Development and analysis of a simple grey-box model of central sleep apnea

Abstract

In this thesis, we develop and analyze a simple grey-box model that describes the pathophysiology of central sleep apnea (CSA). We construct our model following a thorough survey of published approaches. Special attention is given to PNEUMA, a complex, comprehensive model of human respiratory and cardiovascular physiology that brings together many existing physiological models. We perform a sensitivity analysis, concluding that signals of interest in PNEUMA are insensitive to changes in all but approximately twenty parameters. This justifies our goal of developing a small, simple model that captures approximately the same behaviour among signals of interest. The simplicity of our model not only makes it accessible to analytical and intuitive exploration, but also opens up the possibility that its parameters could be reliably estimated from a patient's data records. This could be of great value in developing patient-specific or state-specific treatments for CSA. Our model describes the dynamics of the alveolar gas exchange, blood gas transport, and cerebral gas exchange processes, which together determine the cerebral and arterial partial pressures of carbon dioxide, given ventilation as input. Our model of the ventilatory controller senses both the cerebral and arterial carbon dioxide partial pressures and issues a ventilatory drive command from which the level of ventilation is determined, closing the loop. We develop a linearized small-signal model of our system and determine conditions for its stability. We conclude by comparing the stability predictions suggested by our linear analysis to the stability properties of our original nonlinear model, with promising results.