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This thesis is concerned with the application of system identification techniques to the analysis of complex physiological systems. The techniques are applied to neuronal spike-train data obtained from elements of the neuromuscular system. A brief description of the neuromuscular system is given in chapter 1, along with a more detailed discussion of the muscle spindle, which is the component of the neuromuscular system which this study deals with. In addition, some possibilities for system identification studies of the muscle spindle are discussed. The identification procedure is based on statistical methods for the treatment of point-process data. The point-process representation of a spike-train is introduced in chapter 2 with definitions of time and frequency domain point-process parameters. Estimates for these parameters are given, along with expressions for their asymptotic distributions. The linear point-process system identification model is introduced and estimates are described for the model parameters in terms of the previously defined point-process parameters. These point-process and linear parameter estimates are applied to muscle spindle spike-train data. In the analysis of a single spike-train certain important features only show up in the frequency domain, and for input and output spike-trains a linear transfer function type description is constructed in the frequency domain. The mathematical model of this transfer function is used as the basis for an analogue computer simulation of a subsystem of the muscle spindle. This consists of a linear first order filter followed by an encoder which generates output spikes. Data logged from the simulation is processed in the same manner as experimental data, and the effect of varying the simulation parameters on the linear model estimates is looked at. It is shown that in general the linear model description reflects the properties of the linear filter in the simulation, and varying the simulation parameters can be used to accurately match results from simulated data with those obtained from real data. Chapter 3 compares the point-process approach with a more conventional filtering and sampled data approach to estimate power spectra. The filtering of spike-trains with broad band spectra is investigated, and this shows up a pitfall in the choice of filter cut-off frequency. It is concluded that the point-process approach is preferable due to shorter computational times, and the well documented statistical propeties of the point-process estimates. The application of the point-process techniques described in chapter 2 to the analysis of more general spike-train data is considered in chapter 4. Three techniques for measuring the degree of coupling between two spike-trains are compared, and the point-process frequency domain measure is found to be the most sensitive. This measure is also applied to a data set containing a strong single periodicity, and the ability to detect coupling at a single harmonic is demonstrated. The analysis of coupling between spike-trains in the frequency domain is extended to deal with multiple spike-trains, and the ability to distinguish genuine coupling from the effect of a common input is shown to be a powerful tool which can be used to investigate communications pathways in neural systems. Finally, one special feature of the muscle spindle response to a spike-train input is analysed using the simulation. It is demonstrated that the point-process approach can produce results about a particular phenomenon from a single experiment much more rapidly than using a repetitive trial and error approach. Chapter 5 considers the extension of the linear point-process identification model introduced in chapter 2. Higher order time and frequency domain point-process parameters are defined and estimates given. In the time domain, a new technique for rapidly generating higher order time domain parameters is developed. The quadratic point-process model is introduced and solutions for its parameters given. These estimates are applied to muscle |
