Computational and Mathematical Methods in Medicine
Volume 10 (2009), Issue 2, Pages 139-154
doi:10.1080/17486700802201592
Original Article

Theoretical Models for the Quantification of Lung Injury Using Ventilation and Perfusion Distributions

B. S. Brook,1 C. M. Murphy,2 D. Breen,3 A. W. Miles,2 D. G. Tilley,2 and A. J. Wilson4

1School of Mathematical Sciences, University of Nottingham, Nottingham, UK
2Department of Mechanical Engineering, University of Bath, Bath, UK
3Department of Anaesthesthetics, Royal Hallamshire Hospital, Sheffield, UK
4Department of Physics, University of Warwick, Coventry, UK

Received 10 March 2007; Accepted 21 March 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper describes two approaches to modelling lung disease: one based on a multi-compartment statistical model with a log normal distribution of ventilation perfusion ratio (V˙/Q˙) values; and the other on a bifurcating tree which emulates the anatomical structure of the lung. In the statistical model, the distribution becomes bimodal, when the V˙/Q˙ values of a randomly selected number of compartments are reduced by 85% to simulate lung disease. For the bifurcating tree model a difference in flow to the left and right branches coupled with a small random variation in flow ratio between generations results in a log normal distribution of flows in the terminal branches. Restricting flow through branches within the tree to simulate lung disease transforms this log normal distribution to a bi-modal one. These results are compatible with those obtained from experiments using the multiple inert gas elimination technique, where log normal distributions of V˙/Q˙ ratio become bimodal in the presence of lung disease.