Japanese Journal of Applied Physics
Vol. 47, No. 5, 2008, pp. 4165–4169#2008 The Japan Society of Applied Physics

Ultrasonic Measurement of Transient Change in Stress–Strain Propertyof Radial Arterial Wall Caused by Endothelium-Dependent Vasodilation
Kazuki I KESHITA, Hideyuki H ASEGAWA, and Hiroshi KANAI
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan(Received November 22, 2007; accepted January 30, 2008; published online May 23, 2008)

The endothelial dysfunction is considered to be an initial step of atherosclerosis. Additionally, it was reported that the smoothmuscle, which constructs the media of the artery, changes its characteristics owing to atherosclerosis. Therefore, it is essential
to develop a method for assessing the regional endothelial function and mechanical property of the arterial wall. There is aconventional technique of measuring the transient change in the diameter of the brachial artery caused by ﬂow-mediateddilation (FMD) after the release of avascularization. For more sensitive and regional evaluation, we developed a method of
measuring the change in the elasticity of the radial artery due to FMD. In this study, the transient change in the mechanicalproperty of the arterial wall was further revealed by measuring the stress–strain relationship during each heartbeat. The minutechange in the thickness (strain) of the radial arterial wall during a cardiac cycle was measured by the phased tracking method,
together with the waveform of blood pressure which was continuously measured with a sphygmometer at the radial artery. The
transient change in stress–strain relationship during a cardiac cycle was obtained from the measured changes in wall thickness
and blood pressure to show the transient change in instantaneous viscoelasticity. From the in vivo experimental results, thestress–strain relationship shows the hysteresis loop. The slope of the loop decreased owing to FMD, which shows that theelastic modulus decreased, and the increasing area of the loop depends on the ratio of the loss modulus (depends on viscosity)
to the elastic modulus when the Voigt model is assumed. These results show a potential of the proposed method for thethorough analysis of the transient change in viscoelasticity due to FMD. [DOI: 10.1143/JJAP.47.4165]
KEYWORDS: ultrasound, atherosclerosis, FMD, stress–strain property, viscoelasticity

1.

Introduction

The main cause of circulatory diseases is considered to beatherosclerosis. Therefore, the quantitative assessment of
atherosclerosis is essential for making an early diagnosis ofthese diseases. The endothelial dysfunction is considered to
be an initial step of atherosclerosis.1) Additionally, it wasreported that the smooth muscle, which constructs the mediaof the artery, changes its characteristics owing to atherosclerosis.2) Consequently, it is important for early preventive
treatment to noninvasively assess the endothelial function
and the mechanical property of the media mainly composedof smooth muscle.
Endothelial cells react to the shear stress caused by theblood ﬂow and produce nitric oxide (NO), which is known
as a vasodepressor material. The smooth muscle is relaxedby the produced NO. This function is important for
maintaining the homeostasis of the vascular system. Smoothmuscle cells in the media are classiﬁed into two types with
diﬀerent functionalities.3) The composite type is proliferative, and the contractional type contracts and relaxes as
responses to chemical and mechanical stimuli. When the
blood vessel has initially formed, smooth muscle cellschange their type from composite to contractional, andcontrol blood ﬂow and blood pressure. On the other hand,
after the vascular system is established, smooth muscle cellschange their characteristics from contractional to composite
owing to atherosclerosis. The composite type is related to thegrowth factor and accelerates the migration of smoothmuscle cells to the intimal layer. Therefore, as describedabove, the evaluation of the endothelial function andcharacteristics of smooth muscle cells is important for the
early diagnosis of atherosclerosis.
For the evaluation of the endothelial function, there is aconventional technique of measuring the transient change in

the inner diameter of the brachial artery caused by ﬂowmediated dilation (FMD) after the release of avascularization.4) For more sensitive and regional evaluation, wedeveloped a method of directly measuring the change inthe elasticity of the intima-media region due to FMD.5) In
this study, the proposed method was applied to themeasurement of the radial artery. There is an inversely
proportional relationship between the percent change in
inner diameter due to FMD and that in the inner diameter of
the artery at rest, because the ﬂow velocity, which aﬀects theshear stress, is inversely proportional to the square of theinner diameter when the pressure and ﬂow volume areconstant.6) Therefore, the radial artery would be a moresuitable site for the measurement of FMD.
Furthermore, the blood pressure can be measured
continuously at the radial artery, which realizes thenoninvasive evaluation of the stress–strain relationshipduring each heartbeat. The transient change in viscoelasticity was investigated from the measured stress–strain
relationship.
2.

