Skip to main content
PMC home page
The Journal of Physiology logoLink to The Journal of Physiology
. 1979 Jul;292:107–134. doi: 10.1113/jphysiol.1979.sp012841

Numerical solution of coupled transport equations applied to corneal hydration dynamics.

S D Klyce, S R Russell
PMCID: PMC1280848  PMID: 490333

Abstract

1. A quantitative basis for the currently accepted theory on the regulation of corneal hydration was derived using the technique of finite element analysis to integrate a set of coupled flow equations. The model was based on non-equilibrium thermodynamics and incorporated the transport and permeability properties of the corneal epithelium and endothelium as well as the gel properties of the central connective tissue layer. 2. Considerable errors were introduced in the prediction of corneal hydration dynamics (unsteady-state behaviour) unless allowance was made for the development of trans-stromal gradients in pressure and solute concentration. 3. Thickness of in vitro rabbit corneal epithelium and stroma were measured with an automatic specular microscope during responses to changes in the osmolarity of the tear-side bathing medium. The time course of these experiments was fitted with the mathematical model to obtain a set of membrane phenomenological coefficients and transport rates. 4. The model with the redetermined membrane parameters was tested by predicting the influence of other variations in boundary conditions with excellent match to several well-documented experimental observations, including an explanation for the slight stromal swelling observed in hibernating mammals. 5. The regulation of corneal stromal hydration can be explained accurately by balance between the dissipative flows across the serial array of corneal layers and the active HCO3 transport by the endothelium, supporting the earlier 'pump-leak' hypothesis. 6. It was found that stromal retardation of fluid flow, as well as gradients in solute concentration, significantly influences the dynamics of corneal stroma hydration. Tissue gel properties may be a more important factor in coupled transport across cell layers than generally appreciated.

