Mathematical modelling of pulsatility in neuroendocrine systems.

The work described in this thesis concerns the mathematical description of the characteristic oscillatory electrical behaviour of certain neurosecretory cells found in the hypothalamus of the mammalian brain. This study concentrates on those cells which secrete the hormone oxytocin. A model first described by Hodgkin and Huxley is used as a starting point for the derivation of a description comprising a system of coupled non-linear partial differential equations. The equations have been based wherever possible on experimental data relevant to the system being studied. Where this has not been possible, alternative models based on data from other, related systems have been used. The thesis starts with a discussion of the physiology of the system under study and presents some background material. The second chapter discusses the process of mathematical modelling of neurones and presents some of the relevant work in the area. The model due to Hodgkin and Huxley is significant and is discussed in detail. The research methodology is then outlined. Experimental procedures for recording the electrical behaviour of nerve cells and methods of recording selected ionic currents are the subject of chapter three. Chapter four presents a discussion of oscillatory behaviour in nerve cells at a general level and outlines the features necessary for a nerve cell to exhibit oscillation. The next three chapters discuss the characteristics of the different ionic currents involved and describe the author's derivation of models of these currents. Chapter Five presents the author's model of the sodium current, Chapter Six, the potassium currents and Chapter Seven, the calcium current. The experimental work undertaken and the results obtained are then presented and discussed.During the course of this study a number of computer programs were written and tested by the author. The program listings appear in the appendix. The thesis is significant and contributes to the body of knowledge in that no other mathematical model of the unique bursting behaviour of oxytocin-secreting cells exists as far as the author is aware.