Traveling waves in excitable media

2012 ◽  
Vol 48 (3) ◽  
pp. 446-448
Author(s):  
T. V. Karamysheva
2018 ◽  
Vol 119 (6) ◽  
pp. 2212-2228 ◽  
Author(s):  
Michael E. Rule ◽  
Carlos Vargas-Irwin ◽  
John P. Donoghue ◽  
Wilson Truccolo

Previous studies on the origin and properties of spatial patterns in motor cortex β-local field potential (β-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether β-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in β-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) β-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) β-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) β-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, β-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient β-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of β-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient β-local field potential (β-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, β-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex β-LFP wave patterns.


1999 ◽  
Vol 60 (1) ◽  
pp. 54-57 ◽  
Author(s):  
Grigory V. Osipov ◽  
James J. Collins

1996 ◽  
Vol 10 (18) ◽  
pp. 2237-2250 ◽  
Author(s):  
B M Sager

2008 ◽  
Vol 107 (2) ◽  
pp. 344-349 ◽  
Author(s):  
E. P. Zemskov ◽  
A. Yu. Loskutov

1997 ◽  
Vol 36 (04/05) ◽  
pp. 290-293
Author(s):  
L. Glass ◽  
T. Nomura

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.


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