Mathematical models of respiratory control in humans
This thesis is concerned with modelling the properties of human ventilation during steady-state conditions and during acute and sustained isocapnic hypoxia. Chapter 1 reviews some of the relevant studies in animals and humans. Chapter 2 describes the origins of the data studied in this thesis. In particular, it describes the experimental apparatus and the technique of dynamic end-tidal forcing used to gather the data, as well as the particular protocols employed. Chapter 3 studies the breath-to-breath variations in ventilation during steady breathing in both rest and during light exercise with the end-tidal gases controlled. The results suggest that: 1) both simple ARMA models and a simple state-space model can describe the autocorrelation present in the data; 2) variations in spectral power were present in the data which cannot be described by these models; and 3) these variations were often due to a uniform modulation and did not significantly affect the coefficients of the models. For these kinds of data, a heteroscedastic form of state-space model provides an attractive theoretical structure for the noise processes. Chapter 4 studies human ventilation during sustained isocapnic hypoxia. Two models are used. The first, developed by Painter et al. (J. Appl. Physiol. 74:2007-2015, 1993) describes hypoxic ventilatory decline (HVD) as a decline in peripheral chemoreflex sensitivity. The second is an extended model which incorporates a component of HVD that is independent of peripheral chemoreflex sensitivity. The models incorporate a parallel noise structure. It is concluded that, in some subjects but not others, there is a component of HVD which is independent of peripheral chemoreflex sensitivity. Chapter 5 studies the human ventilatory response to cyclic isocapnic hypoxia. Both a simple proportional dynamic model suggested by Clement and Robbins (Respir. Physiol. 92:253-175, 1993), and an extended model with an additional non-linear rate-sensitive component are studied. The models incorporate a parallel noise structure. The results show that, although the extended model improves the fit to the data for some subjects, both models failed to explain the data fully, especially the occasional large breaths, which were shown to occur more frequently in some parts of the hypoxic cycle than other parts.