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
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.