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L’artère comme un milieu à microdilatation : une investigation numérique

Abstract : Arteries, like soft biological tissues in general, have an internal structure and a complex organization on several scales. Some phenomena alter this microstructure inducing a modification of their response at the same level of stimuli and therefore their macroscopic behavior. Among these phenomena, there may be mentioned arteriosclerosis, a natural process which is characterized by thickening and lowest deformability of the arterial wall. The arterial wall has stiffened. This stiffening is due in part to the remodeling corresponding to a modification of structure involving synthesis of new constituents with a different organization or reorganization of existing ones. We can also mention atherosclerosis, a pathology resulting in accumulation of lipids, carbohydrates, adipose tissue, etc. creating a plaque called atheroma at the inner wall of the artery. This pathology accelerates arteriosclerosis and subsequently modifies the microstructure by remodeling. The optimization of therapeutic techniques applied to the diseases of the arterial system requires the analysis of the artery considered as a mechanical system. Thus, mathematical modelling of its mechanical behavior is imperative. Given the complexity of its microstructure, we opted for a representation of its behavior in the context of Eringen micromorphic media and more particularly in the context of microdilatation media.The artery, in normal operating conditions, is subjected to small elastic deformations. The solution of field equations for analysing the state of stress and deformation induced by an external stimulus can generally be obtained only numerically. Due to the complexity of the behaviour model, we had to develop a dedicated tool. It is based on a clever coupling of the boundary element method and a collocation point method. The digital tool developed has been validated on a number of simple cases allowing a comparison of numerical and analytical solutions. The analysis of the artery as a homogeneous microdilatation medium is undertaken initially. Then, motivated by the observation of the layered structure of the artery with different mechanical properties, the analysis continues by considering the medium as non-homogeneous. The work was then extended to the study of arteriosclerosis by first simulating the modification of the deformability by a modification of the microstructural characteristics then by the insertion of inert inclusions. An in-depth study of the impact of such areas with different size and position in the arterial wall is conducted. Finally, atherosclerosis and angioplasty are approached by considering a rigid atheroma plaque. The results obtained highlight some clinical observations. In particular, we can mention the remodelling process induced by the local degeneration of the mechanical properties of the artery or by the stent placement whose clinical utility is no longer to be demonstrated. This work should be continued by the effective identification of the microstructural parameters of the artery and by the optimization of the mechanical properties of stents to localize the remodeling area. It will also be necessary to take into account the global anisotropy of the artery.
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Arnaud Voignier. L’artère comme un milieu à microdilatation : une investigation numérique. Matériaux. Université de Lorraine, 2019. Français. ⟨NNT : 2019LORR0233⟩. ⟨tel-02553495⟩

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