Evolution of cardiac computer models. The top panels illustrate, from left to right, the progression from one-dimensional (1D) models to three-dimensional (3D) models, including those that incorporate a representation of gross cardiac anatomy (3D+) and regional variations in myocardial fiber orientation (3D++). In the 1D model of a linear cardiac fiber (oriented vertically), pacing the fiber at cell 1 at a short cycle length induces discordant APD alternans in which the APD pattern at the site of stimulation is (from left to right) short APD, long APD, short APD, etc. However, the initial pattern at the other end of the fiber (cell no. 220) is the opposite: long APD followed by short APD (arrow 1). The next long APD is followed by conduction block (arrow 2). In the 2D simulation, local conduction block, indicated by the light blue region, prevents a wavefront of excitation (red area) from propagating up the right side of the sheet (where all of the cells remain in the rest state, shown in dark blue), but permits propagation up the left side, thereby inducing the formation of a spiral wave of excitation. When transferred to a 3D slab, the 2D spiral wave becomes a 3D vortex. Future challenges to creating a complete model of the heart include incorporation of excitation-contraction coupling and innervation by the sympathetic and parasympathetic limbs of the autonomic nervous system into an anatomically realistic substrate. The 1D image is reprinted with permission from Circ. Res. (8). The 3D image is reprinted with permission from Proc. Natl. Acad. Sci. U. S. A. (17). The 3D+ and 3D++ images are reprinted from Xie et al. (14). The cross-section of the heart is reproduced with permission from Benjamin/Cummings (18).