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An efficient space-splitting method for simulating brain neurons by neuronal synchronization to control epileptic activity

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Abstract

Controlling synchronization of neural networks in brain activity is an important issue in neurodevelopmental disorders such as epileptic seizures. In this paper, we propose an efficient numerical method to simulate nonlinear spatio-temporal neural dynamic models and their synchronizations. In this study, the generalized Lagrange Jacobi Gauss–Lobatto collocation method combined with Trotter operator splitting technique is employed. This method allows us to decouple the nonlinear partial differential equations of neural network models into independent linear algebraic equations of very small dimensions. Moreover, we examine different test cases to indicate the advantages of the proposed method in accuracy, computational cost, and complexity. It is shown that the computational complexity of the proposed method is much smaller than the complexity of pure spectral method. Finally, A GPU implementation is applied on the two dimensional models to accelerate the time consuming simulations.

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Acknowledgements

The authors are very grateful to reviewers for carefully reading this paper and for their comments and suggestions, which have improved the quality of the paper. Also they are grateful to High Performance Computing (HPC) laboratory in IPM to provided us the suitable GPU for simulations. The corresponding author’s work was partially supported by Center of Excellence in Cognitive Neuropsychology (CECN). He sincerely thanks to CECN for their support.

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Authors and Affiliations

  1. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    M. M. Moayeri, S. Latifi & K. Parand

  2. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    A. H. Hadian-Rasanan & J. A. Rad

  3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada

    K. Parand

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  1. M. M. Moayeri
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Moayeri, M.M., Hadian-Rasanan, A.H., Latifi, S. et al. An efficient space-splitting method for simulating brain neurons by neuronal synchronization to control epileptic activity. Engineering with Computers 38, 819–846 (2022). https://doi.org/10.1007/s00366-020-01086-9

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