The preclinical development of
antitumor drugs greatly benefits 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 stochastic model is derived from a set of minimal assumptions formulated at cellular level.
Tumor cells are divided in two groups: proliferating and nonproliferating. The probability that a proliferating cell generates a new cell is a function of the
tumor weight. The probability that a proliferating cell becomes nonproliferating is a function of the plasma
drug concentration. The time-to-death of a nonproliferating cell is a random variable whose distribution reflects the nondeterministic delay between
drug action and cell death. The evolution of the expected value of
tumor weight obeys two differential equations (an ordinary and a partial differential one), whereas the variance is negligible. Therefore, the
tumor growth dynamics can be well approximated by the deterministic evolution of its expected value. The
tumor growth inhibition model, which is a lumped parameter model that in the last few years has been successfully applied to several
antitumor drugs, is shown to be a special case of the minimal model presented here.