Using Lagrangian coherent structures to analyze fluid mixing by cilia

Chaos

Volumn 20, Issue 1, 2010, Pages

  Lukens, Sarah ^a   Yang, Xingzhou ^b   Fauci, Lisa ^a  

^a Tulane University   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; AUDIOVISUAL EQUIPMENT; BIOLOGICAL MODEL; BIOPHYSICS; COMPUTER PROGRAM; EUKARYOTIC FLAGELLUM; HYDRODYNAMICS; METHODOLOGY; MICROFLUIDICS; PHYSIOLOGY; STATISTICAL MODEL; THEORETICAL MODEL; VISCOSITY;

ANIMALS; BIOPHYSICS; CILIA; HYDRODYNAMICS; MICROFLUIDICS; MODELS, ANATOMIC; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; SOFTWARE; VISCOSITY;

EID: 77953487897     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3271340     Document Type: Article

References (35)

1. Afzelius BA. Cilia-related diseases. J. Pathol. 2004, 204:470-477. JPTLAS, 0022-3417, 10.1002/path.1652.
2. Blake JR, Sleigh M. Mechanics of ciliary locomotion. Biol. Rev. Cambridge Philos. Soc. 1974, 49:85-125. BRCPAH, 0006-3231, 10.1111/j.1469-185X.1974.tb01299.x.
3. Brokaw CJ. Simulating the effects of fluid viscosity on the behaviour of sperm flagella. Math. Methods Appl. Sci. 2001, 24:1351-1366. MMSCDB, 0170-4214, 10.1002/mma.184.
4. Dillon R, Fauci L. An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating. J. Theor. Biol. 2000, 207:415-430. JTBIAP, 0022-5193, 10.1006/jtbi.2000.2182.
5. Dillon R, Fauci L, Omoto C. Mathematical modeling of axoneme mechanics and fluid dynamics in ciliary and sperm motility. Dyn. Contin. Discrete Impulsive Syst.: Ser. A - Math. Anal. 2003, 10:745-758. ZZZZZZ, 1201-3390.
6. Dillon R, Fauci L, Omoto C, Yang X. Fluid dynamic models of flagellar and ciliary beating. Ann. N.Y. Acad. Sci. 2007, 1101:494-505. ANYAA9, 0077-8923, 10.1196/annals.1389.016.
7. Dillon R, Othmer H. A mathematical model for the outgrowth and spatial patterning of the vertebrate limb bud. J. Theor. Biol. 1999, 197:295-330. JTBIAP, 0022-5193, 10.1006/jtbi.1998.0876.
8. Ghosh A, Fischer P. Controlled propulsion of artificial magnetic nanostructured propellers. Nano Lett. 2009, 9:2243-2245. NALEFD, 1530-6984, 10.1021/nl900186w.
9. Haller G. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids 2001, 13:3365-3385. PHFLE6, 1070-6631, 10.1063/1.1403336.
10. Khatavkar V, Anderson P, den Toonder J, Meijer H. Active micromixer based on artificial cilia. Phys. Fluids 2007, 19:083605. PHFLE6, 1070-6631, 10.1063/1.2762206.
11. Knowles MR, Boucher RC. Mucus clearance as a primary innate defense mechanism for mammalian airways. J. Clin. Invest. 2002, 109:571-577. JCINAO, 0021-9738.
12. Lindemann C. A model of flagellar and ciliary functioning which uses the forces transverse to the axoneme as the regulator of dynein activation. Cell Motil. Cytoskeleton 1994, 29:141-154. CMCYEO, 0886-1544, 10.1002/cm.970290206.
13. Marshall W, Kintner C. Cilia orientation and the fluid mechanics of development. Curr. Opin. Cell Biol. 2008, 20:48-52. COCBE3, 0955-0674, 10.1016/j.ceb.2007.11.009.
14. Marshall W, Nonaka S. Cilia: Tuning in to the cell's antenna. Curr. Biol. 2006, 16:R604-R614. CUBLE2, 0960-9822, 10.1016/j.cub.2006.07.012.
15. Matsui H, Randell SH, Peretti SW, Davis CW, Boucher RC. Coordinated clearance of periciliary liquid and mucus from airway surfaces. J. Clin. Invest. 1998, 102:1125-1131. JCINAO, 0021-9738, 10.1172/JCI2687.
