Multiscale modelling of the respiratory tract

Abstract : We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the thoracic cage. We prove that this problem has at least one solution locally in time for any data and, in the special case where the spring stiffness is equal to zero, we obtain an existence result globally in time provided that the data are small enough. The behaviour of the global model is illustrated by three-dimensional simulations.
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Léonardo Baffico, Céline Grandmont, Bertrand Maury. Multiscale modelling of the respiratory tract. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2010, pp.59--93. ⟨10.1142/S0218202510004155⟩. ⟨inria-00343629v2⟩

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