Japanese Journal of Applied Physics 48 (2009) 07GJ10REGULAR PAPER

Flow-Mediated Change in Viscoelastic Property of Radial Arterial Wall
Measured by 22 MHz UltrasoundKazuki Ikeshita1 , Hideyuki Hasegawa2;1 , and Hiroshi Kanai1;2
12Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan

Received November 19, 2008; accepted March 22, 2009; published online July 21, 2009
The endothelial dysfunction is considered to be an initial step in atherosclerosis. Additionally, it was reported that the smooth muscle, whichconstructs the media of the artery, changes its characteristics owing to atherosclerosis. Therefore, it is essential to develop a method ofassessing the regional endothelial function and mechanical properties of the arterial wall. To evaluate the endothelial function, aconventional technique of measuring the transient change in the diameter of the brachial artery caused by flow-mediated dilation (FMD)
after the release of avascularization is used. However, this method can not evaluate the mechanical properties of the wall. We previously
developed a method for the simultaneous measurements of waveforms of radial strain and blood pressure in the radial artery. In this study,
the viscoelasticity of the arterial wall was estimated from the measured stress–strain relationship using the least-squares method and thetransient changes in the mechanical properties of the arterial wall ware revealed. From in vivo experimental results, the stress–strain
relationship showed a hysteresis loop and viscoelasticity was estimated by the proposed method. The slope of the loop decreased owing to
FMD, which resulted in the decrease in estimated elastic modulus. The increase in the area of the loop occurred after recirculation, whichcorresponds to the increase in the ratio of the loss modulus (depends on viscosity) to the elastic modulus when the Voigt model is assumed.
In this study, the variance in estimates was evaluated by in vivo measurement for 10 min. The temporal decrease in static elasticity afterrecirculation due to FMD was much larger than the evaluated variance. These results show a potential of the proposed method for thethorough analysis of the transient change in viscoelasticity due to FMD. # 2009 The Japan Society of Applied Physics
DOI: 10.1143/JJAP.48.07GJ10

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 in atherosclerosis.1) Additionally, it was reported thatthe smooth muscle, which constructs the media of the artery,changes its characteristics owing to atherosclerosis.2) Consequently, it is important for an early preventive treatment tononinvasively assess the endothelial function and mechanical properties of the media mainly composed of smoothmuscle.
Endothelial cells react to the shear stress caused by blood
ﬂow and produce nitric oxide (NO), which is known as avasodepressor material. The smooth muscle is relaxed as aresult of the response to the produced NO. This function isimportant for maintaining the homeostasis of the vascularsystem. Smooth muscle cells in the media are classiﬁed into
two types with diﬀerent functionalities.3) The composite
type is proliferative, and the contractional type contracts andrelaxes as responses to chemical and mechanical stimuli.
When the blood vessel is initially formed, smooth muscle
cells change 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 changeE-mail address: ikeshita@us.ecei.tohoku.ac.jp

in the inner diameter of the brachial artery caused by
ﬂow-mediated dilation (FMD) after the release of avascularization.4) For a more sensitive and regional evaluation, wedeveloped a method of directly measuring the change in theelasticity of the intima–media region due to FMD.5)
We propose a method for the evaluation of FMD, which
was previously applied to the measurement of the radial
artery. There is an inversely proportional relationshipbetween the percent change in inner diameter due to FMD
and that in the inner diameter of the artery at rest because theﬂow velocity, which aﬀects the shear stress, is inversely
proportional to the square of the inner diameter when thepressure and ﬂow volume are constant.6) Additionally, theblood pressure (stress) waveform can be continuously
measured in the radial artery, together with the minutechange in thickness (radial strain), which is measured using
the ultrasonic phased tracking method.7) From such measurements, we could determine the stress–strain relationshipduring each heartbeat.8) Therefore, the radial artery would bea more suitable site for the measurement of FMD.
In this study, from the stress–strain relationship during
each heartbeat, the viscoelasticity of the intima–media
region was estimated using the least-squares method, andthe transient change in viscoelasticity due to FMD wasestimated. In addition, the viscoelasticity at rest wasmeasured for 10 min to evaluate the variance in measurements.
2.

