Accurate and efficient simulation of cardiac electrophysiology is essential for understanding arrhythmias and improving clinical modeling. However, the stiffness and multi-scale nature of the underlying equations present significant computational challenges. In this study, we evaluated the Second-Order Semi-Implicit Alternating Direction Implicit (SSI-ADI) method applied to the monodomain model, using the Minimal Ventricular ionic model to represent human ventricular dynamics.
We compared SSI-ADI to two widely used numerical schemes — Forward Euler (FE) and Operator Splitting ADI (OS-ADI) — with respect to accuracy, stability, and parallel performance. While FE was severely limited by stability constraints and OS-ADI achieved only first-order convergence, SSI-ADI demonstrated second-order accuracy and consistently lower numerical errors across a wide range of time steps.
A key result was the ability of SSI-ADI to reach low error levels using significantly larger time steps. For instance, to match the accuracy of OS-ADI at 0.016 ms, SSI-ADI required only 0.128 ms — resulting in an eightfold reduction in simulation time. This practical efficiency, driven by its higher-order convergence, compensates for its higher computational cost per time step.
We further validated performance using a two-dimensional arrhythmia simulation under an S1–S2 stimulation protocol, a standard experimental setup in cardiac modeling. To accelerate the computations, SSI-ADI was implemented in CUDA. Among all tested schemes, it achieved the highest GPU speedup — 12.48x compared to its OpenMP version. This substantial gain stems from the method's structure, which allows all operations in the first phase to be computed independently per grid point, maximizing parallel efficiency.
These results highlight SSI-ADI as an elegant, robust, and scalable method capable of delivering fast, accurate simulations of complex cardiac dynamics — making it a highly attractive tool for computational cardiology.