A Combined Pharmacokinetic–Pharmacodynamic (PK–PD) Model for Tumor Growth in the Rat with UFT Administration

Abstract

A combined pharmacokinetic–pharmacodynamic model was developed to simulate the response of a rat tumor to UFT, a combination of uracil with Tegafur (FT). Tegafur is oral the prodrug of 5-fluorouracil (5-FU), an anti-cancer drug for colon cancer. A physiologically based pharmacokinetic (PBPK) model was developed and fitted to experimental data from literature. Three pharmacodynamic (PD) models were developed to describe the tumor cell growth treated with 5-FU, and a dual transit compartment model gave the best fit. This result may be due to dual mechanisms of action of 5-FU, and the dual transit compartment model is able to simulate these better than the other models. The PBPK and PD models were combined, and various dosing strategies were tested. The optimal ratio of uracil to Tegafur to maximize tumor reduction and minimize systemic toxicity was found to be consistent with previous reports. The model correctly predicted the toxic effect of low dihydropyrimidine dehydrogenase (DPD) level, consistent with clinical tests. Pharmacokinetic modulating chemotherapy (PMC), which combines continuous infusion of 5-FU and periodic administration of UFT was shown to be more effective than the same dose given by continuous infusion only. This model can guide the development of dosing strategies and patient specific 5-FU therapies.

Introduction

Drug development is an expensive, time-consuming process. According to Adams et al., drug development cost ranges from $500 million to $2000 million per new drug, depending on the therapy and the developing firm.¹ Even after the development and approval of drug to the market, the optimal dosing schedule and regimen remain uncertain. For example, the chemotherapeutic drug 5-fluorouracil (5-FU) was developed several decades ago and has been widely used, but the optimal method of using this drug is still under debate.2., 3. Finding an optimal dosing strategy is a difficult, expensive task that involves a large number of patients and a long period of time, especially for oncology drugs. In addition, the inherent metabolic and physiologic variations in patients result in patients responding differently to the same dosing regimen.⁴ Pharmacogenetics, which studies the effect of genetic variations on responses of patients to drugs and attempts to tailor the dosing strategy for each individual patient, attempts to address this issue.5., 6. Considering this individual genetic variation further complicates the problem of dose optimization because it is virtually impossible to perform such a large number of tests on each individual.

A mathematical approach such as a pharmacokinetic–pharmacodynamic (PK–PD) model is a feasible alternative as it can link the administration regimen to patient response in terms of tumor growth.⁷ A physiologically-based pharmacokinetic (PBPK) model can be used to obtain the concentration profiles of a drug in different organs after drug administration, and a pharmacodynamic (PD) model can be used to model the pharmacological effect of the drug, for instance, the response of tumor to oncology drugs. Such an integrative mathematical model can help researchers to predict possible outcomes of various drug candidates, and the benefits of the integrative PBPK–PD model are well recognized.8., 9., 10., 11., 12., 13. The integrative mathematical models can be used to test the effect of individual variation in pharmacokinetic and pharmacodynamic factors, such as clearance rate and tumor response.

In this article, a PBPK model is developed to describe the concentration profiles of a chemotherapeutic drug administered in a rat, and a PD model is developed to describe the tumor growth kinetics in the presence of the drug. The PBPK model and the PD model are then combined together to predict the growth of tumor in a rat. The combined PK–PD model is used to find the optimal combination ratio of the drugs, and to test the effect of variation in the metabolizing enzyme level. Also a new dosing strategy to maximize the drug efficacy is tested. Such a model should be an effective guide towards rapid evaluation of treatment strategies and can be a useful tool for patient specific chemotherapy if levels of key enzymes in an individual are known.