Principles and Experimental Methods

2.1

Estimation of minute change in thickness ofarterial wall for measuring stress–strain
relationship
The arterial wall is composed of three layers, namely,
intima, media and adventitia. The smooth muscle, whichconstructs the media, is the main source of the viscoelasticity of the vessel wall. Therefore, the dilation andcontraction of the artery depend on the characteristics ofthe media. The detailed analysis of the change in the

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K. Ikeshita et al.

The change in thickness, hðtÞ, corresponds to theincremental strain in the arterial radial direction at the time
t due to the pressure increment pðtÞ from the diastolicpressure.

2 cm

10 MHz(Conventional)

2.2
2 cm

22 MHzFig. 1. B-mode images of the radial artery along the longitudinal
axis (left) and in the plane perpendicular to the arterial longitudinal
direction (right).

viscoelasticity of the arterial wall due to FMD requires thein vivo measurement of the stress–strain relationship, which
has not been measured noninvasively thus far.
The blood pressure waveform can only be measured
noninvasively in vivo at the radial artery. However, it is
impossible to measure the strain of the radial arterial wall by
ultrasound at a typical frequency (10 MHz) in conventional
equipment. Therefore, we constructed an acquisition system
for high-frequency ultrasound.8) This system improved thespatial resolution in the axial direction. Therefore, thissystem allows more detailed measurements and analyses.
Figure 1 shows the B-mode images of the radial artery along
the longitudinal axis and in the plane perpendicular to theaxis of the artery.
To determine the stress–strain relationship, the minutechange in the thickness (strain) hðtÞ of the right radial
arterial wall during a cardiac cycle was measured using thephased tracking method.7) Together with the measurement of
RF signals for the estimation of hðtÞ, the waveform of
blood pressure (stress) pðtÞ in the left radial artery wascontinuously measured with a sphygmometer.
To obtain the change in thickness, the velocities of arterywall boundaries (lumen-intima and media-adventitia) were
estimated. The velocity vðtÞ was estimated from the phasec of echoes in two consecutive frames. The phaseshift ðtÞcshift ðtÞ was obtained using the complex cross-correlation
applied to the demodulated signals of RF echoes.
c the average velocity
From the estimated phase shift ðtÞ,v^ðtÞ of the arterial wall at the pulse repetition interval T was
obtained asv^ðtÞ ¼ 

c
c0 
ðtÞ
;
2!0 T

ð2:1Þ

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, A
and B (corresponding to the boundaries of the arterial wall),in the arterial wall along an ultrasonic beam was obtained
from the diﬀerence between displacements, xA ðtÞ and xB ðtÞ,at these two positions ash^ðtÞ ¼ x^A ðtÞ  x^B ðtÞ
Zt¼ ½v^A ðtÞ  v^B ðtÞ dt:
ð2:2Þ
0

Viscoelasticity estimation of arterial wall using
least-squares method
The smooth muscle constructs the media and is the main
source of the viscoelasticity of the arterial wall. We assumed
a viscoelastic model as a mechanical model of the arterial
wall to estimate its viscoelasticity.
There are many types of models for describing theviscoelasticity of the arterial wall. We selected a viscoelastic
model with two components to simply understand theviscoelastic behavior of the arterial wall; one component
corresponds to elasticity and the other to viscosity. In thisstudy, the Voigt model was used because the deformation of
the arterial wall during one cardiac cycle is reproducible
among cardiac cycles, and there is no permanent deformation. The Maxwell model, which is another model with twocomponents, was not used because it should be used for
viscoelastic materials showing a permanent deformation.
By assuming the Voigt model as a viscoelastic model ofthe intima–media region, the stress–strain relationship isgiven by^ðtÞ ¼ Es ðtÞ þ _ ðtÞ þ 0 ;