Full text

PDF
110

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. BRUBAKER R. F., KUPFER C. Microcryoscopic determination of the osmolality of interstitial fluid in the living rabbit cornea. Invest Ophthalmol. 1962 Oct;1:653–660. [PubMed] [Google Scholar]
  2. Bito L. Z., Roberts J. C., Saraf S. Maintenance of normal corneal thickness in the cold in vivo (hibernation) as opposed to in vitro. J Physiol. 1973 May;231(1):71–86. doi: 10.1113/jphysiol.1973.sp010220. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Bito L. Z., Saraf S. The effects of cold on corneal thickness and on aqueous humor and blood plasma composition of Rana pipiens. Exp Eye Res. 1973 Aug 10;16(4):315–325. doi: 10.1016/0014-4835(73)90097-3. [DOI] [PubMed] [Google Scholar]
  4. Bowman K. A., Green K. Hydrostatic pressure effects on deswelling of de-epithelialized and de-endothelialized corneas. Invest Ophthalmol. 1976 Jul;15(7):546–550. [PubMed] [Google Scholar]
  5. DAVSON H. The hydration of the cornea. Biochem J. 1955 Jan;59(1):24–28. doi: 10.1042/bj0590024. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. DUANE T. D. The steady state of corneal hydration. Am J Ophthalmol. 1949 Jun;32(Pt 2)(6):203–207. doi: 10.1016/s0002-9394(14)78373-4. [DOI] [PubMed] [Google Scholar]
  7. Diamond J. M. A rapid method for determining voltage-concentration relations across membranes. J Physiol. 1966 Mar;183(1):83–100. doi: 10.1113/jphysiol.1966.sp007852. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Diamond J. M., Bossert W. H. Standing-gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia. J Gen Physiol. 1967 Sep;50(8):2061–2083. doi: 10.1085/jgp.50.8.2061. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Dikstein S., Maurice D. M. The metabolic basis to the fluid pump in the cornea. J Physiol. 1972 Feb;221(1):29–41. doi: 10.1113/jphysiol.1972.sp009736. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Fischbarg J. Active and passive properties of the rabbit corneal endothelium. Exp Eye Res. 1973 May 10;15(5):615–638. doi: 10.1016/0014-4835(73)90071-7. [DOI] [PubMed] [Google Scholar]
  11. Fischbarg J., Warshavsky C. R., Lim J. J. Pathways for hydraulically and osmotically-induced water flows across epithelia. Nature. 1977 Mar 3;266(5597):71–74. doi: 10.1038/266071a0. [DOI] [PubMed] [Google Scholar]
  12. Friedman M. H. A quantitative description of equilibrium and homeostatic thickness regulation in the in vivo cornea. I. Normal cornea. Biophys J. 1972 Jun;12(6):648–665. doi: 10.1016/S0006-3495(72)86110-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Friedman M. H. A quantitative description of equilibrium and homeostatic thickness regulation in the in vivo cornea. II. Variations from the normal state. Biophys J. 1972 Jun;12(6):666–682. doi: 10.1016/S0006-3495(72)86111-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Friedman M. H. Unsteady transport and hydration dynamics in the in vivo cornea. Biophys J. 1973 Sep;13(9):890–910. doi: 10.1016/S0006-3495(73)86033-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Goldman J. N., Benedek G. B., Dohlman C. H., Kravitt B. Structural alterations affecting transparency in swollen human corneas. Invest Ophthalmol. 1968 Oct;7(5):501–519. [PubMed] [Google Scholar]
  16. Green K., Downs S. J. Corneal membrane water permeability as a function of temperature. Invest Ophthalmol. 1976 Apr;15(4):304–307. [PubMed] [Google Scholar]
  17. Green K., Green M. A. Permeability to water of rabbit corneal membranes. Am J Physiol. 1969 Sep;217(3):635–641. doi: 10.1152/ajplegacy.1969.217.3.635. [DOI] [PubMed] [Google Scholar]
  18. HARRIS J. E., NORDQUIST L. T. The hydration of the cornea. I. The transport of water from the cornea. Am J Ophthalmol. 1955 Nov;40(5 Pt 2):100–110. doi: 10.1016/0002-9394(55)91842-0. [DOI] [PubMed] [Google Scholar]
  19. HEDBYS B. O., DOHLMAN C. H. A new method for the determination of the swelling pressure of the corneal stroma in vitro. Exp Eye Res. 1963 Apr;2:122–129. doi: 10.1016/s0014-4835(63)80003-2. [DOI] [PubMed] [Google Scholar]
  20. HEDBYS B. O., MISHIMA S. Flow of water in the corneal stroma. Exp Eye Res. 1962 Mar;1:262–275. doi: 10.1016/s0014-4835(62)80010-4. [DOI] [PubMed] [Google Scholar]
  21. HEDBYS B. O., MISHIMA S., MAURICE D. M. The inbibition pressure of the corneal stroma. Exp Eye Res. 1963 Apr;2:99–111. doi: 10.1016/s0014-4835(63)80001-9. [DOI] [PubMed] [Google Scholar]
  22. Hedbys B. O., Mishima S. The thickness-hydration relationship of the cornea. Exp Eye Res. 1966 Jul;5(3):221–228. doi: 10.1016/s0014-4835(66)80010-6. [DOI] [PubMed] [Google Scholar]
