Heart Muscle as a Reaction–Diffusion Medium: The Roles of Electric Potential Diffusion, Activation Front Curvature, and Anisotropy

Abstract

This tutorial, the third in a series about electrical dynamics in the heart, reviews laboratory experiments and numerical experiments about a reaction–diffusion partial-differential equation model commonly used to interpret electrophysiological propagation in normal heart muscle. It aims to sort out ostensibly contradictory impressions competing in current literature about the nature, magnitude, and dynamical consequences of activation front curvature within such a uniformly anisotropic tissue, insofar as such idealizations represent normal heart muscle. It is shown that activation fronts do not generally propagate along the perpendicular, and do not attach perpendicularly to no-flux boundaries, and that "critical radius" is a tricky concept except in isotropic media. Much is found to depend, even qualitatively, on the numerical value of the electric diffusion coefficient for normal heart muscle, to which values spanning two orders of magnitude are imputed in the literature. A "correct" value is tentatively identified which seems to lie securely inside the continuum range, so things are rather simpler than they may have appeared (except in diverse cases of unspecifiable abnormality in living specimens and in models). This tutorial is intended as much to provoke inquiry as to lay it to rest: The reader looking for solvable problems will find many unsolved here, with a rich current reference list leading to more.