Third Order Time and Frequency Domain and Mutual Information Analyses For Neuronal Spike Trains

Research on the brain has received considerable attention over the last two decades. Non-randomness of the information flow is widely reported in the study of the brain. Statistical Signal Processing methods have been applied to analyse the dependencies between neuronal recordings. From one side, this makes a great contribution towards further understanding of the brain. On the other side, due the the progress of experimental technology, analysing experimental data becomes a more and more difficult task and hence requires advanced approaches to be developed. Evidence of higher order interactions and nonlinear interactions has been reported in recent experimental findings. This project develops two approaches for statistical signal processing to analyse Multielectrode Array (MEA) data. The first one is a Unified framework of Third Order time and frequency domain analysis (UTO) and the second one is a Mutual Information Function (MIF). These two approaches are described and applied to single unit spike trains to interpret the interactions and dependencies between the spiking neurons. The presence of dependencies are successfully estimated by each approach. In simulations where a modelled neuronal network with 100 neurons, UTO is applied to investigate third order dependencies according to a centre-surrounded pattern of connectivities in the network. The correct pattern of excitatory and inhibitory connections are detected using UTO. Significant values of cumulant estimates are present when third order interactions are present. MIF analysis is also conducted on the simulations. The proposed method computes the Mutual Information (MI) as a function of time lags, along with a Monte-Carlo based calibration method using 100 trials of Poisson spike trains. Significant departure of MI value from the baseline are shown when the dependence exists. UTO and MIF are applied to an experimental MEA spike train data collected from a study of connectivity in a model of kainic acid (KA) induced epileptiform activity for mesial temporal lobe epilepsy (mTLE) in rat. UTO and MIF both successfully highlight the short latency and long latency dependencies existing in the dataset. Therefore, UTO and MIF provide complementary tools to capture dependencies between spike train signals.