Modeling of cardiac electrophysiological mechanisms: from action potential genesis to its propagation in myocardium

The aim of the present paper is to describe the different attempts at modeling cardiac electrophysiological mechanisms, mainly at the membrane and cellular level, from action potential genesis to its propagation in myocardium. The Hodgkin and Huxley model describing the nervous action potential's theoretical reconstruction is first recalled, for it represents the basic model for a large part of cardiac action potential models. These models (Beeler and Reuter, Van Capelle and Durrer, Luo and Rudy) are then successively studied as their main applications by diverse authors. Varied approaches, like the Fitzhugh-Nagumo model (derived from the Bonhoeffer-Van der Pol model of oscillatory systems) or cellular automata models applied to the study of ventricular activation wave propagation and diseases associated with its perturbation, are then presented and discussed. Other, different approaches, such as general studies of excitable media, are evoked. This paper concludes with a critical evaluation of these different methods of electrophysiological cardiac modeling and of the main domains in which they led to significant results and in which they appear able to generate future perspectives.