© 2013

The Respiratory System in Equations


Part of the MS&A — Modeling, Simulation and Applications book series (MS&A)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Bertrand Maury
    Pages 1-11
  3. Bertrand Maury
    Pages 13-52
  4. Bertrand Maury
    Pages 53-95
  5. Bertrand Maury
    Pages 97-146
  6. Bertrand Maury
    Pages 147-180
  7. Bertrand Maury
    Pages 181-213
  8. Bertrand Maury
    Pages 215-224
  9. Back Matter
    Pages 225-278

About this book


The 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.


Fluid mechanics Modeling Resistive trees Respiratory system

Authors and affiliations

  1. 1.Department of Mathematics, UMR CNRS 8628Université Paris-SudOrsayFrance

About the authors

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.

Bibliographic information


“This book models respiratory system using ordinary and partial differential equations. … this is a very good book on an extremely difficult topic.” (E. Ahmed, zbMATH 1312.92005, 2015)

“It is designed as an introduction to mathematical modeling in the particular context of the respiratory system. … this book is a most valuable reference for students and researchers in the fields of applied mathematics, bioengineering and medicine who are interested in the challenging field of modeling how the respiratory system works.” (Marcela Szopos, Mathematical Reviews, September, 2014)