A model of cardiac microstructure and diffusion MRI is presented, and compared with experimental data from ex vivo rat hearts. The model includes a simplified representation of individual cells, with physiologically correct cell size and orientation, as well as intra- to extracellular volume ratio. Diffusion MRI is simulated using a Monte Carlo model and realistic MRI sequences. The results show good correspondence between the simulated and experimental MRI signals. Similar patterns are observed in the eigenvalues of the diffusion tensor, the mean diffusivity (MD) and the fractional anisotropy (FA). A sensitivity analysis shows that the diffusivity is the dominant influence on all three eigenvalues of the diffusion tensor, the MD and the FA. The area and aspect ratio of the cell cross-section affect the secondary and tertiary eigenvalues, and hence the FA. Within biological norms, the cell length, volume fraction of cells and rate of change of helix angle play a relatively small role in influencing tissue diffusion. Results suggest that the model could be used to improve understanding of the relationship between cardiac microstructure and diffusion MRI measurements, as well as in testing and refinement of cardiac diffusion MRI protocols.