Abstract
The authors measured the transfer function (TF) of the left ventricle (LV) in an isolated canine preparation. Here TF indicates the ratio of induced vibration in LV to input vibration when an external mechanical oscillation is applied. TF had a single peak the frequency of which changed from 40 Hz to 80 Hz when LV pressure (LVP) increased from 6 mm Hg to 96 mm Hg. A mathematical model was formulated to estimate the viscoelasticity of the spherical shell. This model was constructed of the material points, elastic components which connected all the material points, and viscous components placed in series with elastic components. Theoretical TF can be computed if the viscoelastic values are given. The value of viscoelasticity at which the theoretical TF best fitted the experimental TF was considered to be the viscoelasticity of the model. The validity of this approach was verified using a silicone spherical shell. The estimated myocardial elasticity was 40 kPa when LVP was 6 mm Hg, 160–170 kPa when LVP was 96 mm Hg and was approximately proportional to LVP, whereas viscosity showed small change. The inclination of elasticity was consistent with previous reports. These results proved that myocardial elasticity can be estimated by analysing the transfer function of the left ventricle.
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References
Advani, S. H. andLee, Y. C. (1970) Free vibrations of fluid-filled spherical shells.J. Sound Vibr.,12, 453–462.
Demer, L. L. andYin, F. C. P. (1983) Passive biaxial mechanical properties of isolated canine myocardium.J. Physiol.,339, 615–630.
Elzinga, G. andWesterhof, N. (1981) ‘Pressure-volume’ relations in isolated cat trabecula.Circ. Res.,49, 388–394.
Ghista, D. N., Sandler, H. andVayo, H. W. (1975) Elastic modulus of the human intact left ventricle: determination and physiological interpretation.Med. & Biol. Eng.,13, 151–161.
Halperin, H. R., Chew, P. H., Weisfeldt, M. L., Sagawa, K., Humphery, J. D. andYin, F. C. P. (1987) Transverse stiffness: a method for estimation of myocardial wall stress.Circ. Res.,61, 695–703.
Jantz, R. andGrimm, A. F. (1973) Deformation of the diastolic left ventricle.Biophys. J.,13, 689–704.
Koiwa, Y., Hashiguchi, R., Ohyama, T., Isoyama, S., Satoh, S., Suzuki, H. andTakishima, T. (1986) Measurement of instantaneous viscoelastic properties by impedance-frequency curve of the ventricle.Am. J. Physiol.,250, H672-H684.
Koiwa, Y., Ohyama, T., Takagi, T., Kikuchi, J., Honda, H., Hashiguchi, R., Shimizu, Y., Butler, J. P. andTakishima, T. (1988) The left ventricular vibration mode in the transfer function method and at the moment of the first heart sound.Front. Med. Biol. Eng.,1, 59–70.
Mirsky, I. andParmley, W. W. (1974) Evaluation of passive elastic stiffness for the left ventricle and isolated heart muscle. InCardiac mechanics: Physiological, clinical and mathematical considerations. John Wiley & Sons Inc., New York, Chap. 11.
Mirsky, I., Janz, R. F., Kubert, B. R., Korecky, B. andTaichman, G. C. (1976) Passive elastic wall stiffness of the left ventricle: a comparison between linear theory and large deformative theory.Bull. Math. Biol.,38, 239–251.
Pinto, J. G. andFung, Y. C. (1973) Mechanical properties of the heart muscle in the passive state.J. Biomech.,6, 597–616.
Sagawa, K. (1978) The ventricular pressure-volume diagram revised.Circ. Res.,43, 677–687.
Suga, H., Sagawa, K. andShoukas, A. A. (1973) Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. —Ibid.,,35, 314–322.
Tani, J., Miyachi, Y., Ohtomo, K., Takishima, T., Koiwa, Y., Ohyama, T., Shimizu, Y., Takagi, T., Kikuchi, J., Honda, H. andHoshi, N. (1989) Identification of left ventricular viscoelastic properties (English abstract).Transcription Jpn. Soc. Mech. Eng. (Series C) 55, 1622–1627.
Templeton, G. H., Mitchell, J. H., Ecker, R. R. andBlomqvist, G. (1970) A method for measurement of dynamic compliance of the left ventricle in dogs.J. Appl. Physiol.,29, 742–745.
Templeton, G. H. andNardizzi, L. R. (1974) Elastic and viscous stiffness of the canine left ventricle. —Ibid.,,36, 123–127.
Templeton, G. H., Wildenthal, K., Willerson, J. T. andReardon, W. C. (1974) Influence of temperature on the mechanical properties of cardiac muscle.Circ. Res.,36, 624–634.
Van Loon, P. (1980) Model parameters of mechanical structures. Ph.D. dissertation, Katholiek Univ. Leuven.
Yeatman, L. A., Parmley, W. W. andSonnenblick, E. H. (1969) Effects of temperature on series elasticity and contractile element motion in heart muscle.Am. J. Physiol.,217, 1030–1034.
Yin, F. C. P., Strumpf, R. K., Chew, P. H. andZeger, S. L. (1987) Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading.J. Biomech.,20, 557–589.
Zienkiewicz, O. C. andCheung, Y. K. (1967)The finite element method in structural and continuum mechanics. 3rd edn. McGraw Hill, New York.
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Tani, J., Yamamoto, H., Honda, H. et al. Estimation of left ventricular myocardial elasticity and viscosity by a thick-walled spherical model. Med. Biol. Eng. Comput. 31, 325–332 (1993). https://doi.org/10.1007/BF02446683
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DOI: https://doi.org/10.1007/BF02446683