Mathematical Modeling in Tumor Growth and Progression (Invasion and Metastasis, 4-5)

This text aims to provide experimental researchers with a survey of mathematical models and theoretical biological tools being pursued to describe tumour heterogeneity, tumour growth and its control and tumour progression. The author's intention is to distribute a set of ideas, notations and nomenclature to a broad audience. The articles cover such diverse areas as tumour growth and phenotypic progression, angiogenic growth in epithelial cell populations of the tumour bed, tumour growth and invasion, the host response and its effect on ultimate tumour growth and the idea that tumour systems can be viewed as evolving in, and reacting to, environments which display a continuously changing energy profile. Implications of the mathematical assumptions are identified and the limitations of these models, their interpretation and their future development are discussed.