Experimental Methods

2.1

Estimation of minute change in thickness of arterial
wall
The minute change in the thickness of the radial arterial
wall hðtÞ at time t during a cardiac cycle was measured by
the phased tracking method.7)
To obtain the change in thickness, the velocities of theartery wall boundaries were estimated. The velocity vðt; dÞ atthe depth d (d: initial depth at t ¼ 0) was estimated from thephase shift ðt; dÞ of echoes in two consecutive frames.
The phase shift ðt; dÞ was obtained using the complex
cross-correlation function rðt; dÞ applied to the demodulated
signal zðt; dÞ of RF echoes asE-mail address: ikeshita@us.ecei.tohoku.ac.jp4165

c dÞ ¼
exp½ jðt;rðt; dÞ
;jrðt; dÞj

ð2:1ÞJpn. J. Appl. Phys., Vol. 47, No. 5 (2008)

rðt; dÞ ¼

M
X

K. IKESHITA et al.

RF signal
z ½t; d þ xðt; dÞ þ mD

m¼M

custom−madeacquisition
system z½t þ T; d þ xðt; dÞ þ mD;
where xðt; dÞ, D,  and M are the displacement of theobject at the depth d in the depth direction, the samplinginterval in the depth direction, a complex conjugate, and ahalf width of the correlation window, respectively. Fromc dÞ, the average velocity
the estimated phase shift ðt;v^ðt; dÞ of the arterial wall during a pulse repetition interval
T was obtained asv^ðt; dÞ ¼ 

c dÞ
ðt;
c0 
;
T
2!0

pulse transmit trigger ultrasonic
ECG

diagnostic
equipment

frame trigger

blood pressure
waveform

ultrasonic probe(transmit: 22 MHz)

sphygmometerleft handð2:2Þ

where !0 and c0 are the center angular frequency of theultrasound wave and the speed of sound, respectively. Thechange in thickness, hðtÞ, between two diﬀerent depths,dA and dB , in the arterial wall along an ultrasonic beam
was obtained from the diﬀerence between displacements,
xðt; dA Þ and xðt; dB Þ, at these two positions ash^ðtÞ ¼ x^ðt; dA Þ  x^ðt; dB Þ
Zt
¼ ½v^ðt; dA Þ  v^ðt; dB Þ dt:
ð2:3Þ

right hand

probe

cuff

0

The change in thickness, hðtÞ, corresponds to theincremental strain in the arterial radial direction at thetime t due to the pressure increment pðtÞ from thediastolic pressure. Therefore, from the maximum changes
in wall thickness hmax ¼ maxt jhðtÞj and pulse pressurepmax ¼ maxt jpðtÞj, which is the diﬀerence between thesystolic and diastolic pressures, the approximate circumferential dynamic elastic modulus Eh (Pa) was obtained as8)


1 r0
pmax
Eh 
þ1
;
ð2:4Þ
hmax
2 h0
h0
where r0 and h0 are the internal radius and wall thickness
at the end diastole, respectively.
2.2 Procedure for in vivo measurement
The right radial artery of a healthy male subject (33years old) was measured. In the measurement of the radial
artery (Fig. 1), ultrasonic RF echoes (transmit: 22 MHz)
were acquired at a sampling frequency of 66.5 MHz and aframe rate of 169 Hz for 2 s. This acquisition was repeatedevery 20 s for 2 min at rest before avascularization andevery 12 s for 3 min after recirculation. Together with theRF signals, the waveform of blood pressure pðtÞ in the leftradial artery was continuously measured with a sphygmometer at a sampling frequency of 169 Hz (frame rate).
In this study, a sphygmometer (Colin JENTOW-7700),
which automatically optimizes the position of the sensor
for blood pressure measurement by detecting the regionalpulsation of the radial artery, was used for the continuous
measurement of the blood pressure waveform pðtÞ for about
10 min. However, the sphygmometer always requires thearterial pulsation to optimize the position of the sensor. In
this measurement, therefore, the sensor of the sphygmometer
was placed in the left arm, in which avascularization was not
induced. The transient change in stress–strain relationshipFig. 1. (Color online) Ultrasonic measurement of radial artery.

during a cardiac cycle due to FMD was obtained from themeasured change in thickness, hðtÞ, of the arterial wall ineq. (2.3) and from the blood pressure pðtÞ.
3.

