Abstract
The standard conception of cardiac conduction is based on the cable theory of nerve conduction, which treats cardiac tissue as a continuous syncytium described by the Hodgkin-Huxley equations. However, cardiac tissue is composed of discretized cells with microscopic and macroscopic heterogeneities and discontinuities, such as subcellular localizations of sodium channels and connexins. In addition to this, there are heterogeneities in the distribution of sympathetic and parasympathetic nerves, which powerfully regulate impulse propagation. In the continuous models, the ultrastructural details, i.e. the microscopic heterogeneities and discontinuities, are ignored by 'coarse graining' or 'smoothing'. However, these ultrastructural components may play crucial roles in cardiac conduction and arrhythmogenesis, particularly in disease states. We discuss the current progress of modelling the effects of ultrastructural components on electrical conduction, the issues and challenges faced by the cardiac modelling community, and how to scale up conduction properties at the subcellular (microscopic) scale to the tissue and whole-heart (macroscopic) scale in future modelling and experimental studies, i.e. how to link the ultrastructure at different scales to impulse conduction and arrhythmogenesis in the heart.