Model Validation and Control Issues in the Respiratory System
This chapter develops static and dynamic models of the chemoreflex control of breathing based on experimental measurements. A graphical concept model of the steady state based on current physiology is built up first, which demonstrates key concepts in the
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Model Validation and Control Issues in the Respiratory System James Duffin
Abstract This chapter develops static and dynamic models of the chemoreflex control of breathing based on experimental measurements. A graphical concept model of the steady state based on current physiology is built up first, which demonstrates key concepts in the control of breathing such as loop gain and its clinical partner CO2 reserve. The Stewart approach to modeling acid-base is used to convert this static model to handle the effects of acid-base changes on respiratory control. Finally, this static model of the chemoreflex control system is incorporated into a dynamic simulation of the control of breathing and acid-base balance using a graphical programming language. The dynamic model demonstrates the instabilities observed during sleep at altitude and the effects of changes in cerebrovascular reactivity on loop gain and stability that are a part of the sleep apnoea syndrome. Hence this chapter will also draw connections to the chapter by Bruce (Chap. 7).
8.1 Introduction 8.1.1 The Respiratory Control System Breathing is responsible for supplying sufficient oxygen (O2 ) for metabolism and eliminating the carbon dioxide (CO2 ) produced by metabolism. The respiratory control system accomplishes this aim by altering pulmonary ventilation so that at equilibrium, i.e., steady state, O2 uptake at the lungs equals O2 consumption by the tissues, and CO2 elimination at the lungs equals CO2 production by the tissues. As Fig. 8.1 illustrates, when pulmonary gas exchange matches metabolism, tissue partial pressures of oxygen (PO2 ) and carbon dioxide (PCO2 ) remain constant, and so J. Duffin () Thornhill Research Inc., 210 Dundas St. W. Suite 200, Toronto, ON, Canada, M5G 2E8 e-mail: [email protected] J.J. Batzel et al. (eds.), Mathematical Modeling and Validation in Physiology, Lecture Notes in Mathematics 2064, DOI 10.1007/978-3-642-32882-4 8, © Springer-Verlag Berlin Heidelberg 2013
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Pulmonary Ventilation O2 Uptake
Tissue Metabolism CO2 Production
Pco2
Po2 O2 in Tissues
CO2 in Tissues
Tissue Metabolism O2 Consumption
Pulmonary Ventilation CO2 Excretion
Fig. 8.1 A conceptual model showing the balance between metabolic requirements and pulmonary gas exchange of O2 and CO2 . Notice the difference in storage compartment sizes for O2 and CO2
the control system is set up to accomplish its main goal by constraining these partial pressures within limits. The diagram also displays the difference in the storage capacities for O2 and CO2 ; as a consequence changes in PO2 are fast but those for PCO2 are slow. What are the constraints for the partial pressures? The requirement for PO2 is relatively simple; it should be kept at a partial pressure that saturates arterial haemoglobin and provides a gradient that is sufficient to supply tissue metabolic requirements for O2 . Since the carriage of oxygen in blood is such that saturation can be achieved over a wide range of PO2 , it need not be closely regulated unless saturati
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