ABSTRACT
This chapter focuses on seminal dynamical models that can be used as a springboard into the rapidly expanding study of evolutionary oncology, or the evolutionary ecology of tumors. Also, although evolution by natural selection is well-recognized as an important process during tumor treatment. More recently, Davide Ambrosi and Francesco Mollica modeled nutrient deficiency in multicell spheroids cultured either free in suspension or embedded in agarose. These models introduce mechanical stress generated within the tumor and externally through the agarose gel under the assumption of an elastic spheroid. Whole autochthonous tumors are often much more difficult to model than laboratory systems, such as multicell spheroids, or special in vivo systems, because their geometries are usually much more irregular. However, breast ductal carcinoma in situ (DCIS) is something of an exception and so has attracted the attention of mathematical oncologists. Mathematical oncology provides a much richer theory than that underlying explanations of these phenomena in standard pathology texts.
