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Issue ESAIM: Proc.
Volume 23, 2008
Mathematical and numerical modelling of the human lung
Page(s) 98 - 113
DOI http://dx.doi.org/10.1051/proc:082307
Published online 26 July 2008

ESAIM: Proc., 2008, Vol. 23, pp. 98-113
DOI: 10.1051/proc:082307

Towards stresses and strains in the respiratory system

Lena Wiechert1, Timon Rabczuk1, 2, Andrew Comerford1, Robert Metzke1 and Wolfgang A. Wall1

1  Chair of Computational Mechanics, Technical University of Munich, Boltzmannstraße 15, D-85747 Garching, Germany
2  Mechanical Engineering Department, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand

timon.rabczuk@canterbury.ac.nz

Published online: 26 July 2008

Abstract
This paper is concerned with coupled problems in the human respiratory system with emphasis on mechanical ventilation. We focus on the modeling aspects of pulmonary alveoli and the lower airways against the background of acute lung diseases. In this connection occurring stresses and strains are of substantial interest.

For the first generations of the bronchial tree, a geometry based on human computer tomography scans obtained from in-vivo experiments is employed. The deformability of airway walls is taken into account to study airflow structures and airway wall stresses for a number of different scenarios. Therefore we carried out fluid-structure interaction (FSI) simulations under transient incompressible flow conditions. Both models for healthy and diseased lungs are studied under normal breathing as well as under mechanical ventilation.

Our alveolar model is based on three-dimensional artificial random geometries generated with the help of a new labyrinthine algorithm ensuring preservation of overall minimal mean pathlength. A polyconvex hyperelastic material model incorporating general histologic information is employed to realistically describe alveolar parenchymal tissue properties. The influence of surface-active agents (the so-called surfactant) on the overall mechanical behavior of pulmonary alveoli is investigated. For this purpose an adsorption-limited model relating surface stresses to the interfacial concentration of surfactant is used.



© EDP Sciences, ESAIM 2008


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