Wave propagation simulation in normal and infarcted myocardium: computational and modelling issues

Simulation of propagating action potentials (PAP) in normal and abnormal myocardium is used for the understanding of mechanisms responsible for eliciting dangerous arrhythmias. One- and two-dimensional models dealing with PAP properties are reviewed in this paper viewed both from the computational and mathematical aspects. These models are used for linking theoretical and experimental results. The discontinuous nature of the PAP is demonstrated through the combination of experimental and theoretically derived results. In particular it can be shown that for increased intracellular coupling resistance the PAP upstroke phase properties (Vmax, dV/dtmax and tau foot) change considerably, and in some cases non-monotonically with increased coupling resistance. It is shown that tau foot) is a parameter that is very sensitive to the cell's distance to the stimulus site, the stimulus strength and the coupling resistance. In particular it can be shown that in a one-dimensional structure the tau foot value can increase dramatically for lower coupling resistance values near the stimulus site and subsequently can be reduced as we move to distances larger than five resting length constants from the stimulus site. The tau foot variability is reduced with increased coupling resistance, rendering the lower coupling resistance structures, under abnormal excitation sequences, more vulnerable to conduction block and arrhythmias. Using the theory of discontinuous propagation of the PAP in the myocardium it is demonstrated that for specific abnormal situations in the myocardium, such as infarcted tissue, one- and two-dimensional models can reliably simulate propagation characteristics and explain complex phenomena such as propagation at bifurcation sites and mechanisms of block and re-entry. In conclusion it is shown that applied mathematics and informatics can help in elucidating electrophysiologically complex mechanisms such as arrhythmias and conduction disturbances in the myocardium.