Probing the relationship between high frequency oscillations and epileptic brain activity through the lens of feedforward inhibition

Abstract

The current variety of treatment options for epilepsy leaves 30% of those who suffer from this chronic neurological disease without a cure. Therefore, this senior thesis project aims to uncover new insights about the brain structure that underlies susceptibility to epilepsy in hopes that a greater understanding of this underlying structure will catalyze the discovery of novel therapeutic methods which target these underlying differences in brain structure. To drive the discovery of new insights about underlying structure, this project addresses the following tension found in the literature: high frequency oscillations occur in both the brains of those with epilepsy and in the brains of those without epilepsy. Only when high frequency oscillations occur in the brains of those with epilepsy does the brain enter a state of unstable dynamics and seizure activity. This suggests that there is a difference in underlying structure between epileptic and non-epileptic brains, and this study uses computational modeling of neuronal firing to characterize these differences. First, based on a firing rate model, we find that within the phase space of the weight values, there is a band of stability from which one might predict the stability of a set of weights. Then, in the next two versions of the model, we add Hebbian plasticity and homeostatic plasticity. Only through the addition of Hebbian plasticity and homeostatic plasticity does high frequency oscillation, the manipulation described in our driving question, have a lasting effect on the weights. With the addition of a rate based Hebbian plasticity model to the base firing rate model, we find that weights can be perturbed from this band of stability through Hebbian plasticity. Adding a weight based homeostatic plasticity model to the base firing rate and Hebbian plasticity model then gives insight into the fact that having a target weight within a certain location with respect to the band of stability can rescue stability of a set of original weights from the destabilizing effects of Hebbian plasticity. Finally, we explore the effect of high frequency oscillation on various weight combinations within the phase space, and we find that certain weight combinations are projected to an unstable state through high frequency oscillation while other weight combinations remain at a stable state even in the face of high frequency oscillation. The unifying characteristic of those weights which remain stable in the face of high frequency oscillation remains an open question. However, in the process of investigating high frequency oscillations, it was found that weights on the edge of the band of stability are more robust to instability through Hebbian plasticity than weights on the band of stability that are further from the edge. These results suggest that the differential response to high frequency oscillation between epileptic and non-epileptic brains can be attributed at least in part to the location of weights with respect to the band of stability.