Cardiac tissue microstructure influences propagation of cardiac electrical excitations under normal and arrhythmic conditions, but quantitative characterisation of this relationship remains a significant research challenge. Reaction-diffusion computational models of cardiac electrophysiology offer a viable approach for studying the influence of microstructure on complex excitation patterns which underlie arrhythmias (Benson et al. 2011). In this study, the influence of tissue microstructure (cardiomyocyte and sheetlet orientations) on organ-scale excitation patterns was investigated using 5 healthy rat ventricle reconstructions, obtained from diffusion tensor MRI (DTI) at 100 μm isotropic resolution (Teh et al. 2016). The primary, secondary, and tertiary eigenvectors from DTI have been shown previously to align with the myocyte, sheetlet plane, and sheetlet normal directions, respectively. The rat action potential duration and its restitution were simulated using the Fenton-Karma 3 variable cellular activation model (Fenton et al. 1998). Scroll wave re-entry was initiated in the 5 anatomical models at 10 prescribed locations for 3 different microstructure scenarios (giving 150 simulations in total): (i) isotropic (no microstructure); (ii) anisotropic (myocyte but no sheetlet microstructure); and (iii) orthotropic (myocyte and sheetlet microstructure). DTI-based microstructure was shown to increase dispersion of repolarisation following pacing at the left ventricular apex. In addition, inclusion of microstructure increased mean number of scroll wave filaments, and fast Fourier transform analysis of pseudo ECG waveforms revealed that anisotropic and orthotropic microstructure favoured the transition from narrow, single-peaked spectra to a broader range of peaks, associated with increased complexity of electrical activity. Arrhythmia dynamics differed between the 5 reconstructions, where myocardial structural variability between datasets could account for whether or not ventricular tachycardia degenerated into ventricular fibrillation, highlighting the important and under-appreciated role of structural variability. This study shows that myocardial structural variability alone can account for large inter-subject variability in arrhythmia dynamics.