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

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 [S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 36; no. 7; pp. 3329 - 3334
Main Authors Simpson, Matthew J., Ellery, Adam J.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2012
Subjects
Approximation
Communities
Diffusion
Maclaurin series
Mathematical analysis
Mathematical models
Michaelis–Menten
Nonlinearity
Oxygen diffusion
Transport
Uptakes
Oxygen diffusion
Maclaurin series
Michaelis–Menten
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Summary: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 [S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theor. Biol. 60 (1976) 449–457] 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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ISSN:0307-904X
DOI:10.1016/j.apm.2011.09.071