Equilibrium model of a vascularized spherical carcinoma with central necrosis: some properties of the solution

Properties of the solutions of a nonlinear time-independent diffusion equation are studied. The equation arises in a model of a spherically symmetric vascularized carcinoma with a central necrotic core. The boundary value problem as posed possesses a constant solution when the nutrient consumption r...

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Bibliographic Details
Published in:Journal of mathematical biology 1993-09, Vol.31 (7), p.735-745
Main Authors: ADAM, J. A, NOREN, R. D
Format: Article
Language:English
Subjects:
Biological and medical sciences
Cell Division
Fundamental and applied biological sciences. Psychology
General aspects
Humans
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Models, Biological
Necrosis
Neoplasms - blood supply
Neoplasms - pathology
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Summary:Properties of the solutions of a nonlinear time-independent diffusion equation are studied. The equation arises in a model of a spherically symmetric vascularized carcinoma with a central necrotic core. The boundary value problem as posed possesses a constant solution when the nutrient consumption rate and deposition rate (from the vascular network) are equal. This solution can lose uniqueness at a critical tumor dimension which corresponds to the onset of instability with respect to deviations from that uniform equilibrium state.
ISSN:0303-6812
1432-1416
DOI:10.1007/BF00160422