Applications of Reduced Order Modeling Techniques in Computational Neuroscience

Human brains are highly nonlinear dynamical systems comprised of neurons that communicate through electrical and chemical synapses. These neurons produce brain rhythms which play a functional role in cognitive processes. The disruption of these cognitive processes through abnormal brain rhythms can result in a variety of neurological disorders, such as Parkinson’s disease, epilepsy, and treatment-resistant depression. This work is motivated by the importance of understanding neural brain rhythms in both experimental and computational settings. In this work, we implement model reduction strategies, specifically phase and phase-amplitude reduction, to explore and analyze neural behavior from a reduced order framework. Using these model reduction techniques, we develop a control strategy that drives a population of synchronized neural oscillators towards a desynchronized state, mirroring the effect of deep brain stimulation on pathologically synchronized neural oscillators. We then examine the impact of synaptic plasticity on critical coupling strength estimates for a population of inhibitory neurons with all-to-all coupling. Finally, we derive terms for a data-driven phase-amplitude model of a complicated network of neuronal subnetworks with a complex coupling structure and additive noise.