Reconstructing the heart

The electrical activity of the heart can be reconstructed at different levels and time scales; for example, its global rhythmicity and irregularity, propagating action potentials and wave fronts, membrane action potentials and ionic currents, and single channel currents. Various different types of mathematical model are used, including eikonal equations, partial and ordinary differential equations, and coupled lattices of maps or ordinary differential equations. These phenomena and models form a hierarchy in which the organ and tissue physiology results from the cellular biophysics. On making discrete approximations of continuous spaces and times, the range of diverse models of cardiac excitation are all examples of synchronous concurrent algorithms (SCAs) and, as such, they may be studied in a unified way from the point of view of parallel deterministic computation. The theory of SCAs provides mathematical methods that may be used for the decomposition, combination and comparison of different types of model in the reconstruction of a hierarchical model of electrical activity in the heart.