A model of tracer transport in airway surface liquid

Bulletin of Mathematical Biology

Volumn 69, Issue 3, 2007, Pages 817-836

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

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Advection; Cilia; Diffusion; Dispersion; Mucus; Tonicity

Indexed keywords

FLUORESCENT DYE;

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; CYSTIC FIBROSIS; EUKARYOTIC FLAGELLUM; HUMAN; LUNG; MATHEMATICAL COMPUTING; METABOLISM; MUCOCILIARY CLEARANCE; MUCUS; TRANSPORT AT THE CELLULAR LEVEL;

BIOLOGICAL TRANSPORT; CILIA; CYSTIC FIBROSIS; FLUORESCENT DYES; HUMANS; LUNG; MODELS, BIOLOGICAL; MUCOCILIARY CLEARANCE; MUCUS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EUKARYOTA;

EID: 33947514701     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-006-9163-z     Document Type: Article

References (20)

1. Barlow, E., 2000. Modelling Muco-Ciliary Transport in the Lung. Master's Thesis, School of Mathematics and Statistics, University of Birmingham, Birmingham, UK.
2. Blake, J.R., Gaffney, E.A., 2001. Modeling aspects of tracer transport in mucociliary flows. In: Salathe, M. (Ed.), Cilia and Mucus: From Development to Respiratory Defense. Marcel Dekker, New York, pp. 291-302.
3. Boucher, R.C., 1994, Human airway ion transport. Part 1. Am. J. Respir. Crit. Care Med. 150, 271-281.
4. Douglas, J., Jr., Peaceman, D., 1955. Numerical solution of two-dimensional heat flow problems. A. I. Chem. E. J. 1, 505-512.
5. Fauci, L., Dillon, R., 2006. Biofluidmechanics of reproduction. Ann. Rev. Fluid Mech. 38(1), 371-394.
6. Fulford, G.R., Blake, J.R., 1986. Muco-ciliary transport in the lung. J. Theor. Biol. 121, 381-402.
7. Leonard, B.P., 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19, 459-98.
8. Lutz, R.J., Litt, M., Charkrin, L.W., 1973. Physical-chemical factors in mucus rheology. In: Gabelnick, H.L., Litt, M. (Eds.), Rheology of Biological Systems. Charles C. Thomas, Springfield, IL, pp. 119-157.
9. Matsui, H., Randell, S.H., Peretti, S.W., Davis, C.W., Boucher, R.C., 1998. Coordinated clearance of periciliary liquid and mucus from airway surfaces. J. Clin. Invest. 102(6), 1125-1131.
10. Mitran, S., 2004. Computation of advection and diffusion of a passive tracer in a prescribed velocity field. Available: http://www.amath.unc.edu/ Faculty/mitran/research/PCL.html.
11. Okada, Y., Takeda, S., Tanaka, Y., Izpisúa Belmonte, J.-C., Hirokawa, N., 2005. Mechanism of nodal flow: A conserved symmetry breaking event in left-right axis determination. Cell 121, 633-644.
12. Quinton, P.M., 1994. Viscosity versus composition in airway pathology (editorial). Am. J. Respir. Crit. Care Med. 149, 6-7.
13. Sanderson, M.J., Sleigh, M.A., 1981. Ciliary activity of cultured rabbit tracheal epithelium: Beat pattern and metachrony. J. Cell Sci. 47, 331-341.
14. Sleigh, M.A., Blake, J.R., Liron, N., 1988. The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137, 726-741.
15. Smith, D.J., Gaffney, E.A., Blake, J.R., 2006a. Discrete cilia modelling with singularity distributions: Application to the embryonic node and the airway surface liquid. To appear in Bull. Math. Biol.
16. Smith, D.J., Gaffney, E.A., Blake, J.R., 2006b. A viscoelastic traction layer model of muco-ciliary transport. Published online first in Bull. Math. Biol. with doi: 10.1007/s11538-005-9036-x
17. Smith, J.J., Travis, S.M., Greenberg, E.P., Welsh, M.J., 1996. Cystic fibrosis airway epithelia fail to kill bacteria because of abnormal airway surface liquid. Cell 85, 229-236.
18. Taylor, G.I., 1951. Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A209, 447-461.
19. Taylor, G.I., 1953. Dispersion of soluble matter in solvent flowing slowly throught a tube. Proc. R. Soc. Lond. A219, 186-203.
20. Toskala, E., 1994. Normal and Pathological Respiratory Cilia. An Experimental and Clinical Study With Special Reference to Scanning Electron Microscopy. PhD Thesis, University of Kuopio, Finland.