Breaking the state of the heart: meshless model for cardiac mechanics

Cardiac modeling has recently emerged as a promising tool to study pathophysiology mechanisms and to predict treatment outcomes for personalized clinical decision support. Nevertheless, achieving convergence under large deformation and defining a robust meshing for realistic heart geometries remain challenging, especially when maintaining the computational cost reasonable. Smoothed particle hydrodynamics (SPH) appears to be a promising alternative to the finite element method (FEM) since it removes the burden of mesh generation. A point cloud is used where each point (particle) contains all the physical properties that are updated throughout the simulation. SPH was evaluated for solid mechanics applications in the last decade but its capacity to address the challenge of simulating the mechanics of the heart has never been evaluated. In this paper, a total Lagrangian formulation of a corrected SPH was used to solve three solid mechanics problems designed to test important features that a cardiac mechanics solver should have. SPH results, in terms of ventricle displacements and strains, were compared to results obtained with 11 different FEM-based solvers, by using synthetic cardiac data from a benchmark study. In particular, passive dilation and active contraction were simulated in an ellipsoidal left ventricle with the exponential anisotropic constitutive law of Guccione following the direction of fibers. The proposed meshless method is able to reproduce the results of three benchmark problems for cardiac mechanics. Hyperelastic material with fiber orientation and high Poisson ratio allows wall thickening/thinning when large deformation is present.