A minimal model describing the effect of drug administration on tumor growth dynamics

The preclinical development of antitumor drugs would greatly benefit from the availability of models capable of predicting tumor growth as a function of the drug administration schedule. For being of practical use such models should be simple enough to be identifiable from standard experiments conducted on animals. In the present paper, a simple mathematical model of tumor dynamics is derived from a set of minimal assumptions formulated at cellular level. In the model there are two classes of tumor cells: proliferating and non-proliferating. Assuming independence between the cells, the mean tumor mass obeys two differential equations: an ordinary and a partial differential one. It is shown that, due to the large number of cells in measured tumor masses, the variance of the mass tumor is negligible compared to its expected value so that the stochastic model can be replaced by a deterministic one. For suitable choice of the model parameters, the proposed minimal model yields the so-called TGI (tumor growth inhibition) model. This is a lumped parameter model, based on only five parameters, that in the last few years has been successfully used to fit and predict the effect of several antitumor drugs