We describe methodologies for: (a) mapping ventricular activation using high-density epicardial electrode arrays; (b) measuring and modelling ventricular geometry and fibre orientation at high spatial resolution using diffusion tensor magnetic resonance imaging (DTMRI); and (c) simulating electrical conduction; using comprehensive data sets collected from individual canine hearts. We demonstrate that computational models based on these experimental data sets yield reasonably accurate reproduction of measured epicardial activation patterns. We believe this ability to electrically map and model individual hearts will lead to enhanced understanding of the relationship between anatomical structure, and electrical conduction in the cardiac ventricles.