Hiltmann, P. and Lory, P. (1983) On oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics. Bulletin of Mathematical Biology, 45, 661-664.

has been cited by the following article:

• TITLE: Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method

  AUTHORS: Devaraj Shanthi, Vembu Ananthaswamy, Lakshmanan Rajendran

  KEYWORDS: Oxygen Diffusion; Michaelis-Menten; Non-Linear Differential Equations; New Homotopy Perturbation Method; Numerical Simulation

  JOURNAL NAME: Natural Science, Vol.5 No.9, September 2, 2013

  ABSTRACT: This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.