Abstract
A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet. We propose a mechanism that can lead to such behavior. The velocity restitution gives the instantaneous velocity of a wave as a function of the time since the passage of the previous wave at a given point in space. Nonmonotonic restitution relationships will lead to situations in which various spacings between circulating waves are possible. In cardiology, the situation in which two waves travel in an anatomically defined circuit is referred to as double-wave reentry. Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy.
Highlights
In an excitable medium, a su ciently large perturbation from rest leads to a propagating excitation wave
A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet
Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy
Summary
A su ciently large perturbation from rest leads to a propagating excitation wave. Examples of excitation waves include action potentials in nerves and heart tissue, oxidation waves in the Belousov Zhabotinsky reaction, and forest res.[1,2] The dynamical properties of the excitation waves depend on the geometry and the nature of the medium. Nonmonotonic velocity restitution curves have been associated with a variety of exotic behaviors in one, two, and three dimensional contexts, such as wavefront bunching,[30] fractionation of the dispersion curve,[28] pulse annihilation,[24] as well as modulation of spiral wave period[29] and stability.[26] Both theoretical and experimental papers dating back to the 1960s have demonstrated multiple waves traveling on one dimensional rings.[5,6,8,13,15,23,24,28,30,32,33] If the velocity restitution is a monotonic increasing function, the only steady con guration is the antipodal one for double-wave reentry. This analysis extends previous studies by considering the role of heterogeneities and by analyzing all the bifurcations and stability of double-wave reentry that arise for oscillatory velocity restitution functions as the ring size varies
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