an artery with atherosclerotic plaque or the carotid sinus
because they are not flat and ultrasonic beams does not incident normal to the

719

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wall in the case of conventional linear scanning. This paper describes a method
for accurately imaging such targets by steering ultrasonic beams.
For the evaluation of dynamic mechanics, arterial elasticity has been
determined by measuring the pulse wave velocity [7] and the rough change inthe diameter of the artery [8]. However, the mechanical property of plaquecannot be directly determined by these methods because they evaluate average
elasticity of the entire circumference. A method to detect the vulnerability ofatherosclerotic plaque with sufficient accuracy has not yet been reported. The
purpose of the present study was to determine the regional elasticity of thearterial wall and tissue characterization. At the last, arterial motion along in its
longitudinal direction, which is lateral to the ultrasound beam, was measured.
2. Methods
2.1. Beam steering for accurate B-mode imaging [9]Figure 1 shows a schematic diagram of the beam steering. The ultrasonic beamscans M positions along the x-axis by conventional linear scanning. The depthof the arterial wall, yi (i =1, 2, ..., M ), at each beam position, xi (i =1, 2, ..., M ),is manually predetermined in the B-mode image obtained by conventional linear
scanning. The interval between the neighboring ultrasonic beams is defined by
Δx = xi+1 - xi. With respect to each position, (xi, yi), of the i-th ultrasonic beam on
the wall, a regional slope, aw,i, of the arterial wall to the surface of the ultrasonicprobe is estimated by the least-squares method using positions, {(xi, yi)}, of
neighboring ±N ultrasonic beams on the arterial wall, as follows:a w ,i =

N
⎛ N
⎞⎛ N
⎞
( 2 N + 1) ∑ x i ⋅ y i − ⎜ ∑ x i ⎟⎜ ∑ y i ⎟i=− N⎝ i = − N ⎠⎝ i = − N ⎠⎛⎞( 2 N − 1) ∑ x i2 − ⎜ ∑ x i ⎟i=− N⎝ i=− N ⎠
N

N

2

.

(1)

From the estimated aw,i, the slope, ai, and the angle, θi, of the beam that isperpendicular to the arterial wall at (xi, yi) are determined as follows:
1

,

(2)

θ i = tan −1 ai .

(3)

ai = −

a w ,i

From the determined θi (rad) and the (xi, yi) of the arterial wall, the center, bi, of
the aperture that transmits an ultrasonic beam to (xi, yi) is given by721

bi = xi −yiy= xi − i .
tan θ iai

(4)

By determining θi and bi (mm) for all positions, {(xi, yi)}, on the wall, all beams
are designed to be perpendicular to the arterial wall.
In this study, θi is assigned in discrete values. Therefore, the discrete beam
angle, θ ′i , that is the nearest to θi is selected from pre-assigned angles of K
beams. The bi of the aperture is calculated again using θ ′i. The bi of the aperture
should be also assigned in a discrete value that depends on the element pitch of
the ultrasonic probe. The discrete transmit position, b′i, of the aperture, which isnearest to bi, is selected, as well as θ ′i. In this way, the ultrasonic beam istransmitted to the position, (x ′i, y ′i), on the wall as perpendicular as possible.
Although the designed ultrasonic beam does not exactly pass through the (xi, yi)
because of the discrete values of b ′i and θ ′i, the difference, |x ′i - xi|, is less thanhalf the element pitch.

Fig. 1. Determination of optimum beam position and angle (N = 1).

2.2. Elasticity estimation and tissue characterization based on axial
motion estimation

2.2.1. Axial motion estimation by “phased tracking method” [10]An ultrasonic beam was sequentially scanned at M positions with a linear-typeultrasonic probe of 7 MHz using conventional ultrasound diagnostic equipment(Toshiba SSH-140A), and multiple (Nm+1) points were preset from the luminal
surface to the adventitia along the m-th ultrasonic beam (m=1, …, M) withconstant intervals of h0=375 μm at a time t0 just before the ejection period. By
dividing the arterial wall into multiple layers, we defined the n-th layer (n =1, …,

