Comparing Surrogate Models for Action Potential Features in Ischemic Conditions

Yan B Werneck1, Lucas Teixeira Oliveira2, Rodrigo Weber dos Santos2, Bernardo Martins Rocha3, Kevin Burrage4, Anders Nygren5, Brodie Lawson6, Joventino de Oliveira Campos2
1PPGMC-UFJF, 2Federal University of Juiz de Fora, 3Universidade Federal de Juiz de Fora, 4Queensland University Technology, 5Schulich School of Engineering, University of Calgary, 6ARC Centre of Excellence for Mathematical and Statistical Frontiers (Queensland University of Technology)


Abstract

Electrophysiological action potential (AP) models are critical for understanding cardiac dynamics, especially in pathological states like ischemia. However, their computational demands limit clinical applications. This study evaluates surrogate modeling approaches—Neural Networks (NNs), Polynomial Chaos Expansions (PCEs), and Gaussian Processes (GPs)—for efficiently emulating AP ischemic conditions and predicting key quantities of interest such as action potential duration, upstroke velocity, and resting potential.

The ten Tusscher 2004 model was parameterized into: Model A, a 3-parameter ischemia model simulating acidosis, hypoxia, and hyperkalemia; and Model B, a 12-parameter model capturing ionic conductance variability. Surrogate models were assessed using accuracy for predicting the quantities of interest, efficiency (training/inference time), and resource use. NNs used GPU-accelerated PyTorch for parallel processing, GPs were implemented with GPyTorch, and PCEs used Chaospy with CPU-only operations. Training datasets ranging from 100 to 5,000 samples were used to evaluate surrogate dependence on data.

NNs outperformed other methods in higher-dimensional parameter spaces, demonstrating scalability and robust accuracy. PCEs provided comparable accuracy for low-dimensional Model A but required larger datasets for similar performance in high-dimensional spaces such as Model B. GPs were effective for simpler parameterizations but struggled with the complexity of high-dimensional data. NNs with smaller architectures offered the fastest inference times while retaining accuracy comparable to the best models. In general, the fastest emulators were up to a million times faster than the TT model, while maintaining relative errors below 1%, highlighting the potential of surrogate use for modeling action potential dynamics.