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Model Validation and Control Issues in the Respiratory System

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Mathematical Modeling and Validation in Physiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2064))

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 \({\text{ CO}}_{2}\) 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).

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Authors and Affiliations

  1. Thornhill Research Inc., 210 Dundas St. W. Suite 200, Toronto, ON, Canada, M5G 2E8

    James Duffin

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  1. James Duffin
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Correspondence to James Duffin .

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Editors and Affiliations

  1. Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Jerry J. Batzel

  2. College of Sciences, Department of Mathematics, King Saud University, King Khalid Road, Diriyah Campus, Riyadh, 11451, Saudi Arabia

    Mostafa Bachar

  3. Institute for Mathematics, and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Franz Kappel

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Duffin, J. (2013). Model Validation and Control Issues in the Respiratory System. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_8

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