  23. Hodson S., Miller F. The bicarbonate ion pump in the endothelium which regulates the hydration of rabbit cornea. J Physiol. 1976 Dec;263(3):563–577. doi: 10.1113/jphysiol.1976.sp011645. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Hodson S. The regulation of corneal hydration by a salt pump requiring the presence of sodium and bicarbonate ions. J Physiol. 1974 Jan;236(2):271–302. doi: 10.1113/jphysiol.1974.sp010435. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Hoshiko T., Lindley B. D. Phenomenological description of active transport of salt and water. J Gen Physiol. 1967 Jan;50(3):729–758. doi: 10.1085/jgp.50.3.729. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Hull D. S., Green K., Boyd M., Wynn H. R. Corneal endothelium bicarbonate transport and the effect of carbonic anhydrase inhibitors on endothelial permeability and fluxes and corneal thickness. Invest Ophthalmol Vis Sci. 1977 Oct;16(10):883–892. [PubMed] [Google Scholar]
  27. KEDEM O., KATCHALSKY A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim Biophys Acta. 1958 Feb;27(2):229–246. doi: 10.1016/0006-3002(58)90330-5. [DOI] [PubMed] [Google Scholar]
  28. Kim J. H., Green K., Martinez M., Paton D. Solute permeability of the corneal endothelium and Descemet's membrane. Exp Eye Res. 1971 Nov;12(3):231–238. doi: 10.1016/0014-4835(71)90143-6. [DOI] [PubMed] [Google Scholar]
  29. Klyce S. D. Electrical profiles in the corneal epithelium. J Physiol. 1972 Oct;226(2):407–429. doi: 10.1113/jphysiol.1972.sp009991. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Klyce S. D. Enhancing fluid secretion by the corneal epithelium. Invest Ophthalmol Vis Sci. 1977 Oct;16(10):968–973. [PubMed] [Google Scholar]
  31. Klyce S. D., Maurice D. M. Automatic recording of corneal thickness in vitro. Invest Ophthalmol. 1976 Jul;15(7):550–553. [PubMed] [Google Scholar]
  32. Klyce S. D., Neufeld A. H., Zadunaisky J. A. The activation of chloride transport by epinephrine and Db cyclic-AMP in the cornea of the rabbit. Invest Ophthalmol. 1973 Feb;12(2):127–139. [PubMed] [Google Scholar]
  33. Klyce S. D. Transport of Na, Cl, and water by the rabbit corneal epithelium at resting potential. Am J Physiol. 1975 May;228(5):1446–1452. doi: 10.1152/ajplegacy.1975.228.5.1446. [DOI] [PubMed] [Google Scholar]
  34. Klyce S. D., Wong R. K. Site and mode of adrenaline action on chloride transport across the rabbit corneal epithelium. J Physiol. 1977 Apr;266(3):777–799. doi: 10.1113/jphysiol.1977.sp011793. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. MASTMAN G. J., BALDES E. J., HENDERSON J. W. The total osmotic pressure of tears in normal and various pathologic conditions. Arch Ophthalmol. 1961 Apr;65:509–513. doi: 10.1001/archopht.1961.01840020511008. [DOI] [PubMed] [Google Scholar]
  36. MAURICE D. M., GIARDINI A. A. Swelling of the cornea in vivo after the destruction of its limiting layers. Br J Ophthalmol. 1951 Dec;35(12):791–797. doi: 10.1136/bjo.35.12.791. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. MAURICE D. M. The permeability of the cornea. Ophthalmic Lit. 1953 Jun;7(1):3–26. [PubMed] [Google Scholar]
  38. MAURICE D. M. The structure and transparency of the cornea. J Physiol. 1957 Apr 30;136(2):263–286. doi: 10.1113/jphysiol.1957.sp005758. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. MISHIMA S., MAURICE D. M. The effect of normal evaporation on the eye. Exp Eye Res. 1961 Sep;1:46–52. doi: 10.1016/s0014-4835(61)80007-9. [DOI] [PubMed] [Google Scholar]
  40. MISHIMA S., MAURICE D. M. The oily layer of the tear film and evaporation from the corneal surface. Exp Eye Res. 1961 Sep;1:39–45. doi: 10.1016/s0014-4835(61)80006-7. [DOI] [PubMed] [Google Scholar]
  41. Maurice D. M. Cellular membrane activity in the corneal endothelium of the intact eye. Experientia. 1968 Nov 15;24(11):1094–1095. doi: 10.1007/BF02147776. [DOI] [PubMed] [Google Scholar]
  42. Mishima S., Hedbys B. O. The permeability of the corneal epithelium and endothelium to water. Exp Eye Res. 1967 Jan;6(1):10–32. doi: 10.1016/s0014-4835(67)80049-6. [DOI] [PubMed] [Google Scholar]
  43. SCHWARTZ B., FELLER M. R. Temperature gradients in the rabbit eye. Invest Ophthalmol. 1962 Aug;1:513–521. [PubMed] [Google Scholar]
  44. SEARS M. L. Miosis and intraocular pressure changes during manometry: mechanically irritated rabbit eyes studied with improved manometric technique. Arch Ophthalmol. 1960 Apr;63:707–714. doi: 10.1001/archopht.1960.00950020709014. [DOI] [PubMed] [Google Scholar]
  45. Stanley J. A., Mishima S., Klyce S. D., Jr In vivo determination of endothelial permeability to water. Invest Ophthalmol. 1966 Aug;5(4):371–377. [PubMed] [Google Scholar]
  46. Trenberth S. M., Mishima S. The effect of ouabain on the rabbit corneal endothelium. Invest Ophthalmol. 1968 Feb;7(1):44–52. [PubMed] [Google Scholar]
  47. Yasuda H., Stone W., Jr Theoretical study of the fluid transport and the hydration of the cornea. J Theor Biol. 1967 Jul;16(1):111–134. doi: 10.1016/0022-5193(67)90056-2. [DOI] [PubMed] [Google Scholar]
  48. Ytteborg J., Dohlman C. H. Corneal edema and intraocular pressure. II. Clinical results. Arch Ophthalmol. 1965 Oct;74(4):477–484. doi: 10.1001/archopht.1965.00970040479008. [DOI] [PubMed] [Google Scholar]

Articles from The Journal of Physiology are provided here courtesy of The Physiological Society

RESOURCES