Thursday, April 12
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Charles S. Peskin
Title: Muscle and Blood: Mechanics and Electrophysiology of the Heart by the Immersed Boundry Method
Abstract: (joint work with David McQueen, Boyce Griffith, and Edward Vigmond)
The heart is a muscular organ equipped with valves that pumps blood around the circulation. It is coordinated by an electrical system intrinsic to the heart itself. The subject of this talk is a mathematical description of the mechanical function and electrophysiology of the heart, and also the computer solution of the governing equations. It turns out that the coupled problems of cardiac mechanics and electrophysiology can be formulated and solved in a similar manner within the framework of the immersed boundary (IB) method. This methodology was originally developed to study fluid-structure interaction of the heart valves, which are thin, flexible, elastic membranes immersed in the flowing blood. The IB method employs a Lagrangian description of immersed elastic structures, and an Eulerian description of the fluid in which they are immersed. The two descriptions are linked by interaction equations that involve the Dirac delta function. The interaction equations describe the application of force to the fluid by the elastic immersed boundary, and the motion of the immersed boundary at the local fluid velocity. In the electrical context, we use a bidomain formulation, with a Lagrangian description of the intracellular space, and an Eulerian description of the extracellular space. Again, there are interaction equations that involve the Dirac delta function. In this case, though, the variables involved in the interaction equations are the transmembrane currents and voltages, instead of the boundary forces and velocities. Results will be shown as computer animations of the beating heart.