Overview
Electrophysiology describes how electrical signals propagate across cardiac tissue, coordinating the synchronized contraction of the heart. When this propagation is disrupted — through structural damage, fibrosis, or ionic abnormalities — arrhythmias emerge. Computational electrophysiology provides a framework for understanding these phenomena mechanistically, connecting subcellular ion channel dynamics to tissue-level voltage propagation.
Technical Formulation
We adopt the monodomain formulation, which models the cardiac tissue as a single homogenized conductor. The governing equation is a nonlinear reaction-diffusion PDE, where the diffusion term drives voltage propagation across the tissue and the reaction term couples to the ion channel dynamics described by the underlying ODE system. The nonlinear reaction term introduces the stiffness characteristic of parabolic systems — fast action potential upstrokes coupled to slower recovery dynamics — requiring stable and accurate time integration. Together with the ion channel models, this forms a tightly coupled PDE-ODE system that must be solved simultaneously across the full cardiac geometry.
Clinical Application
The primary clinical motivation is arrhythmia modeling. By simulating voltage propagation across patient-specific geometries, we can study how structural and ionic heterogeneities give rise to pathological conduction patterns. This forms the electrical component of the full electromechanical pipeline, directly upstream of the mechanical response.
References & Resources
- Key References:
- Keener & Sneyd — Mathematical Physiology — foundational treatment of cardiac electrophysiology
- Quarteroni et al. — Numerical Models for Differential Problems — numerical treatment of reaction-diffusion systems