The Respiratory System in Equations

This book introduces concepts and techniques for mathematical modeling of the respiratory system, using differential equations, resistive networks and other mathematical tools. Offers state-of-the-art modeling techniques, and several detailed exercises.

This book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

Numerous exercises helping the reader to learn quickly Online programs allowing the reader to perform his own computations No prior knowledge on physiology required Includes supplementary material: sn.pub/extras

Auteur
Bertrand Maury is Professor of Mathematics at the Université Paris-Sud, Orsay (France). He is also adjunct Professor at the Ecole Polytechnique, Docent Professor at the University of Jyväskylä (Finland), and junior member of the Institut Universitaire de France. His domains of interest extend from Computational Fluid Dynamics and Numerical Analysis, to modeling in life sciences and Optimal Transportation.

Contenu
Introduction.- Lumped models.- The lung as a resistive tree.- Computing velocity fields.- Gas exchanges.- The lung as an infinite tree.- Data.- Solutions to exercises.- Complements.- Glossary.