Thesis (M.S.)--Villanova University, 2006. / Psychology Dept. Includes bibliographical references.

In the stochastic modeling of neurons, the first passage time problem arises as a natural object of study when considering the inter spike interval distribution. In this report, we study some aspects of this problem as it arises in the context of neuroscience. In the first chapter we describe the basic neurophysiology required to model the neuron. In the second, we study the Poisson model, Stein’s model, and some diffusion models, calculating or indicating methods to compute the density of the first passage time random variable or its moments. In the third and fourth chapters, we study the Fokker-Planck equation, and use it to compute the first passage time in the discrete and continuous time random walk cases. In the final chapter, we study sequences of neurons and the change in the density of the waiting time distributions, and hence in the inter spike intervals, as the output spike train from one neuron is considered as the input in the subsequent neuron.

Oscillatory states in the Electroencephalogram (EEG) reflect the rhythmic synchronous activation in large networks of neurons. Time-frequency methods quantify the spectral content of the EEG as a function of time. As such, they are well suited as tools for the study of spontaneous and induced changes in oscillatory states. We have used time-frequency techniques to analyze the flow of activity patterns between two strongly connected brain structures: the entorhinal cortex and the hippocampus, which are believed to be involved in information storage. EEG was recorded simultaneously from the entorhinal cortex and the hippocampus of behaving rats. During the recording, low-intensity trains of electrical pulses at frequencies between 1 and 40 Hz were applied to the olfactory (piriform) cortex. The piriform cortex projects to the entorhinal cortex, which then passes the signal on to the hippocampus. Several time-frequency methods, including the short-time Fourier transform (STFT), Wigner-Ville distribution (WVD) and multiple window (MW) time-frequency analysis (TFA), were used to analyse EEG signals. To monitor the signal transmission between the entorhinal cortex and hippocampus, the time-frequency coherence functions were used. The analysed results showed that stimulation-related power in both sites peaked near 15 Hz, but the coherence between the EEG signals recorded from these two sites increased monotonically with stimulation frequency. Among the time-frequency methods used, the STFT provided time-frequency distributions not only without cross-terms which were present in the WVD, but also with higher resolutions in both time and frequency than the MW-TFA. The STFT seems to be the most suitable time-frequency method to study the stimulation-induced signals presented in this thesis. The MW-TFA, which gives low bias and low variance estimations of the time-frequency distribution when only one realization of data is given, is suitable for stochastic and nonstationary signals such as spontaneous EEG. We also compared the performance of the MW-TFA using two different window functions: Slepian sequences and Hermite functions. By carefully matching the two window functions, we found no noticeable difference in time-frequency plane between them. / Thesis / Master of Engineering (ME)