ASYMPTOTIC ANALYSIS FOR PERIODIC CARDIAC MUSCLE.
The problem of determining the potential distribution in a strand of cardiac cells is solved using asymptotic analysis. The intracellular, extracellular, and transmembrane potentials are treated as dependent upon the variable X in two ways: first, aperiodically, as determined by the boundary continuous problem; second, periodically, with the small-scale variable y defined only within the unit cell. Asymptotic analysis determines differential equations for the large-scale and the small-scale potential fields. These problems can be solved separately, avoiding the necessity to deal with two disparate scales of the problem at the same time. The method was used to obtain the closed-form solution for a one-dimensional strand of 30 cardiac cells, and can be extended to two- and three-dimensional models.