A two-clones tumor model: Spontaneous growth and response to treatment

Abstract

The paper aims at providing a general theoretical frame bridging the macroscopic growth law with the complex heterogeneous structure of real tumors. We apply the "Phenomenological Universality" approach to model the growth of cancer cells accounting for "populations", which are defined not as biologically pre-defined cellular ensemble but as groups of cells behaving homogeneously with respect to their position (e.g. primary or metastatic tumor), growth characteristics, response to treatment, etc. Populations may mutually interact, limit each other their growth or even mutate into another population. To keep the description as simple and manageable as possible only two populations are considered, but the extension to a multiplicity of cell populations is straightforward. Our findings indicate that the eradication of the metastatic population is much more critical in the presence of mutations, either spontaneous or therapy-induced. Furthermore, a treatment that eradicates only the primary tumor, having a low kill rate on the metastases, is ultimately not successful but promotes a "growth spurt" in the latter.

Keywords: Gompertz; Mathematical model; PUN; Tumor growth.