Young and Aged Neuronal Tissue Dynamics With a Simplified Neuronal Patch Cellular Automata Model

Abstract

Realistic single-cell neuronal dynamics are typically obtained by solving models that involve solving a set of differential equations similar to the Hodgkin-Huxley (HH) system. However, realistic simulations of neuronal tissue dynamics —especially at the organ level, the brain— can become intractable due to an explosion in the number of equations to be solved simultaneously. Consequently, such efforts of modeling tissue- or organ-level systems require a lot of computational time and the need for large computational resources. Here, we propose to utilize a cellular automata (CA) model as an efficient way of modeling a large number of neurons reducing both the computational time and memory requirement. First, a first-order approximation of the response function of each HH neuron is obtained and used as the response-curve automaton rule. We then considered a system where an external input is in a few cells. We utilize a Moore neighborhood (both totalistic and outer-totalistic rules) for the CA system used. The resulting steady-state dynamics of a two-dimensional (2D) neuronal patch of size 1, 024 × 1, 024 cells can be classified into three classes: (1) Class 0–inactive, (2) Class 1–spiking, and (3) Class 2–oscillatory. We also present results for different quasi-3D configurations starting from the 2D lattice and show that this classification is robust. The numerical modeling approach can find applications in the analysis of neuronal dynamics in mesoscopic scales in the brain (patch or regional). The method is applied to compare the dynamical properties of the young and aged population of neurons. The resulting dynamics of the aged population shows higher average steady-state activity 〈a(t → ∞)〉 than the younger population. The average steady-state activity 〈a(t → ∞)〉 is significantly simplified when the aged population is subjected to external input. The result conforms to the empirical data with aged neurons exhibiting higher firing rates as well as the presence of firing activity for aged neurons stimulated with lower external current.