Our understanding of the electrophysiological properties of the heart is incomplete. We have investigated two issues that are fundamental to advancing that understanding. First, there has been widespread debate over the mechanisms by which an externally applied shock can influence a sufficient volume of heart tissue to terminate cardiac fibrillation. Second, it has been uncertain whether cardiac tissue should be viewed as an electrically orthotropic structure, or whether its electrical properties are, in fact, isotropic in the plane orthogonal to myofiber direction. In the present study, a computer model that incorporates a detailed three-dimensional representation of cardiac muscular architecture is used to investigate these issues. We describe a bidomain model of electrical propagation solved in a discontinuous domain that accurately represents the microstructure of a transmural block of rat left ventricle. From analysis of the model results, we conclude that (1) the laminar organization of myocytes determines unique electrical properties in three microstructurally defined directions at any point in the ventricular wall of the heart, and (2) interlaminar clefts between layers of cardiomyocytes provide a substrate for bulk activation of the ventricles during defibrillation.