Simulating the formation of spiral wave in the neuronal system
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O R I G I N A L PA P E R
Simulating the formation of spiral wave in the neuronal system Jun Ma · Bolin Hu · Chunni Wang · Wuyin Jin
Received: 5 December 2012 / Accepted: 9 January 2013 / Published online: 24 January 2013 © Springer Science+Business Media Dordrecht 2013
Abstract Some experimental results have confirmed that a spiral wave could be observed in the cortex of brain. The biological Hodgkin–Huxley neurons are used to construct a regular network with nearestneighbor connection, artificial line defects are generated to block the traveling wave in the network, and the potential mechanism for formation of spiral wave is investigated. A target wave is generated in a local area by imposing two external forcing currents with diversity (I0 − I1 ) in different areas of the network. It is confirmed that spiral wave could be induced by the defects even if no specific initial values are used. A single perfect spiral wave can occupy the network when the coupling intensity exceeds certain threshold; otherwise, a group of spiral waves emerges in the network. Certain channel noise can enhance the diversity (I0 − I1 ) for generating target wave, and then spiral waves are induced by blocking the target wave with
J. Ma () · B. Hu · C. Wang Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China e-mail: [email protected] W. Jin College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050, China W. Jin School of Physics and Mechanical & Electrical Engineering, Shao Guan University, Shaoguan 512005, China
defects under no-flux and/or periodic boundary conditions in the network. Keywords Target wave · Spiral wave · Defects · Network · Factor of synchronization
1 Introduction The application of magnetoencephalography (MEG) and electroencephalogram (EEG) could give a feasible way to identify and measure the brain cortex activities. Sometimes, we focus on the several of electrical activities of neurons by applying the voltage-sensitive dye technology. Some experimental results have confirmed that spiral wave could be observed in the cortex of brain [1–4]. Spiral waves were also discovered in rat intact cortex in vivo, both during the epidural application of carbachol and bicuculline and during sleep-like states [4]. Compared with the spiral waves in the brain slices, spiral waves in vivo are sustained for shorter times. These results support the hypothesis that spiral waves, as an emergency activity pattern, which can organize and modulate cortical population activities may contribute to both normal cortical processing and pathological patterns of activities, such as those found in epilepsy. As it is well known, coherence and/or stochastic resonance could be observed in the neuron or network of neurons due to noise and some bifurcation parameters [5–7]. Electric activities of neurons show distinct regularity when coherence or
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stochastic resonance occurs [8]. More interesting, spiral wave occurs in the network under multiple spatial coherence resonances induced by wh
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