Point Process Analysis Techniques: Theory and Applications to Complex Neurophysiological Systems

Lau, Joe Wing-Nin (1991) Point Process Analysis Techniques: Theory and Applications to Complex Neurophysiological Systems. PhD thesis, University of Glasgow.

Abstract

The main objective of this thesis is the development of analytical techniques and computational procedures for the analysis of complex neuronal networks. The techniques are applied to data obtained from elements of neurophysiological systems and simulated models to illustrate different aspects of these analysis tools. The nerve signals that occur within neuromuscular control systems are widely accepted to be stochastic in nature and are characterised by the times of occurrence of events, typically 1 msec, in duration of fixed amplitude, within the process. This provides the basis for considering these processes as stochastic point processes. The analytical approach adopted is similar to that used in ordinary time series and requires an inter-disciplinary approach involving linear and non-linear system analysis, estimation theory, probability theory and statistical inference. In this thesis a considerable amount of work is devoted to the discussion of these various areas related to the point process analysis techniques. In addition, neurophysiological concepts are discussed to provide a basis for the application of these techniques. These techniques are applied to the analysis of real data obtained from physiological experiments and simulated data generated by model neuronal networks of different complexities. Finally, some possibilities for future work opened up by the present investigation are considered. An introduction together with some historical notes are given in Chapter 1. The objectives of this thesis are set down and some general ideas of a point process and neurophysiology are introduced. The historical notes at the end of Chapter 1 are intended to give a picture of the trend of developments concerning point processes. Chapter 2 presents a simplified account of the relevant neurophysiological background. Some features of the neuromuscular system which lead to the use of point process analysis techniques are discussed. This is followed by a brief description of the organisation of neuromuscular system and some of its elements. The idea that the generation of an action potential occurs when the membrane potential at the trigger zone of a neurone exceeds the threshold forms the basis for the neurone model used in this thesis . The multiple input and output nature of neuromuscular systems in addition to the short duration of an action potential justify the realisation of a spike train as stochastic point process. Chapter 2 is concluded by considering some findings from the application of point process analysis techniques to data recorded from neuromuscular elements. The details of the techniques are then explained in Chapter 3-5. Chapter 3 gives a development of the theory of linear point process system analysis. The formal definitions of the assumptions involved, namely stationarity, mixing, and orderliness are explained. These assumptions are important in simplifying the theories involved and are seen to be valid in our applications. Theories for univariate, bivariate and multi-variate point processes are considered. The asymptotic value of the auto- spectrum of a point process is shown to be a non-zero constant, which marks the distinction from the auto-spectrum of an ordinary time series. Various quantities in both time and frequency domains are introduced and, among them, the coherence function and its partial and multiple forms are explained in particular details. The application of coherence is emphasised in Chapter 6. Since the processes involved are stochastic in nature, appropriate estimation procedures for the time and frequency domain quantities should be used. Chapter 4 is devoted to explaining the estimation procedure used and the statistical properties of these estimates. Also the Poisson point process - which possesses similar properties to Gaussian white noise in the case of ordinary time series - is introduced. The importance of the Poisson point process lies on the fact that it may be used as a 'reference process' to indicate departure of independence within a point process. At the end of Chapter 4, the confidence intervals of the time and frequency domain estimates under the hypothesis of independence are developed. The confidence interval approach forms the basis of inferring whether there is any significant association between processes or within a process. Chapter 5 describes briefly the implementation of the neurophysiological and simulation experiments. The digital algorithm for generating the exponential and Gaussian variables to provide the required stimuli in the experiment are explained. The neurone model, which is the building block of more complicated neuronal networks, is also described. Chapter 6 presents results and discussion. First some simulated spike trains of different structures are analysed using histogram, auto-intensity and auto-spectrum. The histogram is found to be least sensitive in revealing significant information concerning the processes. (Abstract shortened by ProQuest.).

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Computer engineering, Neurosciences
• Date of Award: 1991
• Depositing User: Enlighten Team
• Unique ID: glathesis:1991-78358
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 30 Jan 2020 15:31
• Last Modified: 30 Jan 2020 15:31
• URI: https://theses.gla.ac.uk/id/eprint/78358