Investigating the dynamics of a population of spiking neurons across spatial scales

Abstract

Mean-field models describe bulk neural activity in terms of population-average action potential (spike) rates, but do not attempt to address the variations in the firing activity of individual neurons and the interactions among them. In 2016, Waikato Cortical Modelling group published a purely theoretical model [Steyn-Ross et al, Phys. Rev. E 93.2 (2016): 022402] that provides a more accurate mapping of spiking dynamics, scaling from single neuron to the macroscopic level by regridding the system using a spatial blocking: a bottom-up neural regridding referred to as True-field. A 2D continuum of identical neurons is constructed from a lattice of spiking neurons that are coupled both synaptically (via chemical synapses) and diffusively (via electrical synapses). The spiking behaviour at the single-neuron level is modelled using the Wilson point neuron equations, steered by incoming electrical impulses from adjacent neurons. These equations are then reblocked to form a coarser-spatial resolution by eliminating the high-frequency spatial modes. The existence of diffusive terms in voltage and recovery equations is crucial for this spatial coarse-graining procedure.

The purpose of this thesis is to conduct a preliminary analysis of the True-field model, which has never been tested in simulations before. The coarse-graining procedure employed in this framework results in a set of nonlinear corrections in the model equations. My first challenge is to recover those corrections and conduct numerical investigations to identify the most significant ones. My next challenge is to tune parameters of the True-field model via a comprehensive series of simulations, looking for “realistic” cortical behaviours. Two approaches are used: point simulations of the homogeneous two-neuron cortex, and full 2D grid simulations of a sheet of cortical tissue. Point simulations are straightforward and time efficient but do not provide any information about spatial variations in firing activity; grid simulations allow examination of spatial patterns, but can be challenging to set up, and are computationally expensive in terms of run times and memory requirements. I demonstrate that True-field can reproduce spiking behaviour of a normal brain across multiple levels using a range of blocking ratios: intracellular spiking for low blocking; agglomerated population events (EEG patterns) when blocking is increased. I also show that the model can produce the seizure-like events (SLE) seen in a slice of mouse brain sustained in a bath of artificial cerebro-spinal fluid (aCSF). My grid simulations confirm the generation and propagation of firing activity across the reblocked cortical grid. In conclusion, this new paradigm provides insights about the spiking dynamics of neurons from microscopic to macroscopic levels in a way that neither single-neuron nor mean-field approaches can do.