Mathematical modelling of cilia-driven transport of biological fluids

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 465, Issue 2108, 2009, Pages 2417-2439

  Smith, D J ^a,b   Gaffney, E A ^b,c   Blake, J R ^a,b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b BIRMINGHAM CHILDREN S HOSPITAL NHS FOUNDATION TRUST   (United Kingdom)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Cilia; Mucus; Slender body theory; Stokeslet; Transport; Viscoelastic

Indexed keywords

BENDING (DEFORMATION); BENDING MOMENTS; BODY FLUIDS; COMPUTATION THEORY; COMPUTER SIMULATION; ELASTICITY; LIQUIDS; PARTICLE SEPARATORS; PLASTICITY; RELAXATION PROCESSES; RHEOLOGY; STATISTICAL TESTS; VISCOSITY;

CILIA; MUCUS; SLENDER-BODY THEORY; STOKESLET; TRANSPORT; VISCOELASTIC;

MATHEMATICAL MODELS;

EID: 67749137344     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0018     Document Type: Article

References (36)

1. Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303-310. (doi:10.1017/S0305004100049902)
2. Brokaw, C. J. 2002 Computer simulation of flagellar movement. VII. Coordination of dynein by local curvature control can generate helical bending waves. Cell Motil. Cytoskel. 53, 102-124. (doi:10.1002/cm.10067)
3. Cartwright, J. H. E., Piro, N., Piro, O. & Tuval, I. 2007 Embryonic nodal flow and the dynamics of nodal vesicular parcels. J. R. Soc. Interface 4, 49-55. (doi:10.1098/rsif.2006.0155)
4. Clarke, R. J., Jensen, O. E., Billingham, J. & Williams, P. M. 2006 Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Proc. R. Soc. A 462, 913-933. (doi:10.1098/rspa.2005.1607)
5. Dillon, R. H., Fauci, L. J. & Yang, X. 2006 Sperm motility and multiciliary beating: an integrative mechanical model. Comput. Math. Appl. 52, 749-758. (doi: 10.1016/j.camwa.2006.10.012)
6. Fauci, L. & Dillon, R. 2006 Biofluidmechanics of reproduction. Ann. Rev. Fluid Mech. 38, 371-394. (doi:10.1146/annurev. fluid.37.061903.175725)
7. Fu, H. C., Powers, T. R. & Wolgemuth, C. W. 2007 Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99, 258101. (doi:10.1103/PhysRevLett.99.258101)
8. Fu, H. C., Powers, T. R. & Wolgemuth, C. W. 2008 Beating patterns of filaments in viscoelastic fluids. Phys. Rev. E 78, 041913. (doi:10.1103/PhysRevE.78.041913)
9. Fulford, G. R. & Blake, J. R. 1986 Muco-ciliary transport in the lung. J. Theor. Biol. 121, 381-402. (doi:10.1016/S0022-5193 (86) 80098-4)
10. Fulford, G. R., Katz, D. F. & Powell, R. L. 1998 Swimming of spermatozoa in a linear viscoelastic fluid. Biorheology 35, 295-309. (doi:10.1016/S0006-355X (99) 80012-2)
11. Gheber, L. & Priel, Z. 1998 Effect of viscosity on metachrony in mucus propelling cilia. Cell Motil. Cytoskel. 39, 9-20. (doi:10.1002/(SICI) 1097-0169 (1998) 39:1<9::AID-CM2>3.0. CO;2-3)
12. Gueron, S. & Levit-Gurevich, K. 2001 A three-dimensional model for ciliary motion based on the internal 9 +2 structure. Proc. R. Soc. Lond. B 268, 599-607. (doi:10.1098/rspb.2000.1396)
13. Gueron, S. & Liron, N. 1998 Computations of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions. Biophys. J. 74, 1658-1676. (doi:10.1016/S0006-3495 (98) 77879-8)
14. Hancock, G. J. 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. Lond. A. 217, 96-121. (doi:10.1098/rspa. 1953.0048)
15. Hines, M. & Blum, J. J. 1978 Bend propagation in flagella. I. Derivation of equations of motion and their simulation. Biophys. J. 23, 41-57. (doi:10.1016/S0006-3495 (78) 85431-9)