Results

3.1 Calibration of time delay
The delay of the strain from the applied stress isdetermined on the basis of the viscoelasticity of the material.
The experimental apparatus employed in this study has two
factors, which lead to undesirable time delays.
(1) The sphygmometer incorporates a low pass ﬁlter(LPF), which leads to a time delay in the output of
the waveform of blood pressure. The time delay of theanalog LPF depends on the inverse of the cutoﬀ
frequency.
(2) The blood pressure is measured in the left radial artery,whereas the strain is measured in the right radial artery.
In this study, the time delay 1 due to factor (1) isevaluated by simultaneously measuring the pulsation of theleft radial artery using the sphygmometer and a pressure
sensor with a much smaller time delay (maximum frequency
response: 20 kHz). The pressure sensor was manually placed
and used for measurement during a short period (2 s) at
almost the same place as the sphygmometer on the skinsurface over the radial artery. The time delay 2 due to factor(2) is evaluated by measuring the waveforms of velocities ofthe left and right radial arterial walls by the ultrasonicphased-tracking method.
Figure 2(1-a) shows the waveforms measured using the
sphygmometer and the pressure sensor. The waveform
measured using the sphygmometer was delayed by about
25 ms from that measured using the pressure sensor. Thus,
1  25 ms.

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Jpn. J. Appl. Phys., Vol. 47, No. 5 (2008)

τ1 = 25ms(1)
normalized blood pressure

K. IKESHITA et al.

pressure sensor
sphygmometer

(a)

1

(b)

0.8

25 ms

0.6
0.4
0.2
0

0

200

400

600

800

1000

0

200

400

600

800

time [ms](2)velocity [ vi (t) ]10.0012

correlation [vi (t) and v’i (t)](b)

10.0004

0.4

0

–0.4

–0.0004
0.0012

–0.8
–1
0.8

0.00080.0004

0

200
400
600
800
time delay [ms] from R–wave

1000

200

1

0

–1
0

150

τ L =150ms

τ R =150ms(b)

τ R =150ms

(c)
0.7

0.4
100

–0.8
–0.0004

0.4
100

0.4

–0.4

0

(c)

0.7

τ L =150ms

0(a)correlation

correlation

0.0008correlation

velocity [m/s]

(3)

0.8

correlation

velocity [m/s](a)v’i (t)1000
time [ms]

100

200
300
400
500
time delay [ms] from R–wave

200
150
time delay [ms] from R–wave

600

Fig. 2. (1) Correction of delay caused by experimental system. For (2) left and (3) right radial arteries, (a) velocities of arterial walls,(b) correlation functions, and (c) enlarged views of (b).

