APPM Department Colloquium - Travis Austin

Travis Austin, Tech-X Corporation

Discontinuous Cardiac Activation Modeling using Fast Multilevel Solvers

The ventricles are the core pumping chambers of the heart, responsible for pumping deoxygenated blood from the heart to the lungs and oxygenated blood from the heart to the rest of the body. Both left and right ventricles are composed of cardiac cells that have bioelectrical-mechanical capabilities responsible for the pumping action of the ventricles. The bioelectrical activity of the cells is based on the movements of ions (sodium, potassium, calcium, etc.) across cell walls that alter the membrane potential. Physically the cells are cylindrical-shaped and lie end-to-end in fibers which are then grouped into sheets such that effective ventricular equations (the bidomain equations) which couples microscopic cell level activity to macroscopic diffusion.

Most models that are employed to study cardiac bioelectrical activation assume that cardiac ventricular tissue is continuous and a continuous conductivity value is therefore used in the diffusion equation. In the early 1990s researchers at the University of Auckland showed through careful tissue dissection and imaging that there are larger scale discontinuities that can not be ignored if one one is interested in particular questions dependent on tissue structure. In particular, it is believed that models of defibrillation are completely dependent on the inclusion of these finer scale structures. Yet these detailed models affect the properties of the finite element matrices used in the modeling and require the use of more sophisticated linear solvers. This talk describes the background of discontinuous cardiac activation modeling and the current use of Black Box Multigrid for solving the discontinuous cardiac activation problems on structured grids.