An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

Simpson, Matthew & Ellery, Adam (2012) An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell. Applied Mathematical Modelling, 36(7), pp. 3329-3334.

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We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

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ID Code: 46433
Item Type: Journal Article
Refereed: Yes
Keywords: Oxygen, Oxygen diffusion, Michaelis-Menten, Maclaurin Series
DOI: 10.1016/j.apm.2011.09.071
ISSN: 0307-904X
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2012 Elsevier Inc.
Copyright Statement: This is the author’s version of a work that was accepted for publication in Applied Mathematical Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematical Modelling, Volume 36, Issue 7, (July 2012). DOI: 10.1016/j.apm.2011.09.071
Deposited On: 12 Oct 2011 23:31
Last Modified: 31 Aug 2013 08:00

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