Annals of Biomedical Engineering

, Volume 18, Issue 1, pp 19–36

Mathematical models of the spatial distribution of retinal oxygen tension and consumption, including changes upon illumination

  • Laura M. Haugh
  • Robert A. Linsenmeier
  • Thomas K. Goldstick


To better understand oxygen utilization by the retina, a mathematical model of oxygen diffusion and consumption in the cat outer, avascular retina was developed by analyzing previously recorded profiles of oxygen tension (PO2) as a function of retinal depth. Simple diffusion modelling of the oxygen distribution through the outer retina is possible because the PO2 depends only on diffusion from the choroidal and retinal circulations and on consumption within the tissue. Several different models were evaluated in order to determine the best one from the standpoints of their ability to represent the data and to agree with physiological reality. For the steady state one-dimensional diffusion model adopted (the special three-layer diffusion model), oxygen consumption was constant through the middle layer and zero in the layers near the choroid and near the inner retina. On the average, the oxygen consuming layer, as found by nonlinear regression for each profile, extended from about 75% to 85% of the retinal depth from the vitreous. This is a narrow band through the mid-region of the photoreceptors. Oxygen consumption of the entire avascular retina, determined from fitting eight PO2 profiles measured in light-adapted retinas, averaged 2.7 ml O2(STP)/(100 g tissue · min), while the value determined from fitting thirty-two PO2 profiles measured in dark-adapted retinas averaged 4.4 ml O2(STP)/(100 g tissue · min). Consumption in the light was thus only 60% of that in the dark. This suggests that the outer retina is at greater risk of hypoxic injury in the dark than in the light, a fuinding of considerable clinical significance.


