Effect of shape on pressure-volume relationships of ellipsoidal shells

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.