The primary purpose of the heart is to act as a regular, rhythmic pump in order to maintain the circulation of blood throughout the body. This mechanical activity is driven by electrical activity at the cell-level, through the intricate processes comprising excitationcontraction coupling. Disruption to these processes can result in rhythm disturbances (arrhythmias), which are potentially fatal, but the underlying mechanisms are complex, dynamic and multi-scale. Thus, they are difficult to experimentally dissect, and have been a major focus in the field of computational biology. Detailed quantitative descriptions of cardiac electrophysiology have been developed over the past 60 years that allow the simulation of healthy and pathophysiological excitation, permitting detailed computational investigation of the complex processes that result in pro-arrhythmic behaviour. However, despite the rat being the most widely used animal model in cardiovascular research, existing computational models of rat ventricular electrophysiology are unable to account for stochastic subcellular calcium dynamics, which are known to trigger arrhythmias. The aims of this thesis were to: (i) develop a new computational model of rat ventricular electrophysiology including stochastic spatio-temporal calcium cycling dynamics; and (ii) use this model to explore how ion channel remodelling observed in heart failure results in pro-arrhythmic activity at the single cell level, and the mechanisms underlying the unique restitution characteristics of the rat ventricular action potential. A recent rat ventricular electrophysiology model was coupled to a stochastic, spatiotemporal calcium cycling model. The new model reproduced various experimental action potential and calcium handling dynamics from the literature for rat ventricular myocytes, and revealed that electrical remodelling in heart failure increases the propensity for spontaneous calcium release events and lowers the threshold for generation of delayed afterdepolarisations, both of which are pro-arrhythmic. In addition, the restitution properties of rat ventricular myocytes are the result of a complex balance between altered repolarising potassium current kinetics and calcium handling properties, including the sodium-calcium exchanger. The model developed in this thesis has provided insight into pro-arrhythmic and ratedependent phenomena in rat ventricular myocytes, and is suitable for future single cell and tissue simulations.