Modeling Growth of Tumors and Their Spreading Behavior Using Mathematical Functions

Computer simulations of the spread of malignant tumor cells in an entire organism provide important insights into the mechanisms of metastatic progression. Key elements for the usefulness of these models are the adequate selection of appropriate mathematical models describing the tumor growth and its parametrization as well as a proper choice of the fractal dimension of the blood vessels in the primary tumor. In addition, survival in the bloodstream and evasion into the connective spaces of the target organ of the future metastasis have to be modeled. Determination of these from experimental models is complicated by systematic and unsystematic experimental errors which are difficult to assess. In this chapter, we demonstrate how to select the best-suited mathematical function to describe tumor growth for experimental xenograft mouse tumor models and how to parametrize them. Common pitfalls and problems are described as well as methods to avoid them.