Diastolic Pressure-volume Relations and Distribution of Pressure and Fiber Extension Across the Wall of a Model Left Ventricle

A model for left ventricular diastolic mechanics is formulated that takes into account noneligible wall thickness, incompressibility, finite deformation, nonlinear elastic effects, and the known fiber architecture of the ventricular wall. The model consists of a hollow cylindrical mass of muscle bound between two plates of negligible mass. The wall contains fiber elements that follow a helical course and carry only axial tension. The fiber angle (i.e., helical pitch) is constant along the length of each fiber but varies through the wall in accordance with the known distribution of fiber orientations in the canine left ventricle. To simplify the analysis and reduce the number of degrees of freedom, the anatomic distribution of fiber orientations is divided into a clockwise and counterclockwise system. The reference configuration for the model corresponds to a state in which, by hypothesis, the transmural pressure gradient is zero, the tension is zero for all fibers across the wall, and all fibers are assumed to have a sarcomere length of 1.9 micrometer. This choice of reference configuration is based on the empirical evidence that canine ventricles, fixed in a state of zero transmural pressure gradient and dissected, demonstrate sarcomere lengths between 1.9 and 2.0 micrometer in inner, middle, and outer wall layers, while isolated ventricular muscle bundles are observed to have zero resting tension when the sarcomere length ranges from 1.9 to 2.0 micrometer. An equation representing the global condition for equilibrium is derived and solved numerically. It is found that the model's pressure-volume relation is representative of diastolic filling in vivo over a wide range of filling pressures, and the calculated midwall sarcomere lengths in the model compare favorably with published experimental data. Subendocardial fibers are stretched beyond Lmax even at low filling pressures, i.e., 5 mm Hg, while fibers located between 60-80% of wall thickness extend minimally between 5 and 12 mm Hg. The hydrostatic pressure field within the wall is highly nonlinear. The pressure rises steeply in the subendocardial layers so that the net gain in pressure in the inner third of the wall is 85% of the filling pressure. It is demonstrated that these results are independent of heart size for a family of heart models that are scale models of each other. They are, however, critically dependent on the existence of longitudinally oriented fibers in the endocardial and epicardial regions of heart wall.