Conceptual frameworks for mathematical modeling of tumor growth dynamics

The paper discusses the applicability of some empirical and functional mathematical models of tumor growth to multicell tumor spheroids which are a three-dimensional experimental paradigm of prevascular tumors. A new mathematical model based on receptor-mediated regulation of growth is developed and tested and two additional functional models (autostimulation, competing populations) are analyzed. It is demonstrated that these models, defined by two autonomous differential equations, can describe spontaneous tumor regression. The concept of tumor magnification factor, a quantifier of positive feedback mechanisms, is elaborated.