Non-invasive evaluation of Poisson’s ratio ofarterial wall using ultrasound
H. Hasegawa, H. Kanai, N. Chubachi and Y. Koiwa

Similarly, small velocity signals vIN(t) = vA(t) on the anterior walland vP(t) on the posterior wall of the artery are simultaneously measured and the change in inner diameter, ∆d(t), of the blood vessel withamplitudes of several hundred micrometres is also obtained by integrating the difference between these two velocity signals:

Indexing terms: Ultrasonic measurement, Biomedical measurement
A new method for non-invasively evaluating the Poisson ratio of anarterial wall using ultrasound is presented.

Introduction: In the early stage of atherosclerosis, fibrous spots several millimetres in diameter are scattered on the surface of the artery.
After growth of these spots, the arterial wall becomes homogeneously hard in the final stage of atherosclerosis. A major concern inthe early diagnosis of atherosclerosis has been, therefore, to develop
a non-invasive method for evaluating the elasticity of each local areaon the arterial wall.
In this Letter, velocity signals on the surface of the intima andadventitia are simultaneously measured and any change in the thickness of the arterial wall is accurately obtained by integrating the difference between these two velocity signals. Similarly, small velocity
signals on the surface of the anterior and the posterior wall aresimultaneously measured and a change in the diameter of the lumen
is obtained by integrating the difference between these signals. Basedon these changes in thickness and diameter, the Poisson ratio of thewall is evaluated. From in vivo experiments, the Poisson ratio isobtained for human carotid artery and abdominal aorta.
Principle: Small velocity signals, vIN(t) and vAD(t), on the intima andadventitia of the arterial wall are accurately measured using ultrasound by the following procedure [1]. RF pulses with angular frequency, ω0 = 2πf0, are transmitted at a time interval of ∆T from anultrasonic transducer on the skin surface. Defining the acoustic
velocity as c0, the instantaneous distance of an object on the arterial
wall from the ultrasonic transducer is denoted by x(t) = c0 · τ(t),where τ(t) is the instantaneous period required for one-way transmission from the ultrasonic transducer to the object. The ultrasonicpulse reflected by the object is received by the same ultrasonic transducer and is amplified. Applying quadrature demodulation to thesignal, the resultant in-phase and quadrature signals are simultaneously A/D converted and then separated into the response signals{y(x; t)} for each transmitted pulse, where x denotes the distance ofthe object from the ultrasonic transducer.
The phase θ(x; t) of the resultant sectional complex signal y(x; t)
is given by ω0 multiplied by twice the delay time τ(t):The amplitude of the change in thickness, ∆h(t), of the arterial wall is<100 µm and ∆h(t) varies in time. Thus, such minute changes inthickness cannot be measured by the B-mode or M-mode images
obtained in standard ultrasonic diagnostic equipment. From ∆h(t)and ∆d(t), the strain in radial direction, eH(t), and the strain in circumferential direction, eD(t), are defined bywhere hD and dD are the arterial wall thickness and arterial diameterat the end of diastole, respectively.
From these two values, the Poisson ratio σ(t) is given bywhich shows the instantaneous Poisson ratio. In this Letter, however,the following average Poisson ratio σ 0 during one cardiac cycle isevaluated:

where tS is the instant when the blood pressure becomes maximum
during systole.

The phase difference ∆θ(x; t) between the demodulated signals y(x;t) and y(x; t + ∆T) of the received signals for the successively transmitted pulses in the interval ∆T is given by

where ∆x(t) = x(t + ∆T) – x(t) is the displacement of the object in theperiod ∆T at a time t. By dividing the displacement ∆x by the period∆T, the average velocity, denoted by v(t + ∆T/2), of the object during
the period ∆T is given by the phase difference ∆θ(x; t):

From the resultant velocity signals vIN(t) and vAD(t), the change inthickness, ∆h(t), of the arterial wall with amplitudes of several
micrometers is accurately obtained by integrating the difference
between these signals:

The minimum value of the measurable vibration velocity is 0.5mm/s
and the time interval T0 of integration equals 222 µs. Thus, by multiplying these two values, the lowest value of the change in thickness isfound to be ~0.1 µm.

