G. R. Fulford and J. R. Blake, Muco-ciliary Transport in the Lung, J Theor Biol, vol.121, pp.381-402, 1986.

A. Wanner, M. Salathe, O. 'riordan, and T. G. , Mucociliary clearance in the airways, Am J Respir Crit Care Med, vol.154, p.8970383, 1996.

M. R. Knowles and R. C. Boucher, Mucus clearance as a primary innate defense mechanism for mammalian airways, J Clin Invest, vol.109, p.11877463, 2002.

J. V. Fahy and B. F. Dickey, Airway mucus function and dysfunction, N Engl J Med, vol.363, issue.23, p.21121836, 2010.

M. J. Sanderson and M. A. Sleigh, Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony, J Cell Sci, vol.47, p.7263784, 1981.

M. A. Sleigh, J. R. Blake, and N. Liron, The propulsion of mucus by cilia, Am Rev Respir Dis, vol.137, issue.13, p.3278666, 1988.

L. Gheber and Z. Priel, On metachronism in ciliary systems: a model describing the dependence of the metachronal wave properties on the intrinsic ciliary parameters, Cell Motil Cytoskeleton, vol.16, issue.3, p.2364445, 1990.

L. Gheber and Z. Priel, Extraction of cilium beat parameters by the combined application of photoelectric measurements and computer simulation, Biophys J, vol.72, issue.97, p.8994632, 1997.

D. B. Hill, V. Swaminathan, A. Estes, J. Cribb, E. T. O'brien et al., Force Generation and Dynamics of Individual Cilia under External Loading, Biophys J, vol.98, p.20085719, 2010.

M. Salathe, Regulation of mammalian ciliary beating, Annu Rev Physiol, vol.69, p.16945069, 2007.

M. Bottier, S. Blanchon, G. Pelle, E. Bequignon, D. Isabey et al., A New Index for Characterizing Micro-bead Motion in a Flow Induced by Ciliary Beating: part I, Experimental Analysis, PLoS Comput Biol, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01579454

D. J. Smith, E. A. Gaffney, and J. R. Blake, Modelling mucociliary clearance, Resp Physiol Neurobi, vol.163, pp.178-188, 2008.

J. Blake, A model for the micro-structure in ciliated organisms, J Fluid Mech, vol.55, 1972.

E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep Prog Phys, vol.72, issue.9, p.96601, 2009.

W. L. Lee, P. G. Jayathilake, Z. Tan, D. V. Le, H. P. Lee et al., Muco-ciliary transport: Effect of mucus viscosity, cilia beat frequency and cilia density, Comput Fluid, vol.49, issue.1, pp.214-221, 2011.

S. M. Mitran, Metachronal wave formation in a model of pulmonary cilia, Comput Struct, vol.85, p.19169426, 2007.

X. Yang, R. H. Dillon, and L. J. Fauci, An Integrative Computational Model of Multiciliary Beating, Bull Math Biol, vol.70, issue.4, p.18236120, 2008.

S. R. Keller, Fluid mechanical investigations of ciliary propulsion. California Institute of Technology, 1975.

J. R. Blake and H. Winet, On the mechanics of muco-ciliary transport, Biorheology, vol.17, p.7407342, 1980.

D. J. Smith, E. A. Gaffney, and J. R. Blake, Discrete Cilia Modelling with Singularity Distributions: Application to the Embryonic Node and the Airway Surface Liquid, Bull Math Biol, vol.69, issue.5, p.17473955, 2007.

S. Childress, Mechanics of Swimming and Flying, 1981.

S. M. Ross and S. Corrsin, Results of an analytical model of mucociliary pumping, J Appl Physiol, vol.34, issue.3, pp.333-373, 1974.

J. R. Velez-cordero and E. Lauga, Waving transport and propulsion in a generalized Newtonian fluid, J NonNewton Fluid, vol.199, pp.37-50, 2013.

X. N. Shen and P. E. Arratia, Undulatory Swimming in Viscoelastic Fluids, Phys Rev Lett, vol.106, p.21668264, 2011.

B. Liu, T. R. Powers, and K. S. Breuer, Force-free swimming of a model helical flagellum in viscoelastic fluids, Proc Natl Acad Sci USA, vol.108, p.22106263, 2011.

M. Dasgupta, B. Liu, H. C. Fu, M. Berhanu, K. S. Breuer et al., Speed of a swimming sheet in Newtonian and viscoelastic fluids, Phys Rev E, vol.87, p.13015, 2013.

E. Lauga, Propulsion in a viscoelastic fluid, Phys Fluids, vol.19, 2007.

H. Fu, W. Wolgemuth, and T. R. Powers, Swimming speeds of filaments in nonlinearly viscoelastic fluids, Phys Fluids, vol.21, 2009.

J. Teran, L. Fauci, and M. Shelley, Viscoelastic Fluid Response Can Increase the Speed and Efficiency of a Free Swimmer, Phys Rev Lett, vol.104, p.20366685, 2010.

L. Zhu, M. Do-quang, E. Lauga, and L. Brandt, Locomotion by tangential deformation in a polymeric fluid, Phys Rev E, vol.83, p.11901, 2011.

L. Zhu, E. Lauga, and L. Brandt, Self-propulsion in viscoelastic fluids: Pushers vs. pullers, Phys Fluids, vol.24, issue.5, 2012.
DOI : 10.1063/1.4718446
URL : http://arxiv.org/pdf/1212.0123

G. S. Beavers and D. D. Joseph, Boundary conditions at a naturally permeable wall, J Fluid Mech, vol.30, issue.1, pp.197-207, 1967.

V. S. Verma and S. M. Tripathee, A planar model for muco-ciliary transport in the human lung: effects of mucus visco-elasticity, cilia beating and porosity, IJMMPS, vol.1, issue.1, 2013.

M. A. Chilvers and C. O'callaghan, Analysis of ciliary beat pattern and beat frequency using digital high speed imaging: comparison with the photomultiplier and photodiode methods, Thorax, vol.55, p.10722772, 2000.