Mathematical model of prevascular growth of a spherical carcinoma
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Computer simulations on multiprobe freezing of irregularly shaped tumors
Computers in Biology and Medicine
Hopf bifurcation in a solid avascular tumour growth model with two discrete delays
Mathematical and Computer Modelling: An International Journal
Individual-based approaches to birth and death in avascu1ar tumors
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
A gradient-driven mathematical model of antiangiogenesis
Mathematical and Computer Modelling: An International Journal
Modelling the role of cell-cell adhesion in the growth and development of carcinomas
Mathematical and Computer Modelling: An International Journal
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
Mathematical and Computer Modelling: An International Journal
Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth
Journal of Scientific Computing
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The growth and development of solid tumours occurs in two distinct stages-the avascular growth phase and the vascular growth phase. During the former growth phase the tumour remains in a diffusion-limited, dormant state of a few millimetres in diameter (cf. multicell spheroids, carcinoma in situ) while during the latter growth phase, invasion and metastasis may take place. In order to accomplish the transition from avascular to vascular growth, solid tumours may secrete diffusible substances known as tumour angiogenesis factors (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events. Capillary sprouts are formed which migrate towards the tumour, eventually penetrating it and permitting vascular growth to take place. This paper will present several mathematical models which deal with the various stages of growth and development of solid tumours.