• dynamical model
• neural model
• naural network model
• glia

The work is presented in five main chapters. The first one is a general overview of neural and glial physiology. More specifically, the neuron-glia interaction at the synaptic level and the regulation of the released neurotransmitters are the evidence that the non- neural cells must be included in the models for a more accurate description of the human brain functionality. In the second chapter, the adopted mathematical models of the brain’s elements are described, as well as the method used to derive insight information of synaptic transmission and network dynamics.
Afterwards, we present the analysis of the microscopic and mesoscopic levels of descrip-
tion. Chapter 3 is dedicated to the tripartite synapses. It is reported the well-described scenario of simple bipartite and open-loop tripartite synapses. Starting from these results we investigate the effect of gliomodulation in homosynaptic connection and deduce a possible procedure to its mean field description. In Chapter 4 we focus on the network dynamics. For the sake of clarity, we describe both neuron and neuron-glia models to investigate the:
• effects of short-term plasticity in excitatory/inhibitory neural network;
• effects of a single activation of astrocyte in neuron-glia network;
• long-term effects induced by glial cells in neuron-glia network.
The original results obtained in this thesis concern the description of the mean field procedure of homosynaptic transmission, the modulation of excitatory/inhibitory balance and the regulation of network oscillations induced by persistent astrocytic activity. More specifically, we identify a glia-induced frequency filtering of periodic external input. In conclusion, we propose future perspectives aiming to improve the knowledge of the functional activity of human brain domains.