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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.

A perspective transformation is developed whereby an object in space as viewed from an arbitrary point can be projected into a plane and plotted. Families of curves which can be used to define such an object are discussed and examples are given. An algorithm which eliminates the plotting of hidden portions of the object is discussed.

A thick-wall spherical model for the rat left ventricle was used to deduce passive wall stiffness from diastolic pressure-volume data. This was done for rats in three age classes: young (1 mo), adult (17 mo) and old (17 mo). The model was based on finite deformation elasticity theory consistent with the magnitude of observed deformation. A least-squares procedure was used to determine elastic constants in postulated nonlinear stress-stretch relations for the myocardium. It was found that at a given level of stress, wall stiffness for ventricles in the young age class was consistently greater than wall stiffness in the other two classes. In addition, the difference in wall stiffness between rats in the adult and old age classes was found to be approximately 10%.

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