Geodesic
Multiscale modelling of the respiratory track: a theoretical framework
C. Grandmont1 ; B. Maury2 ; A. Soualah3
1 INRIA, Projet REO Rocquencourt, BP 105 78153 Le Chesnay Cedex, France
2 Laboratoire de mathématiques, Université Paris-Sud Bâtiment 425, bureau 130, 91405 Orsay Cedex, France
3 Laboratoire de mathéématiques , Université Paris-Sud Bâtiment 425, bureau 130, 91405 Orsay Cedex, France
ESAIM. Proceedings, Tome 23 (2008), pp. 10-29.

Voir la notice de l'article provenant de la source EDP Sciences

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 diaphragm muscl. We prove that this problem has at least one solution locally in time for any data and, in the special case where the external forces are equal to zero and if the initial conditions are small enough, that the solution exists globally in time. Note moreover that, in the case where the spring stiffness is equal to zero, we obtain an existence result globally in time provided, once again, that the data are small enough. The behaviour of the global model is illustrated by two-dimensional simulations.
DOI : 10.1051/proc:082302

C. Grandmont 1 ; B. Maury 2 ; A. Soualah 3

1 INRIA, Projet REO Rocquencourt, BP 105 78153 Le Chesnay Cedex, France
2 Laboratoire de mathématiques, Université Paris-Sud Bâtiment 425, bureau 130, 91405 Orsay Cedex, France
3 Laboratoire de mathéématiques , Université Paris-Sud Bâtiment 425, bureau 130, 91405 Orsay Cedex, France 
@article{EP_2008_23_a2,
     author = {C. Grandmont and B. Maury and A. Soualah},
     title = {Multiscale modelling of the respiratory track: a theoretical framework},
     journal = {ESAIM. Proceedings},
     pages = {10--29},
     publisher = {mathdoc},
     volume = {23},
     year = {2008},
     doi = {10.1051/proc:082302},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:082302/}
}
TY  - JOUR
AU  - C. Grandmont
AU  - B. Maury
AU  - A. Soualah
TI  - Multiscale modelling of the respiratory track: a theoretical framework
JO  - ESAIM. Proceedings
PY  - 2008
SP  - 10
EP  - 29
VL  - 23
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc:082302/
DO  - 10.1051/proc:082302
LA  - en
ID  - EP_2008_23_a2
ER  - 
%0 Journal Article
%A C. Grandmont
%A B. Maury
%A A. Soualah
%T Multiscale modelling of the respiratory track: a theoretical framework
%J ESAIM. Proceedings
%D 2008
%P 10-29
%V 23
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc:082302/
%R 10.1051/proc:082302
%G en
%F EP_2008_23_a2
C. Grandmont; B. Maury; A. Soualah. Multiscale modelling of the respiratory track: a theoretical framework. ESAIM. Proceedings, Tome 23 (2008), pp. 10-29. doi : 10.1051/proc:082302. http://geodesic.mathdoc.fr/articles/10.1051/proc:082302/

Cité par Sources :