Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.