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Spatiotemporal activities of neural network exposed to external electric fields

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Abstract

Neural electrical activities are due to the movement of ions in/out of the neuron and can be modulated by an external electric field. Moreover, clinical evidences reveal that the modulated activities of brain tissue by an external electric field are associated with normal or pathological brain functions. In this paper, we investigated the spatiotemporal activities of a network of neurons considering an AC electric field. It is shown that the external electric field has a significant impact on the activities of the neural network. The strong external electric field facilitates the neuron firing action potentials and enhances the mean firing rate of the network, but disrupts the synchronicity of the activities of the neural network. The information entropy revealed that the external field is capable of changing the amount of information in the neural network and the interspike internals distribution can also be changed by the external field regardless the network parameters. It is observed a v-shape resonant area in the \(E_\mathrm{appl}\)-f (field intensity–field frequency) parameter space, where the neural network exhibits a high firing rate but weak synchronicity and low value of information entropy. Moreover, the effect of the electric field on the spatiotemporal activities of the neural network is detected in different connection fraction and network size. Our current work gives the insight into the effect of the external electric field on the spatiotemporal activities of the neural network.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China with Grants No. 11447027, and the Fundamental Research Funds for the Central Universities with No. GK20 1503025.

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Authors and Affiliations

  1. College of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710119, China

    Hengtong Wang

  2. Center of Soft Matter Physics and its Application, Beihang University, Beijing, 100191, China

    Yong Chen

  3. School of Physics and Nuclear Energy Engineering, Beihang University, Beijing, 100191, China

    Yong Chen

Authors
  1. Hengtong Wang
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  2. Yong Chen
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Correspondence to Hengtong Wang.

Appendix

Appendix

1.1 Description of the neuronal model

The neuron in our neural network is chosen as the Hodgkin–Huxley conductance-based model, which describes how action potentials are initiated and propagated in a single neuron. Here, the neuron is treated as a single-patch model, and the current along the axon is ignored. To make the model closely match the real nervous system, the angle (\(\theta \)) between the field line and the exterior normal direction of the patches has a uniform distribution, based on the complex structure neural network and neurons.

On the other hand, we consider the action of the exogenous electric fields at the cellular level as a membrane voltage perturbation and introducing an additive correction term \(V_E\) for the reversal potential. In fact, the external fields interact with the ions in the neuron and induce a reset of the distribution of ions both inside and outside membranes. Thus, the reversal potential should be modified. Based on the theory of the electric field (induced by ion distribution) force just balances the diffusion force at equilibrium, in the current model, we suppose that force induced by an external electrical field \(V_E\) is balanced by the changes in distribution of ions. Thus, the final reversal potential \(E_\mathrm{ion}^\mathrm{final}\) (with effect of an external field) can be simply written as: \(E_\mathrm{ion}^\mathrm{final}=-V_E+E_\mathrm{ion}\). Here, \(E_\mathrm{ion}\) is the reversal potential without of an external field.

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Wang, H., Chen, Y. Spatiotemporal activities of neural network exposed to external electric fields. Nonlinear Dyn 85, 881–891 (2016). https://doi.org/10.1007/s11071-016-2730-4

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