Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T12:41:21.006Z Has data issue: false hasContentIssue false

MODELLING HYDROGEN CLEARANCE FROM THE RETINA

Published online by Cambridge University Press:  25 January 2018

D. E. FARROW*
Affiliation:
Mathematics and Statistics, Murdoch University, Murdoch WA 6150, Australia email [email protected], [email protected]
G. C. HOCKING
Affiliation:
Mathematics and Statistics, Murdoch University, Murdoch WA 6150, Australia email [email protected], [email protected]
S. J. CRINGLE
Affiliation:
Lions Eye Institute, 2 Verdun St, Nedlands WA 6009, Australia email [email protected], [email protected]
D.-Y. YU
Affiliation:
Lions Eye Institute, 2 Verdun St, Nedlands WA 6009, Australia email [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The human retina is supplied by two vascular systems: the highly vascular choroidal, situated behind the retina; and the retinal, which is dependent on the restriction that the light path must be minimally disrupted. Between these two circulations, the avascular retinal layers depend on diffusion of metabolites through the tissue. Oxygen supply to these layers may be threatened by diseases affecting microvasculature, for example diabetes and hypertension, which may ultimately cause loss of sight.

An accurate model of retinal blood flow will therefore facilitate the study of retinal oxygen supply and, hence, the complications caused by systemic vascular disease. Here, two simple models of the blood flow and exchange of hydrogen with the retina are presented and compared qualitatively with data obtained from experimental measurements. The models capture some interesting features of the exchange and highlight effects that will need to be considered in a more sophisticated model and in the interpretation of experimental results.

MSC classification

Type
Research Article
Copyright
© 2018 Australian Mathematical Society 

References

Alder, V. A., Yu, D. Y., Cringle, S. J. and Su, E. N., “Experimental approaches to diabetic retinopathy”, Asia-Pac. J. Ophthalmol. 4 (1992) 2025; http://research-repository.uwa.edu.au/en/publications/experimental-approaches-to-diabetic-retinopathy(a439eaca-237f-423f-874d-19f00138b070).html.Google Scholar
Arciero, J. C., Causin, P. and Malgoroli, F., “Mathematical methods for modeling the microcirculation”, AIMS Biophys. 4 (2017) 362399; doi:10.3934/biophy.2017.3.362.CrossRefGoogle Scholar
Friedland, A. B., “A mathematical model of transmural transport of oxygen to the retina”, Bull. Math. Biol. 40 (1978) 823837; doi:10.1007/BF02460609.Google Scholar
Friedman, E., Smith, T. R. and Kuwabara, T., “Retinal microcirculation in vivo ”, Invest. Ophthalmol. Vis. Sci. 3 (1964) 217226; http://iovs.arvojournals.org/article.aspx?articleid=2203699.Google ScholarPubMed
Goldman, D., “Theoretical models of microvascular oxygen transport to tissue”, Microcirculation 15 (2008) 795811; doi:10.1080/10739680801938289.Google Scholar
Guidoboni, G., Harris, A., Cassani, S., Arciero, J., Siesky, B., Amireskandari, A., Tobe, L., Egan, P., Januleviciene, I. and Park, J., “Intraocular pressure, blood pressure and retinal blood flow autoregulation: a mathematical model to clarify their relationship and clinical relevance”, Invest. Ophthalmol. Vis. Sci. 55 (2014) 41054118; doi:10.1167/iovs.13-13611.Google Scholar
Kety, S. S., “The theory and applications of the exchange of inert gas at the lungs and tissues”, Pharmacol. Rev. 3 (1951) 141; http://pharmrev.aspetjournals.org/content/3/1/1.Google Scholar
Leonard, B. P., “A stable and accurate convective modelling procedure based on quadratic upstream interpolation”, Comput. Methods Appl. Mech. Engrg. 19 (1979) 5998; doi:10.1016/0045-7825(79)90034-3.CrossRefGoogle Scholar
Secomb, T. W., “Blood flow in the microcirculation”, Annu. Rev. Fluid Mech. 49 (2017) 443461; doi:10.1146/annurev-fluid-010816-060302.CrossRefGoogle Scholar
Winchell, G. A., “Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat”, Master’s Thesis, Northwestern University, Evanston, USA, 1983; https://books.google.com.au/books?id=CAKoGwAACAAJ.Google Scholar
Yu, D. Y., Alder, V. A. and Cringle, S. J., “Measurement of blood flow in rat eyes by hydrogen clearance”, Amer. J. Physiol. (Heart Circ. Physiol.) 261(30) (1991) H960H968; https://www.ncbi.nlm.nih.gov/pubmed/1887939.CrossRefGoogle ScholarPubMed