Figures 2(2-a) and 2(3-a) show the wall velocities vi ðtÞ ofthe left and right radial arteries, respectively, for seven andeight cardiac cycles consecutively measured using ultrasound. The waveforms are ECG-triggered. Figures 2(2-b)
and 2(3-b) show the correlation functions between the
waveforms of the wall velocities vi ðtÞ (i ¼ 1, 2, . . ., 7 or 8) of
seven or eight heartbeats and the waveform v0 i ðtÞ during theperiod indicated by the dotted lines in Figs. 2(2-a) and2(3-a). Figures 2(2-c) and 2(3-c) show the enlarged views of
the periods between the dotted lines in Figs. 2(2-b) and2(3-b). As shown in Figs. 2(2-c) and 2(3-c), there is almost
no diﬀerence between the time delay from the R-wave in theleft arm L and that in the right arm R when the samplingintervals Ts of velocity waveforms are 0.33 ms, because thetime delay 2 means the diﬀerence between L and R , thatis, 2 < Ts  1 . The same procedure can be applied toother subjects to evaluate the diﬀerence in the arrival time ofthe pulse wave between the left and right arms prior to themeasurement of FMD.
3.2 In vivo experimental results for healthy subjects
RF data for 2 s obtained by each acquisition included atleast an entire cardiac cycle. Consequently, the changes inthickness hðtÞ and blood pressure pðtÞ were obtained for atleast one cardiac cycle in each measurement to estimate theelasticity Eh of the radial arterial wall.
Figure 3 shows the results of the measurement of thechange hðtÞ in the intima-media thickness of the rightradial artery in a healthy 33-year-old male for 2 s. As
shown in Fig. 3(a), the initial positions k and l of thelumen-intima and media-adventitia boundaries of theposterior wall were determined manually on the M-mode
image by referring to the RF echo from the posterior wall
sampled at 66.5 MHz. Then, the instantaneous positions ofthese points were automatically tracked, as shown by thelines, by the phased tracking method. Figures 3(b) and 3(c)show the electrocardiogram and blood pressure waveformpðtÞ, respectively. The time delay 1 in the waveform of theblood pressure pðtÞ was corrected, as described in theprevious section. Figures 3(d) and 3(e) show the estimatedvelocities at k and l, respectively. The change in the
thickness of the intima-media region, hðtÞ, was calculatedby the temporal integration of the diﬀerence between thesevelocities, as shown in Fig. 3(f). The minute change inthickness, hðtÞ, for two cardiac cycles was measured with
suﬃcient reproducibility. The stress–strain characteristicsof the intima-media region of the radial artery for eachmeasurement were obtained using the measured bloodpressure waveform [Fig. 3(c)] and the change in thickness[Fig. 3(f)].
Figure 4(a) shows the transient change in inner diameterd, which was manually determined by referring to the RFecho obtained at each R-wave of ECG, and that in theelasticity Eh of the intima-media region. Figure 4(a) showsthat the percent change in measured elasticity Eh is muchlarger than that in diameter d measured by the conventional
method. Moreover, the increase in inner diameter wasmeasured after the decrease in elasticity, and a diﬀerence
was observed between the time of the maximum increase in
inner diameter d and that of the maximum decrease inelasticity Eh . The elasticity Eh began to recover to its
original value before avascularization when the diameter

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Jpn. J. Appl. Phys., Vol. 47, No. 5 (2008)

K. IKESHITA et al.

(a)depth 2.5 mm

k
l

(b)

ECG
116 mmHg(c)blood pressure 0
38 mmHg
2 mm/s(d)

0−2 mm/s
2 mm/s(e)

0−2 mm/s
10 μ m(f)

0−10 μ m
0

0.5

1.0

1.5

time [s]Fig. 3. (Color online) (a) M-mode image of radial artery (healthy 33-year-old male). (b) Electrocardiogram. (c) Blood pressure
waveform pðtÞ. (d) Velocity at lumen-intima boundary (LIB). (e) Velocity at media-adventitia boundary (MAB). (f) Change in
intima-media thickness of posterior wall, hðtÞ.

(a) avascularization recirculation
300 s
2200 inner diameterelasticity [kPa]

3.2

1800
1400

600

(1)

200 0 60 120 0
time [s](b)130blood pressure [mmHg]

2.9

(5)
(2)

120
110
100
90
80
70
60

2.6

(4)

2.3

(3)
40

80

(5)

(1) (2) (4)120 160 2.0
time [s]inner diameter [mm]3.5elasticity

1000

Figure 4(b) shows the transient change in stress–strain
relationship between the change in thickness and the bloodpressure. The change in stress–strain relationship shows thehysteresis property. The time when each hysteresis loop was
measured is indicated by an arrow in Fig. 4(a).
The slope and area A of the hysteresis loop changed
gradually. The slope of the loop decreased owing to FMD,
which shows that the elastic modulus decreased. In addition
to the change in slope, the change in the area A of thehysteresis loop is shown in Fig. 5. Figure 5 shows that the
maximum area of the loop Amax immediately follows
recirculation and the area of the loop comes aroundgradually. The area of the loop depends on the ratio of theloss modulus ! (!: angular frequency of strain, :viscosity) to the static elastic modulus Es when the Voigt
model is assumed. The maximum decrease in elasticity Ehwas measured at 22 s after the release of the cuﬀ, and the
maximum area of the loop Amax was found immediately
following recirculation (7 s), which results from the decreasein elastic modulus Es and the increase in viscosity .

(3)

4 2 0 −2 −4 −6 −8 −10 −12change in thickness during heartbeat [μm]4.