722Nm) as being between two contiguous points, n and n+1, along each beam. For
measurement of the change in thickness of each of the Nm layers, theinstantaneous depth xm,n(t) of the n-th point along the m-th beam wassimultaneously tracked by applying the phased tracking method [10] to thereceived ultrasound. The minute decrease of several tenths of a micrometer inthickness of the n-th layer resulting from the arrival of the pressure wave at the
beginning of the ejection period was determined by Δhm,n(t) = xm,n+1(t) - xm,n(t) h0.
2.2.2. Radial strain and elasticity estimated by axial displacements
From the ratio of the maximum decrease in thickness during one heartbeat,Δhm,n,max=maxt|Δhm,n(t)|, to the initial thickness, h0, of the n-th layer, themaximum deformation of the n-th layer was obtained by Δεm,n,max=Δhm,n,max /h0.
Since the deformation was sufficiently small and was in the linear regime, it
showed incremental strain in the radial direction. By assuming that the arterial
wall is incompressible and that the blood pressure is applied normal to eachlayer, the elastic modulus of the n-th layer along the m-th beam, Eθ,m,n, isapproximately given by [11]1 ⎛ ρm, n, 0 Nm − n +1⎞ Δ p⎟
Eθ, m, n ≅ ⎜⎜+2 ⎝ h0Nm ⎟⎠ Δ εm,n,max(n = 1,..., Nm; m = 1,..., M ) ,(5)where ρm,n,0 is the initial inner radius of curvature of the n-th layer along the mth beam at time t0. We assumed that the pressure in the arterial wall decreases
linearly with the distance from the intimal side to the adventitia and that thearterial wall is almost isotropic.
For the region with a length of 18 mm (M = 60) along the axis of the artery,the regional elasticity Eθ,m,n was estimated on the cross-sectional image. Since
the reflected ultrasound was received at a sampling interval of 100 ns (=75 μm
along depth direction) after the quadrature demodulation, we further divided
each layer with a thickness of h0 into 5 points, shifted the initial depth of eachlayer by 1/5 of h0 and applied the above procedure to each depth. Thus, Eθ,m,n
was estimated at intervals of 75 μm in the depth direction and 300 μm in thelongitudinal direction of the arterial wall.
2.2.3. Arterial tissue characterization based on elasticity [12-14]
In this study, an elasticity image is classified using the likelihood function Li(i=1: lipid, 2: blood clot, 3: fibrous tissue, 4: calcified tissue) of the elasticity

723

distributions. To obtain the likelihood function of the elasticity distribution ofeach tissue, the elasticity distribution is translated using the normal distribution
to obtain the probability distribution. From in vitro experiments, the elasticity
distribution of each tissue, i, is obtained as illustrated in Fig. 2(a). The elasticity
distribution of each tissue consists of Ji data points with respective elastic
moduli (i =1: lipid, 2: blood clot, 3: fibrous tissue, 4: calcified tissue). Using alldata 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. 2(b).
In this sequence, the j-th datum ( j=1, ..., J1) has the corresponding elastic
modulus Ej (Ej<Ej+1) where j is named the elasticity number. It is clear in Fig.
2(a) that the mean elastic modulus of the distribution is largely different fromthe elastic modulus of the (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 (radial strain) of the arterial wall due to aheartbeat is measured using ultrasound. The measured change in thickness isexpressed by the sum of the actual change in thickness Δh and noise e of themeasurement system, and the elastic modulus is proportional to the reciprocal
1/(Δh+e) of the measured change in thickness. Therefore, the variance of theestimated elastic moduli increases with decreasing actual change in thickness(increasing elastic modulus) in comparison with the case of increasing change inthickness (decreasing elastic modulus). As a result, the elasticity distribution isbroadened at a high elastic modulus. Thus, as shown in Fig. 2(c), the normal
distribution is assumed with respect to the elasticity number j so that theprobability around the center of the ascending sequence made becomes the
maximum.

Fig. 2. Illustration of allocation of elasticities of elasticity distribution to boxes of normal
distribution. (a) Original elasticity distribution of the tissue. (b) Ascending sequence of elastic
modulus of elasticity distribution. (c) Probability distribution obtained using normal distribution.

The probability distribution of each tissue was obtained by allocating all thedata of Ji points of each tissue i to boxes of the normal distribution. The number

724

0.4

frequency [%]40

probability

60
(a−1)
50
lipid
40
_ 40 kPa
81+
30(N=425)
20
10
0 0
0.5
1
elastic modulus [MPa]

0.4

0.2
0.1

0

0

21 28 44 83 133192 245
elastic modulus [MPa]

(c−1)

3

fibrous tissue_ 0.63 MPa
1.0 +(N=5979)

2
1
0

(d−1)
calcified tissue_ 1.2 MPa
2.0 +(N=579)

3
2
1

0.2
0.1

1

2
3
4
5
elastic modulus [MPa]

