  Starting from the concept of binary interactions between pairs of particles,
a kinetic framework for the description of the action potential dynamics on a
neural network is proposed. It consists of two coupled levels: the description
of a single brain region dynamics and the interactions among different regions.
On one side, the pairwise interaction between neurons exchanging membrane
potential is statistically described to account for the unmanageable number of
neuron synapses within a single brain region. On the other, the network
connections accounting for the brain region topology are represented and
studied using concepts of the graph theory. Equilibrium and stability of the
obtained macroscopic systems are analyzed as well as numerical simulations of
the system dynamics are performed in different scenarios. In particular, the
latter allows us to observe the influence of the discrete network topology on
the membrane potential propagation and synchronization through the different
regions, in terms of its spiking characteristics.
