Discrete lung sounds: crackles (rales) as stress-relaxation quadrupoles

We modeled discrete emission of sound from lung parenchyma as a point source in an ideal medium. The point source, a quadrupole, represents the stress anomaly in lung parenchyma in the neighborhood of a collapsed airway, and its time course when the airway opens. The dynamics of the airway opening event are characterized by a single time constant. The ideal medium, lung parenchyma, was modeled as a homogeneous linearly elastic lossless nondispersive continuum of infinite extent undergoing infinitesimal strains. Despite its simplicity, this elementary model leads to predictions of crackle waveforms, spectral densities, and spatial intensity distributions which are consistent with observations. In particular, the model predicts changes of waveform shape and polarity with observation position relative to the source, dramatic influences of transduction processes, and successive increases in zero crossing time intervals.