Optimization for Bursting Neural Models

Abstract

This thesis concerns parameter estimation for bursting neural models. Parameter estimation for differential equations is a difficult task due to complicated objective function landscapes and numerical challenges. These difficulties are particularly salient in bursting models and other multiple time scale systems. Here we make use of the geometry underlying bursting by introducing defining equations for burst initiation and termination. Fitting the timing of these burst events simplifies objective function landscapes considerably. We combine this with automatic differentiation to accurately compute gradients for these burst events, and implement these features using standard unconstrained optimization algorithms. We use trajectories from a minimal spiking model and the Hindmarsh-Rose equations as test problems, and bursting respiratory neurons in the preBotzinger complex as an application. These geometrical ideas and numerical improvements significantly enhance algorithm performance. Excellent fits are obtained to the preBotzinger data both in control conditions and when the neuromodulator norepinephrine is added. The results suggest different possible neuromodulatory mechanisms, and help analyze the roles of different currents in shaping burst duration and period.