Mathematical models of the steps involved in the systemic delivery of a chemotherapeutic to a solid tumor: From circulation to survival

Abstract

The efficacy of an intravenously administered chemotherapeutic for treatment of a solid tumor is dependent on a sequence of steps, including circulation, extravasation by the enhanced permeability and retention effect, transport in the tumor microenvironment, the mechanism of cellular uptake and trafficking, and the mechanism of drug action. These steps are coupled since the time dependent concentration in circulation determines the concentration and distribution in the tumor microenvironment, and hence the amount taken up by individual cells within the tumor. Models have been developed for each of the steps in the delivery process although their predictive power remains limited. Advances in our understanding of the steps in the delivery process will result in refined models with improvements in predictive power and ultimately allow the development of integrated models that link systemic administration of a drug to the probability of survival. Integrated models that predict outcomes based on patient specific data could be used to select the optimum therapeutic regimens. Here we present an overview of current models for the steps in the delivery process and highlight knowledge gaps that are key to developing integrated models.

Keywords: Chemotherapy; Drug delivery; Enhanced permeability and retention effect; Mathematical models; Pharmacokinetics; Survival models; Tumor growth.