Noninvasive estimation of left-ventricular
end-diastole elasticity by analysing heart
wall vibrations
H. Kanai, S. Nakaya, H. Honda and Y. Koiwa
A new noninvasive method was previously presented for themeasurement of the left ventricular (LV) end-diastolic pressure(EDP) by combining Mirsky’s method and the experimentallyderived relationship. The eigenfrequency was determined byapplying a short-time Fourier transform to the velocity signal on thehuman heart wall which is transcutaneously measured in vivo by thephased tracking method using ultrasound. In the Letter the authors
estimate the elasticity of the heart wall for several human patients.

Introduction: Left ventricular (LV) pressure and its elasticity are significant parameters necessary for the clinical diagnosis of heart diseases. In particular, knowledge of the LV end-diastolic pressure(EDP), PED, is usually needed to assess LV functioning in clinical settings; a noninvasive method to measure this was previously presented [1]. The eigenfrequency was found by using a short-time
Fourier transform to the velocity signal on the human heart wall [2]which is measured transcutaneously in vivo by the phased tracking
method [3] using ultrasound. However, the LV EDP, the normal
value of which lies between 5 and 12mmHg, cannot be obtained
from the blood pressure measured at the brachial artery. Furthermore, the LV end-diastolic elasticity (EDE) EED cannot be noninvasively measured. To measure the LV pressure of a patient, invasive
catheterisation is essential. Although the accuracy of this measurement has been confirmed, such cardiac catheterisation is difficult toapply at the bedside. Therefore, a noninvasive technique for measuring of LV EDP, PED, and its elasticity, EED, is needed.
Based on dimension analysis and Advauni and Lee’s equation [4],by assuming that the LV wall vibration at the end-diastole is approximated by the free vibration of an elastic shell, Honda et al. [5] haveexperimentally derived a simple relationship between Young’s modulus E [Pa] of the LV wall, the LV internal radius r [m], the LV wall
thickness h [m], the myocardial density ρ [kg/m3], and the LV instantaneous mode-2 eigenfrequency f2 [Hz] as follows:

In vivo experimental results: Fig. 1a and b show a typical example ofthe electrocardiogram (ECG) and the vibration y(t), respectively, on
the LV side of the interventricular septum (IVS) measured by thephased tracking method of a 60 year old male patient (A) withmitral regurgitation (MR). By referring to the cross-sectional Bmode image, the direction of the ultrasonic beam is set so that thebeam is perpendicular to the IVS during the measurement. Fig. 1cshows the time-frequency distribution of y(t) of Fig. 1b. The instantaneous eigenfrequency f2 of mode 2 is determined for the fiveinstants at the end-diastole. With the determined f2, the LV EDP PED
is calculated for each instant t as shown by the squares in Fig. 1dusing eqns. 2 and 3. The resultant pressure estimate, PED , closely
coincides with the actual value, PED, which is shown by the solid linein Fig. 1d, directly measured by a catheter in the LV. In the otherfour patients and three young healthy subjects, the same procedure
was applied, the results being summarised in Table 1; catheterisation
was not used in the healthy subjects. The average difference between
PED and PED ranges from –4.6 to 3.6mmHg, which is sufficientlysmall.

where the coefficient A(h/r) is a function of h/r and is independent ofelasticity. From Honda’s experiment [4], the values of A(h/r) aredetermined for various values of h/r and it is experimentally foundout that A(h/r) does not strongly depend on the values of h/r. By
assuming a myocardial density ρ of 1.02 × 103 [kg/m3], eqn. 1 isapproximated byFig. 1 In vivo experimental results for 60 year old male patient (A)It is worth noting that the elasticity E of the shell is noninvasively
estimated without measuring the LV EDP when r, h, and f2 are measured.
In Mirsky’s method [6], on the other hand, the LV elastic stiffness
EQ [Pa] is given by

where V = 4πr3/3 [m3] and VW = 4π((r + h)3 – r3)/3 [m3] are the internal and wall volumes, respectively, σM = V/VW × (1 + (r + h)3/2R3)PED[Pa] is the stress on the LV wall, and R = r + h/2. The coefficients αand β satisfy the relationship dPED/dV = α · PED + β. It is experimentally found that β is negligibly small and α is given by PED = 57.32eαV.
By assuming that the E of eqn. 2 is equal to the EQ of eqn. 3, theLV EDP PED is determined from the eigenfrequency f2 of the LV wall
vibration, where the internal radius r, and the thickness h, are easily
measured by echocardiography. The LV wall vibration y(t) is transcutaneously measured by the novel phased tracking method [3]developed in our laboratory using ultrasound. By applying a shorttime Fourier transform to the resultant y(t), its eigenfrequency f2 isdetermined at the end-diastole. At the same time, the LV EDE EED is
obtained from eqn. 2.

