AVALANCHES IN THE LUNG - A STATISTICAL-MECHANICAL MODEL

We study a statistical mechanical model for the dynamics of lung infla tion which incorporates recent experimental observations on the openin g of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tr ee, we analytically derive the exponents describing the size distribut ion of the first avalanches and test the analytical solution by numeri cal simulations. We find that the treelike structure of the airways, t ogether with the simplest assumptions concerning opening threshold pre ssures of each airway, is sufficient to explain the existence of power -law distributions observed experimentally.