A Minimal Model of Tumor Growth Inhibition in Combination Regimens Under the Hypothesis of No Interaction Between Drugs

One important issue in the preclinical development of an anticancer drug is the assessment of the compound under investigation when administered in combination with other drugs. Several experiments are routinely conducted in xenograft mice to evaluate if drugs interact or not. Experimental data are generally qualitatively analyzed on empirical basis. The ability of deriving from single drug experiments a reference response to the joint administrations, assuming no interaction, and comparing it to real responses would be key to recognize synergic and antagonist compounds. Therefore, in this paper, the minimal model of tumor growth inhibition (TGI), previously developed for a single drug, is reformulated to account for the effects of noninteracting drugs and simulate, under this hypothesis, combination regimens. The model is derived from a minimal set of basic assumptions that include and extend those formulated at cellular level for the single drug administration. The tumor growth dynamics is well approximated by the deterministic evolution of its expected value that is obtained through the solution of an ordinary and several partial differential equations. Under suitable assumptions on the cell death process, the model reduces to a lumped parameter model that represents the extension of the very popular Simeoni TGI model to the combined administration of noninteracting drugs.