ð2:3Þwhere ^ðtÞ is the stress modeled by the Voigt model and ðtÞ,
_ ðtÞ, Es , and  are the strain, strain rate, static elasticity, andviscosity, respectively. In the in vivo measurement, themeasured strain ðtÞ is the incremental strain due to the pulsepressure, whereas the measured stress includes the bias
stress (diastolic blood pressure). Therefore, 0 is added to theright-hand side of eq. (2.3) as the bias stress corresponding
to diastolic pressure.
The parameters in eq. (2.3), Es , , and 0 , are estimatedusing the least-squares method by minimizing the meansquared error  between the measured ðtÞ and model ^ðtÞ
stresses and deﬁned by ¼ Et f½ðtÞ  ^ðtÞ2 g;

ð2:4Þ

where Et ½   indicates the averaging operation during a
cardiac cycle. The parameters E^s , ^ , and ^0 that minimize 
are determined by setting the partial derivatives of  withrespect to Es , , and 0 to zero as
@
¼ 0;
@Es

@
¼ 0;
@

@
¼ 0:
@0

ð2:5Þ

To solve the simultaneous equations, the optimum parameters that minimize  are determined.
2.3 Procedure for in vivo measurement
The right radial arteries of two healthy male subjects(subject A: 35 years old and subject B: 22 years old) were
measured. In these measurements, ultrasonic RF echoes(transmit: 22 MHz) were acquired at a sampling frequencyof 66.5 MHz for 2 s and the frame rate was about 160 Hz.8)
The acquisition for the evaluation of FMD was repeatedevery 20 s for 2 min at rest before avascularization and every
12 s for 3 min after recirculation. Together with the measurement of RF signals, the waveform of blood pressure pðtÞ in

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K. Ikeshita et al.

the left radial artery was continuously measured with asphygmometer (Colin Jentow-7700). Additionally, for theevaluation of reproducibility, RF data and the blood pressure
waveform at rest were measured every 1 min for 10 min. In
this study, a sphygmometer, which automatically optimizes
the position of the sensor for blood pressure measurement bydetecting the regional pulsation 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 the arterial pulsation to optimize theposition of the sensor. In this measurement, therefore, thesensor of the sphygmometer was placed in the left arm, inwhich avascularization was not induced.
The experimental apparatus employed in this study
showed undesirable time delays. We corrected the timedelay between stress and strain to determine the stress–strain
relationship that depended on only the viscoelasticity of
the arterial wall.8) The transient change in stress–strain
relationship during a cardiac cycle due to FMD was obtained
from the measured change in the thickness hðtÞ of thearterial wall and from the blood pressure pðtÞ.
3.

Blood Pressure [mmHg]

120

75

0

–2

–4
–6
–8
Change in Thickness [μm]–10

Figures 3(a) and 3(b) show the time sequence of the blood
ﬂow velocities and stress–strain relationships of subject A,
respectively. Blood velocity clearly increased immediately
after recirculation and the stress–strain relationship started tochange. Sixty seconds after recirculation, blood velocity
returned to its original value and the stress–strain relationship also came around gradually.
Figure 4(a) shows the transient changes in the means andstandard deviations (SDs) of the static elasticity Es andviscosity  averaged by 5 ultrasonic beams. These parameters were estimated from the stress–strain relationships
obtained from subject A (the ﬁrst measurement). The
transient change in static elasticity Es was similar to thatin a diﬀerent elastic parameter reported in the literature.5)
The minimum static elasticity Es was measured at 35 s after
the release of the cuﬀ. The maximum pecentage change instatic elasticity Es was about 57% (770 kPa). Moreover, theviscosity , which was evaluated noninvasively by the
proposed method, increased after recirculation. The measured viscosity was in the same range as the viscosity at the
carotid artery reported in the literature (in vitro measurement).9) The maximum viscosity  at 35 s after recirculation
was about 21 kPas, which was about 94% (10 kPas) larger
than the mean at rest.

