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Modeling, numerical analysis and simulations of breathing

Justine Fouchet-Incaux 1, 2
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : In this thesis, we study the modelling of the human mechanical ventilation and the nu- merical analysis of linked systems. Direct simulations of air flow in the whole airways are impossible (complex geometry, unavailable meshes). Then a reduced area of interest can be considered, working with reduced geometries and artificial boundaries. One can also use reduced models, simple but realistic. If one try to make 3D numerical simulations where the fluid flow is described by the Navier-Stokes equations, various issues are raised: • If we consider that ventilation is the result of pressure drops, the associated bound- ary conditions are Neumann conditions. It leads to theoretical questions in terms of existence and uniqueness of solution and numerical issues in terms of scheme choice and appropriate numerical methods. • When working in a truncated domain, it may be necessary to take into account non-described phenomena with appropriate models. Here we consider 0D models. These 3D/0D couplings imply numerical instabilities that we mathematically and numerically study in this thesis. Furthermore, when we focus on forced breathing, linear usual models are invalidated by experiments. In order to observe the differences between the experimental and numer- ical results, it is necessary to take into account several types of non-linearities, such as deformation of the domain or the Bernoulli phenomenon. A reduced model approach is adopted in this work. Finally, we sought to validate the obtained models by comparing numerical and experimental results in the context of interdisciplinary work. Achieving model and simulate these flows allow to better understand phenomena and parameters that come into play in diseases (asthma, emphysema ...). A medium-term objective is to study the influence of helium-oxygen mixture in the aerosol deposition. In the longer term, the application of these models to pathological situations could afford to build decision support tools in the medical field (understanding of pathology, therapy optimization ...).
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  • HAL Id : tel-01575952, version 1

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Justine Fouchet-Incaux. Modeling, numerical analysis and simulations of breathing. Numerical Analysis [math.NA]. Université Paris-Sud 11, 2015. English. ⟨tel-01575952⟩

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