Muscle and Blood: Computer Simulation of the Heart by the Immersed Boundary Method
Charles Peskin, Courant Institute of Mathematical Sciences<br /> New York University
Computer simulation of the beating human heart requires the simultaneous solution of equations of motion that couple together the fluid mechanics of the blood, the elasticity of the flexible heart valve leaflets, and the active, time-dependent elasticity of the muscular heart walls. The immersed boundary (IB) method was created to solve this problem. It regards the cardiac tissue as a part of the fluid in which additional, elastic forces are applied. These forces are generated by a collection of immersed elastic fibers that model the muscle fibers of the heart walls and the collagen fibers that give the heart valve leaflets their strength. Results will be shown as a computer animation of the beating heart. Not included in these simulations is the electrical activity that coordinates and controls the heartbeat, but we shall discuss how the IB framework can be generalized to solve the electrical problem, too.
References (available at http://www.math.nyu.edu/faculty/peskin):
McQueen DM and Peskin CS: Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity. In: Mechanics for a New Millennium (Proc. ICTAM 2000), H. Aref and J.W. Phillips, eds., Kluwer Academic Publishers, 2001.
Peskin CS: The immersed boundary method. Acta Numerica 11:479-517, 2002
Abstract Author(s): Charles S. Peskin, David M. McQueen, and Boyce E. Griffith