Regularity of node distribution impacts conduction velocities in finite element simulations of the heart

The monodomain model and finite element method are often used together to compute electrical excitation conduction in cardiac tissue. It is known that the choice of using mass lumping as well as the used ionic current integration method affect the resulting conduction velocities (CVs), especially at coarse resolutions. We describe how the regularity of node arrangement in tetrahedral grids also affects simulated CVs in a similar magnitude. We compare activation times (ATs) over a distance of 21.4 mm at different resolutions to a high resolution reference solution from a previously published benchmark. We show that triangulated grids are able to be within 10% of the reference solution up to a grid resolution of 0.6 mm, while results from regular grids already diverge by more than that at 0.4 mm. At 0.7 mm, a regular grid yields an AT of 80.01 ms, where a triangulated grid with less nodes results in 47.52 ms (reference solution 42.82 ms). We investigate how gradual perturbation of nodes from a regular grid effects AT, finding that CV monotonically increases with degree of node perturbation.