Retina Oxygen Oxygen consumption Model 


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  1. 1.
    Alder, V.A.; Cringle, S.J.; Constable, I.J. The retinal oxygen profile in cats. Invest. Ophthalmol. Vis. Sci. 24:30–36; 1983.PubMedGoogle Scholar
  2. 2.
    Bill, A. Circulation in the eve. In Renkin, E.M.; Mickel, C.C., eds. Handbook of Physiology. The cardiovascular system IV. Bethesda, MD: American Physiology Society; 1984; pp. 1001–1034.Google Scholar
  3. 3.
    Brown, K.T. Optical stimulator, microelectrode advancer and associated equipment for intraretinal neurophysiology in closed mammalian eyes. Opt. Soc. Am. J. 54:101–109; 1964.Google Scholar
  4. 4.
    Brown, K.T. The electroretinogram: Its components and their origins. Vision Res. 8:633–677; 1968.PubMedGoogle Scholar
  5. 5.
    Clark, D.K.; Erdmann, W.; Halsey, J.H.; Strong, E. Oxygen diffusion, conductivity and solubility coefficients in the microarea of the brain. Adv. Exp. Med. Biol. 94:225–232; 1978.Google Scholar
  6. 6.
    Cohen, L.H.; Noell, W.K. Relationships between visual function and metabolism. In: Graymore C.N., ed. Biochemistry of the retina. New York: Academic Press, Inc.; 1965: pp. 36–49.Google Scholar
  7. 7.
    Dollery, C.T., Bulpitt, C.J.; Kohner, E.M. Oxygen supply to the retina from the retinal and choroidal circulations at normal and increased arterial oxygen tensions. Invest. Ophthalmol. 8:588–594; 1969.PubMedGoogle Scholar
  8. 8.
    Ganfield, R.A.; Nair, P.; Whalen, W.J. Mass transfer, storage and utilization of oxygen in cat cerebral cortex. Am. J. Physiol. 219:814–821; 1970.PubMedGoogle Scholar
  9. 9.
    Goldstick, T.K. Oxygen transport. In: Brown, J.H.U.; Gann, D.S., eds. Engineering principles in physiology, vol. II, New York: Academic Press, Inc.; 1973: pp. 257–282.Google Scholar
  10. 10.
    Haugh, L.M. A model of oxygen distribution and consumption in the cat retina in light and darkness. Biomedical Engineering Department, Northwestern University, Evanston, IL; 1988. Thesis. 152 pp.Google Scholar
  11. 11.
    Haugh, L.M.; Linsenmeier, R.A.; Goldstick, T.K. Spatial heterogeneity of oxygen consumption in the cat in light and darkness. Invest. Ophthalmol. Vis. Sci., Suppl. 29:413; 1988.Google Scholar
  12. 12.
    Hubbard, R. The respiration of the isolated rod outer limb of the frog retina. J. Gen. Physiol. 37:373–379; 1954.PubMedGoogle Scholar
  13. 13.
    Kimble, E.A.; Svoboda, R.A.; Ostroy, S.E. Oxygen consumption and ATP changes of the vertebrate photoreceptor. Exp. Eye Res. 31:271–288; 1980.PubMedGoogle Scholar
  14. 14.
    Ladman, A.J. The fine structure of the rod-bipolar cell synapse in the retina of the albino rat. J. Biophys. Biochem. Cytol. 4:459–465; 1958.PubMedGoogle Scholar
  15. 15.
    Landers, M.B., III. Retinal oxygenation from the choroidal circulation. Trans. Am. Ophthalmol. Soc. 76:528–556; 1978.PubMedGoogle Scholar
  16. 16.
    Linsenmeier, R.A. Effects of light and darkness on oxygen distribution and consumption in the cat retina. J. Gen. Physiol. 88:521–542; 1986.CrossRefPubMedGoogle Scholar
  17. 17.
    Linsenmeier, R.A.; Yancey, C.M. Improved fabrication of double-barreled recessed cathode oxygen microelectrodes. J. Appl. Physiol. 63(9):2554–2557; 1987.PubMedGoogle Scholar
  18. 18.
    Linsenmeier, R.A.; Yancey, C.M. Effects of hyperoxia on the oxygen distribution in the intact cat retina. Invest. Ophthalmol. Vis. Sci. 30:612–618; 1989.PubMedGoogle Scholar
  19. 19.
    Prince, J.H.; Diesem, C.D.; Eglitis, I.; Ruskell, G.L. Anatomy and histology of the eye and orbit in domestic animals. Springfield, IL: Charles C Thomas; 1960.Google Scholar
  20. 20.
    Purves, M.J. The physiology of the cerebral circulation. Cambridge, MA: Cambridge University Press; 1972.Google Scholar
  21. 21.
    Reading, H.W.; Sorsby, A. The metabolism of the dystrophic retina. I. Comparative studies on the glucose metabolism of the developing rat retina, normal and dystrophic. Vision Res. 2:315–325; 1962.CrossRefGoogle Scholar
  22. 22.
    Robertis, E.D. Electron microscope observations on the submicroscopic organization of the retinal rods. J. Biophys. Biochem. Cytol. 2:319–329; 1956.Google Scholar
  23. 23.
    Robinson, B. NLREG nonlinear regression subroutine package. Evanston, IL: Vogelback Computing Center, Northwestern University; 1972.Google Scholar
  24. 24.
    Roh, H.-D.; Goldstick, T.K.; Linsenmeier, R.A. Spatial variation of the local tissue oxygen diffusion coefficient measured in situ in the cat retina and cornea. Adv. Exp. Med. Biol. in press.Google Scholar
  25. 25.
    Schneiderman, G.; Goldstick, T.K. Oxygen electrode design criteria and performance characteristics: recessed cathode. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 45:145–154; 1978.Google Scholar
  26. 26.
    Sjostrand, F.S. The ultrastructure of the inner segments of the retinal rods of the guinea pig eye as revealed by electron microscopy. J. Cell. Comp. Physiol. 42:45–70; 1953.Google Scholar
  27. 27.
    Steinberg, R.H.; Linsenmeier, R.A.; Griff, E.R. Retinal pigment epithelial cell contributions to the electroretinogram and electrooculogram. In: Osborne, N.N.; Chader, G.J., eds. Progress in retinal research, vol. 4, Oxford: Pergamon Press; 1985: pp. 33–66.Google Scholar
  28. 28.
    Steinberg, R.H.; Walker, M.L.; Johnson, W.M. A new microelectrode positioner for intraretinal recording from the intact mammalian eye. Vision Res. 8:1521–1523; 1968.PubMedGoogle Scholar
  29. 29.
    Thews, G. Ein Verfahren zur Bestimmung des O2-Diffusionskoeffizienten, der O2-Leitfahigkeit und des O2-Loslichkeitskoeffizienten in Gehirngewebe. Pflugers Arch. Gesamte Physiol. Menschen Tiere. 271:227–244; 1960.PubMedGoogle Scholar
  30. 30.
    Tornquist, P.; Alm, A. Retinal and choroidal contribution to retinal metabolism in vivo. A study in pigs. Acta Physiol. Scand. 106:351–357; 1979.PubMedGoogle Scholar
  31. 31.
    Tsacopoulos, M.; Baker, R.; Levy, S. Studies on retinal oxygenation. Adv. Exp. Med. Biol. 75: 413–416; 1976.PubMedGoogle Scholar
  32. 32.
    Vogel, M. Postnatal development of the cat retina. Berlin: Springer-Verlag; 1978.Google Scholar
  33. 33.
    Whalen, W.J.; Riley, J.; Nair, P. A microelectrode for measuring intracellular PO2. J. Appl. Physiol. 23:798–801; 1967.PubMedGoogle Scholar
  34. 34.
    Yancey, C.M.; Linsenmeier, R.A. Oxygen distribution and consumption in the cat retina at increased intraocular pressure. Invest. Ophthalmol. Vis. Sci. 30:600–611; 1989.PubMedGoogle Scholar
  35. 35.
    Zuckerman, R.; Weiter, JJ. Oxygen transport in the bullfrog retina. Exp. Eye Res. 30:117–127; 1980.CrossRefPubMedGoogle Scholar

Copyright information

© Pergamon Press plc 1990

Authors and Affiliations

  • Laura M. Haugh
    • 1
  • Robert A. Linsenmeier
    • 1
  • Thomas K. Goldstick
    • 1
    • 2
    • 3
  1. 1.Department of Biomedical EngineeringNorthwestern UniversityEvanston
  2. 2.Department of Neurobiology and PhysiologyNorthwestern UniversityEvanston
  3. 3.Department of Chemical EngineeringNorthwestern UniversityEvanston

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