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Conséquences de l’asymétrie et de la compliance des bronches sur les propriétés hydrodynamiques du poumon, applications à la kinésithérapie respiratoire

Abstract : The lung is an organ whose the role is to transport oxygen from the ambient air to the blood and to extract carbon dioxide from the blood. It is a tree-like structure of bronchi, the bronchial tree, connected to an exchange surface, the acini.The bronchial bifurcations are asymmetric: the bronchi divides into two daughter bronchi of different sizes. The topology of the tree is asymmetric : the number of bifurcations that connect the trachea to the acini is not constant. The bronchi wall is deformable (compliance) and their geometries are affected by the transmural pressure, i.e., the pressure difference between the surrounding tissue and the air flowing inside the bronchi. These characteristics affect the hydrodynamic properties of the tree.As an interface with the external air, it is constantly in contact with external particles. The bronchial mucus plays a protective role by capturing these particles. Normally, the mucus is naturally drained out of the lung. The mucus should not stagnate in the bronchi because stagnation increases the probability of developing an infection. When stagnation occurs, chest physiotherapy is often prescribed. The physiotherapists usually perform technics using the air shear stress to stimulate the mucus extraction. However, the expiratory conditions that allow to mobilize the mucus are not clearly defined.This thesis is based on three steps that allow to analyze the influence of the bifurcations asymmetry and of the compliance on the distribution of the shear stress induced by the airflow in the bronchi. Our three studies use a 0D model for each bronchus. The air hydrodynamic into each bronchus is simplified, either with a Poiseuille flow or with a “modified Poiseuille” flow that includes some inertial effects.The first step consists in understanding the air shear stress repartition in a symmetric tree with compliant bronchi. We show that this repartition exhibits a maximum whose location and amplitude depend on the flowrate in the trachea and on the pressure in the pulmonary tissue. This study shows also that one partial obstruction might “hide” others localized deeper in the lung. The comparison of our results with a typical yield shear stress of the mucus allows to develop, in the limits of our model, idealized chest physiotherapy technics for mucus draining.The second step aims at understanding the link between the bifurcation’s asymmetry and the hydrodynamics in a fractal and rigid tree. We propose in this part the hypothesis that the pulmonary asymmetry selection is linked to the optimization of a cost linked to the tree’s hydrodynamic resistance, under a constraint on the tree’s volume. Our analysis allows to propose a scenario that explains the difference in asymmetry observed between mammals.Finally, the third step aims at studying the shear stress repartition in a tree with asymmetric bifurcations and compliant bronchi. We show that the distribution of the air shear stress induced by a Poiseuille flow in trees with symmetric bifurcations and with asymmetric bifurcations have similar behaviors. However, the asymmetric case presents a spread of the shear stresses in the distal part of the tree, and bronchi with similar properties can have very different shear stresses.This research, based on the alliance of mathematics, physics, biology and medicine, allowed to improve our understanding of both the bifurcation asymmetry, the bronchi compliance and their effect on the airflow hydrodynamic. Particularly, this allowed to further understand the influence of the air shear stress on the mucus flow during chest physiotherapy.
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Submitted on : Friday, October 8, 2021 - 9:31:12 AM
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  • HAL Id : tel-03239006, version 3

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Jonathan Stephano. Conséquences de l’asymétrie et de la compliance des bronches sur les propriétés hydrodynamiques du poumon, applications à la kinésithérapie respiratoire. Physique mathématique [math-ph]. Université Côte d'Azur, 2021. Français. ⟨NNT : 2021COAZ4035⟩. ⟨tel-03239006v3⟩

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