STABILITY ANALYSIS OF THE RESPIRATORY CHEMICAL CONTROL SYSTEM USING MODELS OF CARBON-DIOXIDE

In this dissertation, short-term periodicities (STP) of ventilation are examined using mathematical models of the respiratory chemical control system. The system dynamical characteristics, proposed as a mechanism underlying STP, are studied using both deterministic (stability analysis) and stochastic (spectral analysis) techniques.; A minimal model of CO{dollar}sb 2{dollar} dynamics is developed as a first-order difference differential equation to obtain an explicit stability index (SI) of the system. SI maps relevant physiological variables: CO{dollar}sb 2{dollar} controller gain and intercept, metabolic rate, inspired level of CO{dollar}sb 2{dollar}, cardiac output, lung-chemoreceptor circulation delay, tissue volume, and blood-gas partition coefficient into a single parameter. Numerical simulations validated the use of SI to determine the degree of either sustained or transient STP.; Based on the technique of CO{dollar}sb 2{dollar} rebreathing, a scheme is presented to estimate two of the key physiological variables needed to evaluate SI, namely tissue volume and blood-gas partition coefficient.; Spectral techniques are used to analyze the system responses to uncorrelated noise imposed on system parameters, such as blood flow, metabolic rate, and ventilation. The findings suggest that the peripheral component of ventilation (via the carotid body chemoreceptors) exhibits an underdamped behavior (in the time domain) which produces a corresponding peak in the power spectrum of ventilation. In addition, there is a strong negative correlation between central (via the medullary chemoreceptors) and peripheral components of ventilation, resulting in a total ventilation which is less variable than the direct sum of its components.; The study supports the hypothesis that certain types of STP may be attributable to the characteristics of the feedback control of CO{dollar}sb 2{dollar} dynamics.