Mathematical model of prevascular growth of a spherical carcinoma
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
On the numerical solution of mathematical models of cancer growth and optimal cancer therapy
BIOCOMPUCHEM'09 Proceedings of the 3rd WSEAS International Conference on Computational Chemistry
A numerical algorithm for avascular tumor growth model
Mathematics and Computers in Simulation
Journal of Computational Physics
Some inverse problems raised from a mathematical model of ductal carcinoma in situ
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
The role of growth factors in avascular tumour growth
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core
Journal of Scientific Computing
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In this paper, a mathematical model is presented to describe the evolution of an avascular solid tumour in response to an externally-supplied nutrient. The growth of the tumour depends on the balance between expansive forces caused by cell proliferation and cell-cell adhesion forces which exist to maintain the tumour's compactness. Cell-cell adhesion is incorporated into the model using the Gibbs-Thomson relation which relates the change in nutrient concentration across the tumour boundary to the local curvature, this energy being used to preserve the cell-cell adhesion forces. Our analysis focuses on the existence and uniqueness of steady, radially-symmetric solutions to the model, and also their stability to time-dependent and asymmetric perturbations. In particular, our analysis suggests that if the energy needed to preserve the bonds of adhesion is large then the radially-symmetric configuration is stable with respect to all asymmetric perturbations, and the tumour maintains a radially-symmetric structure-this corresponds to the growth of a benign tumour. As the energy needed to maintain the tumour's compactness diminishes so the number of modes to which the underlying radially-symmetric solution is unstable increases-this corresponds to the invasive growth of a carcinoma. The strength of the cell-cell bonds of adhesion may at some stage provide clinicians with a useful index of the invasive potential of a tumour.