• Computational Neuroscience
• Connectome
• Large-Scale Network
• Neural Field

The development of new experimental techniques in parallel with a continuous increase of computational power, has allowed to build biologically grounded neural models, ranging from highly detailed single neurons to large scale neural populations, the latter used generally to investigate whole brain dynamics.
Among large scale neural networks, the so-called neural mass network has acquired a considerable relevance. In this kind of network, each node identifies a neuronal population with its own intrinsic dynamics. In the continuous limit, with the addition of the spatial dimension, the set of these nodes can be described through Neural Field Equations (NFEs).
In this thesis, at first, we have studied cortical dynamics in rest condition, by implementing a neural mass network, endowed with a connectivity obtained from experimental data. Next, we have introduced the spatial dimensions, which in the continuous limit, lead to the NFEs.
In NFE models, connectivity is often decomposed into two contributions: one short-range, spatially invariant, the other one long-range spatial-dependent. The short-range term is then approximated by a diffusion term. The heterogeneous term represents the long-distance connections between different regions of the brain. The extension to the NFEs, among other advantages, allows a certain freedom in defining the heterogeneous term.
We have investigated two patterns for the heterogeneous term: point-to-point connectivity, where only one point is identified for each region and subregion connectivity, where for each region there is a cluster of heterogeneous points. The strengths and the distribution of the connections are given by the Structural Connectivity (SC), or Structural Connectome, obtained from experimental data.
We have implemented the NFEs on a spherical surface, by means of algorithms, called Freesurfer, which maps the surface of the cerebral cortex onto a spherical surface.
The simulations are performed in rest state condition, which, at behavioural level, refers to situations where the subject is awake, with eyes closed and thinking about nothing. We have then defined the simulated Blood-Oxygen-Level-Dependent (BOLD) signal, which is related to the Functional Connectivities (FCs) matrix, obtained from the correlation between the simulated BOLD, in a certain time window, in different regions. Similarly, we have defined the Functional Connectivity Dynamics (FCD) matrix, obtained from the correlation between the FCs at different time windows. Finally, we have shown that our NFEs admit solutions such that the FCD matrix obtained from these solutions is qualitatively similar to those obtained from functional Magnetic Resonance Imaging (fMRI) measurements.
The arguments treated in the thesis are organized as follows: In the Introduction, we briefly describe the neuron, the functional unit of the nervous systems. In the second chapter, we give an overview of the different approaches used to describe single neuron dynamics and neural population dynamics. Then, we build neural mass and neural field models, in which the firing rate equations are derived exactly in the case of a Quadratic Integrate-and-Fire network, in the thermodynamic limit.
In the Results and Conclusions section we report and discuss the simulations results. More technical mathematical details and derivations are reported in the Appendices.