Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-09T04:33:42.696Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of non-polar lipids on tear film dynamics

Published online by Cambridge University Press:  04 April 2014

M. Bruna  and
C. J. W. Breward
M. Bruna*
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
C. J. W. Breward
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we examine the effect that physiological non-polar lipids, residing on the surface of an aqueous tear film, have on the film evolution. In our model we track the evolution of the thickness of the non-polar lipid layer, the thickness of the aqueous layer and the concentration of polar lipids which reside at the interface between the two. We also utilise a force balance in the non-polar lipid layer in order to determine its velocity. We show how to obtain previous models in the literature from our model by making particular choices of the parameters. We see the formation of boundary layers in some of these submodels, across which the concentration of polar lipid and the non-polar lipid velocity and film thickness vary. We solve our model numerically for physically realistic parameter values, and we find that the evolution of the aqueous layer and the polar lipid layer are similar to that described by previous authors. However, there are interesting dynamics for the non-polar lipid layer. The effects of altering the key parameters are highlighted and discussed. In particular, we see that the Marangoni number plays a key role in determining how far over the eye the non-polar lipid spreads.

JFM classification

Biological Fluid Dynamics: Biomedical flows Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 565 - 605
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aydemir, E., Breward, C. J. W. & Witelski, T. P. 2011 The effect of polar lipids on tear film dynamics. Bull. Math. Biol. 73 (6), 1171–1201.CrossRefGoogle ScholarPubMed
Berger, R. E. & Corrsin, S. 1974 A surface tension gradient mechanism for driving the pre-corneal tear film after a blink. J. Biomech. 7 (3), 225–238.CrossRefGoogle ScholarPubMed
Berke, A. & Mueller, S. 1996 Einfluss des Lidschlages auf die Kontaktlinse und die zugrundeliegenden Kräfte. Die Kontaktlinse 1, 17–26.Google Scholar
Berke, A. & Mueller, S. 1998 The kinetics of lid motion and its effects on the tear film. In Lacrimal Gland, Tear Film, and Dry Eye Syndromes 2: Basic Science and Clinical Relevance (ed. Sullivan, D. A., Dartt, D. A. & Meneray, M. A.), Advances in Experimental Medicine and Biology, vol. 438, pp. 417–424. Plenum.CrossRefGoogle Scholar
Braun, R. J. 2012 Dynamics of the tear film. Annu. Rev. Fluid Mech. 44, 267–297.CrossRefGoogle Scholar
Braun, R. J. & Fitt, A. D. 2003 Modelling drainage of the precorneal tear film after a blink. Math. Med. Biol. 20 (1), 1–28.CrossRefGoogle ScholarPubMed
Braun, R. J. & King-Smith, P. E. 2007 Model problems for the tear film in a blink cycle: single-equation models. J. Fluid Mech. 586, 465–490.CrossRefGoogle Scholar
Bron, A. J., Tiffany, J. M., Gouveia, S. M., Yokoi, N. & Voon, L. W. 2004 Functional aspects of the tear film lipid layer. Exp. Eye Res. 78 (3), 347–360.CrossRefGoogle ScholarPubMed
Chen, J., Green-Church, K. B. & Nichols, K. K. 2010 Shotgun lipidomic analysis of human meibomian gland secretions with electrospray ionisation tandem mass spectrometry. Invest. Ophthalmol. Vis. Sci. 51 (12), 6220–6231.CrossRefGoogle Scholar
Dey, D., Boulton-Stone, J. M., Emery, A. N. & Blake, J. R. 1997 Experimental comparisons with a numerical model of surfactant effects on the burst of a single bubble. Chem. Engng Sci. 52 (16), 2769–2783.CrossRefGoogle Scholar
Dieckow, J. & Argüeso, P. 2012 The human tear film. In Ocular Surface: Anatomy and Physiology, Disorders and Therapeutic Care (ed. Martin Herranz, R. & Corrales Herran, R. M.), chap. 2. CRC Press.Google Scholar
Heryudono, A., Braun, R. J., Driscoll, T. A., Maki, K. L., Cook, L. P. & King-Smith, P. E. 2007 Single-equation models for the tear film in a blink cycle: realistic lid motion. Math. Med. Biol. 24 (4), 347–377.CrossRefGoogle Scholar
Holly, F. J. & Lemp, M. A. 1977 Tear physiology and dry eyes. Surv. Ophthalmol. 22 (2), 69–87.CrossRefGoogle ScholarPubMed
Johnson, M. E. & Murphy, P. J. 2004 Changes in the tear film and ocular surface from dry eye syndrome. Prog. Retin. Eye Res. 23 (4), 449–474.CrossRefGoogle ScholarPubMed
Jones, M. B., Fulford, G. R., Please, C. P., McElwain, D. L. S. & Collins, M. J. 2008 Elastohydrodynamics of the eyelid wiper. Bull. Math. Biol. 70 (2), 323–343.CrossRefGoogle ScholarPubMed
