On the analysis of oxygen diffusion and reaction in biological systems

DOI10.1016/0025-5564(87)90110-6zbMath0613.92011OpenAlexW1984440408WikidataQ113886445 ScholiaQ113886445MaRDI QIDQ1820082

William E. King, David S. Schultz

Publication date: 1987

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(87)90110-6

zbMATH Keywords

tumorssingle celloxygen consumptionMichaelis-Menten kineticsorthogonal collocationanisotropic systemsanalysis of oxygen diffusion and reactionmultiregion biological systemsoxygenation of a multicell spheroidsingle-cell analysistime-dependent flux boundary conditiontransient and steady-state solutions

Mathematics Subject Classification ID

Physiological, cellular and medical topics (92Cxx)

Related Items (4)

Existence, uniqueness, and stability for a class of diffusion problems ⋮ Mathematical model of prevascular growth of a spherical carcinoma ⋮ Diffusion regulated growth characteristics of a spherical prevascular carcinoma ⋮ Mathematical models of tumor growth. IV: Effects of a necrotic core

Cites Work

• On oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics
• Complementary variational principles for diffusion problems with Michaelis-Menten kinetics
• A comment on Lin's paper on nonlinear diffusion in biological systems
• A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics
• Analysis of a nonlinear diffusion problem with Michaelis-Menten kinetics by an integral equation method
• A model for the growth of a solid tumor with non-uniform oxygen consumption
• Nonlinear diffusion in biological systems

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