ELECTRONICS LETTERS

13th May 1999

Vol. 35

a Electrocardiogram (ECG)b Vibration signal y(t) on IVS
c Estimated mode 2 eigenfrequency f2 around end-diastole, which issuperimposed on time-frequency distribution, obtained by short time
Fourier transform of y(t)d Actual LV EDP, PED and estimated PED, PED at five instants in enddiastoleFig. 2 Correlation between estimated LV EDE EED [kPa] and ratio, PED/VED [mmHg/ml], for five patients in Table 1

No. 10

The LV EDE EED of eqn. 2 is presented in the lowest row of Table
1. According to the LV elastic stiffness, EM, obtained in the in vitro
experiments [6], the average value of EM is 24.6 ± 2.2kPa for 13
healthy subjects, and 134.8 ± 2.1kPa for six patients with congestive
cardiomyopathy. Also in Table 1, for the patients with dilated cardiomyopathy (DCM), MR, or old myocardial infarction (OMI), the LV
EDE estimates are similarly increased, that is, the passive chambercompliance is decreased; in patient (B), a diuretic was applied and it
would be effective.
Table 1: In vivo experimental results for five patients and threehealthy subjects
Patients
Age
Diagnosis
GenderSubject ID

Healthy2125
2563
44615760
MR DCM-OMI DCM DCM DCM
female male male male male malemalemale(D) (E) (F) (G) (H)(C)(B)(A)

LV volume VED [m,]17935
LV radius rED [mm]LV wall thickness hED [mm] 120.34
hED/rED0.346
A(h/r)

268
4080.200.343

859785229 310 137
222322324238121011912120.32 0.29 0.28 0.5 0.43 0.55
0.345 0.344 0.343 0.348 0.347 0.349

Eigenfrequency f2 [Hz]Actual EDP PED [mmHg]

302316930302425281327–

24–

23–

EDP estimate PED [mmHg]
Error ∆P [mmHg]262.3

8–1.228–3.6

21–4.6

173.6

13–

11–

10–

EDE estimate EED [kPa]96361148971302622LV obtained by the transcutaneous measurement of vibrations onthe LV surface and their spectral analysis to determine the instantaneous mode-2 eigenfrequency. These in vivo experimental results
indicate that the elasticity noninvasively estimated in this Letter will
become an effective parameter for the evaluation of the heart function.

© IEE 1999
Electronics Letters Online No: 19990531
DOI: 10.1049/el:19990531

H. Kanai and S. Nakaya (Department of Electrical Engineering,
Graduate School of Engineering, Tohoku University, Sendai 980-8579,
Japan)
H. Honda and Y. Koiwa (First Department of Internal Medicine, Tohoku
University School of Medicine, Sendai 980-8574, Japan)

References
123The ratio PED/VED [mmHg/ml] of the LV EDP PED, directly measured by the catheterisation, to the LV end-diastolic volume VED,measured by angiocardiography, has been employed to evaluate thecardiac function. Fig. 2 shows the relationship of the estimates EEDand the ratio PED/VED for the five patients in Table 1. There is a correlation between them.

456Conclusions: In this Letter, we have proposed a new method for estimating the LV EDE based on the sizes and the eigenfrequency of the

ELECTRONICS LETTERS

13th May 1999

Vol. 35

17 March 1999

SATO, M., KANAI, H., CHUBACHI, N., HONDA, H., and KOIWA, Y.: ‘Method

for noninvasive estimation of left ventricular end diastolic pressure
based on analysis of heart wall vibration’, Electron. Lett., 1996, 32,(11), pp. 949–950
HONDA, H., NAKAYA, S., KAMADA, H., HASEGAWA, H., DEMACHI, J.,
CHIKAMA, H., SUGIMURA, K., YAMAMOTO, Y., KUMASAKA, N., TAKITA, T.,
IKEDA, J., KANAI, H., KOIWA, Y., and SHIRATO, K.: ‘Non-invasive
estimation of human left ventricular end-diastolic pressure’, Med.
Eng. Phys., 1998, 20, pp. 485–488
KANAI, H., SATO, M., KOIWA, Y., and CHUBACHI, N.: ‘Transcutaneous
measurement and spectrum analysis of heart wall vibrations’, IEEETrans., 1996, UFFC-43, (5), pp. 791–810
ADVAUNI, S.H., and LEE, Y.C.: ‘Free vibrations of fluid-filled sphericalshells’, J. Sound Vibrat., 1970, 12, pp. 453–462
HONDA, H., KOIWA, Y., TAKAGI, K., KIKUCHI, J., HOSHI, N., TAKISHIMA, T.,
and BUTLER, J.P.: ‘Noninvasive measurement of left ventricularmyocardial elasticity’, Am. J. Physiol., 1994, 266, pp. H881–H890
MIRSKY, I., GHISTA, D.N., and SANDLER, H.: ‘Cardiac mechanics:
Physiological, clinical, and mathematical considerations’ (John Wiley
Inc, New York, 1974), pp. 331–358

No. 10