Bulletin ofMathematicalBiology Vol. 47, No. 1, pp. 53-70, 1985. Printed in Great Britain 0092-8240/85S3.00 + 0.00 Pergamon Press Ltd. 9 1985 Society for Mathematical Biology DISTRIBUTION OF STRESSES IN THE LEFT VENTRICULAR WALL OF THE INTACT HEART 9 J. C. MISRA and S. I. SINGH Department of Mathematics, Indian Institute of Technology, Kharagpur, India The left ventricle is modelled as a prolate spheroid of viscoelastic material with an aim to demonstrate the qualitative effects of anistropy and nonhomogeneity in the calculation of intact ventricular wall stresses. The pericardial pressure is accounted for in the analysis and an attempt is made to examine to what extent this influences the ventricular stresses. Numerical results are also obtained by computing the analytical expressions derived through the analysis. 1. Introduction. In recent years much attention has been focused on the health and disease of the heart for reviving the human or subhuman heart in order to defeat death and prolong life. On the other hand, the possible inability to detect certain cardiovascular diseases with medical examination suggests that cardiologists should have a better knowledge of the mechanics and performance of the myocardium in order to develop more sophisticated diagnostic techniques. As a consequence, there is an increasing interest in this area with due attention to the calculation of forces and stresses de- veloped in the wall of the left ventricle. Several attempts have been made to estimate left ventricular wall stresses by different investigators (Sandler and Dodge, 1963; Wong and Rautaharju, 1968; Ghista and Sandler, 1969; Mirsky, 1969, 1970, 1973; Gould et al., 1972; Janz and Grimm, 1973; Pao et al., 1974) by considering different models. Such studies are helpful for assessing left ventricular performance, but in all the above mentioned studies (excepting the one by Mirsky, 1970), the cardiac muscle has been treated as an isotropic homogeneous and elastic material. Although an initial attempt was made by Mirsky (1970) to examine the effect of aniso- tropicity as well as inhomogeneity of the ventricular wall tissues on the generated stresses in the wall, the damping material behaviour of the wall tissues was completely ignored by him. Experimental investigations, however, indicate that from the mechanical point of view, cardiac muscle in the passive state is anisotropic (Grant, 1965; Streeter and Bassett, 1966 and Streeter et al., 1969), inhomogeneous and viscoelastic (Buchthal and Kaiser, 1951; 53