Mathematical modeling of the electrical activity of a single cardiac cell and of strands of cardiac cells are problems of fundamental interest in the area of electrophysiology. New and increasingly comprehensive data on the electrophysiological behavior of single, isolated cardiac myocytes have facilitated the development of more 'complete' models and are used here for the development of mathematical characterizations of cells exhibiting 'normal' electrophysiologic behavior as well as those exhibiting 'depressed' activity. Simulation and parameter estimation techniques are utilized to investigate model-generated single cell electrical behavior and to adjust this behavior to best fit observed responses. Suitably 'identified' models may be used in further simulations of electrical activity in linear strands of resistively coupled cardiac cells. It is hoped that together with advances in experimental methods, these methods for analysis and adjustment of model behavior will provide new and meaningful insight into the mechanisms of cardiac electrical activity.