Control theory inspired considerations of the mathematical models of defibrillation

One efficient approximate solution of the bidomain equations, which are used as a mathematical model of the heart tissue electrical properties, has been described. Moreover, the selected algorithm for discretization of partial differential equations, consisting of the method of separation of variables and modal analysis technique, results in the state space representation of cardiac electrical activities, which makes the model suitable for applications of modern control theory. Also, the finite-dimensional model reveals the connection to the older models of defibrillation - simple circuit equivalents. Finally, an optimal controller designed for the generalized version of a simple parallel resistor-capacitor circuit has been applied to one- and three-mode expansions of the bidomain model.