Multiscale modelling of the respiratory tract

Léonardo Baffico (1) , Céline Grandmont (2) , Bertrand Maury (3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 REO - Numerical simulation of biological flows
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Finite Element Method; Navier-Stokes equations; local existence; coupling of models; ventilation process; Finite Element Method.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Léonardo Baffico, Céline Grandmont, Bertrand Maury. Multiscale modelling of the respiratory tract. [Research Report] 2008, pp.33. ⟨inria-00343629v1⟩