Dynamics of Sustained Reentry in a Loop Model with Discrete Gap
Phys. Rev. E., 76:021928, 2007.
The dynamics of reentry is studied in a one-dimensional loop of model cardiac cells with discrete intercellular gap junction resistance (R). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For R below a limiting value, propagation is found to change from period-1 to quasiperiodic (QP) at a critical loop length (Lcrit) that decreases with R. Quasiperiodic reentry exists from Lcrit to a minimum length (Lmin), which also shortens with R. The decrease of Lcrit(R) is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with R. An increase of R does not seem to increase the number of possible QP solutions since, as in the continuous cable, only two QP modes of propagation were found despite an extensive search through alternative initial conditions.
The contraction of the heart is initiated by an electrical impulse that propagates over the heart muscle to activate each muscle cell. Propagated activation is carried out by the cells themselves, which, once activated, activate their neighbours in turn. Once a cell is activated, it cannot be re-activated for a while. Therefore, once all cells have been activated, the heart can relax and pause until the next beat. In diseased hearts, activation can be so delayed that some cells are ready for the next activation before all others are activated. It is then possible that the activation "re-enters" and goes on forever, making the heart beat too fast and ineffective. This can be lethal if it is not stopped in time by defibrillation of the heart.
This paper is a mathematical study of re-entry in a one-dimensional loop. This is a highly simplified model of re-entry in a real heart. However, the events in such a simple model are already very complicated. Only when such relatively simple models are well understood, we can hope to gain a better understanding of more complicated situations. Basic studies like these are therefore important to obtain a good understanding of the events in a real heart.
This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
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