Mechanism of spiral formation in heterogeneous discretized excitable media

Abstract

Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.

Spontaneous formation of unidirectional path

“…Our numerical results showed unidirectional propagation always appeared at the spiral core as reported on the previous paper (Kinoshita et al, 2013). To clarify the cause of unidirectional behavior, we focused on the inhibitor concentration around the path and found a spatial asymmetric profile.…”

“…These cells were placed randomly in BZ reaction field (see Supplement). Figure 1 shows the previous results [15], which illustrate that the unidirectional path was generated spontaneously with the spatial heterogeneity of excitability. Although our previous study [15] indicated that certain distributions of suppression cells could spontaneously generate the unidirectional path, the mechanism and the specific structure necessary to create unidirectional path have not been elucidated.…”

“…In addition, a unidirectional path could be generated stochastically by spatial arrays of suppressed cells [15]. In our previous experiment [15], we chose the ruthenium-catalyzed BZ system because the properties of the reaction kinetics (oscillatory, excitation, and suppression states) can be conveniently controlled by adjusting the light intensity [12,[16][17][18][19][20].…”

“…Therefore, in the current study, to clearly identify the mechanism for the spontaneous formation of unidirectional path in the experiment [15], we simulate the Oregonator model, which was modified for photosensitive BZ reaction [21,22], with a heterogeneous reaction field. This simulated system represents the same condition for the spatial arrays of the suppression cells as that utilized in the previous experiment ( Figure 1) [15].…”

Reentry produced by small-scale heterogeneities in a discrete model of cardiac tissue

“…by spontaneous formation of spirals due to ectopic beats. The accumulation of the heterogeneities in a particular region of the system may generate reentries [18,19] due to the formation of a source-sink mismatch [20,21]. On the other hand, heterogeneities can be also employed as virtual electrodes to generate a large number of new waves to suppress fibrillatory electrical activity [22,23].…”