Classification: 74D05, 74Q10, 76S05, 92B05

Keywords: Poiseuille flow, dyadic tree, kernel operator, damped wave equation, human lungs

@article{M2AN_2006__40_1_201_0, author = {Grandmont, C\'eline and Maury, Bertrand and Meunier, Nicolas}, title = {A viscoelastic model with non-local damping application to the human lungs}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {40}, number = {1}, year = {2006}, pages = {201-224}, doi = {10.1051/m2an:2006009}, zbl = {pre05038398}, mrnumber = {2223510}, language = {en}, url = {http://www.numdam.org/item/M2AN_2006__40_1_201_0} }

Grandmont, Céline; Maury, Bertrand; Meunier, Nicolas. A viscoelastic model with non-local damping application to the human lungs. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 1, pp. 201-224. doi : 10.1051/m2an:2006009. http://www.numdam.org/item/M2AN_2006__40_1_201_0/

[1] Analyse fonctionnelle. Théorie et applications. Masson (1993). | MR 697382 | Zbl 0511.46001

,[2] A multiscale/multimodel approach of the respiration tree, in Proc. of the International Conference, “New Trends in Continuum Mechanics” 8-12 September 2003, Constantza, Romania Theta Foundation Publications, Bucharest (2005). | Zbl 1187.92030

, and ,[3] A one-dimensional model for the propagation of pressure waves through the lung. J. Biomechanics 35 (2002) 1081-1089.

, and ,[4] A 3D virtual environment for modeling mechanical cardiopulmonary interactions. Med. Imag. An. 2 (1998) 169-195.

, and ,[5] Constitutive equations for the lung tissue. J. Biomech Eng. 105 (1983) 374-380.

,[6] Micro-macro modelling of arrays of spheres interacting through lubrication forces, Prépublication du Laboratoire de Mathématiques de l'Université Paris-Sud (2005) 46.

and ,[7] Non-homogeneous Boundary Value Problems and Applications, I. Springer-Verlag, New York (1972). | Zbl 0223.35039

and ,[8] A distributed nonlinear model of lung tissue elasticity. J. Appl. Phys. 82 (1997) 32-41.

and ,[9] Interplay between flow distribution and geometry in an airway tree. Phys. Rev. Lett. 14 (2003) 90.

, , and ,[10] The optimal bronchial tree is dangerous. Nature 427 (2004) 633-636.

, , and ,[11] Multilevel norms for ${H}^{-1/2}$. Computing 61 (1998) 235-255. | Zbl 0930.65120

,[12] Mechanical model of the inspiratory pump. J. Biomechanics 35 (2002) 139-145.

, , and ,[13] Stress-strain analysis and the lung. Fed. Proc. 41 (1982) 130-135.

,