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Next generation neural mass models : working memory, all-brain modelling and multi-timescale phenomena

Authors
  • Taher, Halgurd
Publication Date
Dec 09, 2021
Source
HAL
Keywords
Language
English
License
Unknown
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Abstract

In this thesis we report new extensions and applications of next generation neural mass models. Montbrió, Pazó, and Roxin (MPR) have shown that the collective behavior of an ensemble of quadratic integrate and fire (QIF) neurons can be described in terms of the mean membrane potential and firing rate in an exact manner, reducing the dimension of the problem from an infinitely large microscopic network to a low dimensional macroscopic description. Since the neural mass gives access to the mean membrane potentials, it can be used as a proxy for local field potential and EEG signals.One contribution of this thesis is the implementation of short-term synaptic plasticity (STP) into the MPR model. Based on a synaptic theory of working memory (WM), we reproduce WM mechanisms using a QIF network and its exact mean-field limit in a multi-population setup. In particular, we report agreement between the behavior of the network and the extended neural mass model and we make a comparison between our model and experimental results on cortical oscillations associated to WM tasks. The neural mass model exhibits oscillations in the β-γ range during memory loading and maintenance, as also observed in experiments, while we encounter empty β-γ bands using a heuristic model. Furthermore we report how these power bands are formed by resonances among fundamental frequencies, which are linked to the number of items retained in memory. We also provide an analytical estimate for the maximal WM capacity of around five items.The second contribution is the application of a multi-population model in order to test clinical hypothesis of seizure propagation. We use structural connectomes obtained from dMRI scans of healthy subjects and epileptic patients. We describe how seizure-like events can be modeled as a recruitment from low activity to high activity states. External inputs can trigger such an event and lead to a cascade of recruitments, hence mimicking the spatio-temporal propagation of seizures. The numerical results suggest that epileptic patients are more susceptible to extensive recruitment events than healthy subjects. We also find good agreement between the first brain areas to be recruited in our model and the pre-surgical assessment of recruited secondary networks.As a third contribution we study the network and neural mass in presence of STP using slow-fast dynamics. Depending on the amplitude of a slow periodic current applied to the population, the collective behavior can be either in a regime of subthreshold oscillations or bursting, i.e., alternating between a quasi-static drift and fast large amplitude oscillations. The two regimes are separated by a narrow parameter interval, resembling a canard explosion. In this region we report jump-on canards, which approach otherwise repelling invariant sets. We study their impact on the emergence of bursting. For intermediate timescale separations bursting emerges in a continuous manner via a spike-adding mechanisms mediated by mixed-type-like torus canards, trajectories which evolve nearby families of repelling equilibria and limit cycles. For stronger timescale separation the continuous transition is blocked by jump-on canards. The mechanisms observed in the neural mass are also responsible for the emergence of bursting in the network. To summarize, this thesis puts next generation neural mass models into a broader context of modeling in neuroscience and provides new perspectives for future work. This includes approaches to take better models of STP into account and ideas for exact neural masses based on biologically plausible neuron models.

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