Simplified cellular automata model of neuronal patch dynamics with generalized non-linear cell response

Authors

  • Reinier Xander A. Ramos ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Johnrob Y. Bantang ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

Hodgkin-Huxley (HH) and other computational neuronal models are adequate methods in describing the dynamics of a single neuron. However, the HH model consist of four ordinary differential equations (ODEs) to solve for the neuronal response. Hence, simulating a large network of HH neurons would require very powerful computing devices. A model based on cellular automata (CA) has been recently made possible resulting to a simplistic way of simulating many neurons without requiring large computational resource. In this study, we introduce a non-linear CA that generalizes the response of the neuron compatible with empirical data via a nonlinearity parameter b. The resulting simple model is used to study a neuronal patch of 104 (N = 10000) neurons in a 2D lattice with periodic boundary conditions. The phase space diagrams show that in the limit that the activation function becomes linear (b → 1+), the system transitions from an active steady-state (Class 1) to a quiescent steady-state (Class 0) at a0 ≈ 0.5. Actual spatio-temporal neuronal responses simulations are obtained by translating the activation probability into dynamical transitions between the three standard neuronal cell (discrete) states: 1) Q = quiescent or inactive; 2) F = firing or spiking; 3) R = refractory period, such that Q → F → R → Q.

About the Speaker

Johnrob Y. Bantang, National Institute of Physics, University of the Philippines Diliman

Associate Professor

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Issue

Article ID

SPP-2021-PB-03

Section

Poster Session B (Complex Systems, Photonics, and Interdisciplinary Topics)

Published

2021-10-02

How to Cite

[1]
RXA Ramos and JY Bantang, Simplified cellular automata model of neuronal patch dynamics with generalized non-linear cell response, Proceedings of the Samahang Pisika ng Pilipinas 39, SPP-2021-PB-03 (2021). URL: https://proceedings.spp-online.org/article/view/SPP-2021-PB-03.