Modélisation physique des voies aériennes supérieures pour le Syndrome d'Apnées Obstructives du Sommeil. (Physical modelling of the upper airway for Obstructive Sleep Apnea Syndrome)

Le Syndrome d'Apnees Obstructives du Sommeil est caracterise par la survenue frequente d' episodes d' obstruction des voies aeriennes superieures. L'interet d'une modelisation physique est qu'elle autorise une comprehension plus fine du phenomene, et laisse esperer une amelioration des traitements. Le but a donc ete de concevoir, puis de valider, un algorithme de simulation numerique de l'interaction entre les tissus vivants et le flux d'air a l'origine d'un episode apneique. Afin d'alleger les calculs et de reduire le temps de simulation, des hypotheses simplificatrices ont ete envisagees. D'une part, en ce qui concerne les tissus vivants, la methode des elements finis permet une prediction realiste de leur deformation. Le cadre des petites perturbations et de l'elasticite lineaire implique de plus un calcul rapide de la reponse mecanique. D'autre part, la simulation de l'ecoulement d'air se fait via une formulation asymptotique des equations de Navier-Stokes (equations de Navier-Stokes Reduites / Prandtl), qui facilite la resolution numerique. Afin de valider hypotheses physiques et methode de resolution numerique, une maquette in-vitro a ete utilisee. Celle-ci permet de reproduire, dans des conditions controlees, une interaction entre flux d'air et paroi deformable analogue a celle qui se produit a la base de la langue en debut d'obstruction. Une mesure precise de la deformation du conduit d'ecoulement est obtenue a l'aide d'une camera digitale. Une serie de comparaisons quantitatives a montre qu'en depit des simplifications effectuees, l'erreur entre prediction et mesures est faible. Finalement, pour se rapprocher de la realite clinique, des modeles de voies aeriennes superieures de quatre patients apneiques ont ete construits a partir de radiographies sagittales. Des comparaisons entre simulations a partir de radiographies pre-operatoires et post-operatoires ont montre que les predictions etaient globalement coherentes avec les consequences du geste chirurgical. Elles ont pu egalement mettre en evidence certaines limites de notre approche, dues a la complexite du phenomene.

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