Mixture dynamics: Combination therapy in oncology

In recent years combination therapies have become increasingly popular in most therapeutic areas. We present a qualitative and quantitative approach and elucidate some of the challenges and solutions to a more optimal therapy. For tumor growth this involves the study of semi-mechanistic cell-growth/kill models with multiple sites of action. We introduce such models and analyze their dynamic properties using simulations and mathematical analysis. This is done for two specific case studies, one involving a single compound and one a combination of two compounds. We generalize the notion of Tumor Static Concentration to cases when two compounds are involved and develop a graphical method for determining the optimal combination of the two compounds, using ideas akin to those used in studies employing isobolograms. In studying the dynamics of the second case study we focus, not only on the different concentrations, but also on the different dosing regimens and pharmacokinetics of the two compounds.