Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons.

Yuangen Yao,Chengzhang Ma,Jun Ma,Haiyou Deng,Ming Yi,Irene Sendiña-Nadal

doi:10.1371/journal.pone.0171273

Abstract

Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed.

Highlights

The neuronal system plays a pivotal role in regulating physiological behaviors [1,2,3], which consists of a large number of neurons
As previously described in the section of introduction, as a reasonable and random excitation model, bounded noise has been widely applied in many fields
The present study focuses bounded noise and shortcuts on selection of spiral waves in SW networks of HH Neurons

Summary

Introduction

The neuronal system plays a pivotal role in regulating physiological behaviors [1,2,3], which consists of a large number of neurons. Recent studies have suggested that neuronal networks may share small-world (SW) topologies [6, 7], and neuronal dynamics can present and form complex spatial and temporal patterns [6]. Yang et al explored the impact of bounded noise and shortcuts on the spatiotemporal dynamics of SW neuronal networks, and founded that noise always impair spatial synchronization among coupled neurons, and yet CR occurs at an appropriately noise. Motivated by the above results, investigating the impacts of bounded noise and shortcuts on spiral waves in a SW neuronal network is very interesting and important. We mainly investigate roles of bounded noise and shortcuts on formation of spiral waves in a SW network of Hodgkin-Huxley (HH) neurons. The spatiotemporal dynamics of HH neurons in a SW network is governed by the following differential equations [44]

VijÞ þ D εklijðVkl À kl

Findings

Conclusion