6

(d−2)

0.3
0.2
0.1
0

0

(c−2)

0.3

0
0.09 0.30 0.71 1.6
3.0
0.19 0.45 1.1
2.2
elastic modulus [MPa]
0.4

1
2
3
4
elastic modulus [MPa]4frequency [%]0.4
probability

4

probablity

frequency [%]00.5
1elastic modulus [MPa]

0

(b−2)

0.3

10

0

0.1
12 22 50 83 131183
elastic modulus [MPa]blood clot
_ 56 kPa
95 +(N=301)

20

0.2

0

(b−1)

30

(a−2)

0.3

probability

frequency [%]of boxes, {Bi}, of the normal distributions is determined so that the number ofdata in the box for a box number, which is located at threefold the standard
deviation of the box number from the mean (mean ± 3×SD), becomes one. As
shown in Fig. 2(c), the number of data, Di,h (h=1, ..., Bi), included in each box isdetermined by following the line of the normal distribution. Then, the (Ji /2)-thdatum is included in the box with the highest probability. By allocating all thedata of Ji points of each tissue to boxes of the corresponding normal distribution,
the mean elasticity Ēi,h of the data included in each box is obtained.

0.53 0.73 1.2 2.1 4.0
elastic modulus [MPa]4.8

Fig. 3. Elasticity distribution and probability distribution of each tissue. (a) Lipid, (b) blood clot, (c)fibrous tissue, and (d) calcified tissue.

Figures 3(a-1), 3(b-1), 3(c-1), and 3(d-1) show the elasticity distributions
for lipids, blood clots, fibrous tissue, and calcified tissue, respectively, and Figs.
3(a-2), 3(b-2), 3(c-2), and 3(d-2) show the respective probability distributions,pi (Ēi,h), whose horizontal axis was labeled by the mean elasticity Ēi,h of the725

corresponding box Bi,h. When the elastic modulus Em,n measured at depth nalong the m-th ultrasonic beam is closest to the mean elasticity Ēi,h of the box
Bi,h, the probability p′i (Em,n) with respect to the elastic modulus Em,n wasdetermined to be pi (Ēi,h). For each pixel with the corresponding elastic modulus
Em,n, the region of interest (ROI) Rm,n of ±450 mm in the depth direction and±450 mm in the longitudinal direction of the artery is assigned. Thus, there are
up to 36 elastic moduli in the ROI. Using the probability distribution p’i (Em,n),the log likelihood function ln(Li) for the i-th class is obtained with respect toelasticities in Rm,n as

ln Li =∑ ln p ' ( E ).

( k ,l )∈Rm ,n

i

k ,l

(6)

However, the size of an ROI varies at the edge of an elasticity 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 the class thathas the largest likelihood.
For comparison, the elasticity image is also classified by the Mahalanobis
distance between the elasticity value of each single pixel and the elasticity
distribution of each tissue (mean±SD: lipids 81±40 kPa, blood clots 95±56 kPa,fibrous tissue 1.0±0.63 MPa, calcified tissue 2.0±1.2 MPa).
2.3. Lateral motion estimation [15]Using an ultrasonic probe of 10 MHz, an ultrasound beam scans the carotid
artery in its longitudinal direction at 70 positions with intervals of 0.1 mm. At
each position, RF echoes are acquired at a sampling frequency of 40 MHz. Let
us define the RF signal at beam position b and depth d in n-th frame. A B-mode
image can be constructed with a 2-dimensional (radial-longitudinal of theartery) data set obtained by one scanning, which is called as frame. To reduce
the spacing between RF lines, which is a factor limiting the spatial resolution in
the measurement of the displacement which is lateral to the ultrasonic beam,
K RF lines, rf ′n(d, b + k/(K +1)), are interpolated between original RF lines,
rfn(d, b), using the linear interpolation as follows:k ⎞ ( K + 1 − k ) rf n ( d , b ) + k ⋅ rf n ( d , b + 1)⎛
rf 'n ⎜ d , b +
.
⎟=
K +1⎠
K +1
⎝
( k = 1, 2, ..., K )(7)

