A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology

Abstract

Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev‐Panfilov model and the ten Tusscher‐Noble‐Noble‐Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

“…The normalized time corresponds to the solution time of a given approach divided by the solution time from the first approach. As expected, for the same time step, the semi‐implicit scheme requires nearly half the computational time of the fully implicit Scheme 43 . Additionally, the introduction of MQ does not significantly alter the computational time.…”

“…The CV results for GQ and NQ yield similar behavior as that observed by Krishnamoorthi et al 32 with the GQ overestimating the CV for coarse meshes and the NQ underestimating the CV for coarse meshes. As mentioned in our previous work, 43 the CV error is mainly caused by an underestimation of the spatial gradient and an overestimation of the transmembrane potential due to linear interpolation. After all, the magnitude of the spatial gradient that can develop in coarse linear elements is limited and, thus, can lead to a smaller CV in coarse elements.…”

“…First, an example considering the CV which develops for different conductivities and quadratures is considered in Figure 4. As presented in our previous work, 43 the conductivity can have a large effect on the convergence of the CV based on the spatial discretization. Therefore, it is worth considering different conductivities with the various quadrature approaches, especially since electrophysiology problems often have anisotropic conductivities.…”

“…The CV was shown to converge when using a high order and a large number of quadrature points. In our previous work, 43 we noted that the difference between the quadrature rules in hexahedral and tetrahedral elements leads to different effects on the convergence of the CV based on the spatial discretization. Finally, Krishnamoorthi et al 32 presented results for the CV with the use of an internal state variable (ISV) approach with Gauss–Legendre quadrature (herein referred to as Gauss quadrature) and nodal quadrature (quadrature points located at the nodes).…”

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

“…With an average spatial discretization of 0.6 mm of the electrophysiological domain Ω EP , we use a coarser mesh than all values tested in [100]. Recently, Woodworth et al published in [137] a convergence study for the monodomain problem coupled to the cell model of ten Tusscher et al [138]. The spatial discretization needed to be in the convergence region is out of scope of the technical requirements for the simulations of this work.…”