Control-Relevant Modeling of the Antitumor Effects of 9-Nitrocamptothecin in SCID Mice Bearing HT29 Human Colon Xenografts

Abstract

The mathematical model structure selected to describe system behavior is at least partially dependent on the proposed use of the model. In this paper, a pharmacokinetic(PK)/pharmacodynamic (PD) model for use in drug delivery algorithm synthesis is developed. The antitumor agent 9-nitrocamptothecin (9NC) was administered orally to severe combined immunodeficient (SCID) mice bearing subcutaneously implanted HT29 human colon xenografts, and the effect of 9NC on those xenografts was characterized. Different PK model structures were considered in characterizing the dynamics of the drug concentration in the plasma. Akaike’s Information Criterion (AIC) was used to select the model structure maximizing fit accuracy while simultaneously minimizing the number of model parameters. The resulting PK model was a set of coupled linear ordinary differential equations able to describe the nonlinear dynamic behavior (e.g. plateauing, etc.) of the drug concentrations observed in the plasma. Pharmacodynamics were modeled by characterizing tumor growth in both the untreated and drug-treated animals. The resulting PK/PD model related drug administration to effect, and this model has a structure that facilitates future control algorithm synthesis. Control algorithms in this context would directly utilize PK/PD model predictions. These predictions would be used to determine the amount and frequency of drug administration in order to reduce the tumor burden without violating clinically relevant constraints. This methodology could then be used to aid the clinician in selecting dose levels and schedules, and extension to patient tailored treatment may eventually be feasible with this approach.