title: Neural field models with a dendritic dimension
Creators: name: Culmone, Viviana
Publisher: name: University of Reading
Year: 2019

description: Neural field models (NFMs) describe the spatio-temporal evolution of neuronal populations as a continuous excitable medium. The resulting tissue-level description can be employed to fit data from macroscopic recordings of electrocortical brain ac-tivity like the electroencephalogram (EEG) and local field potentials (LFPs). The standard neural field approach models the cortex as a two-dimensional sheet, ne-glecting the actual cortical depth. Although a small number of studies have con-sidered the anatomical cortical layers to model different connectivity patterns, their mathematical description does not commonly use the cortical depth to determine the model dynamics. Therefore, within the framework of neural field theory, the impact of dendrites on brain activity remains far from being exhaustively explored. In the present work, we extend the geometry of a two-dimensional (2D) NFM to incorporate a dendritic dimension for the excitatory neural populations, repre-senting the cortical depth. Dendritic trees are modelled as linear cables, spatially discretized in multiple subsections (compartments). Spatio-temporal patterns of the new cortical model are studied for systems consisting of either a single or multiple microcolumns. A powerful approximation, extended from the one for the 2D NFM, is introduced to predict the power spectral density of the mean membrane potential from the Jacobian matrix of the linearized system evaluated at a singular point. Our numerical analysis reveals a variety of dynamics, ranging from those characterized by "flat" power spectra without alpha rhythmicity due to signal loss over the tree, up to sharp alpha resonances corresponding to proximity to a Hopf bifurcation. The research focuses on the identification of plausible EEG dynamics, e.g., those exhibit-ing a dominant alpha activity, conceived as the central rhythm of spontaneous EEG. Crucial to this endeavour has been the careful tuning of key dendritic parameters introduced with the three-dimensional (3D) geometry, such as the "synaptic factor" (i.e. synaptic conductance) and the membrane length constant, and wider parameter sweeps using the Particle Swarm Optimization (PSO) technique. The dynamics are mainly studied for a single microcolumn systems with different dendritic configurations (e.g. varying conductance and length constant) during synchronous and asynchronous synaptic activation in either a single or multiple dendritic domains. Our results explain the impact of key dendritic parameters on the 3D NFM dynamics. Heuristics characterizing these effects can be regarded as representative of the well-known phenomenon of "dendritic democracy", classically indicating the normalisation of post-synaptic somatic potentials compensating for dendritic filtering activity. While several experimental studies have investigated the genesis of this compensation, to date this phenomenon has not be explored concerning a potential interplay with the alpha rhythm. Our findings suggest that physiological conditions enhancing the onset of action potentials in active models also promote alphoid dynamics in our passive neural field models including the dendritic dimension. In particular, synaptic strength has to increase with distance from the soma. We found several parameter configurations giving rise to alpha rhythmicity in the 3D geometry, Dynamical analysis highlights the impact of the key dendritic parameters at different cortical depths on the genesis of alpha rhythm, providing a clearer insight into the dendritic mechanisms and cortical dynamics. Indeed, the model can be used as a valid starting point for NF studies aiming to encompass further dendritic properties, implement more detailed connctivity schemes and incorporate data from depth electrode recordings.