In vivo experimental results for two healthy
subjects
RF data for 2 s obtained by each acquisition included at leastan entire cardiac cycle. Therefore, the changes in thicknesshðtÞ and blood pressure pðtÞ were obtained for at least one
cardiac cycle in each measurement for estimating theviscoelastic parameters of the radial arterial wall.
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. Figure 2
shows the transient change in stress–strain relationshipbetween the change in thickness and the blood pressure of
subject A. The stress–strain relationship showed hysteresis
property and gradually changed its shape. The slope of thehysteresis loop decreased owing to FMD, which shows thatthe elastic modulus decreased. In addition to the change inslope, the area of the loop clearly increased after recirculation. The area of the loop depended on the ratio of the loss
modulus ! (!: angular frequency of strain, : viscosity) tothe static elastic modulus Es when the Voigt model was
assumed.

radial artery

90

Fig. 2. (Color online) Transient change in relationship (hysteresis)
between blood pressure pðtÞ and change in thickness hðtÞ measured
in the radial artery in vivo.

3.1

(a)

105

60

Results

at restbefore avascularization
7s
20 s
35 s
65 s

recirculationECG

0.4 m/sblood velocity(b)Blood Pressure [mmHg]

7s

23 s

31 s

60 s

120

120

120

120

120

105

105

105

105

105

90

90

90

90

90

75

75

75

75

75

60

0

–2

–4

–6

–8

–10

Change in Thickness [μm]Fig. 3.

60

0

–2

–4

–6

7s

–8

–10

60

0

–2

–4

20 s

–6

–8

–10

60

0

–2

–4

–6

35 s

–8

–10

60

0

–2

–4

–6

–8

–10

65 s

(Color online) Time sequence of transient change in the blood velocity (a) and stress–strain hysteresis (b).

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Jpn. J. Appl. Phys. 48 (2009) 07GJ10
avascularization(5 min)recirculation

rest

20

700

10

Elasticity
30

60 120rest

avascularization(5 min)

60

90

120

150

elasticity [kPa]

30

1400

20

700

10

Elasticity

avascularizationrest(5 min)

(c)

60

90

120

150

700

10

Elasticity
30

60

60

90

150

90

120

150

180
time [s]

2000
1500
1000
500

20

0
120

0

static elasticity

2

4

40

20

0

30

Es

0
0

1400

0

0

2500

recirculation30

60 12060 1203000

180
time [s]21000Elasticity

Fig. 5. (Color online) Transient change in means and SDs ofestimated static elasticity Es and viscosity  measured in anothersubject (subject B).

0

Viscosity

2800
elasticity [kPa]

30

10

0

recirculation

2100

0

700

180
time [s]40

60 12020

0Viscosity

0

1400

0

2800

0

30

static elasticity [kPa]

(b)

0

0

40

2100

Viscosity [kPa ·s]

0elasticity [kPa]1400

viscosity [kPa ·s]

30viscosity [kPa ·s]elasticity [kPa]

Viscosity

2100

recirculation

Viscosity

2800

40

2800

avascularization(5 min)viscosity [kPa ·s]

rest

viscosity [kPa ·s](a)K. Ikeshita et al.

180
time [s]Fig. 4. (Color online) Transient change in means and SDs ofestimated static elasticity Es and viscosity  measured in subject A:(a) first, (b) second, and (c) third measurements.

Figures 4(b) and 4(c) show the transient changes in themeans and SDs of the static elasticity Es and viscosity 
measured in the same subject on other days (the second andthird measurements in subject A). The maximum percentagechange in static elasticity Es observed at 11 s afterrecirculation was about 36% (360 kPa) in the second
measurement, and that at 7 s after recirculation was about
50% (490 kPa) in the third measurement. The maximum
increase in viscosity  at 35 s after recirculation was about
73% (11 kPas) in the second measurement and that at 73 s
after recirculation was about 240% (23 kPas) in the third
measurement from the means at rest.
Figure 5 shows the transient change in the means and SDsof the static elasticity Es and viscosity  measured in anothersubject (subject B). The maximum percentage change instatic elasticity Es at 19 s after recirculation was about 55%(570 kPa). The maximum increase in viscosity  at 44 s afterrecirculation was about 571% (23 kPas) from the mean at

η

6
8
10
measurement No.