16. Murase M. The Dynamics of Cellular Motility 1992, (Wiley, Chichester).
17. Nonaka S, Shiratori H, Saijoh Y, Hamada H. Determination of left-right patterning of the mouse embryo by artificial nodal flow. Nature (London) 2002, 418:96-98. NATUAS, 0028-0836, 10.1038/nature00849.
18. Okada Y, Takeda S, Tanaka Y, Belmonte J, Hirokawa N. Mechanism of nodal flow: A conserved symmetry breaking event in left-right axis determination. Cell 2005, 121:633-644. CELLB5, 0092-8674, 10.1016/j.cell.2005.04.008.
19. Otto SR, Yannacopoulos AN, Blake JR. Transport and mixing in stokes flow: The effect of chaotic dynamics on the blinking Stokeslet. J. Fluid Mech. 2001, 430:1-26. JFLSA7, 0022-1120, 10.1017/S0022112000002494.
20. Peng J, Dabiri J. An overview of a Lagrangian method for analysis of animal wake dynamics. J. Exp. Biol. 2008, 211:280-287. JEBIAM, 0022-0949, 10.1242/jeb.007641.
21. Peng J, Dabiri J. The 'upstream wake' of swimming and flying animals and its correlation with propulsive efficiency. J. Exp. Biol. 2008, 211:2669-2677. JEBIAM, 0022-0949, 10.1242/jeb.015883.
22. Peskin CS. The immersed boundary method. Acta Numerica 2002, 11:479-518. ZZZZZZ, 0962-4929, 10.1017/S0962492902000077.
23. Purcell EM. Life at low Reynolds numbers. Am. J. Phys. 1977, 45:3-11. AJPIAS, 0002-9505, 10.1119/1.10903.
24. Schweickert A, Weber T, Beyer T, Vick P, Bogusch S, Feistel K, Blum M. Cilia-driven leftward flow determines laterality in xenopus. Curr. Biol. 2007, 17:60-66. CUBLE2, 0960-9822, 10.1016/j.cub.2006.10.067.
25. Shadden S, Lekien F, Marsden J. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 2005, 212:271-304. PDNPDT, 0167-2789, 10.1016/j.physd.2005.10.007.
26. Shadden SC, Taylor CA. Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Eng. 2008, 36:1152-1162. ABMECF, 0090-6964, 10.1007/s10439-008-9502-3.
27. Shah A, Ben-Shahar Y, Moninger T, Kline J, Welsh M. Motile cilia of human airway epithelia are chemosensory. Science 2009, 325:1131-1134. SCIEAS, 0036-8075, 10.1126/science.1173869.
28. Sleigh MA, Blake JR, Liron N. The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 1988, 137:726-741. ARDSBL, 0003-0805.
29. Smith DJ, Gaffney EA, Blake JR. Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 2008, 163:178-188. 10.1016/j.resp.2008.03.006, 1569-9048.
30. Strathmann R, Grunbaum D. Good eaters, poor swimmers: Compromises in larval form. Integr. Comp. Biol. 2006, 46:312-322. ICBNDB, 1540-7063, 10.1093/icb/icj031.
31. Talbot P, Geiske C, Knoll M. Oocyte pickup by the mammalian oviduct. Mol. Biol. Cell 1999, 10:5-8. MBCEEV, 1059-1524.
32. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos 1990, (Springer, New York).
33. Wilson M, Peng J, Dabiri J, Eldredge J. Lagrangian coherent structures in low Reynolds number swimming. J. Phys.: Condens. Matter 2009, 21:204105. JCOMEL, 0953-8984, 10.1088/0953-8984/21/20/204105.
34. Witman GB. Ciliary and Flagellar Membranes 1990, 1. Bloodgood, R. A., in, edited by (Plenum, New York)
35. Yang X, Dillon R, Fauci L. An integrative computational model of multiciliary beating. Bull. Math. Biol. 2008, 70:1192-1215. BMTBAP, 0092-8240, 10.1007/s11538-008-9296-3.