Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Abstract

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Figure 1.

(a) Schematic showing the dimensions of the simulation domain. The stimulus was applied within the cube marked S. (b) Summary of points at which activation time was evaluated. Activation times at points P₁–P₉ were evaluated and are available in the electronic supplementary material. Plots of the activation time were evaluated along the line from P₁ to P₈ and plots of the activation along the plane shown are provided in two dimensions.

Figure 2.

Activation times along the blue line depicted in figure 1b between points P₁ and P₈ for solutions with Δt=0.005 ms and Δx=0.1 mm (red line), 0.2 mm (green line) and 0.5 mm (blue line). Plot labels correspond to code indexing listed in table 4.

Figure 3.

Activation time at point P₈ depicted in figure 1b for every combination of spatial and temporal refinement. Plot labels correspond to code indexing listed in table 4. (Online version in colour.)

Figure 4.

Activation times on the plane depicted in figure 1b, for codes as indexed in table 4. For each code, the upper and lower planes correspond to the solutions with Δx=0.5 mm and Δt=0.005 ms and Δx=0.1 mm and Δt=0.005 ms, respectively. The activation times are represented by the colour map from dark blue (0 ms) to red (130 ms) with contour bands at 10 ms intervals.