Probing the sub-thalamic nucleus: development of bio-markers from very Local Field Potentials

Abstract

Deep Brain Stimulation (DBS) surgery for neuro-psychiatric disorders involves the insertion of Micro Electrode Recording (MER) targeting probes into a specific location in the patient's brain to confirm the precise location of the candidate nucleus for the stimulation therapy.The unique geometry and electrical properties of these MERs probes, when inserted into neuron dense tissue such as the Sub-thalamic Nucleus (STN) results in the acquisition of signals which typically contain contributions from the spiking behaviour of multiple nearby neurons in addition to a low frequency component similar to the Local Field Potentials (LFP) generated by more distant neurons (over length scales smaller than typical LFPs). We refer to these signals acquired from the MER probes, which contain both some of the nearby (resolvable) spikes and these smaller scale LFPs as very Local Field Potentials (vLFPs).The unique signal contributions to the vLFPs raise the immediate question what contribution of the signal is best used in order to characterise (in terms of identifying the underlying physiology or detecting changes of) the state of the STN. In this thesis we develop methodologies to analyse vLFPs using both model based and model free analysis of the entire (nearby spiking, distant spiking and non-spiking contributions) vLFP and only the nearby spiking neurons.We apply concepts from Mori-Zwanzig non-equillibrium kinetic theory to develop modelfree estimates of the entire vLFP. With this approach we show that the Non-Markov Parameter (NMP) can be used to identify statistically significant changes in the electrical behaviour of the STN when presented with different neuro-linguistic stimuli. We show that these changes are due to variations in the low frequency bands associated with the power spectrum of the vLFP.We then develop a model-based analysis of the entire vLFP using the renewal theory of stochastic processes. We show that when the ensemble of neural processes forming the vLFP satisfy the assumptions of an independent renewal process model, given a measurement of ii the power spectrum, the common probability distribution driving the spiking statistics of the individual neurons can be identified. We show with simulation that, when the assumptions of the model are satisfied, this approach can outperform state of the art spike sorting algorithms in the challenging situation of identifying the spiking statistics when an unknown number of neurons with near identical spike shapes contribute to the vLFP.Finally we develop spike-only analysis by constructing spike sorting strategies using convex optimisation and clustering theory to identify the precise timing and shapes of the spikes associated with individual neurons nearby to the MER probe. With this approach the spike detection and clustering is performed using a Basis Pursuit De-Noising (BPDN) strategy which is a subset of ℓ 1 regularised least squares techniques. We show that this method outperforms state of the art spike sorting algorithms for a range of signal to n...