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

DOI10.1016/j.apm.2011.09.071zbMath1252.34031OpenAlexW2092106366MaRDI QIDQ693427

Adam J. Ellery, Matthew J. Simpson

Publication date: 7 December 2012

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.09.071

zbMATH Keywords

Michaelis-Menten-MacLaurin seriesoxygen diffusion

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Qualitative investigation and simulation of ordinary differential equation models (34C60) Physiological flow (92C35)

Related Items

An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics ⋮ A new mixed MADM-collocation approach for solving a class of Lane-Emden singular boundary value problems ⋮ Oxygen diffusion in a spherical cell subject to nonlinear Michaelis–Menten kinetics: Mathematical analysis by two exact methods ⋮ Modeling of reaction-diffusion transport into a core-shell geometry ⋮ Optimized direct Padé and HPM for solving equation of oxygen diffusion in a spherical cell ⋮ Unnamed Item

Cites Work

• B-spline solution of non-linear singular boundary value problems arising in physiology
• Analytical bounding functions for diffusion problems with Michaelis- Menten kinetics
• The numerical solution of nonlinear singular boundary value problems arising in physiology
• On the convergence of a fourth-order method for a class of singular boundary value problems
• Singular non-linear two-point boundary value problems: existence and uniqueness
• Application of he's homotopy perturbation method for solving the Cauchy reaction-diffusion problem
• Solving frontier problems of physics: the decomposition method
• Numerical modeling of oxygen diffusion in cells with Michaelis-Menten uptake kinetics
• Assessment of a non-traditional operator split algorithm for simulation of reactive transport
• Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model
• Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method
• An efficient algorithm for solving nonlinear age-structured population models by combining homotopy perturbation and Padé techniques
• Models for the Growth of a Solid Tumor by Diffusion
• Tumour angiogenesis: the gap between theory and experiments