Mathematical Biosciences and Engineering (MBE)

Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study
Pages: 1107 - 1126, Issue 5, October 2015

doi:10.3934/mbe.2015.12.1107      Abstract        References        Full text (5989.7K)           Related Articles

Ling Xu - Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, United States (email)
Yi Jiang - Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, United States (email)

1 B. A. Afzelius, Ultrastructural basis for ciliary motility, Eur J Respir Dis Suppl., 128 (1983), 280-286.
2 S. A. Baba, Regular steps in bending cilia during the effective stroke, Nature, 282 (1979), 717-720.
3 C. Barton and S. Raynor, Analytical investigation of cilia induced mucous flow, Bull Math Biophys., 29 (1967), 419-428.
4 J. R. Blake, A note on the image system for a stokeslet in a no slip boundary, Proc. Gamb. Phil. Soc., 70 (1971), 303-310.
5 J. R. Blake, A model for the micro-structure in ciliated organisms, J. Fluid Mech., 55 (1972), 1-23.
6 B. Button, L.-H. Cai, C. Ehre, M. Kesimer, D. B. Hill, J. K. Sheehan, R. C. Boucher and M. Rubinstein, A periciliary brush promotes the lung health by separating the mucus layer from airway epithelia, Science, 337 (2012), 937-941.
7 A. Braiman and Z. Priel, Efficient mucociliary transport relies on efficient regulation of ciliary beating, Respir Physiol Neurobiol., 163 (2008), 202-207.
8 D. L. Brown, R. Cortez and M. L. Minion, Accurate projection methods for the incompressible Navier Stokes equations, J. Comput Phys., 168 (2001), 464-499.       
9 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, 55 (2000), 314-317.
10 M. A. Chilvers, A. Rutman and C. O'Callaghan, Ciliary beat pattern is associated with specific ultrastructural defects in primary ciliary dyskinesia, J Allergy Clin Immunol., 112 (2003), 518-524.
11 J. R. Clamp, Chemical aspects of mucus. General considerations, Br Med Bull., 34 (1978), 25-27.
12 R. Cortez, The method of regularized Stokeslets, SIAM J. Sci. Comput., 23 (2001), 1204-1225.       
13 R. Cortez, L. Fauci and A. Medovikov, The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming, Phys. Fluids, 17 (2005), 031504, 21pp.       
14 R. H. Dillon, L Fauci, C. Omoto and X. Yang, Fluid dynamic models of flagellar and ciliary beating, Ann N Y Acad Sci., 1101 (2007), 494-505.
15 S. H. Donaldson, W. D. Bennett, K. L. Zeman, M. R. Knowles, R. Tarran and R. C. Boucher, Mucus clearance and lung function in cystic fibrosis with hypertonic saline, N. ENGL. J. MED., 354 (2006), 241-250.
16 J. Elgeti and G. Gompper, Emergence of metachronal waves in cilia arrays, PNAS, 110 (2013), 4470-4475.
17 D. Eshel and Z. Priel, Characterization of metachronal wave of beating cilia on forg's palate epithelium in tissue culture, J. Physiol., 388 (1987), 1-8.
18 L. Fauci, C. Peskin, A Computational Model of Aquatic Animal Locomotion, J. Comput Phys., 77 (1988), 85-108.
19 H. Flores, E. Lobaton, S. Mendez-Diez, S. Tlupova and R. Cortez, A study of bacterial flagellar bundling, Bull Math Biol., 67 (2005), 137-168.       
20 W. M. Foster, E. Langenback and E. H. Bergofsky, Measurement to tracheal and bronchial mucus velocities in man: relation to lung clearance, J Appl Physiol Respir Environ Exerc Physiol., 48 (1980), 965-971.
21 M. Friedman, R. Dougherty, S. R. Nelson, R. P. White, M. A. Sackner and A. Wanner, Acute effects of an aerosol hair spray on tracheal mucociliary transport, Am Rev Respir Dis., 116 (1977), 281-286.
