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

作者：Simpson Matthew J^*; Ellery Adam J

来源：Applied Mathematical Modelling, 2012, 36(7): 3323-3328.

DOI：10.1016/j.apm.2011.09.071

• Oxygen diffusion
• Michaelis-Menten
• Maclaurin series

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%26apos;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.

• 出版日期2012-7