Residual stress produced by ventricular volume reduction surgery has little effect on ventricular function and mechanics: A finite element model study

Abstract

Objectives: Residual stress is the stress (force per unit area) that remains when all external loads (eg, left ventricular chamber and pericardial pressures) are removed. It has been suggested that ventricular volume reduction surgery can reconstitute the residual stress-strain state of the left ventricle. To determine the extent to which residual stress is involved, we used a mathematical (finite element) model to simulate the effect of volume reduction operations on left ventricular stroke volume/end-diastolic pressure (Starling) relationships, as well as on regional distributions of stress in the local muscle fiber direction (fiber stress). Methods: The nonlinear stress-strain relationship for the diastolic myocardium was anisotropic with respect to the local muscle fiber direction. An elastance model for active fiber stress was incorporated in an axisymmetric geometric model of the dilated, poorly contractile left ventricular wall. Results: When residual stress is implemented in the model simulation of volume reduction operations, the additional decrease in stroke volume at fixed left ventricular end-diastolic pressure is small (10% volume reduction: 20% at 1 mm Hg and 2.0% at 20 mm Hg; 20% volume reduction: 2.2% at 1 mm Hg and 3.1% at 20 mm Hg). Furthermore, there is little change in the mean fiber stress throughout the left ventricular wall (10% volume reduction: +1.0% at end-diastole and -0.3% at end-systole; 20% volume reduction: +2.1% at end-diastole and -1.0% at end-systole). Conclusions: These results suggest that residual stress produced by volume reduction operations has little effect on left ventricular function and the mean fiber stresses at end-diastole and end-systole.