Effects of spatial segmentation in the continuous model of excitation propagation in cardiac muscle.

Abstract

Spatial segmentation is essential for the numerical simulation of excitation propagation in cardiac muscle. This study evaluated the effects of spatial segmentation on action potential and on the velocity of propagation in a continuous one-dimensional model of cardiac muscle [intracellular and extracellular resistivities along (L) and transverse (T) to the muscle fibers: 402 omega(cm) (R(e), L), 3,620 omega(cm) (R(e), T), 48 omega(cm) (R(e), L), and 126 omega(cm) (R(e), T), J of Physiol 255:335-346, 1976) and either Luo-Rudy (L-R, Circ Res 68:1501-1526, 1991) or Beeler-Reuter (B-R, J Physiol 268:177-210, 1977) ionic currents. Related cable equations for active membrane are derived. Spatial segmentations of < 31.2 microm (L, L-R), < 11.5 microm (T, L-R), < 44.7 microm (L, B-R), and < 16.5 microm (T, B-R) were required for < 1% errors in the characteristic parameters of action potential. Similarly, spatial segmentations of < 54.5 microm (L, L-R), < 20.1 microm (T, L-R), < 84.3 microm (L, B-R), and < 31.2 microm (T, B-R) were required for < 1 % errors in the velocity of conduction. In general, spatial segmentations of < 26.9% and < 50.8% of the space constant of a fully activated membrane gave < 1.0% errors in the characteristic parameters of action potential and in the velocity of propagation, respectively, for both membranes. The action potential duration was relatively insensitive to the spatial segmentation. Our analysis suggests that lambda(full is a better criterion for the selection of spatial segmentation in numerical simulation than the space constant of the resting membrane.