Avalanche Dynamics of Crackle Sound in the Lung

We analyze a sequence of short transient sound waves, called “crackles,” which are associated with explosive openings of airways during lung inflation. The distribution of time intervals between consecutive crackles $\Delta t$ shows two regimes of power law behavior. We develop an avalanche model which fits the data over five decades of $\Delta t$. We find that the regime for large $\Delta t$ is related to the dynamics of distinct avalanches in a Cayley tree, and the regime for small $\Delta t$ is determined by the dynamics of crackle propagation within a single avalanche. We also obtain a mean-field solution of the model which provides information about lung inflation.