Mathématiques en biologie et médecine
The Current-Lifted Monodomain Model for Numerical Computations of the Heart Pacing
Rioux, Myriam
Université Laval

The response of the heart to an external electrical current stimulus remains a very active subject of research, e.g. for investigating defibrillation and pacing mechanisms. The bidomain model has always been recognized to be the only model suitable for these specific modelling applications. In this work, we describe a monodomain model with a source term that is derived from a lifting principle applied to the resolution of the electrostatic balance equation in the parabolic-elliptic formulation of the bidomain equations. The final model is a monodomain equation with lifted current, hence the appellation current-lifted monodomain (CLM). It allows any contribution of the current to be solved separately, making possible to account for unequal anisotropy ratios, the excitation via the intracellular, the extracellular, and the extracardiac media.  As this extra part of the calculation is performed once before all time iterations, the CLM performs as well as the standard monodomain model, i.e. about ten times faster than the bidomain model. For proving the use of the CLM model, virtual electrode polarizations (VEP) are simulated. VEP represents a whole class of phenomena strongly related to unequal anisotropy ratios, where the extracellular cardiac stimulation by an unipolar electrode induces characteristic regions of membrane polarization other than those in the vicinity of the electrode. Finally, the important advancement of this work is the replacement of the bidomain model for long-duration simulations with current stimulation, e.g., investigations of fibrillation mechanisms where current stimulations turn out to be an effective treatment

Lundi, 17 juin, 16h30
Salle Du Manège