The Respiratory System in Equations

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • Bertrand Maury

   Pages 1-11

3. Lumped models

   • Bertrand Maury

   Pages 13-52

4. The lung as a resistive tree

   • Bertrand Maury

   Pages 53-95

5. Computing velocity fields

   • Bertrand Maury

   Pages 97-146

6. Gas exchanges

   • Bertrand Maury

   Pages 147-180

7. The lung as an infinite tree

   • Bertrand Maury

   Pages 181-213

8. Data

   • Bertrand Maury

   Pages 215-224

9. Back Matter

   Pages 225-278

   PDF

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.

• Fluid mechanics
• Modeling
• Resistive trees
• Respiratory system
• ordinary differential equations
• fluid- and aerodynamics

“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)

• Department of Mathematics, UMR CNRS 8628, Université Paris-Sud, Orsay, France

  Bertrand Maury

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.

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