Cardiac electrophysiology models based on continuous-time Markov chains (CTMCs) provide detailed representations of ion channel dynamics and are essential for investigating cellular mechanisms underlying action potentials. However, their high computational cost often limits their applicability in large-scale or real-time simulations. This work addresses this challenge by introducing a high-performance computational method designed to speed up the numerical solution of CTMC-based cardiac models.
The proposed method builds on the matrix exponential framework by integrating the uniformization technique, which reformulates the exponential of the infinitesimal generator matrix into a rapidly convergent series. This transformation improves numerical stability and facilitates efficient computation. To further reduce simulation times, the method was implemented on Graphics Processing Units (GPUs), taking advantage of NVIDIA Tensor Cores via the Warp Matrix Multiply-Accumulate (WMMA) API. Tensor Cores offer hardware-level acceleration for mixed-precision matrix operations, making them well-suited for repeated matrix-matrix multiplications inherent to the uniformization method.
The framework was evaluated using the Bondarenko model for mouse ventricular myocytes, which employs four Markovian formulations to represent key ionic currents. Three sets of simulations were conducted, each with 1000, 10000, and 100000 independent cellular instances, to assess scalability and performance. The Tensor Core-accelerated implementation achieved speedups of up to 148 times relative to the CPU baseline and up to 1.5 times compared to a standard CUDA-based GPU implementation. These gains were especially prominent in large-scale scenarios, confirming the method's ability to handle extensive parallel workloads efficiently.
In conclusion, the integration of uniformization with Tensor Core acceleration enables robust and scalable simulations of complex electrophysiological models. This approach significantly reduces computational cost while preserving numerical accuracy, positioning it as a promising solution for high-throughput or real-time cardiac simulations. Future developments may extend this methodology to other Markov-based models and full-organ simulations.