Mathematical models tumor growth

Such discrepancy is observed in many other cases [12, 13] as well as in cases of tumors growth considered above. Obviously, mathematical model of growth (8) is a very rough approximation. It may be used for rough estimation, for example for classification of population development [16, 17] and also for description of experimental data on separate sections of growth curves. 

The study of tumor growth forms the foundation for many of the basic principles of modem cancer chemotherapy. The growth of most tumors is illustrated by the Gompertzian tumor growth curve (Fig. 124-5). Gompertz was a German insurance actuary who described the relationship between age and expected death. This mathematical model also approximates tumor-cell proliferation. In the... 

Mathematical models that correlate neovascularization with growth of tissue are limited in number. Liotta et al. (1977) developed a mathematical model which describes the spatial and temporal growth of vessels and cancer cells in a transplanted tumor by two coupled partial differential equations with nonlinear birth and death rate terms. While these authors made no attempt to fit their data quantitatively, their model simulates the density of tumor cells and endothelial cells qualitatively and predicts the onset of necrosis in tumors. 

Fxmctional models were later generated to predict tumor growth in terms of cell kinetics and/or cell-cell interactions. More importantly, these models allow for the incorporation of growth inhibition and stimulation by autocrine (tumor-derived), paracrine (microenvironment), or humoral/exogenous mediators. While the mathematical derivation of these relationships is beyond the scope of this chapter, it clearly represents an effort to model receptor-mediated processes, auto-stimulation, negative and positive feedback loops, and dynamic processes between competing subpopulations of... 

Bajzer, Z., Marusic, M. and Vuk-Pavlovic, S., Conceptual frameworks for mathematical modeling of tumor growth djmamics. Math. Comput. Modelling, 23(6),... 

Molina-Pena R, Alvarez MM. A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth. PLoS One. 2012 7 (2) e26233. 

---