Significant tissue structures exist in cardiac ventricular tissue that are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhymogenesis and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements, we use tissue-specific structure and mathematical modelling. Our models have enabled us to consider key hypotheses regarding discontinuous activation. We also consider the future developments of our intact tissue experimental programme.