Direct numerical simulation of expiratory crackles: Relationship between airway closure dynamics and acoustic fluctuations

This paper investigates the relationship between airway closure dynamics and acoustic fluctuations in expiratory crackles using direct numerical simulation. A unified mathematical model is proposed to deal with flow in an airway, elastic deformation of the airway wall, surface tension driven motion of the liquid film that lines the airway, and their acoustic fluctuations because of material compressibility. Airway closure is induced by increasing the surrounding pressure, then the source of the pressure fluctuations is measured over time. Our results show that the airway closure occurs suddenly because of a bridge formation of the liquid film, and high energy transfer occurs between the kinetic energy, the surface energy of the liquid interface, and the elastic energy of the airway wall, invoking a large acoustic fluctuation that causes the expiratory crackles. Nonlinear behavior is observed in terms of the airway wall stiffness; the dynamic motion of the airway closure becomes moderate and both the energy transfer and acoustic fluctuations are dramatically reduced with an increase in airway wall stiffness.