Analysis and Physiological Monitoring of the Human Left Ventricle

Abstract

Mathematical models of the human left ventricle are presented to determine the physiological response-oriented mechanical parameters of the LV, which have diagnostic significance. These parameters are (i) the rheological parameters of the left ventricular muscle, namely the instantaneous values of stiffness of series elasticity, parallel elasticity, and the stress-strain rate relationship for the contractile unit that characterizes the deviatric stress-strain response of a left ventricular muscle element, (ii) the effective modulus of the LV, and (iii) the state of stress in the LV. The rheological parameters are obtained from a continuum model of the LV whose stress state equilibrates the chamber pressure and whose strain state equals the instantaneous strains in the actual LV, obtained from instantaneous changes in the geometry of the LV (as noted from cineangiocardiography); the constitutive equations for the model incorporate the known existing rheological models for the isolated cardiac muscle. The effective moduli of the LV are obtained by correlating the fundamental frequency of vibration of a spherical model of the LV with the corresponding frequencies of the second component of the first heart sound and the third heart sound; thus the values of representative moduli (and hence indices of the left ventricular stiffnesses) at systole and diastole are obtained. The stress state in the LV is obtained by utilizing single plane cineangiocardiographic information of the irregular geometry of the LV in anteroposterior projection. Plane stress finite element analysis of this planor irregular geometry of the LV is done and the resulting stresses are reduced by a factor, heuristically determined to make allowance for the actual 3-dimensional geometry of the LV; the stresses obtained thus bring out effects of irregular boundary of varying (and at times high) curvature.