Each interval of 2 RF lines is shown by Δxe (K) = 0.1/(K + 1) [mm]. Then, thelateral displacement, xl (n), is estimated using the correlation function, γ (n; Δm,726Δl), between two frames including interpolated RF echoes. The correlation
function between n-th and (n+ΔN)-th frames including interpolated RF lines isobtained with respect to each axial and lateral shifts, Δmn and Δln, of the regionof interest (ROI) in the (n+ΔN)-th frame relative to the position of ROI in the nth frame. The axial and lateral displacements between n-th and (n+ΔN)-thframes are determined from the axial and lateral shifts, Δmn and Δln, which givethe maximum correlation coefficient. In this study, the ROI size is 5.8 mm× 0.2mm, and the interval for calculating the correlation is 52 ms (ΔN = 10). Δmn andΔln are changed from -0.08 mm to 0.08 mm and from -0.2 mm to 0.2 mm,
respectively.
Lateral and axial average velocities, vl (n) and vr (n), between n-th and(n+ΔN)-th frames are calculated by lateral and axial shifts, Δln and Δmn,
respectively. Lateral and axial displacements, Δxl (n) and Δxr (n), between n-thand (n+1)-th frames are calculated by lateral and axial average velocities vl (n)and vr (n). Lateral and axial displacements, xl (n) and xr (n), at each frame are
estimated by accumulating instantaneous displacements, Δxl (n) and Δxr (n),during a frame interval obtained from average velocities, vl (n) and vr (n). The
position of ROI in the (n+1)-th frame is determined by the lateral and axial
displacements, xl (n) and xr (n).
3. Results
3.1. Accurate B-mode imaging of carotid sinus

3.1.1. Basic experiment using a phantom
The shape of the phantom simulates the arterial wall at the carotid sinus and thephantom has a hollow. The width of the hollow is 15 mm, and the depth is 2.5
mm. The phantom was fixed in a water bath and it was measured using
diagnostic equipment (Aloka SSD-6500) with a conventional linear-typeultrasonic probe at 10 MHz. The distance from the surface of the ultrasonicprobe to the surface of the phantom was 13 mm. 105 ultrasonic beams withintervals, Δx, of 0.2 mm are transmitted in a frame, and the beam angle, θ ′i, waschanged by 2º frame by frame from θ ′i (1)=70º to θ ′i (21)=110º during 21
frames. Therefore, the elapsed time for acquiring the RF data of 21 frames was
165 ms in the case of a frame rate of 127 Hz in this experiment. Ultrasonic RF
echoes were acquired at a sampling frequency of 40 MHz. Figure 4(a) shows a
B-mode image of the object obtained by conventional linear scanning using 105
ultrasonic beams (θ ′i (11)=90º). The surface of the phantom was manually727

assigned at 105 positions {(xi, yi)} (i =1, 2, ..., 105) on the B-mode image[dotted line in Fig. 4(a)]. The beam, with angle θi and transmit position bi, that isperpendicular to the surface of the phantom was determined using {(xi, yi)}. The
yellow lines in Fig. 4(b) show the calculated optimum beams. Then, the beamwith θ ′i and b′i was selected. Figure 4(c) shows a B-mode image constructedfrom the ultrasonic RF echoes obtained using the calculated beams with {( θ ′i,b′i)}. As shown in the areas surrounded by circles in Fig. 4(a), the surface of thephantom could not be imaged clearly in the areas where the ultrasonic beams
incline from a vertical direction by more than 20° as shown in the B-mode
image obtained by conventional linear scanning. On the other hand, strong
reflected echoes were obtained in such areas using the proposed method, and thephantom was imaged over the entire scanned area, as shown in Fig. 4(c).

Fig. 4. (a) B-mode image obtained by conventional linear scanning (red line: assigned silicone
surface). (b) Calculated beams (yellow lines) superimposed on B-mode image. (c) B-mode image
obtained by proposed method.

3.1.2. In vivo measurement at a carotid artery
A human common carotid sinus of a 25-year-old male was measured in thelong-axis plane. To reduce the elapsed time for acquiring RF data, ultrasonicbeams were transmitted every 5° from θ ′i (1)=70° to θ ′i (9)=110° and discrete
steered angles, {θ ′k}, were changed frame by frame during nine frames.
Ultrasonic RF data were acquired during nine frames (82 ms at a frame rate of
110 Hz) just before the time of the R-wave of the electrocardiogram. Figure 5(a)shows a B-mode image obtained by conventional linear scanning, composed of
105 ultrasonic beams with intervals, Δx, of 0.2 mm (θ ′i (5)=90º). The red line in
Fig. 5(b) shows the assigned (xi, yi) of the posterior wall, and the yellow lines inFig. 5(b) show the calculated optimum beams. Figure 5(c) shows a B-mode
image constructed from the ultrasonic RF echoes obtained using the calculated
beams with {(θ ′i, b′i)}. As shown by the area surrounded by a circle in Fig. 5(a),728

the intima-media complex could not be imaged clearly by conventional linear
scanning in the area where the ultrasonic beams incline from the perpendicular
direction relative to the wall by more than 2.5º. However, sufficient reflectedechoes were obtained from such an area using the proposed method, and theintima-media complex was almost imaged over the entire scanned area as shownin Fig. 5(c).

