CRPC-TR99806-S						August 1999

Title: Simulating Electrical Action Potential Propagation in the Heart
with Parallel Computation

Author: Christa Erwin

Submitted November 1999

Abstract:

     One of the central questions in the field of cardiac dynamics is the
mechanism of the decay of ventricular tachycardia, characterized by spiral
waves of electrical activity, to fibrillation, characterized by
"incoherent" electrical wave behavior, resulting in failure of the heart's
pumping action.  This problem is being chipped away at from various
perspectives by various groups in physiology, mathematics, physics and
engineering.  Numerical simulation, coupled with experimental feedback, is
a necessary and powerful tool in this area, as in many other growing areas
of computational science.
     The focus of this summer project was to explore the effect of
geometry and fiber architecture of the left ventricle on electrical wave
dynamics.  This question was movivated by earlier munerical experiments
performed in a rectangular slab model of the ventricle, which showed that
the rotating anistropy inherent in cardiac tissue could lead to wave
instablility.  This rotating anistropy is pictured in Figure 1 (from [4]
and [5]).  Our goal was to construct a minimally realistic geometrical
model of the left ventricle and to simulate electrical wave propagation in
this three-dimensional model.
     Dissection results reveal a nested layered geometry for the left
ventricle, where a single macroscopic muscle fiber bundle starting at the
basal plane outside the midwall (toward the epicardium) traverses down
toward the apex on an outer surface, and at some point before reaching the
apex, changes direction, traverses back along an inner surface reinserting
at the basal plane inside the midwall (toward the endocardium) [6].  The
simple fact that electrical propagation along a fiber is several times
faster than perpendicular to it suggests that this nested architecture can
be important in the propagaion of electrical waves in the heart.  In
particular, transmural propagation can still be achieved in a nested
geometry even when propagation perpendicular to the fiber is weakened or
cut off.
     A geometrical model of the left ventricle has been developed by Sima
Setayeshgar in the Applied Mathematics Department at the California
Institute of Technology [1], based on previous works [2], [3].  In this
model, the fiber surfaces are given by nested cones, and the fiber
trajectories by geodesics on these surfaces, consistent with experimental
observation.  Figure 2 shows the fiber trajectories on one fiber surface.
     The objective of this summer project was to investigate the effect of
the realistic (a) nested conical geometry and (b) fiber architecture of
the left ventricle on action potential propagation, using the above model.
In the process, the project provided an introduction to the following:

     - Numerical methods for scientific computing, in particular, finite
       difference solutions to nonlinear partial differential equations

     - Parallel computing using MPI

     - HTML form submission and CGI programming as a front-end for running
       parallel code on Caltech's Boewulf machine.

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Christa Erwin
CRPC Summer Research Program in Parallel Computing for Undergraduate Women
California Institute of Technology