Chest physiotherapy is a set of techniques, mostly empirical, used to help the draining of the mucus from the lung in pathological situations. The choice of the techniques, and their adjustment to the patients or to the pathologies, remains as of today largely empirical. High Frequency Chest Wall Oscillation (HFCWO) is one of these techniques, performed with a device that applies oscillating pressures on the chest. However, there is no clear understanding of how HFCWO devices interact with the lung biomechanics. Hence, we study idealised HFCWO manipulations applied to a mathematical and numerical model of the biomechanics of the lung. The lung is represented by an airway tree connected to an homogeneous elastic medium. We highlight that the biophysics of the idealised HFCWO is driven by two dimensionless numbers. We show that the stress applied to the mucus plays the role of a buffer for the mucus yield stress, hence reducing the amount of stress needed to mobilize the mucus. The stress is the addition of two stresses with different physical origin and of the same order of magnitude: a stress due to the airway wall deformation and a stress due to the air-mucus interactions. Our model predicts the existence of an optimal range of HFCWO working frequencies that is in agreement with the frequencies actually used during HFCWO oscillations. Moreover, our model suggests that analyzing the mouth airflow during HFCWO could allow to estimate the compliance and the hydrodynamic resistance of the lung of a patient.
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