Effect of intravenous drug administration mode on drug distribution in a tumor slab: A Finite Fourier Transform analysis

Abstract

Cancer therapy using chemotherapeutic drugs frequently involves injection of the drug into the body through some intravenous mode of administration, viz, continuous (drip) infusion or single/multiple bolus injection(s). An understanding of the effect of the various modes of administration upon tumor penetration of drug is essential to rational design of drug therapy. This paper investigates drug penetration into a model tumor of slab geometry (between two capillaries) in which the overall transport rate of drug is limited by intra-tumor transport characterized by an effective diffusion coefficient. Employing the method of Finite Fourier Transforms (FFT), analytical solutions have been obtained for transient drug distribution in both the plasma and the tumor following three modes of administration, viz, continuous infusion, single bolus injection and equally-spaced equal-dose multiple bolus injections, of a given amount of drug. The qualitative trends exhibited by the plasma drug distribution profiles are consistent with reported experimental studies. Two concepts, viz, the dimensionless decay constant and the plasma/tumor drug concentration trajectories, are found to be particularly useful in the rational design of drug therapy. The dimensionless decay constant provides a measure of the rate of drug decay in the plasma relative to the rate of drug diffusion into the tumor and is thus characteristic of the tumor/drug system. The magnitude of this parameter dictates the choice of drug administration mode for minimizing drug decay in the plasma while simultaneously maximizing drug transport into the tumor. The concentration trajectories provide a measure of the plasma drug concentration relative to the tumor drug concentration at various times following injection. When the tumor drug concentration exceeds the plasma drug concentration, the drug will begin to diffuse out of the tumor. Knowledge of the time at which this diffusion reversal occurs is especially useful for optimum scheduling of subsequent bolus injections in a multiple bolus dosing regimen. There are no reported applications of the FFT method to solve repeated input functions in either the chemical engineering or pharmaceutical science literature. Thus, the application of FFT method to solve multiple bolus injections is a unique one. Use of this FFT based analysis as a predictor tool can limit the number of costly experiments which are being done now to achieve this purpose. Even though the model in its present form is simplified, the analysis thereof has nevertheless led to a better understanding of the various factors that must be taken into account for rational design of drug therapy.