Three topics of importance to modeling the integrative function of the heart are reviewed. The first is modeling of the ventricular myocyte. Emphasis is placed on excitation-contraction coupling and intracellular Ca²⁺ handling, and the interpretation of experimental data regarding interval-force relationships. Second, data on use of diffusion tensor magnetic resonance (DTMR) imaging for measuring the anatomical structure of the cardiac ventricles are presented. A method for the semi-automated reconstruction of the ventricles using a combination of gradient recalled acquisition in the steady state (GRASS) and DTMR images is described. Third, we describe how these anatomically and biophysically based models of the cardiac ventricles can be implemented on parallel computers.