Wall shear stress distribution in a compliant airway tree

Abstract

The airflow in the bronchi applies a shear stress on the bronchial mucus, which can move the mucus. The air–mucus interaction plays an important role in cough and in chest physiotherapy (CP). The conditions under which it induces a displacement of the mucus are still unclear. Yet, the air–mucus interaction justifies common technics of CP used to help the draining of the mucus in prevalent diseases. Hence, the determination of the distribution of the shear stress in the lung is crucial for understanding the effects of these therapies and, potentially, improves their efficiency. We develop a mathematical model to study the distribution of the wall shear stress (WSS) induced by an air flow exiting an airway tree. This model accounts for the main physical processes that determine the WSS, more particularly the compliance of the airways, the air inertia, and the tree structure. We show that the WSS distribution in the tree depends on the dynamics of the airways deformation and on the air inertia. The WSS distribution in the tree exhibits a maximum whose amplitude and location depend on the amount of air flow and on the “tissue” pressure surrounding the airways. To characterize the behavior of the WSS at the tree bifurcations, we derive new analytical criteria related to the airway size reduction in the bifurcations. Our results suggest that a tuning of the airflow and of the tissue pressure during a CP maneuver might allow to control, at least partially, the air–mucus interaction in the lung.

Bronchial Clearance Physiotherapy in Pediatrics. A Controlled, Randomized, Multicenter Study of the Short-Term Effects on Respiration during Outpatient Care for Infants with Acute Bronchiolitis

“…Otherwise, investigators study, whether food intake in the preceding 24 hours, could serve as an indicator of hypoxia in infants with bronchiolitis. 27 IET taken in isolation may impact the airway tree hydrodynamic resistance caused by hypersecretion and its rheological transformations, 14,15 the latter being one of the three causes of airflow obstruction observed in bronchiolitis, which also include inflammation and potential bronchial hyperreactivity. 13,26 The reduction of airway tree hydrodynamic resistance could explain the short-term clinical Table 3 The Wang score variation in the two groups…”

“…The increase in airflow takes place at different pulmonary volumes to discern the location of air/mucus interaction. 15 To monitor expiratory airflow, two clinical indicators were used: an audible indicator (an increase in wet or productive coughing sounds) and a tactile indicator (vibrations under the hand on the thorax). 23 Using both indicators guides the physiotherapist's movements.…”

“…13 Coughing, which only impacts the first bronchial divisions, is the only way that infants have to clear the airways of mucus. Previous modeling-based studies 14,15 have shown how CP techniques to modulate exhalation flows could affect the entire airway tree by increasing the pressure that air exerts on the mucus during exhalation and by immediately reducing hydrodynamic resistance. 14 This background leads to put forward the hypothesis that CP would improve the mucus airway obstruction parameters of children receiving care in outpatient settings.…”

Modélisation de l’interaction air/mucus dans l’arbre bronchique. Volume pulmonaire vs débit d’air : contraintes de cisaillement dans l’arbre bronchique

“…Dans la partie proximale, les bronches ont tendance à être comprimées, ce qui augmente le cisaillement avec la profondeur de l'arbre bronchique. Cependant, à partir d'une certaine profondeur, la pression de l'air devient suffisante pour s'opposer à la pression du tissu environnant et les bronches ne sont plus comprimées, voire se dilatent [20]. Celles-ci ne peuvent donc pas être complètement fermées [20].…”

“…Cependant, à partir d'une certaine profondeur, la pression de l'air devient suffisante pour s'opposer à la pression du tissu environnant et les bronches ne sont plus comprimées, voire se dilatent [20]. Celles-ci ne peuvent donc pas être complètement fermées [20]. Dans le cas où une zone est obstruée, la pression de l'air dans la partie distale à l'obstruction est augmentée par rapport au cas non obstrué à même débit d'air, dilatant encore plus les bronches.…”