  Chest physiotherapy is an empirical technique used to help secretions to get
out of the lung whenever stagnation occurs. Although commonly used, little is
known about the inner mechanisms of chest physiotherapy and controversies about
its use are coming out regularly. Thus, a scientific validation of chest
physiotherapy is needed to evaluate its effects on secretions.
  We setup a quasi-static numerical model of chest physiotherapy based on
thorax and lung physiology and on their respective biophysics. We modeled the
lung with an idealized deformable symmetric bifurcating tree. Bronchi and their
inner fluids mechanics are assumed axisymmetric. Static data from the
literature is used to build a model for the lung's mechanics. Secretions motion
is the consequence of the shear constraints apply by the air flow. The input of
the model is the pressure on the chest wall at each time, and the output is the
bronchi geometry and air and secretions properties.
  In the limit of our model, we mimicked manual and mechanical chest
physiotherapy techniques. We show that for secretions to move, air flow has to
be high enough to overcome secretion resistance to motion. Moreover, the higher
the pressure or the quicker it is applied, the higher is the air flow and thus
the mobilization of secretions. However, pressures too high are efficient up to
a point where airways compressions prevents air flow to increases any further.
Generally, the first effects of manipulations is a decrease of the airway tree
hydrodynamic resistance, thus improving ventilation even if secretions do not
get out of the lungs. Also, some secretions might be pushed deeper into the
lungs; this effect is stronger for high pressures and for mechanical chest
physiotherapy. Finally, we propose and tested two adimensional numbers that
depend on lung properties and that allow to measure the efficiency and comfort
of a manipulation.
