Mathematical Modelling of the electrical activity of the heart from ion-channels to the body surface: Forward and Inverse problems

Meaningful computer based simulations of electrocardiograms (ECGs), linking models of the electrical activity of the heart to ECG signals, are a necessary step towards the development of personalized cardiac models from clinical ECG data. An ECG simulator is, in addition, a valuable tool for building a virtual data base of pathological conditions, to test and train medical devices but also to improve the knowledge on the clinical significance of some ECG signals. In this talk we will present a 3D multi-scale mathematical model based on reaction diffusion equations, named bidomain equations, representing the propagation of the electrical wave in the heart domain. These equations are coupled to a set of dynamic systems representing the electrical activity of cardiac cells. The heart model is then coupled to the Laplace equation representing the diffusion of the electrical potential in the torso. As examples of application, we will first show how this mathematical model could be used in drug cardio-toxicity assessment in safety pharmacology. Then we will show the potential of this mathematical model to improve the diagnosis of cardiac pathologies like ventricular tachycardia and fibrillation by solving various electrocardiography imaging inverse problems.