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 treelike 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.

• Received 10 March 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.2192