Two formulas are presented for estimating local average circumferential stress in the left ventricle from the cavity pressure and various quantities, available from the angiogram, which characterize the size and shape of the cavity and ventricular wall. The advantages of these formulas are as follows: 1) they are based on thick-wall shell theory; 2) they are intended for application at positions in the ventricular wall other than the base; and 3) they are based on a more general representation of ventricular geometry than a sphere, cylinder, or ellipsoid. Except for one location, both formulas predict average circumferential stresses that agree to within 25% with the corresponding stresses in a finite element model of an aneurysmal ventricle. In addition, at the equator of a thick-wall ellipsoid, the formulas are identical in form to a previously derived formula that has been shown to predict stresses that are in fair to good agreement with measured stresses in the open-chest dog heart.

A finite-element model is used to analyze the mechanical behavior of the left ventricle. The ventricle is treated as a heterogeneous, linearly elastic, thickwalled solid of revolution. The inner third of the ventricular wall is assumed to be transversely isotropic with a longitudinal Young's modulus, transverse modulus, and shear modulus of 60 g/cm 2 , 30 g/cm 2 , and 15.5 g/cm 2 , respectively. In the outer two-thirds of the ventricular wall the myocardium is assumed to be isotropic with a Young's modulus of 60 g/cm 2 . Polsson's ratio is assumed to be equal to 0.45 throughout the ventricular wall. The valvular ring at the base of the ventricle is simulated by a homogeneous layer cf collagen. The model appears to predict gross free-wall deformation in the left ventricle of the potassium-arrested rat heart fixed in situ. The presence of a relatively compliant transversely isotropic region near the endocardial surface results in significantly lower axial and circumferential stresses in this region than are present in a homogeneous, isotropic model. The presence of a simulated valvular ring results in a concentration ofrelatively large stresses near the base of the ventricle.

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Previous theoretical procedures for determining the slope and intercept of the stiffness-stress relationship of the passive myocardium from diastolic pressure-volume (P-V) data assume that the eccentricity of the left ventricle (LV) is invariant. In this study a mathematical model for an ellipsoidal membrane was developed that does not contain that constraint. The model predicts a small (less than 10%) but significant decrease in eccentricity as transmural pressure increases. This result was confirmed by the use of a thick-wall finite element model. The implications of this result are as follows. 1) The slope and intercept of the stiffness-stress relationship of unconstrained ellipsodial shells can be determined by fitting a spherical model to the P-V relationships exhibited by the shells. 2) An ellipsoidal model that assumes that the eccentricity of such shells is invariant for all pressures would predict erroneous intercepts. 3) If the eccentricity of the diastolic LV initially decreases relative to its value at zero transmural pressure, then a thick-wall spherical model may be adequate for determining the slope and intercept of the myocardial stiffness-stress relationship.