Fig. 5. (a) B-mode image obtained by conventional linear scanning. (b) Assigned posterior wall
surface (red line) and calculated beams (yellow lines) superimposed on B-mode image of (a). (c) Bmode image obtained by the proposed method.

3.2. Elasticity of extracted arteries measured in vitro and tissue
characterization

Figure 6(a) shows an elasticity image measured in vitro, and Fig. 6(b) shows thepathological image of the corresponding section. Lipids, blood clots, and fibrous
tissue are indicated by yellow, red, and blue dashed lines, respectively. In Fig.
6(c), the elasticity image was classified based on the Mahalanobis distance
between a single elasticity value of a pixel and the elasticity distribution of eachtissue. In Fig. 7, the elasticity image was classified based on the likelihood
between the elasticity distribution of each small region (not a single pixel) andthat of each tissue. In comparison with the result of the classification based on asingle elasticity value shown in Fig. 6(c), misclassified regions were reduced
using the likelihood function between elasticity distributions as shown in Fig. 7.
Figure 8 shows the tissue classification image obtained by analyzing thepathological 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 longitudinal direction of the arterial wall, and each mth 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,

729

and calcified tissue based on RGB values in each region in the pathologicalimage [13]. The regions classified as lipids, blood clots, fibrous tissue, andbackground were stained yellow, red, blue, and gray, respectively.

Fig. 6. (a) Elasticity image. (b) Corresponding pathological image. (c) Classification results based on
the elasticity value of each pixel.

Fig. 7. Classification results based on the elasticity distribution of each small region.

Fig. 8. Classification results based on the pathological image.

730

The correctness of the classification of each pixel was evaluated bycomparing tissue classification images shown in Figs. 6(c) and 7 with that in Fig.
8 based on the pathological image. Using the likelihood, pixels classified into
lipids was found to cluster, and correctly classified pixels were increased (lipids:
32.9%, blood clots: 21.0%, fibrous tissue: 72.8%) in comparison withclassification based on a single elasticity value (lipids: 32.9%, blood clots:
17.4%, fibrous tissue: 64.2%).
3.3. In vivo lateral motion estimation in carotid artery

Figure 9 shows B-mode images of the same carotid artery of a 23-year-old
healthy male. In the initial frame (at 0 s), the region of interest (ROI) was
manually assigned as shown in Fig. 9(a). As shown in Fig. 9, the scan plane wasalmost parallel to the longitudinal direction of the artery. Therefore, in this case,the estimated axial and lateral displacements correspond to motions in the radial
and longitudinal direction of the artery.

Fig. 9. B-mode images of a carotid artery. (a) At 0 s. (b) At 52 ms.

Figure 10(a) shows the electrocardiogram, and Figs. 10(b) and 10(c) show
the estimated lateral and axial displacement, respectively. In Fig. 10(b), theestimated lateral displacement was much improved by increasing the number ofinterpolated RF lines whereas the estimation of the axial displacement was not
influenced. Figure 11 shows the relationship between the longitudinal and radialdisplacements during cardiac cycles. In cardiac systole, the posterior wall moves
in the depth direction due to the diameter expansion, and it moves toward theheart. Such a longitudinal motion of the artery was considered to be due to the
motion of the heart and not due to blood flow because blood flows in the distal
direction in systole (opposite to the estimated displacement).

731

Fig. 10. (a) Electrocardiogram. (b) Estimated longitudinal displacement of the arterial wall. (c)Estimated radial displacement.

Fig. 11. Relationship between the longitudinal and radial displacements during cardiac cycles.

732

4. Conclusion

In this study, methods were proposed for accurate imaging of the carotid sinus
which cannot be assumed as a straight cylindrical shell, measuring mechanicalproperties of the arterial wall based on the axial motion estimation, and detailed
analysis of the artery motion based on the lateral motion estimation. Suchmethods for detailed analysis of the morphology and dynamic mechanics of theartery have potential for providing useful information on diagnosis ofatherosclerosis.
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