Dispersal of hydrogen in the retina – a three-layer model





mathematical model, blood flow, hydrogen clearance, retinal circulation


Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.


doi: https://doi.org/10.1017/S1446181122000050

Author Biographies

Wafaa Mansoor, Murdoch University

Mathematics & Statistics, Murdoch University, Perth, WA, Australia.

Graeme Charles Hocking, Murdoch University

Professor, Mathematics & Statistics, Murdoch University, Perth, WA, Australia.

Duncan Farrow, University of Western Australia

School of Physics, Mathematics and Computing, University of Western Australia, Perth, WA, Australia.





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