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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

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Program

MSC4d
James Duffin
Departments of Anaesthesia & Physiology, University of Toronto
Title Modeling interactions between the control of cerebral blood flow and the chemoreflex control of breathing: implications for stability
Abstract The regulation of brain (central) hydrogen ion concentration involves both the control of blood gas carbon dioxide tensions by altering pulmonary ventilation, as well as the control of cerebral blood flow by altering cerebrovascular resistance. Cerebral blood flow is sensitive to changes in arterial blood gas tensions and particularly to carbon dioxide, while pulmonary ventilation is sensitive to the hydrogen ion concentrations at both peripheral and central respiratory chemoreceptors. The central respiratory chemoreceptor stimulus is determined partly by cerebral blood flow; increases in cerebral blood flow wash out central carbon dioxide to lower the central hydrogen ion concentration, and this cerebrovascular reactivity thus helps regulate and maintain central hydrogen ion concentration. These two control systems therefore interact. Modeling this interaction requires measurement of the respiratory chemoreflex characteristics independent of the effects of cerebrovascular reactivity. This goal can be accomplished by using a rebreathing method that controls the peripheral and central respiratory chemoreceptor stimuli, in terms of carbon dioxide and oxygen gas tensions, independent of both pulmonary gas exchange and cerebral blood flow. Combining the results from a large number of rebreathing tests to produce the response characteristics of an average subject has yielded parameter estimates for a chemoreflex control model. This model has been applied to interpret the changes in respiratory chemoreflex regulation observed in several experimental conditions including sleep, the acute response to hypoxia incorporating hypoxic ventilatory decline, and the facilitation of ventilation by intermittent hypoxia and long-term hypoxic facilitation. Extension of this model to include the relations between the partial pressure of carbon dioxide controlled by pulmonary ventilation and the hydrogen ion concentrations sensed by the peripheral and central chemoreceptors has allowed the model to reproduce the influence of acid-base changes on the control of breathing, including the adaptation to altitude. The physiology of cerebrovascular control is not yet fully understood, and measurement techniques are still in development. Nevertheless, recent experiments have provided the basis of a model of cerebrovascular reactivity. When combined with the chemoreflex model, a steady state model of respiratory control is produced that is capable of predicting the changes in respiratory stability that matches recent experimental findings using pharmacologically-induced changes in cerebrovascular reactivity. A dynamic model with these features offers further insights into the interactions between the chemoreflex control of breathing and the control of cerebral blood flow.
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