VOLUME DISTRIBUTIONS OF AVALANCHES IN LUNG-INFLATION - A STATISTICAL-MECHANICAL APPROACH

Citation
Mk. Sujeer et al., VOLUME DISTRIBUTIONS OF AVALANCHES IN LUNG-INFLATION - A STATISTICAL-MECHANICAL APPROACH, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(3), 1997, pp. 3385-3394
Citations number
27
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
ISSN journal
1063651X
Volume
56
Issue
3
Year of publication
1997
Part
B
Pages
3385 - 3394
Database
ISI
SICI code
1063-651X(1997)56:3<3385:VDOAIL>2.0.ZU;2-1
Abstract
To study the dynamics of lung inflation, we introduce a statistical me chanical model that incorporates experimental observations that, durin g lung inflation from low volumes, (i) each individual airway segment opens when the external inflation pressure reaches a critical opening threshold corresponding to that segment and (ii) airway opening in the lung occurs in cascades or by avalanches. The model includes realisti c asymmetry of the bronchial tree, tissue elasticity, and airway and a lveolar dimensions. We perform numerical simulations of lung inflation to study the effects of these attributes on the volume distributions of both the first and all avalanches for three different distributions of critical opening threshold pressures: (a) a generation-independent , (b) a slightly generation-dependent, and (c) a highly generation-dep endent distribution. For both the first and all avalanches we find tha t the volume distribution is a power law, except for the highly genera tion-dependent threshold distribution. Asymmetry and realistic airway and alveolar dimensions slightly modify the scaling region, but retain a power-law behavior as long as the distribution of threshold pressur es is generation independent or slightly generation dependent. Also, f or such a distribution of threshold pressures, the scaling exponent of the most realistic model (the asymmetric tree with realistic airway a nd alveolar dimensions and tissue elasticity) is 2, which is the value obtained both analytically using percolation theory and from simulati ons on a Cayley tree. Thus the power-law behavior and the scaling expo nents are a consequence of finite-size effects and a distribution of t hreshold pressures that is generation independent or slightly generati on dependent. We also predict the pressure-volume relationship of the model, which is easily and noninvasively accessible in clinical settin gs. The results of the avalanche size distributions and pressure-volum e curves support the notion that at low lung volumes, the distribution of the critical opening threshold pressures in the normal lung is mos t likely wide with negligible generational dependence.