title: A simple analytical model of action potential duration profile in electrotonically-coupled cells.
abstract: Electrotonic interactions between cardiac cells modulate the dispersion of action potential duration (APD). This paper provides a complete mathematical analysis of a simple model of exponential-shaped repolarization in a network of electrotonically-coupled cells with different intrinsic APDs. The forward problem consists in computing the APD map in the coupled system from the intrinsic APD map. A closed-form algebraic formula is derived for the forward problem. The inverse problem, inferring the intrinsic APDs from an APD map, is proved to have a unique solution (if any). Perturbation analysis leads to an efficient and accurate Newton-based solver for this specific inverse problem. Finally, an analytical expression is obtained for the convolution filter that solves the forward problem in one dimension. This mathematical framework forms a solid theoretical basis for future development and validation of repolarization parameter estimation techniques in detailed models of cardiac tissue.
authors.affiliation: Université de Montréal, Département de Physiologie Moléculaire et Intégrative, Montréal, Canada; Hôpital du Sacré-Coeur de Montréal, Centre de Recherche, Montréal, Canada. Electronic address: vincent.jacquemet@umontreal.ca.
authors.forename: Vincent
authors.initials: V
authors.lastname: Jacquemet
mesh_terms: D000200:Action Potentials; D008955:Models, Cardiovascular
keywords: Action potential duration; Cardiac electrophysiology; Computer modeling; Electrotonic coupling; Inverse problem; Parameter estimation