Biomathematics / Computational Biology Colloquium
Computational Modeling of Cardiac Electromechanics
Speaker: Simone Rossi, Mathematics Department, The University of North Carolina at Chapel Hill
Location: Warren Weaver Hall 1314
Date: Tuesday, April 24, 2018, 12:30 p.m.
Thanks to the advances in computational and experimental methods of the last 20 years, today it is possible to study the whole heart function with anatomically accurate models. Unfortunately, the mathematical models describing the heart have mostly remained the same and their limitations have not been overcome.
In this talk, I will focus on the modeling and computational challenges of describing the electrophysiology, the mechanics and the electromechanics of the heart. In particular, I will present a novel hyperbolic model of cardiac electrophysiology: using Cattaneo's fluxes we address the issue of signals propagating at infinite speed in the parabolic equations of cardiac electrophysiology. I will shortly describe a computational efficient method to solve the equation of incompressible elastodynamics: using a variational multiscale analysis, we developed a simple linear finite element method that can easily handle complex geometries, such as those found in cardiac mechanics. I will show how the coupling between the electrophysiology and the mechanics can be performed using an active-strain formulation: in the active-strain formulation, the active contraction of the muscle is introduced in the mechanical model by a multiplicative decomposition of the deformation gradient tensor. The active-strain model for cardiac contraction can incorporate the rearrangement of the muscular cells naturally providing a more accurate representation of the ventricular transmural strains.