A Mathematical Model for the Sounds Produced by Knuckle Cracking

The articular release of the metacarpophalangeal joint produces a typical cracking sound, resulting in what is commonly referred to as the cracking of knuckles. Despite over sixty years of research, the source of the knuckle cracking sound continues to be debated due to inconclusive experimental evidence as a result of limitations in the temporal resolution of non-invasive physiological imaging techniques. To support the available experimental data and shed light onto the source of the cracking sound, we have developed a mathematical model of the events leading to the generation of the sound. The model resolves the dynamics of a collapsing cavitation bubble in the synovial fluid inside a metacarpophalangeal joint during an articular release. The acoustic signature from the resulting bubble dynamics is shown to be consistent in both magnitude and dominant frequency with experimental measurements in the literature and with our own experiments, thus lending support for cavitation bubble collapse as the source of the cracking sound. Finally, the model also shows that only a partial collapse of the bubble is needed to replicate the experimentally observed acoustic spectra, thus allowing for bubbles to persist following the generation of sound as has been reported in recent experiments.