Crackles

In a very general way, crackle is an abrupt and discrete event which follows a small change in the state of a given system. Crackling behavior are found in a wide variety of systems as earthquakes [8], magnetic material [22], crumpled elastic sheet [13], mammalian lung [14] etc, and there is much current interest [23]. Usually, crackles are events which span many orders of magnitude in size and the distribution of sizes form a power law. In particular, the short ``explosive'' transient waves called pulmonary crackle, which are among the many lung sounds generated in the airways in a diseased lung during breathing, behaves as a power law in the distribution of sizes and in the distribution of time interval between consecutive events [4,2]. Often in the clinical field, pulmonary diagnosis is based on analysis of acoustical signals, since the generated acoustic energy produced by the air flow during inspiration and expiration correlates with pulmonary dysfunction. However, analysis of lung sound is based largely on empirical observations without solid theoretical foundations and are not fully understood [18].

Pulmonary crackles are short ``explosive'' transient waves, which are among the many lung sounds generated in the airways in a diseased lung during breathing. They are characterized by a rapid initial pressure deflection, called a spike, followed by a short duration ringing (see Fig.1). Crackles have long been used as a qualitative diagnostic tool, since the acoustic properties of crackles correlate with certain pulmonary dysfunctions [18]. The time series of crackle events are complex and two power laws have been discovered one in the distribution of crackle size amplitudes [4], and one in the time interval between consecutive events [2]. However, analysis of lung sound is based largely on empirical observations without solid theoretical basis and are not fully understood.

Figure 1: Experimental data. (a) The continuous line is the time series of sound pressure $S(t)$ during the first inflation of a dog lung lobe from the collapsed state recorded at a rate of $22,050$Hz; (b) magnified segment of $S(t)$ with consecutive spikes. The inter-spike interval $\Delta t \approx 0.2$s of this segment corresponds to the time difference between two spikes; and (c) another segment from (a) with $\Delta t \approx 0.02$s; [2].