Modeling shear stress distribution in a deformable airway tree

Jonathan Stephano (1, 2, 3) , Benjamin Mauroy (1, 4, 2, 3)

1 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 VADER Center
4 CNRS - Centre National de la Recherche Scientifique

The interaction between air and mucus in the bronchial tree can play an important role on mucus transport at high ventilation regimes, such in exercise, chest physiotherapy or cough. In order to improve our understanding of this interaction , we analysed with modelling approaches the distribution of shear stress in airway trees during expiration. We use models with the minimal possible complexity in order to keep the models tractable and in order to identify the driving phenomena. We explore how the shear stress induced by air can overcome mucus typical yield stress and how it might be distributed in the tree. Our models allow to highlight several behaviors, and show that both tree structure and bronchi deformation play a crucial role in the way mucus is affected by air. In particular, we determined, in the limit of our models , that the shear stress distribution exhibits a bell-like profile along the tree whose properties are directly related to lung's geometry, tissue pressure and to the amount of air flow.

Mots clés: Bronchial tree; shear stress; mucus yield stress; mathematical model; fluid mechanics; bronchi mechanics

Domaines: Biophysique [physics.bio-ph]; Biomécanique [physics.med-ph]; Mécanique des fluides [physics.class-ph]

Jonathan Stephano, Benjamin Mauroy. Modeling shear stress distribution in a deformable airway tree. 27th Canadian Congress of Applied Mechanics, May 2019, Sherbrooke, Canada. ⟨hal-02389639v1⟩