The Neurodynamics of Epilepsy: Synaptic regulation and reversal potential modulation during seizures in a neural field model with conductance-based synapses
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KeywordsEpileptic Seizure Reversal Potential Bifurcation Analysis Homeostatic Mechanism Electrophysiological Experiment
Recent experimental results have shown that during the initiation and termination of epileptic seizures there is a significant change in the micro-ionic environment of cortical neurons  that affects network balance between excitation and inhibition. This is evident through non-synaptic changes in the micro-ionic environment such as the excitatory and inhibitory reversal potentials and conductances that have been measured over the course of a seizure in an in vitro mouse model . Although this phenomenon of a change in reversal potentials during seizures has recently been simulated numerically using a relatively small number of detailed multi-compartmental spiking models , it has not yet been modelled using larger scale mesoscopic neural field models within an analytical framework. This is because the majority of these models use current-based synapses, which do not take the reversal potentials into account  as they are more difficult to incorporate in mesoscopic models of brain dynamics.
We present an analysis of a neural field model with conductance-based synapses that takes into account the reversal potentials and the nonlinear multiplicative effect that they have on the associated conductance. The conductance-based synapses model is derived, analysed and juxtaposed with the current-based synapses model and the results interpreted physiologically.
A comparative bifurcation analysis of both models reveals that there are significant differences in the oscillatory behaviours that correspond to epileptic seizures . In the conductance-based synapses model, there are endogenous anti-epileptic regulatory or control mechanisms that operate on the synaptic scale, whereas previously these were thought to be mainly on the network level; for example, in terms of feedback, feed-forward and surround inhibition . Further, upon modulation of the reversal potentials, the new model exhibits seizure behaviour that initiates and terminates due to non-synaptic ionic mechanisms, similar to that measured in recent experiments .
Seizure dynamics in the brain are modulated by both synaptic regulatory mechanisms and non-synaptic homeostatic mechanisms, which play key roles during seizure initiation, spread and termination . These mechanisms have been investigated using a novel analytical neural field model which has provided insights into understanding epileptic brain dynamics that are not currently observable in electrophysiological experiments and numerical simulations alone.
This work was supported by ARC Linkage Project #LP0560684 and an SVHM REF grant.
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