Use of mathematical models to understand anticancer drug delivery and its effect on solid tumors.

The transport of anticancer drugs and their effect on tumor cells involve a number of physical and biochemical processes. Mathematical modeling provides a tool to help us understand the interaction of these complex processes, thereby contributing to the improvement and optimization of drug delivery. This article starts with a discussion of the biological and physiological properties of tumors, which are often found as barriers to anticancer drug transport and effect. A broad spectrum of mathematical models is reviewed to give an overview of the current state of modeling approaches and different categories of models are outlined. These include pharmacokinetic and transport-based models for the prediction of temporal and temporal-spatial profiles of antidrug concentrations, as well as empirical or deterministic models to describe the effect of drug. We conclude that the systematic elucidation and integration of cellular signal transduction with the biophysical aspects of drug transport will lead to a better understanding of the entire drug-delivery process.