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A study of phase resetting, mutual entrainment, and modified ventricular parasystole using a model of coupled heart cells Foster, Toni


Several aspects of cardiac electrophysiology including phase-resetting and entrainment are investigated through the dynamic interactions of coupled mathematical models of cardiac cells. Unlike previous studies of cell interaction which have used simplified models of a general cardiac cell or oscillators characterized only by their phase transition curves the present work incorporates the more physiologically realistic cell models of the Hodgkin-Huxley type. Furthermore, this caricature of the heart includes models representing cells from each of the major components of the heart's electrical conduction system, the SA node, AV node, Purkinje fibre network, and ventricular myocardium. Since there does not exist a model for an AV node cell, a new model is created by modifying the SA node cell equations. Because spontaneously firing cardiac cells exhibit a wide range of oscillation frequencies, certain physiologically based parameters in the model equations were altered to produce a similar range of intrinsic frequencies in the model cells. These model cells are coupled by assuming that direction-dependent and purely resistive coupling currents flow between them. Furthermore, these coupling currents incorporate a time delay rep-resenting the intercell impulse propagation time which is significant between different regions of the heart. Each of the conduction components, the SA and AV nodes, Purkinje fibre network, and ventricular myocardium, can be modelled with either one or several of their model cells. These model components can then be coupled with appropriate conductances and propagation time delays to model the spread of waves of excitation from one region of the heart to another. When cells interact, their intrinsic cycles may be perturbed. These alterations or phase-shifts which determine the ultimate rhythm of coupled cells are studied for various combinations of the model cells and different strengths of interaction. In each case results are plotted in a phase response curve whose shape is found to depend on such things as coupling conductance and cell frequency. Phase-resetting is a prerequisite to the entrainment of cells in which there are m cycles of one cell for every n cycles of another. The phenomenon of entrainment is studied as part of the behavior of a healthy heart where it provides the mechanism by which cells synchronize to produce a single wave of excitation for each heartbeat. Mutual entrainment is also studied in a commonly occurring pathological situation, modulated ventricular parasystole. It is demonstrated that the particular pattern of m:n entrainment is dependent on the differences in the intrinsic frequencies of the cells and on the strength of the interaction. Results obtained using different types of model cells located in different regions of the heart are compared and contrasted to those of previous studies of adjacent cells which are identical.

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