Background: The monodomain equation is a well-established model in cardiac electrophysiology, describing the propagation of electrical activity in cardiac tissue. Its numerical solution on fine spatial and temporal scales remains computationally demanding when simulating large tissue domains, such as virtual patient population analyses. Accelerated solvers are therefore essential for enabling such large-scale or near-real-time simulations.
Aims: This research aims to develop a highly optimized monodomain simulator that fully exploits modern CPU and GPU architectures. The goal is to significantly reduce simulation times while preserving numerical accuracy, facilitating simulations on realistic cardiac geometries and supporting more demanding applications in personalized medicine and large-scale studies.
Methods: The solver is implemented in C and CUDA to allow the use of GPUs. For the ODE model we used the ten Tusscher–Panfilov 2006 cell model, here GPU acceleration is achieved using CUDA kernels for the Rush-Larsen scheme combined with lookup tables to enhance efficiency. The PDE solver employs GPUs for both right-hand side assembly and the conjugate gradient method. Performance and accuracy were evaluated using the standardized Niederer benchmark, as well as additional simulations on realistic geometries to assess scalability and physiological relevance. Simulation times were broken down into solver components across various spatial resolutions.
Results: On an NVIDIA A100 GPU, the solver achieves a 10× speedup for the ODE component and a moderate speedup for the PDE part. Work is ongoing to further optimize PDE performance. Accuracy remains consistent with established benchmarks.
Conclusions: The new software demonstrates improved computational performance compared to existing tools, particularly in fine-resolution simulations, without compromising numerical accuracy. The optimized GPU implementation will be used to run large-scale, patient-specific simulations in populations with congenital heart disease, enabling more efficient in-silico studies.