Pinto Leite, MF; (2017) Dynamical mean field modelling and estimation of neuronal oscillations. Doctoral thesis , UCL (University College London).

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Abstract

Oscillations in neural activity are a ubiquitous phenomenon in the brain. They span multiple timescales and correlate with a myriad of physiological and pathological conditions. Given their intrinsic dynamical nature, mathematical and computational modelling tools have proven to be indispensible in order to interpret and formalize the mechanisms through which these oscillations arise. In this Thesis, I developed a new methodological framework that allows the assimilation of experimental data into biophysically plausible models of neural oscillations. Motivated by the fast oscillatory activity (30 ~ 130 Hz) at the onset of focal epileptic seizures, I started by investigating, via means of bifurcation analyses, whether such fast oscillations can be plausibly described by conductance-based neural mass models. Neural mass models have enjoyed success in describing several forms of epileptiform activity (e.g. spike-and-wave seizures and interictal spikes), but I found that, in order to generate such fast oscillations, the parameters of this family of models would have to depart significantly from biophysical plausibility. These results motivated the exploration of full mean-field models of spiking neurons to characterise this type of dynamics. I hence proposed a variant of a mean-field neural population model based on the Fokker-Planck equation of conductance-based, stochastic, leaky integrate-and-fire neurons. This modelling approach was chosen for its capacity to describe arbitrary network configurations and predict firing rates, trans-membrane currents and local field potentials. I introduced a new numerical scheme that makes the computational cost of integrating the ensuing partial differential equations scale linearly with the number of nodes of the networks. These advances are crucial for the practical implementation of model inversion schemes. I then built upon the literature of Dynamic Causal Modelling to develop a Bayesian model inversion algorithm applicable to dynamical systems in limit cycle regimes. I applied the scheme to the mean-field models described above, using experimental data recordings of carbachol-induced gamma oscillations, in the CA1 region of mice hippocampal slice preparations. The estimated model was able to make accurate predictions about independent data features; namely inter-spike-interval distributions. Also, the inverted models were qualitatively compatible with the observation that excitatory pyramidal cells and inhibitory interneurons play equally important roles in the dynamics of these oscillations (as opposed to interneuron-dominated gamma oscillations). I also explored the applicability of this inversion scheme to neural mass models of electroencephalographically recorded spike-and-wave seizures in humans. In conclusion, the work presented in this thesis provides significant new contributions to model based analyses of neuronal oscillatory data, and helps to bridge single-neuron measurements to network-level interactions.

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