Abstract
A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as ‘defects’ on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.
Highlights
It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are considered, and it is confirmed that spiral waves are induced in the network in the presence of noise
1) A target wave could be developed to occupy the network by imposing external forcing currents with diversity or blocking partial ion channels of potassium in a fraction of neurons of the network
2) A spiral wave could be induced to occupy the network when the target wave is broken by the artificial defects and keeps robust to channel noise and certain additive Gaussian white noise
Summary
Beautiful spatiotemporal patterns can be observed in reactiondiffusion systems [1,2,3,4,5,6,7,8,9,10,11,12,13] and networks of coupled oscillators and/ or neurons [14,15,16,17,18,19,20,21,22,23,24,25]. It is argued that the realistic defects in the network could result from the effect of channel block because the effect of ion channel blocking in neurons in local area is very similar to the effect of artificial defects on blocking the target wave to induce a spiral wave.
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