This paper presents a morphological analysis of fibrotic scarring in non-ischemic dilated cardiomyopathy, and its relationship to electrical instabilities which underlie reentrant arrhythmias. Two dimensional electrophysiological simulation models were constructed from a set of 699 late gadolinium enhanced cardiac magnetic resonance images originating from 157 patients. Areas of late gadolinium enhancement (LGE) in each image were assigned one of 10 possible microstructures, which modelled the details of fibrotic scarring an order of magnitude below the MRI scan resolution. A simulated programmed electrical stimulation protocol tested each model for the possibility of generating either a transmural block or a transmural reentry. The outcomes of the simulations were compared against morphological LGE features extracted from the images. Models which blocked or reentered, grouped by microstructure, were significantly different from one another in myocardial-LGE interface length, number of components and entropy, but not in relative area and transmurality. With an unknown microstructure, transmurality alone was the best predictor of block, whereas a combination of interface length, transmurality and number of components was the best predictor of reentry in linear discriminant analysis.