Background: The system of transverse and longitudinal sarcolemmal tubules (T-system) is observed to remodel in two cardiovascular conditions of increasing incidence: atrial fibrillation (AF) and heart failure (HF). The relationship between these conditions, wherein patients with HF often develop AF, and vice versa, confounds this problem further. Dysfunctional calcium regulation, as a result of altered T-system morphology, has been suggested to underlie disruptions in excitation-contraction coupling, as well as an increase in the frequency of arrhythmic events at the cellular scale; however, these mechanisms and their importance remain to be fully described. Methods: A contemporary computational model describing rabbit atrial electrophysiology (Aslanidi, et al. 2009) was integrated with our novel model describing stochastic spatio-temporal Ca2+ dynamics (Colman et al. 2017). In isolation to other potential forms of atrial remodelling, morphological T-system remodelling associated with HF was simulated through removing sarcolemmal ion-channel currents from individual calcium release units (CRUs), either assigned randomly or in pre-defined regions of varying extent. Rapid pacing protocols were applied to induce Ca2+ transient alternans, and load the Sarcoplasmic Reticulum (SR) with Ca2+: the resulting statistics of spontaneous release events were analysed. Results: The model reproduced rabbit atrial action potential and Ca2+ transient morphology associated with healthy cardiac function. Variation in T-system density and organisation, in isolation, demonstrated an inverse correlation between T-system density and the susceptibility of spontaneous Ca2+ release events, determined by an interaction of localised SR Ca2+ loading and reduced efflux, promoting successful Ca2+ wave propagation. Lower T-system density also promotes Ca2+ alternans, by alternating successful and failed propagations of Ca2+ into regions without T-tubules. Conclusion: A novel model of rabbit atrial electrophysiology has been developed, that includes a stochastic spatio-temporal description of Ca2+ handling. Investigations using this model suggest that alterations in T-system morphology may play an important role in the predisposition of atrial myocytes to arrhythmic events in the presence of HF. The model presents a powerful research tool to explore how these cell-level phenomena manifest at the tissue level and result in arrhythmias.