Viscosity

15
10
5
0
0

2

4

6
8
10
measurement No.

Fig. 6. (Color online) Means and SDs of static elasticity Es andviscosity  for 10 min in vivo measurements.

rest. The temporal decrease in elasticity Es and the increasein viscosity  were observed also in the another subject.
For the evaluation of reproducibility, RF data and theblood pressure waveform at rest were measured every 1 minfor 10 min. Figure 6 shows the means and SDs of themeasured static elasticity Es and viscosity . The SDs wereobtained from 30 ultrasonic beams. Horizontal dashed lines
show the means of the parameters.
Figure 6 shows the means and SDs of the parameters.
Table I shows the means and SDs of the parameters
averaged for 10 min. For the static elasticity Es , themaximum diﬀerence from the mean was about 200 kPa(17% of mean). The maximum change in static elasticity
due to FMD (770, 360, 490, and 570 kPa) was muchlarger than this value. For the viscosity , the variation inmean was 5 kPas. The maximum change in viscosity due
to FMD (10, 11, 23, and 23 kPas) was also much larger

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Table I. Means and SDs of parameters for 10 min in vivo measurements.
Static elasticity Es(kPa)

Viscosity (kPas)Average1225.1

11.6

SD

640.1

5.0

than this value. However, the patterns of the changes in thestatic elasticity Es and viscosity  after recirculation, and thetime for observing the maximal changes in these parameters
were diﬀerent among these measurements.
4.

Discussion

To reveal the change in the stress–strain relationship of thearterial wall due to FMD, as shown in Figs. 2 and 3, thetransient change in the relationship between the bloodpressure and the change in the thickness of the intima–media
region (correspond to the stress and strain, respectively)
during a cardiac cycle and the time sequence of thehysteresis loop and blood velocity were obtained. Figures 4
and 5 show the viscoelasticity estimated by the least-squares
method.
Figure 2 shows the gradual transient change in stress–
strain relationship due to FMD. The relationship shows
hysteresis property, which is caused by the viscoelasticity of
the arterial wall. Figures 3–5 show the gradual changes inshape and area of the loop, and the parameters (Es and ),
immediately measured after recirculation together with theincrease in blood velocity. The temporal increase in blood
ﬂow velocity indicates the temporal increase in shear stresson the arterial wall. After the blood ﬂow velocity camearound, the stress–strain relationship and estimated parameters gradually came around. These results suggest that thetransient change in viscoelasticity was caused by FMD.
Figure 6 shows the mean and SD of each parametermeasured every 1 min for 10 min at rest. The maximum
changes in static elasticity Es (770, 360, and 490 kPa) andviscosity  (10, 11, and 23 kPas) due to FMD obtained
from subject A were much larger than their ﬂuctuations atrest. The maximum changes in these parameters measured
in subject B (static elasticity Es : 570 kPa and viscosity :

23 kPas) were also much larger than their ﬂuctuations.
However, the ﬂuctuation in the mean of the estimatedviscosity  was large even at rest in the same subject
Fig. 6. One of the reasons for this is the noise containedin the strain rate that is ampliﬁed by the temporal diﬀerentiation of the measured strain. Therefore, it is necessary
to improve the precision in the measurement of strain rateby further investigation for the reduction in variance in theestimated viscosity. As described above, although there
are many aspects of this study that should be further
investigated, the obtained results show that the method
described in this paper can detect the changes in theviscoelastic properties of the arterial wall due to FMD. Sucha method would be beneﬁcial for the detection of early-stage
atherosclerosis.
5.

Conclusions

In this study, we measured the transient change in the stress–
strain relationship of the intima–media region of the radial
artery due to FMD. From the measured stress–strain
relationship, we estimated the viscoelasticity of the arterywall noninvasively. The proposed method showed a potential for the thorough analysis of the transient changes in themechanical properties of the intima–media region caused by
FMD in addition to the evaluation of the endothelial
function.

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