Non-linear model of cancer growth and metastasis: a limiting nutrient as amajor determinant of tumor shape and diffusion

A new approach for modelling the spatio-temporal evolution of tumors is pre sented. To test its validity, a very basic model is considered, which, in s pite of its simplicity, is capable of generating a multiplicity of morpholo gies and growth and migration rates. From an in-vivo scenario of basic life processes, cancer cell proliferation is described as a competition for bas ic nutrients. The chosen mathematical treatment and simulation techniques p ermit a direct implementation of the local nonlinear couplings existing bet ween the various cell populations and the free and bound nutrient concentra tion. A discussion of the results and proposed improvements and application s of the model is also presented. (C) 1999 Harcourt Publishers Ltd.