Computer models of the human heart can lead to a better understanding of cardiac function. Since the objective of many of these models is to be used in a clinical setting, a compromise between computational cost and numerical accuracy is needed. Due to the high mathematical complexity of the underlying model, the finite element discretization commonly used may not be the optimal balance between efficiency, reliability, and accuracy.
To investigate the impact of different spatial discretization schemes on cardiac mechanics, we realized a benchmark configuration that considers the hyper-elastic problem of inflating and actively contracting an idealized left ventricle with transversely isotropic and nearly incompressible properties. In this study, we examined the influence of three different finite elements — conforming Galerkin, discontinuous Galerkin, and enriched Galerkin elements — by investigating the cavity volume and apex shortening for four mesh refinements. Furthermore, we compare the various spatial discretizations concerning the number of degrees of freedom and computational time. All simulations were conducted using both linear and quadratic elements for all methods.
We demonstrate that the conforming Galerkin scheme leads to the occurrence of locking phenomena for coarse mesh resolutions using linear elements. However, locking can be mitigated by using finer mesh resolutions, higher-order elements, or by adopting the discontinuous or enriched Galerkin elements.
Discontinuous Galerkin finite elements have notably more degrees of freedom compared to the conforming Galerkin method, while enriched Galerkin discretization has only one additional per element. However, both enriched and discontinuous Galerkin schemes cause higher computational costs, particularly the discontinuous Galerkin method. Furthermore, simulations utilizing the enriched Galerkin and discontinuous Galerkin schemes demonstrate enhanced robustness and stability compared to the conforming method.
In conclusion, the enriched Galerkin approach offers a favorable balance between computational efficiency and numerical robustness in cardiac modeling applications.