On the use of the bidomain equations for computing the transmembrane potential throughout the heart wall: An inverse problem

In this paper we will explain how one may use the bidomain model to solve the inverse ECG problem in which the transmembrane potential throughout the myocardium is used as the unknown source. The accurate and efficient numerical solution of this problem can, for example, provide valuable insight into the electrophysiological nature of arrhythmias, the location and extent of ischemia and infarction, and can lead to new medical imaging devices. This inverse problem is ill-posed, i.e. it is unstable and, even under ideal conditions, it can be shown that the transmembrane potential cannot be uniquely identified from body surface potential maps (BSPMs) - additional information is needed. The purpose of this paper is to show how the bidomain equations can be combined with apriori information and suitable numerical techniques to partially enforce uniqueness as well as stability in this inverse problem.