An analytical study of the physiology and pathology of the propagation of cardiac action potentials

Abstract

Many cardiac diseases are caused by the abnormal propagation of electrical waves. Previous experimental and modelling work is reviewed, then a detailed study of the mathematics of cardiac propagation is presented. Pathologies are examined in the context of the models by varying parameters in the models to mimic different pathological states. Ionic models of cells are simplified to form analytically tractable models of the propagation of electrical cardiac waves. The roles that sodium channel activation and inactivation play in determining the conduction velocity are studied in detail, and the roles of resting potential currents in conduction block are calculated. The effect of curvature on the conduction velocity is examined, and the conditions in which curvature leads to conduction block and fibrillation are discussed. Hyperkalaemia (important during ischaemia) is modelled, and the model correctly describes the bi-phasic relation between propagation velocity and extracellular potassium.