ETD

• Complex Systems
• Neural Dynamics
• Neural Network

The brain is a paradigmatic example of a complex system exhibiting emergent collective dynamical behaviours arising from the nonlinear interactions of billions of neurons. This complexity has made the brain a subject of intense interdisciplinary study, bringing together insights from physics, biology, neuroscience, mathematics and computer science.
To characterise the dynamical properties of neural networks, researchers often use in-vitro cultures, simplified biological systems that allow us to stimulate neurons and to record their electrical activities in a controlled environment. In this thesis, a neural network of coupled Adaptive Exponential Integrate-and-Fire (AdEx) neuronal models was employed to investigate, in-silico, the dynamics of such cultured networks. A particular emphasis was devoted to shedding light on the dynamical mechanisms underlying the emergence of synchronised neural activity and the role of inhibitory synaptic coupling in shaping network behaviour.
Starting with homogeneous networks of isolated populations of coupled excitatory (or inhibitory) neurons, we investigated the corresponding basic electrical activity patterns that can be generated by the presence of purely excitatory (or inhibitory) synaptic coupling. We manage to describe the specific behaviour of these pure configurations: network bursting for purely excitatory and partial suppression for purely inhibitory.
A network burst is a finite period during which the network exhibits high activity, bounded by windows of low-frequency activity, which were the focus of our subsequent work. We first investigated how excitatory-inhibitory feedback influences and reshapes the network bursting regime found in the homogenous excitatory configuration. Then, we incorporated noise into our neuron models to improve biological realism and introduce variability in otherwise nearly identical networks.
The last part of the thesis work was used to simulate networks that aim to explain remarkable findings from recent experimental data obtained from neuronal cultures. These results were collected and published by the Bio@SNS Laboratory at the Institute of Biophysics of CNR in Pisa, with whom we collaborated during this work.
This work demonstrated how simplified mathematical models can successfully capture and explain some sophisticated electrical patterns of living brain tissue. We also showed how network bursts are phenomena strictly connected to two necessary features: excitation and adaptation; purely inhibitory networks and non-adaptive neurons are unable to perform network bursting activity. The last result we achieved is that random connectivity is unable to reproduce key behaviours of neuronal cultures, such as avalanches; explanations for such phenomena must be researched in local wiring processes and network inhomogeneity. We commit to improving our analysis in this direction in future works.