ELECTRONICS LETTERS

13th February 1997

Vol. 33

Fig. 1 Vibration signals measured in human carotid artery of normal
young subject
a M-mode
b ECG
c PCG
d Small velocity signal vIN(t) = vA(t) on intima
e Small velocity signal vAD(t) on adventitia
f Small velocity signal vP(t) on posterior wall
g Change in thickness, ∆h(t), of anterior wallh Change in diameter, ∆d(t), of lumen

In vivo experimental results: Fig. 1 shows the in vivo experimental
results obtained by applying the proposed method to the human
carotid artery in a normal young subject. Figs. 1d, e, and f show thevelocity signals vIN(t) = vA(t), vAD(t), and vP(t), respectively. Figs. 1gand h show the change in thickness, ∆h(t), of the anterior wall andNo. 4

the change in diameter, ∆d(t), of the lumen. Each signal has sufficient reproducibility even for the minute change in thickness, ∆h(t),with 10µm. Fig. 2 shows the relationship between the strain eH(t) in
the radial direction and the strain eD (t) in the circumferential direction. The average Poisson’s ratio σ 0, which is the gradient of thedashed line in Fig. 2, is 0.12.

variation of the average Poisson ratio, σ 0, of the two types of arteries.
Measurement of the change in thickness, ∆h(t), of the arterial walland the change in diameter, ∆d(t), of the lumen is effective for tworeasons. (i) These values are measured with high spatial resolution(in the axial direction of the artery) of the focal area of the ultrasonicbeam. (ii) Since the spatial resolution in the depth direction of theultrasonic beam is also high, the change in thickness of the intima,media, and adventitia can be separately measured.
Conclusions: In this Letter, the change in thickness, ∆h(t), of the arterial wall and the change in diameter, ∆d(t), of the blood vessel are
accurately and non-invasively obtained using ultrasound. The
minute change of several micrometres in thickness is measured with
sufficient reproducibility. From in vivo experimental results withrespect to the human carotid artery and the human abdominal aortaof the same normal young subject, there is variation of the average
Poisson’s ratio, σ 0, of the two types of arteries. A spatial resolutionof several millimetres is achieved by the proposed method which is
sufficient for diagnosis of the fibrous spots on the arterial wall in theearly stage of atherosclerosis. Therefore, the proposed method has
potential for the evaluation of local elasticity of the arterial wall.

Fig. 2 Relationship between strain, eH(t), in radial direction and strain,eD(t), in circumferential direction for carotid artery and abdominal aorta
of same normal young subject
Gradient of each trajectory shows average Poisson’s ratio σ 0(i) systole(ii) carotid artery(iii) abdominal aorta(iv) diastole

13th February 1997

2 January 1997

H. Hasegawa, H. Kanai and N. Chubachi (Department of ElectricalEngineering, Faculty of Engineering, Tohoku University, Sendai 980-77,Japan)
Y. Koiwa (First Department of Internal Medicine, Tohoku University,
School of Medicine, Sendai 980-77, Japan)

Similarly, the proposed method is applied to the human abdominal aorta, and the change in thickuess, ∆h(t), of the anterior wall andthe change in diameter, ∆d(t), of the lumen are obtained. The relationship between the strain eH(t) in radial direction and the straineD(t) in circumferential direction is shown in Fig. 2 and the average
Poisson’s ratio, σ 0, is determined to be 0.46. These results show theELECTRONICS LETTERS© IEE 1997
Electronics Letters Online No: 19970219

Vol. 33

References
1KANAI, H., SATO, M., KOIWA, Y.,

and CHUBACHI, N.: ‘Transcutaneous
measurement and spectrum analysis of heart wall vibrations’, IEEETrans. Ultrason. Ferroelectron. Freq. Control, 1996, 43, (9), pp. 791–810

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