(Color online) (a) Transient changes in elasticity EhFig. 4.
of intimamedia region of radial artery and inner diameter d. (b) Transient change
in relationship (hysteresis) between blood pressure pðtÞ and change inthickness hðtÞ.

began to increase (at 40 s after recirculation). The time andmagnitude of these percent changes are comparable to thosereported in the literature.5)
To reveal the change in the stress–strain relationship of
the arterial wall due to FMD, the blood pressure pðtÞ and thechange in the thickness of the intima-media region, hðtÞ,during a cardiac cycle during FMD were measured.

Discussion

Figure 4(a) shows the transient changes in the innerdiameter d and elasticity Eh of the intima-media region of theradial artery due to FMD. To reveal the change in the stress–
strain relationship of the arterial wall due to FMD, thetransient change in the relationship between the change in the
blood pressure pðtÞ and the change in the thickness of theintima-media region, hðtÞ, (respectively correspond to thestress and strain) during a cardiac cycle and that in the area ofhysteresis loop are shown in Figs. 4(b) and 5, respectively.
Figure 4(b) shows the gradual transient change in stress–
strain relationship. The relationship shows the hysteresis
property, and it is caused by the viscoelasticity of the arterial

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area of hysteresis loop [mmHg · μm]

Jpn. J. Appl. Phys., Vol. 47, No. 5 (2008)

avascularization

300

K. IKESHITA et al.

recirculation

300 s

area of hysteresis loop

Amax

200
Fig. 5. Transient changes in areas A of hysteresis
loops shown in Fig. 4(b).

100

0

0

60

120

0

40

80

120

time [s]time [s]wall. By deﬁning the applied stress as  ¼ 0 cos !t, thestrain of a viscoelastic material explained using the Voigt
model can be expressed as ¼ 0 cosð!t  Þ;!
 ¼ tan1
:
Es

160

ð4:1Þ

the transient change in stress–strain relationship by the
proposed method showed the suitability of the proposed
method for the clariﬁcation of the transient changes in thefunctional and mechanical characteristics of the intimamedia region during FMD.
5.

By assuming that Es and  are independent of the magnitudeof stress, the area A of the hysteresis loop is calculated asI
A ¼  d ¼ 0 0 sin :
ð4:2Þ
PActually, the stress should be expressed as  ¼ ! 0 cos !t.
Therefore, the area of the hysteresis loop depends on thephase lags  of strains  from stresses , at multiple
frequencies ( f ¼ !=2).
In Fig. 5, the maximum area of the loop was found
immediately following recirculation (7 s). It was consideredthat the viscosity  at 7 s is larger than that at 22 s, because
the area at 7 s is larger than that at 22 s whereas the slope(corresponds to elasticity) at 7 s is similar to that at 22 s.
After 22 s, the area of the loop, A, decreased to that at rest, as
the slope (= elasticity) increased to that at rest. Although thephysiological meanings of the decrease in elasticity and theincrease in the area of the stress–strain loop that begin
immediately after recirculation prior to the dilation ofdiameter should be further investigated, the measurement ofConclusions

In this study, we measured the transient change in the
stress–strain relationship of the intima-media region of theradial artery due to FMD. The proposed method showed apotential of the thorough analysis of the transient change inmechanical property caused by FMD in addition to theevaluation of the endothelial function.
1) R. Ross: New Engl. J. Med. 340 (1999) 115.
2) Y. Matsuzawa: Nippon Rinsho 51 (1993) 1951 [In Japanese].
3) M. Yamamoto and K. Yamamoto: Nippon Rinsho 51 (1993) 1980
[in Japanese].
4) M. C. Corretti, T. J. Anderson, E. J. Benjamin, D. Celermajer, F.
Charbonneau, M. A. Creager, J. Deanﬁeld, H. Drexler, M. GerhardHerman, D. Herrington, P. Vallance, J. Vita, and R. Vogel: J. Am. Coll.
Cardiol. 39 (2002) 257 [Errata; 39 (2002) 1082].
5) T. Kaneko, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 46 (2007)
4881.
6) K. E. Pyke and M. E. Tschakovsky: J. Physiol. 568 (2005) 357.
7) H. Kanai, M. Sato, Y. Koiwa, and N. Chubachi: IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 43 (1996) 791.
8) H. Hasegawa, H. Kanai, N. Hoshimiya, and Y. Koiwa: J. Med. Ultrason.
31 (2004) 81.

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