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2018 | 113 | 169-184
Article title

Mathematical Model of Oxygen Transport in Cornea

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EN
Abstracts
EN
The aim of present work is the development of a quasi-steady state model for the time course concentration profile describing the oxygen diffusion and consumption in a multilayered corneal tissue and investigation of the effect of various model parameters on the oxygen concentration for open and closed eyes. A simple mathematical model for the oxygen transport in multilayered corneal tissue was developed using Fick’s law of diffusion, Michaelis-Menten kinetics of metabolism. A Crank-Nicolson finite difference scheme of the equation describing the oxygen diffusion and consumption was written, in which spatial diffusive terms of the equation were approximated by central differences while the temporal terms were approximated by average of forward and backward time differences. A system of linear equations obtained from the Crank-Nicholson finite differences schemes was solved by the Thomas Algorithm in which successive improve approximate results are obtained.
Discipline
Year
Volume
113
Pages
169-184
Physical description
Contributors
author
  • Harcourt Butler Technological University, Kanpur, India
author
  • Krishna Institute of Engineering & Technology, Ghaziabad, India
author
  • Dr. A.P.J. Abdul Kalam Technical University, Lucknow, Uttar Pradesh, India
References
  • [1] W.R. Amberson, The influence of oxygen tension on the respiration of unicellular organisms. Biol. Bull 55 (1968) 79-85.
  • [2] R.E. Bar., M Hennesse, and V.G: Murphy, Diffusion of oxygen at the endothelial surface of the rabbit cornea. J. Physiol 270 (1977) 1-8.
  • [3] J.J. Blum, Concentration profiles in and around capillaries. Am. J. Physiol 198 (1960) 991-998.
  • [4] I, Fatt and M.I. Bieber. The steady state distribution of oxygen and carbon dioxide in the in vivo cornea. The open eye in air and the closed eye. Exptl Eye Res. 19 (1968) 103-112.
  • [5] Fatt, The steady state distribution of oxygen and carbon dioxide in the in vivocornea II. The open eye in nitrogen and the covered eye. Exptl. Eye. Res. 7 (1968) 413-430.
  • [6] Fatt, J. Giasson Claude and D. Muller Thomas, Non-steady state diffusion in a multilayered tissue initiated by manipulation of chemical activity at the boundaries. Biophys J. 74 (1998) 475-486
  • [7] D. Freeman Ralph and I Fatt. Oxygen permeability of the limiting layers of cornea. Biophys J. 12 (1972) 233-247.
  • [8] S.H. Lin, Oxygen tension in the vivo cornea. Bull. Math Biol, 38 (1976) 269-275.
  • [9] Judith Morris, The physiological causes of contact lens complications. Optometrytoday 3 (1999) 28-33.
  • [10] Polse. A Kennth and Marriane Decker, Oxygen tension under a contact lens. Invest Ophthalmol. Vis Sci. 18 (1979) 188-193.
  • [11] G.H. Takahashi, I. Fatt, and T.K. Goldstick. Oxygen consumption rate of tissuemeasurement by a micropolarographic method. J. Gen Physiol. 50 (1967) 317-335.
  • [12] B. M. Walse: Oxygen requirements of chironmid Larvae. J Exptl. Biol. 25 (1948) 35-44.
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-124ce9da-d75b-42d2-b284-a09de0799dd9
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