Jones, M. B., McElwain, D. L. S., Fulford, G. R., Collins, M. J. & Roberts, A. P. 2006 The effect of the lipid layer on tear film behaviour. Bull. Math. Biol. 68 (6), 1355–1381.CrossRefGoogle ScholarPubMed
Jones, M. B., Please, C. P., McElwain, D. L. S., Fulford, G. R., Roberts, A. P. & Collins, M. J. 2005 Dynamics of tear film deposition and draining. Math. Med. Biol. 22 (3), 265–288.CrossRefGoogle ScholarPubMed
Kaufman, P. L., Alm, A. & Adler, F. H. 2003 Adler’s Physiology of the Eye: Clinical Application. 10th edn. Mosby.Google Scholar
King-Smith, P. E., Fink, B., Hill, R., Koelling, K. & Tiffany, J. 2004 The thickness of the tear film. Curr. Eye Res. 29 (4–5), 357–368.CrossRefGoogle ScholarPubMed
Lemp, M. A. 2007 The definition and classification of dry eye disease: report of the definition and classification subcommittee of the international dry eye workshop (2007). Ocul. Surf. 5 (2), 75–92.Google Scholar
Li, L. & Braun, R. J. 2012 A model for the human tear film with heating from within the eye. Phys. Fluids 24 (6), 062103.CrossRefGoogle Scholar
Liu, H., Begley, C., Chen, M., Bradley, A., Bonanno, J., McNamara, N. A., Nelson, J. D. & Simpson, T. 2009 A link between tear instability and hyperosmolarity in dry eye. Invest. Ophthalmol. Vis. Sci. 50 (8), 3671–3679.CrossRefGoogle ScholarPubMed
MacDonald, E. A. & Maurice, D. M. 1991 The kinetics of tear fluid under the lower lid. Exp. Eye Res. 53 (4), 421–425.CrossRefGoogle ScholarPubMed
Maki, K. L., Braun, R. J., Driscoll, T. A. & King-Smith, P. E. 2008 An overset grid method for the study of reflex tearing. Math. Med. Biol. 25 (3), 187–214.CrossRefGoogle Scholar
Maki, K. L., Braun, R. J., Ucciferro, P., Henshaw, W. D. & King-Smith, P. E. 2010 Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions. J. Fluid Mech. 647, 361–390.CrossRefGoogle Scholar
Matar, O. K., Craster, R. V. & Warner, M. R. E. 2002 Surfactant transport on highly viscous surface films. J. Fluid Mech. 466, 85–111.CrossRefGoogle Scholar
McCulley, J. P. & Shine, W. E. 1997 A compositional based model for the tear film lipid layer. Trans. Am. Ophthalmol. Soc. 95, 79–93.Google ScholarPubMed
McCulley, J. P. & Shine, W. E. 2004 The lipid layer of tears: dependent on meibomian gland function. Exp. Eye Res. 78 (3), 361–365.CrossRefGoogle ScholarPubMed
Mudgil, P. & Millar, T. J. 2011 Surfactant properties of human meibomian lipids. Invest. Ophthalmol. Vis. Sci. 52 (3), 1661–1670.CrossRefGoogle ScholarPubMed
Nagyova, B. & Tiffany, J. M. 1999 Components responsible for the surface tension of human tears. Curr. Eye Res. 19 (1), 4–11.CrossRefGoogle ScholarPubMed
Nichols, J. J., Mitchell, G. L. & King-Smith, P. E. 2005 Thinning rate of the precorneal and prelens tear films. Invest. Ophthalmol. Vis. Sci. 46 (7), 2353–2361.CrossRefGoogle ScholarPubMed
Nicolaides, N., Kaitaranta, J. K., Rawdah, T. N., Macy, J. I., Boswell, F. M. & Smith, R. E. 1981 Meibomian gland studies: comparison of steer and human lipids. Invest. Ophthalmol. Vis. Sci. 20 (4), 522–536.Google ScholarPubMed
Ockendon, H. & Ockendon, J. R. 1995 Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Peng, C.-C., Cerretani, C., Braun, R. J. & Radke, C. J. 2014 Evaporation-driven instability of the precorneal tear film. Adv. Colloid Interface Sci. 206, 250–264.CrossRefGoogle ScholarPubMed
Tiffany, J. M. 1978 Individual variations in human meibomian lipid composition. Exp. Eye Res. 27 (3), 289–300.CrossRefGoogle ScholarPubMed
Tiffany, J. M. & Dart, J. K. G. 1981 Normal and abnormal functions of meibomian secretion. R. Soc. Med. Intl Congr. Symp. 40, 1061–1064.Google Scholar
Trefethen, L. N.2011 Chebfun Version 4.2. The Chebfun Development Team, http://www.chebfun.org/.Google Scholar
Wolff, E. 1946 The muco-cutaneous junction of the lid-margin and the distribution of the tear fluid. Trans. Ophthal. Soc. UK 66, 291–308.Google Scholar
Wong, H., Fatt, I. & Radke, C. J. 1996 Deposition and thinning of the human tear film. J. Colloid Interface Sci. 184 (1), 44–51.CrossRefGoogle ScholarPubMed
Yokoi, N., Yamada, H., Mizukusa, Y., Bron, A. J., Tiffany, J. M., Kato, T. & Kinoshita, S. 2008 Rheology of tear film lipid layer spread in normal and aqueous tear-deficient dry eyes. Invest. Ophthalmol. Vis. Sci. 49 (12), 5319–5324.CrossRefGoogle ScholarPubMed
Zubkov, V. S., Breward, C. J. W. & Gaffney, E. A. 2012 Coupling fluid and solute dynamics within the ocular surface tear film: a modelling study of black line osmolarity. Bull. Math. Biol. 74 (9), 2062–2093.CrossRefGoogle Scholar
Zubkov, V. S., Breward, C. J. W. & Gaffney, E. A. 2013 Meniscal tear film fluid dynamics near Marx’s line. Bull. Math. Biol. 75 (9), 1524–1543.CrossRefGoogle ScholarPubMed