Excitable chemical reaction systems. II. Several pulses on the ring fiber

Double-wave reentry in excitable media

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.

Wave grouping of a meandering spiral induced by Doppler effects and oscillatory dispersion

A new type of meandering spiral pattern, in which the dense waves form groups while the sparse waves keep evenly spaced, is observed in a spatial open reactor using a ferroin-catalyzed Belousov-Zhabotinsky reaction. Such a phenomenon is related to both the Doppler effect of a meandering spiral and the oscillatory dispersion relation of the system. Simulation in the two-dimensional Oregonator reaction-diffusion model with an oscillatory dispersion relation gives very similar results.

The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model

Propagation speed of an impulse is influenced by previous activity. A pulse following its predecessor too closely may travel more slowly than a solitary pulse. In contrast, for some range of interspike intervals, a pulse may travel faster than normal because of a possible superexcitable phase of its predecessor's wake. Thus, in general, pulse speeds and interspike intervals will not remain constant during propagation. We consider these issues for the Hodgkin-Huxley cable equations. First, the relation between speed and frequency or interspike interval, the dispersion relation, is computed for particular solutions, steadily propagating periodic wave trains. For each frequency, omega, below some maximum frequency, omega max, we find two such solutions, one fast and one slow. The latter are likely unstable as a computational example illustrates. The solitary pulse is obtained in the limit as omega tends to zero. At high frequency, speed drops significantly below the solitary pulse speed; for 6.3 degrees C, the drop at omega max is greater than 60%. For an intermediate range of frequencies, supernormal speeds are found and these are correlated with oscillatory swings in sub- and superexcitability in the return to rest of an impulse. Qualitative consequences of the dispersion relation are illustrated with several different computed pulse train responses of the full cable equations for repetitively applied current pulses. Moreover, changes in pulse speed and interspike interval during propagation are predicted quantitatively by a simple kinematic approximation which applies the dispersion relation, instantaneously, to individual pulses. One example shows how interspike time intervals can be distorted during propagation from a ratio of 2:1 at input to 6:5 at a distance of 6.5 cm.