Neural Computation and Sensory Systems Group
Department of Physiological Sciences
The Medical School
Newcastle upon Tyne
NE2 4HH
Submitted to the University of Newcastle upon Tyne for the Degree of Doctor of Philosophy
June 1997
Artificial neural networks have been used in a number of different ways in medicine and medically related fields. This thesis examines one aspect of their use, that of using neural networks for the task of biomedical systems identification. This involved the use of the white noise approach to systems identification, which is common in engineering approaches, and allows the systems under study to be represented in a functional sense, for example by a Volterra series.
A number of theoretical and practical aspects of the application of neural networks are examined in this thesis. Firstly conditions relating to network learning are examined, with the finding that both the number of hidden nodes, network architecture and the initial conditions of the network (in terms of the initial random weight ranges) are important in determining if a neural network will learn a particular problem. A technique for the functional analysis of trained networks is presented and utilised to try and determine the relationship between the network error measure and accuracy in a functional sense. An alternative training method, Expanding Range Approximation, is investigated as a method of ensuring a good functional approximation, and is found to provide a similar functional accuracy to classical backpropagation training, with the benefit that it is not as sensitive to the initial conditions of the network.
Secondly, a known nonlinear dynamic system, the Wiener cascade is used as a way of validating the technique for calculating a Volterra series representation from a particular form of neural network, a time-delayed neural network (TDNN). The comparison of analytic and empirical solutions from the cascade reveals that the TDNN methodology is unable to cope with periodic systems or with systems where there is dependence on time or free flow.
The applications to biomedical systems commence with a study of the Hodgkin-Huxley model of neurones. Using a reduced form of the full model which is equivalent to the situation when the sodium channel is blocked; approximate analytic solutions are presented, using a Carleman linearisation methodology to represent the state-space form of the model as a Volterra series. Numerical simulations of the model using different depolarising dc offsets of the noise characterisation signal reveal that the solutions of the model in terms of Volterra series are local around the position in state-space. In practice this means that they depend on the value of the potassium activation state variable in the model. In fact increasing the value of this, by applying larger depolarising input currents has the same effect as increasing the maximal value of the potassium conductance. Approximate analytic solutions are used to confirm these findings.
The next application involves attempting to directly calculate, from experimental stimulus response data, a neural network based model, which can be expressed in terms of a Volterra series describing the potassium channels in the membrane of the snail Helix aspersa. The aim of this approach is to allow a comparison between a parametrically derived model, based on Hodgkin-Huxley kinetics and one calculated by a neural network direct from experimental data. Unfortunately this aim is not realised within the realms of this thesis, due to problems in training the neural networks.
The final application involves a much more complex system, the human Biceps stretch reflex. This acts as further confirmation of the limitations in the applicability of TDNN to system identification; as this system is believed to contain both nonlinear and non-stationary aspects. It is not surprising therefore that, whilst networks are able to produce a good fit of the data their equivalent functions are not a valid representation of processing in the system.