  Chest physiotherapy is a set of techniques 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 a fluid--structure interaction model
based on an airway tree that is coupled to an homogeneous elastic medium. We
show that our model is driven by two dimensionless numbers that drive the
effect of the idealised HFCWO manipulation on the model of the lung. Our model
allow to analyze the stress applied to an idealised mucus by the air--mucus
interaction and by the airway walls deformation. This stress behaves as a
buffer and has the effect of reducing the stress needed to overcome the
idealised mucus yield stress. Moreover, our model predicts the existence of an
optimal range of the working frequencies of HFCWO. This range is in agreement
with the frequencies actually used by practitioners during HFCWO maneuvers.
Finally, our model suggests that analyzing the mouth airflow during HFCWO
maneuvers could allow to estimate the compliance and the hydrodynamic
resistance of the lung of a patient.
