Flutter in collapsible tubes: a theoretical model of wheezes

Abstract

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.