Probing Brain Networks: Perturbation Models and their Role in Understanding Brain Structure and Function

The activity of our brain is continually affected by external perturbations, ranging from processing sensory information to dealing with structural alterations due to injuries or diseases. Additionally, targeted stimulations, such as pharmacological treatments, surgical interventions, or electrical stimulation, can help reveal how different brain regions communicate and serve as effective medical therapies. Developing analytical models and data-driven approaches to understand the effects of these perturbations is thus crucial for advancing our knowledge of brain function and devising clinical applications. In this thesis, we focus on developing perturbation models for meso- and macroscale brain networks, aiming to explore how different scales of brain organization respond to external and internal disturbances. We begin by examining the role of macroscale structural connectivity in shaping dynamical patterns, by computing a measure of dimensionality using diffusive perturbations. Locally, this measure correlates with brain organization gradients, while on a global scale, it reveals altered emergent dynamical patterns and behavioral capacities due to stroke. To further investigate the interplay between network structure and dynamics, we introduce a distance metric based on the spatiotemporal evolution of perturbations within general nonlinear dynamics. This framework enables us to identify the conditions for the emergence of functional communities, particularly within the brain. Next, we add biological details to the connectivity structure by examining how populations of excitatory and inhibitory neurons encode information from time-varying external signals, demonstrating that the balance between excitation and inhibition adjusts the system's optimal timescale of response. Finally, we employ optimal transport techniques on neurophysiological data collected during a cognitive task to reveal that the cost of transitions between different conditions correlates with task demands, thereby providing insights into the brain's functional reconfiguration in response to environmental changes.