Lastly, in multiple-dose regimens and controlled release delivery systems, it is important to know the amount of drug accumulating over the dosing interval. The accumulation factor R gives a quantitative indication of the fraction of drug that remains in the body after the first dose compared with the amount of drug that accumulates at steady state. Equation (1.54) gives the expression for R:

p,max,1st dose x e

1.7 Applications of Pharmacokinetics in the Design of Controlled Release Delivery Systems

1.7.1 Design challenges for controlled release delivery systems

Of the many design goals that need to be achieved in a successful controlled delivery system, two are closely related to pharmacokinetics: (1) the achievement of a sufficient input flux of drug and (2) the achievement of a desired drug concentration-time profile. While both goals require the balancing of design parameters and biopharmaceutical properties of the drug, the first goal is governed primarily by system design (input), and the second is governed primarily by the physiology of the body (disposition). Therefore, it is not surprising that pharmacokinet-ics, which is the convolution of input and disposition, can be of great help in the design of controlled release delivery systems. In the following subsections, the challenges of achieving these two goals from a pharmaco-kinetics perspective will be explored.

Achievement of a sufficient input flux of drug. The achievement of sufficient input drug flux is probably the greatest challenge to designing a successful controlled release delivery system. While some controlled release delivery systems face even greater design challenges, such as in pulsatile drug delivery39,40 or tissue/site-specific drug targeting (improved local bioavailability), sufficient achievable input flux is still the predominant design issue. To calculate the necessary input flux Jin to achieve a desired Cp,ss, only the systemic clearance Cl needs to be known (Eq. (1.55):

If the input flux cannot closely match the amount of drug being lost per unit time, then the desired Cp ss will not be achieved. The human body superbly insulates the systemic circulation from exogenous input through many anatomical barriers (e.g., lipid bilayers, ciliated epithe-lia, cornified stratum, cellular tight junctions) and physiological barriers [e.g., wide-ranging gut pH and the presence of gut, hepatic, and renal drug-metabolizing enzymes (CYPs, GST) and efflux transporters (P-glycoprotein, MRP)] (see Chap. 2). These barriers can severely limit both the extent (AUC) and the rate of input (&abs) or simply bioavailability. Numerous techniques, many discussed in subsequent chapters, seek to improve the extent (kinetic exposure profile) and/or input rate by achieving a sufficient input flux. Input flux generically can be increased by (1) increasing the absorption site surface area (e.g., larger patch area, absorption in small intestine versus stomach), (2) using permeability enhancers (e.g., ethanol) to selectively modulate barrier properties, (3) creating prodrug entities (e.g., ester conjugates, PEG conjugates, chemical targeting groups) to increase absorption and/or to decrease metabolic/chemical degradation, (4) administering the drug via a route not susceptible to first-pass metabolism, (5) targeting the drug to a specific region or tissue, thus effectively reducing the amount of drug needed systemically, or (6) increasing drug potency. Although increasing drug potency does not really increase input drug flux, if one is able to increase the potency of a drug then, the desired Cp,ss would be effectively lowered, thus reducing the necessary input flux— and thus indirectly "increasing" the relative input flux. Of these six general techniques for improving input flux, the first five are highly related to the design of the delivery system and the pharmacokinetics of zero- and firstorder inputs.

Achievement of a desired drug concentration-time profile. Although physiological processes govern the disposition of drug in the body, several pharmacokinetic parameters are still useful for evaluating drugs as candidates for controlled release delivery systems. In addition to potency, the pharmacokinetic parameters systemic clearance Cl, volume of distribution Vd, and the elimination rate constant K or half-life t1/2 can provide useful information in the design of delivery systems. One important link and design consideration between Cl and Vd and controlled release delivery systems is t1/2. The half-life indicates how quickly Cp can be modulated intentionally upward or downward; in other words, halflife indicates how well the shape of Cp can be controlled (Fig. 1.20). The shorter the half-life, the more closely Cp will mimic the shape of the input. The solid line indicates the shape and time course of the administered input of two different hypothetical drugs that variy only in halflife. The dotted and dashed lines show the resulting concentration-time profiles for each drug, the shorter and longer half-life, respectively. From a controllability perspective, the biopharmaceutical properties of the drug with a shorter half-life make it more desirable for controlled release delivery systems.

Although it may appear that drug delivery systems with efficacies requiring only a single steady-state drug concentration may not benefit directly from increased concentration-time controllability, one also should consider the following two pharmacokinetic benefits: the shorter the half-life, the less time is needed to reach steady state, and the less time is need to fully eliminate the drug (e.g., in an overdose). In therapies requiring complex drug concentration-time profiles (e.g., diseases requiring pulsatile delivery), the controllability of Cp is paramount to a successful system.

Ideal drug candidate for controlled release delivery systems. From a phar-macokinetic and pharmacodynamic perspective, the ideal drug candidate for controlled release delivery systems would have high potency and

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