8. Survey of Research in Modeling the Human Respiratory and Cardiovascular Systems

Abstract

Previous chapter Next chapter Frontiers in Applied Mathematics Research Directions in Distributed Parameter Systems8. Survey of Research in Modeling the Human Respiratory and Cardiovascular SystemsF. Kappel and J. J. BatzelF. Kappel and J. J. Batzelpp.187 - 218Chapter DOI:https://doi.org/10.1137/1.9780898717525.ch8PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutExcerpt In this chapter we examine some major issues concerning the modeling of the respiratory and cardiovascular control systems as well as review some of the important models which have been developed to address these issues. The physiological processes that control the ventilation rate V˙A are fairly well understood and we will look at a number of mathematical models that have been devised to describe this control. The cardiovascular control system, on the other hand, involves a more complex set of interrelationships involving a number of factors including heart rate, blood pressure, cardiac output and blood vessel resistance. At the current time the description of these control relationships is far from complete. We will consider several important areas in cardiovascular control and some of the modeling approaches that have been used to understand the control process. One approach to studying the cardiovascular and respiratory systems considers the introduction of optimality conditions into the design of these systems and application of optimal control theory to the modeling process. Many physiologists assume that optimization is a basic feature in the evolution of biological systems (e.g., see Kenner [42], Swan [79] or Taylor [81]). It is reasonable to consider, for example, whether such systems have evolved in such a way as to minimize energy expenditure. Finally, after we have discussed the respiratory and cardiovascular systems separately, we will consider the interaction and interrelations of these two systems. Previous chapter Next chapter RelatedDetails Published:2003ISBN:978-0-89871-548-4eISBN:978-0-89871-752-5 https://doi.org/10.1137/1.9780898717525Book Series Name:Frontiers in Applied MathematicsBook Code:FR27Book Pages:xvii + 266Key words:control theory, distributed parameter systems