Selection of Multiarmed Spiral Waves in a Regular Network of Neurons

Abstract

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.

Autapse-Induced Spiral Wave in Network of Neurons under Noise

“…In this way, some researchers show great interests in detecting the formation and transition of patterns in network of neurons [9]–[19]. It was reported that spiral wave can be found in the cortex of brain [20]–[22], and then some theoretical investigations [23], [24] have been presented to explore the potential formation mechanism of spiral wave and multi-armed spiral wave in the network of neurons, indeed, these results [24] have confirmed that intermediate channels blocking in neurons in a local area of neuronal network can induce emergence of spiral wave, and the stability of multiarmed spiral wave was also discussed. It was also confirmed that artificial defects [25] can block travelling wave to induce perfect spiral wave under appropriate coupling intensity between neurons, and breakup of spiral wave occurs with strong noise or channel noise [26], [27] being used.…”

Formation of multi-armed spiral waves in neuronal network induced by adjusting ion channel conductance

“…In a word, the way to induce local heterogeneity is different from the case as shown in Ref. 43, thus another mechanism to explain the emergence of multi-armed spiral waves in excitable media can be discussed in a numerical way.…”

“…As a result, it is important to investigate the stability of multi-armed spiral wave in the excitable media. Hu et al 43 attempted to reproduce the occurrence of multi-armed spiral waves in a network of neurons and the stability of multi-armed spiral waves was also discussed analytically. They found that a group of target waves can be emitted from local heterogeneity by imposing external forcing currents with diversity on the network, and then these target waves can convert into spiral waves due to continuous collision.…”

Emitting waves from defects in network with autapses

“…The dynamical properties of electric activities, stochastic resonance, coherence and synchronization of neurons have been investigated extensively [3][4][5][6][7][8][9][10][11][12][13][14]. Furthermore, the collective behaviors of neuronal network have also been investigated by detecting the spatiotemporal pattern selection, transition of spatial distribution , such as pulse wave [20] in a ring network, target wave [30], spiral wave [16][17][18][19][31][32][33][34] in a two-dimensional array with different topological structures. In fact, in realistic neuronal system, the effect of other factors should be considered, for example, the action potential is also dependent on the gliocyte and it is interesting to study the cooperative behaviors of neuron and astrocyte [35].…”