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Study of a visco-elastic model of the human lung and application to the High Frequency Chest Wall Oscillation

Abstract : The human lung is a complex organ playing the role of interface for the vital gas exchanges (oxygen and carbon dioxide) between the ambient air and the blood. It is composed of two interconnected structures assuring the correct circulation of the air produced by the ventilation: the tracheo-bronchial tree and the lung's parenchyma, a porous medium where the gas exchanges between the air and the blood occur. Being reachable by external pollutants, the lung is protected among others by a specific secretion, also called the pulmonary mucus. The latter can accumulate and obstruct the airways in case of specific respiratory diseases. That can then alter and disturb the proper functioning of the lung. The use of therapeutic methods is then essential for the patient to maintain a good quality of life. The High Frequency Chest Wall Oscillation (HFCWO) is a respiratory technique, being part of the chest physiotherapy, that dispenses automated therapy which mobilizes the mucus and favors its expectoration. It is based on the application of small amplitude pressures at a relatively high frequency on the chest's patient. This mechanical treatment seems efficient but its use and effects on human lungs are based on empirical knowledge and are consequently not well understood as of today. The comprehension of this therapy rests on the study of the lung, complex system where specific behaviors occur. In that way, the mathematical modeling can be an useful tool. This thesis takes an interest in building and understanding a mathematical and numerical model of the lungs adapted to study the influences of the HFCWO on the human lungs. It is exploited to propose new insight on the use of this technique. Our work is based on the coupling between two idealized models: a 0D model of an airway tree that mimics the tracheo-bronchial tree and a multi-D homogeneous elastic medium that mimics the lung's parenchyma. The latter is used with its unidimensional formulation in most of this work. Our goal is to study the physics of the coupling between the air fluid dynamics in the airway tree and the deformation of the elastic medium, and to analyze the stresses felt by the mucus inside the tree. First, based on literature data, we show the efficiency of the model at mimicking ventilation at rest in healthy and non-healthy lungs. Meanwhile, we take an interest at understanding the role of its parameters. Then, with a dimensionless formulation of the model and comparative numerical simulations, we propose the use of a specific variable also known as the quality factor. Defined from the parameters of the lungs, this variable can suggest the capability of the lung to resonate with stimulations whose it is submitted. From the data observed in the literature, we suggest a range of frequencies that maximizes the effects of the HFCWO and potentially the displacement of the mucus in the tree. We show that this interval is directly linked to the fundamental natural frequency of the elastic material. The natural frequencies computed with our model are similar to the resonance frequencies deduced from clinical studies found in the literature. The end of the work propose prospects for improvement of the model such as the use of 3D lungs geometries constructed from CT-scan, the use of a splitting method to optimize the numerical time calculation or the establishment of a clinical study of the air flows at mouth induced by the HFCWO.
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Submitted on : Monday, November 22, 2021 - 9:28:20 AM
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Michaël Brunengo. Study of a visco-elastic model of the human lung and application to the High Frequency Chest Wall Oscillation. Mechanics [physics]. Université Côte d'Azur, 2021. English. ⟨NNT : 2021COAZ4069⟩. ⟨tel-03438925⟩

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