A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model

Abstract

In this paper a highly parallel method is developed for simulating the elastodynamics of a four-chamber human heart with patient-specific geometry. The heterogeneous hyperelastic model is discretized by a finite element method in space and a fully implicit adaptive method in time, and the resulting nonlinear algebraic systems are solved by a scalable domain decomposition algorithm. The deformations of the cardiac muscles are quite complex due to the realistic geometry, the heterogeneous hyperelasticity of the cardiac tissue, and the myocardial fibers with active stresses. Moreover, the deformations in different chambers and at different phases of the cardiac cycle are very different. To simulate all the muscle movements including the atrial diastole, the atrial systole, the isovolumic contraction, the ventricular ejection, the isovolumic relaxation, and the ventricular filling, the temporal-spatial mesh needs to be sufficiently fine, but not too fine so that the overall computing time is manageable, we introduce a baseline mesh in space and a two-level time stepping strategy including a uniform baseline time step size to obtain the desired time accuracy and an adaptive time stepping method within a baseline time step to guarantee the convergence of the nonlinear solver. Through numerical experiments, we investigate the performance of the proposed method with respect to the material coefficients, the fiber orientations, as well as the mesh sizes and the time step sizes. For an unstructured tetrahedral mesh with more than 200 million degree of freedoms, the method scales well for up to 16,384 processor cores for all steps of an entire cardiac cycle.