Modeling conduction in the ventricles

Two models of electrical conduction in the cardiac ventricles are considered. The first model considered is that of a strand of ventricular muscle which uses the one-dimensional cable equation with the Beeler-Reuter model to represent the transmembrane currents. The effect of periodic stimulation on the strand is numerically simulated, and it is found that as simulation frequency is increased, the rhythms of synchronization are successively encountered. It is shown that this sequence of rhythms can be accounted for by considering the response of the strand to premature stimulation. This involves deriving a one-dimensional finite-difference equation or "map" from the response to premature stimulation, and then iterating this map to predict the response to periodic stimulation.The second model states that the highly ramified His-Purkinje system is reminiscent of a fractal branching structure, and that the ventricular myocardium is activated in a "fractal" (time-scale invariant) fashion, since it is activated via the His-Purkinje system. A 1/$f sp alpha$ power spectrum can sometimes be linked to fractal processes. The averaged power spectrum of single QRS complexes falls off as 1/$f sp alpha$ ($ alpha sim$ 4)