Next generation neural activity models: bridging the gap between mesoscopic and microscopic brain scales

Byrne, Aine (2017) Next generation neural activity models: bridging the gap between mesoscopic and microscopic brain scales. PhD thesis, University of Nottingham.

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Neural mass and neural field models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by neurobiological considerations, they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. In this thesis we consider the θ-neuron model that has recently been shown to possess an exact mean-field description for smooth non-pulsatile interactions, and show that the inclusion of a more realistic synapse model leads to a mean-field model, that has many of the features of a neural mass model, coupled to a further dynamical equation that describes the evolution of network synchrony.

We have carried out extensive analysis on the model for both a single and a two population system. Importantly, unlike its phenomenological counterpart this next generation neural mass model is an exact macroscopic description of the underlying microscopic spiking neurodynamics, and is therefore a natural candidate for use in large scale human brain simulations. Using our reduced model, we replicate a human MEG power spectrogram to demonstrate that the model is capable of reproducing transitions from high amplitude to low amplitude signals, which are believed to be caused by changes in the synchrony of the underlying neuronal populations.

We then shift our focus to a spatially extended model and construct a next generation neural field model. Using both Turing instability analysis and numerical continuation techniques we explore the existence and stability of spatio-temporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Coombes, Stephen
Kypraios, Theodore
Keywords: mathematics; neuroscience; neural mass model; magnetoencephalography; beta rebound; synchrony
Subjects: Q Science > QA Mathematics
Q Science > QP Physiology > QP351 Neurophysiology and neuropsychology
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 44661
Depositing User: Byrne, Aine
Date Deposited: 14 Dec 2017 04:40
Last Modified: 15 Dec 2017 16:02

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