22 L. Gheber, A. Korngreen and Z. Priel, Effect of viscosity on metachrony in mucus propelling cilia, Cell Motil Cytoskeleton, 39 (1998), 9-20.
23 J. Kim and P. Moin, Application of a fractional step method to incompressible Navier-Stokes equations, J. Comput Phys., 59 (1985), 308-323.       
24 M. R. Knowles and R. C. Boucher, Mucus clearance as a primary innate defense mechanism for mammalian airways, J Clin Invest., 109 (2002), 571-577.
25 M. C. Lai and C. S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput Phys., 160 (2000), 705-719.       
26 R. L. Leopold, M. J. O'Mahony, X. J. Lian, A. E. Tilley, B. G. Harvey and R. G. Crystal, Smoking is associated with shortened airway cilia, PloS One, 4 (2009), e8157.
27 R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady and Time Dependent Problems, {SIAM}, 2007.       
28 A. Livraghi and S. H. Randell, Cystic fibrosis and other respiratory diseases of impaired mucus clearance, Toxicol Pathol, 35 (2007), 116-129.
29 P. M. Low, C. L. Luk, M. J. Dulfano and R. J. Finch, Ciliary beat frequency of human respiratory tract by different sampling techniques, Am Rev Respir Dis., 130 (1984), 497-498.
30 M. R. Marino and E. Aiello, Cinemicrographic analysis of beat dynamics of human respiratory cilia, Cell Motility, 2 (1982), 35-39.
31 H. Matsui, S. H. Randell, S. W. Peretti, C. W. Davis and R. C. Boucher, Coordinated clearance of periciliary liquid and mucus from airway surfaces, J Clin Invest., 102 (1998), 1125-1131.
32 M. Salathe, Cilia and Mucus, from Development to Respiratory Defense, CRC Press, 2001.
33 S. M. Mitran, Metachronal wave formation in a model of pulmonary cilia, Comput Struct., 85 (2007), 763-774.
34 P. G. Noone, M. W. Leigh, A. Sannuti, S. L. Minnix, J. L. Carson, M. Hazucha, M. A. Zariwala and M. R. Knowles, Primary ciliary dyskinesia: Diagnostic and phenotypic features, Am J Respir Crit Care Med, 169 (2004), 459-467.
35 C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput Phys., 25 (1977), 220-252.       
36 E. M. Purcell, Life at low Reynolds number, AIP Conf. Proc., 28 (1976), p49.
37 W. S. Sale and P. Satir, Direction of active sliding of microtubules in Tetrahymena cilia, PNAS, 74 (1977), 2045-2049.
38 M. J. Sanderson and M. A. Sleigh, Ciliary activity of cultured rabbit tracheal epithelium: Beat pattern and metachrony, J Cell Sci., 47 (1981), 331-347.
39 P. Satir, Studies on cilia: II. examination of the distal region of the ciliary shaft and the role of the filaments in motility, J Cell Biol., 26 (1965), 805-834.
40 A. Schmid and M. Salathe, Ciliary beat co-ordination by calcium, Biol Cell, 103 (2011), 159-169.
41 P. R. Sears, K. Thompson, M. R. Knowles and C. W. Davis, Human airway ciliary dynamics, Am J Physiol Lung Cell Mol Phyiol., 304 (2013), L170-L183.
42 M. A. Sleigh, Ciliary function in transport of mucus, Eur J Respir Dis. Suppl., 128 (1983), 287-292.
43 M. A. Sleigh, Adaptations of ciliary systems for the propulsion of water and mucus, Comp Biochem Physiol A Comp Physiol., 94 (1989), 359-364.
44 G. Taylor, Analysis of the Swimming of Microscopic Organisms, Proc. R. Soc. Lond. A, 209(1951), 447-461.
45 E. O. Tuck, A note on a swimming problem, J. Fluid Mech., 31 (1968), 305-308.
46 E. Tuomanen, The surface of mammalian respiratory cilia: interactions between cilia and respiratory pathogens, Ciliary and Flagellar Membranes, (Ed: Bloodgood RA) (1990), 363-388. Springer US.
47 X. Yang, R. H. Dillon and L. J. Fauci, An integrative computational model of multiciliary beating, Bull Math Biol., 70 (2008), 1192-1215.       

Go to top