Pharmacodynamic Aspects of Systemic Drug Delivery

Abstract

Some of the most common cases of drug delivery (i.v. bolus, first-order absorption and zero-order absorption) are evaluated with respect to the relationship between extent and/or rate of drug absorption and pharmacodynamic outcome. Each case is evaluated after a single dose and at steady state after multiple dosing in a one-compartment body model. The pharmacodynamic model used is the E_max-model with and without an effect compartment. The area under the effect-time curve (AUCe) is used as a cumulative measure for overall drug activity. After first-order absorption, AUC_e can vary as a function of absorption rate between a minimum, the AUC_E of the equivalent i.v. bolus, E_max/k_e*ln[1+D/(E₅₀*Vd)], and a maximum, E_max*D/(E₅₀*CL). After multiple dosing, the degree of fluctuation of the pharmacodynamic effect will depend on the dose and will always be less than the degree of pharmacokinetic fluctuation. A dosing rate (DR₅₀=CL*E₅₀/f_u) is proposed that allows calculation of the dose necessary to produce and maintain 50% of the maximum effect and that can easily be adapted to obtain any fraction of the desired effect. Zero-order input rate is optimal to achieve the maximum cumulative effect with a minimal amount of drug. For multiple dosing, a multiple dose factor (MDF) is introduced that allows calculation of the additional dose needed to maintain a certain minimum level of effect at all times. The relationships between drug delivery and pharmacodynamic effect should be appreciated and preferable over mere blood levels in the development of drug delivery systems and the design of rational dosage regimens. During the past 30 years significant knowledge has been gained on the issue of bioavailability as measured by systemic concentrations of drugs. For the most common case of drugs which follow linear pharmacokinetics, the area under the curve (AUC) is directly proportional to the amount of drug absorbed. Therefore, AUC is an excellent indicator of the extent of drug absorption. For equal amounts absorbed, AUC is constant and independent of the rate of absorption. Furthermore, AUC allows prediction of the average steady state levels during multiple dosing. The rate of absorption is usually characterized by the time (t_max) and magnitude (C_max) of the peak level or by means of appropriate absorption rate constants. The rate of absorption determines the degree of fluctuation during multiple dosing.

With the advent of PK-PD modeling in recent years, it has become common to measure not only the resulting plasma levels for different dosage forms, but also to quantify the resulting drug effects as a function of time. Just like in the case of pharmacokinetics, the area under the effect-time curve (AUCe) can be used as a cumulative measure of drug activity. The goal of this paper is to evaluate some of the most common cases of drug delivery with respect to the relationship between drug delivery and pharmacodynamic outcome.