16. Ivic, A., Onyeaka, H., Girling, A., Brewis, I. A., Ola, B., Hammadieh, N., Papaioannou, S. & Barratt, C. L. R. 2002 Critical evaluation of methylcellulose as an alternative medium in sperm migration tests. Hum. Reprod. 17, 143-149. (doi:10.1093/humrep/17.1.143)
17. Knowles, M. & Boucher, R. C. 2002 Mucus clearance as a primary innate defense mechanism for mammalian airways. J. Clin. Invest. 109, 571-577.
18. Lauga, E. 2007 Propulsion in a viscoelastic fluid. Phys. Fluids 19, 083104. (doi:10.1063/1.2751388)
19. Lighthill, M. J. 1964 Introduction to Fourier analysis and generalised functions, pp. 11-12, 16-18. Cambridge, UK: Cambridge University Press.
20. Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86, 705-726. (doi:10.1017/S0022112078001354)
21. Liron, N. & Mochon, S. 1976 The discrete-cilia approach to propulsion of ciliated micro-organisms. J. Fluid Mech. 75, 593-607. (doi:10.1017/S0022112076000402)
22. Matsui, H., et al. 2006 A physical linkage between cystic fibrosis airway surface dehydration and pseudomonas aeruginosa biofilms. Proc. Natl Acad. Sci. 103, 18 131-18 136. (doi:10.1073/phas.0606428103)
23. Nonaka, S., Tanaka, Y., Okada, Y., Takeda, S., Harada, A., Kanai, Y., Kido, M. & Hirokawa, N. 1998 Randomization of left-right asymmetry due to loss of nodal cilia generating leftward flow of extraembryonic fluid in mice lacking KIF3B motor protein. Cell 95, 829-837. (doi:10.1016/S0092-8674 (00) 81705-5)
24. Normand, T. & Lauga, E. 2008 Flapping motion and force generation in a viscoelastic fluid. Phys. Rev. E. 78, 061907. (doi:10.1103/PhysRevE.78.061907)
25. Phan-Thien, N. 2002 Understanding viscoelasticity. Berlin, Germany: Springer.
26. Phan-Thien, N. & Fan, X.-J. 2002 Viscoelastic mobility problem using a boundary-element method. J. Non-Newt. Fluid Mech. 105, 131-152. (doi:10.1016/S0377-0257 (02) 00079-4)
27. Raya, Á. & Izpisúa Belmonte, J. C. 2006 Left-right asymmetry in the vertebrate embryo: from early information to higher-level integration. Nat. Rev. Genet. 7, 283-293. (doi:10.1038/nrg1830)
28. Rogers, D. F. 2004 Airway mucus hypersecretion in asthma: an undervalued pathology. Curr. Opin. Pharm. 4, 241-250. (doi:10.1016/j.coph. 2004.01.011)
29. Sanderson, M. J. & Sleigh, M. A. 1981 Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony. J. Cell Sci. 47, 331-341.
30. Sleigh, M. A., Blake, J. R. & Liron, N. 1988 The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137, 726-741.
31. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2007a Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid. Bull. Math. Biol. 69, 1477-1510. (doi:10.1007/s11538-006-9172-y)
32. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2007b A viscoelastic traction layer model of muco-ciliary transport. Bull. Math. Biol. 69, 289-327. (doi:10.1007/s11538-005-9036-x)
33. Smith, D. J., Blake, J. R. & Gaffney, E. A. 2008a Fluid mechanics of nodal flow due to embryonic primary cilia. J. R. Soc. Interface 5, 567-573. (doi:10.1098/rsif.2007.1306)
34. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2008b Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 163, 178-188. (doi:10.1016/j.resp. 2008.03.006)
35. Smith, D. J., Gaffney, E. A., Blake, J. R. & Kirkman-Brown, J. C. 2009a Human sperm accumulation near surfaces: a simulation study. J. Fluid Mech. 621, 289-320. (doi:10.1017/S0022112008004953)
36. Smith, D. J., Gaffney, E. A., Gadêlha, H., Kapur, N., Kirkman-Brown, J. 2009b Bend propagation in the flagella of migrating human sperm, and its modulation by viscosity. Cell Motil. Cytoskel. 66, 220-236. (doi:10.1002/cm.20345)