Simulation of Left Ventricular Dynamics Using a Low-Order Mathematical Model

The eventual goal of this study is to develop methods for estimating dynamic stresses in the left ventricle (LV) that could be used on-line in clinical settings, based on routinely available measurements. Toward this goal, a low-order theoretical model is presented, in which LV shape is represented using a small number of parameters, allowing rapid computational simulations of LV dynamics. The LV is represented as a thick-walled prolate spheroid containing helical muscle fibers with nonlinear passive and time-dependent active contractile properties. The displacement field during the cardiac cycle is described by three time-dependent parameters, using a family of volume-preserving mappings based on prolate spheroidal coordinates. Stress equilibrium is imposed in weak form and the resulting force balance equations are coupled to a lumped-parameter model of the circulation, leading to a system of differential–algebraic equations, whose numerical solution yields predictions of LV pressure and volume, together with spatial distributions of stresses and strains throughout the cardiac cycle. When static loading of the passive LV is assumed, this approach yields displacement and stress fields that closely match results from a standard finite-element approach. When dynamic motion with active contraction is simulated, substantial variations of fiber stress and strain through the myocardium are predicted. This approach allows simulations of LV dynamics that run faster than real time, and could be used to determine patient-specific parameters of LV performance on-line from clinically available measurements, with the eventual goal of real-time, patient-specific analysis of cardiac parameters.