Avalanches in the lung: A statistical mechanical model

TL;DR

This paper presents a statistical mechanical model for lung inflation dynamics, explaining experimentally observed power-law distributions of airway opening events through an avalanche mechanism mapped onto percolation theory.

Contribution

It introduces an exact analytical solution for avalanche size distribution in lung airway opening, linking airway structure to observed power-law behavior.

Findings

Power-law distribution of airway opening avalanches explained

Analytical exponents derived for avalanche sizes

Numerical simulations confirm analytical predictions

Abstract

We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the tree-like structure of the airways together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.