Propagation of Parametric Uncertainty in Aliev-Panfilov Model of Cardiac Excitation

Models of cardiac electrophysiology are useful for studying heart functions and cardiac disease mechanisms. However, cardiac models often have a great level of complexity, and it is often computationally prohibitive to simulate tissue and organ activities in a real-time fashion. To address the challenge, simplified models such as Aliev-Panfilov model are developed to reduce model complexity, while providing necessary details of cardiac functions. Simplified models may induce uncertainty, which can deteriorate the accuracy and reliability of cardiac models. In addition, model parameters are calibrated with noisy data and cannot be known with certainty. It is important to assess the effect of parametric uncertainty on model predictions. For the probabilistic, time-invariant parametric uncertainty, a generalized polynomial chaos (gPC) expansion-based method is presented in this work to quantify and propagate uncertainty onto model predictions. Using gPC, a measure of confidence in model predictions can be quickly estimated. As compared with sampling-based uncertainty propagation techniques, e.g., Monte Carlo (MC) simulations, the gPC-based method in this work shows its advantages in terms of computational efficiency and accuracy, which has the potentials for dealing with complicated cardiac models, e.g., 2D tissue and 3D organ models.