Mathematical Modeling in Tumor Growth and Progression

This special issue of Invasion and Metastasis is meant to provide experimental researchers with a survey of mathematical models and theoretical biological tools presently being pursued to describe tumor heterogeneity, tumor growth and its control, and tumor progression. While comprehensive, the articles remain intelligible. The authors' aim is to distribute a fairly exclusive set of ideas, notations, and nomenclature to a broader audience in a way that is easily understood and digested. The articles cover such diverse areas as tumor growth and phenotypic progression, angiogenic growth in epithelial cell populations of the tumor bed, tumor growth and invasion, the host response and its effect on ultimate tumor growth, and the vision that tumor systems can be viewed as evolving in, and reacting to, environments which display a continuously changing energy profile. Much of the mathematical detail is referenced, and relevant experimental data are highlighted where appropriate. Implications of the mathematical assumptions are identified, and the limitations of these models, their interpretation, and their future development are discussed. Offering a set of valuable tools, this collection of reviews will be appreciated by cancer biologists and cell biologists interested in the theoretical framework around which their results can be interpreted. It also serves as an excellent overview for any biologist with an interest in biomathematics, mathematical modeling, and/or computer simulation.