Drug Kinetics

By P. G. WELLING

1 Introduction

The continuing search for new and improved drugs, and the consequent introduction into clinical practice of increasingly potent therapeutic agents, re-emphasizes the need for a greater quantitative understanding of the processes of drug absorption, distribution, metabolism, and excretion and the rates at which these events occur.

This chapter is presented in a similar form to its predecessors in Volumes 2 and 3, and attempts to describe major observations, conclusions, and accomplishments from studies on drug kinetics during the review period. The literature coverage is not as exhaustive as in Volume 3. However, the writer has attempted to include sufficient material for the reader to appreciate the most recent trends in this area of research.

The maturity of the study of drug kinetics may be reflected in the recent publishing of textbooks on pharmacokinetics, fundamentals of clinical pharmacokinetics, biopharmaceutics and pharmacokinetics. Other useful texts include monographs on biopharmaceutics and drug interactions, and pharmacokinetics, drug metabolism, and drug interaction.

Increasing acceptance of the importance of a knowledge of drug kinetics in therapy is also indicated by the contents of various symposia on clinical pharmacokinetics, pharmacology and pharmacokinetics, individualization of drug therapy, and pharmacokinetics and drug effects. Several reviews have been published relating to clinical aspects of pharmacokinetics, drug level-response relationships, the use of computers in drug therapy, and the influence of environmental and body temperature and age on drug pharmacodynamics and pharmacokinetics.

During the review period, theoretical and practical approaches to the kinetics associated with drug interactions have been described, and further evidence has been presented of the importance of non-linear pharmacokinetics in the correct analysis of some in vivo data, particularly in cases of saturable processes. Theoretical papers have appeared concerning polygenic factors in drug kinetics, the use of eigenvector decomposition in multicompartment modeling, kinetic treatment of non-uniform and variable dosage regimens, data treatment in mammillary models of n compartments with different routes of administration, and also the use of hydrodynamic diffusion analogue models in the solution of pharmacokinetic problems.

Dedrick has discussed problems associated with relating animal data to man in terms of physical and chemical factors. Some aspects of the present status of bioavailability and tissue distribution studies habe been reviewed by Garrett, while Wagner has reviewed the evidence of non-linear phenomena in drug kinetics and has presented guidelines for correct analysis of drug disposition in this light. As in all physical and chemical phenomena, a limiting factor in distinguishing linear and non-linear processes is the noise level in, and reproducibility of, collected data. These problems will continue to give rise to interpretation inconsistencies with studies conducted in biological systems in vivo. Words of warning have been sounded regarding the statistical validity of some types of computer fitting and also methodology and design of pharmacokinetic studies.

Drug Absorption. — The importance of the route of administration in drug absorption and disposition has been reviewed by Gibaldi and Perrier and by Riegelman and Rowland. The latter authors emphasize the importance of the 'first-pass' effect for p.o. dosed drugs and showed that the hepatic extraction of a drug during absorption is controlled by Michaelis–Menten-type kinetics and also the concentration of drug exposed to the liver per unit time. Other authors have described the influence of gastric emptying, various physiological factors, and also antacids on gastro-intestinal drug absorption rates.

In vitro and in situ studies in rats have provided further evidence of the importance of solvent drag on intestinal drug absorption and the negative influence of K+ on drug absorption due to water uptake by epithelial cell mernbranes.

Nayak and Benet have described an elegant series of experiments designed to study the gastro-intestinal absorption of drugs in the rhesus monkey. By means of suitably implanted Foley catheters, drug absorption from the stomach and intestine can be determined from either liquid or solid dosage forms. Examples of the preparations for stomach and intestinal absorption studies are reproduced in Figure 1.

Although some difficulties were encountered in the maintenance of these preparations over prolonged periods, they provide an excellent basis for drug absorption studies from specific sites in the gastro-intestinal tract.

The Loo–Riegelman method for calculating drug absorption rates has been criticized by Boxenbaum and Kaplan, who showed that substitution of a two-term Taylor expansion to simplify absorption terms may lead to serious calculation errors. Various other aspects of the Loo–Riegelman absorption method in compartment model systems have been presented by Wagner, who also discussed the application of the Wagner–Nelson absorption method to both one- and two-compartment model data in the presence and absence of competing reactions at absorption sites. A further method for calculating the rate and extent of drug absorption has been described, which is based on the integration of the model-independent Kwan–Till method and either of the previously cited model-dependent methods. This procedure utilizes both plasma and urine data and incorporates one or more internal checks, which facilitate more accurate interpretation of absorption and distribution processes.

As an alternative to these rather complex methods, a more simple model-independent procedure has been proposed for calculating drug absorption rates. In this method, the general solution for the absorption rate constant, ka, is given by equation (1), where Mn is the slope of the terminal regression of the logarithm of

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

either the plasma concentration or urinary drug-excretion curves, intercept (i.v.) and intercept (l°) are the antilogarithms of the respective ordinate intercepts after i.v. and first-order input, and D2 and D1 are the i.v. and first-order drug doses respectively. The relative simplicity of this method makes it attractive, but it does require i.v. data and its accuracy has yet to be fully tested.

Other reported drug-absorption studies include a systems approach to vaginal drug delivery and the influence of blood flow and solvent effects on i.m. drug absorption. Percutaneous drug absorption has been reviewed by Riegelman and Idson.

The advantages of intra-arterial drug infusions have been evaluated in some detail in terms of increased drug delivery and effectiveness in a particular target organ or tissue. The relative advantage of arterial versus venous infusion approaches are discussed in terms of total drug delivery and effect at the site of action as in equations (2) and (3).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In these equations C0 is the amount of drug in arterial blood entering the site of activity, E]Cb(t)] is the pharmacologic effect at any time (t) resulting from an amount of drug Cb at the active site, and Rd and Re are the ratios of total drug delivery and effect respectively resulting from arterial and venous infusion. The authors describe the various relationships that are possible between Rd and Re, and the influence these relationships may have on the relative advantages of regional and systemic drug delivery. Various applications of control theory principles in drug delivery have been discussed by Smolen.

Bioavai1ability. — The unsatisfactory situation still existing in the area of drug bioavailability and bioequivalence is summarized in the recommendations from a Drug Bioequivalence Study Panel to the Office of Technology Assessment, United States Congress. These recommendations outline major problem areas regarding drug bioequivalence and shortcomings in current testing procedures and suggest various steps to be taken to ensure uniformity of marketed drug products. Examples of drug bioinequivalence continue to be reported, but there is still no international agreement on which products should be tested or the correct methods to be used in the testing procedures. In an attempt to inform health practitioners of potential bioavailability problems, the U.S. Academy of Pharmaceutical Sciences has published a series of bioavailability monographs for selected drugs. These monographs serve an excellent purpose, but they can provide only information available from reported studies. In many instances this information is fragmentary and inadequate. A clear understanding and adequate control of the bioequivalence problem are hindered by non-uniform definition of terms and methods of data interpretation. Some of the present misconceptions regarding bioavailability are discussed by Ogilvie and by Cabana and Dittert. The latter authors stress the importance of obtaining clinical pharmacokinetic information at an early stage during drug development in order to design a dosage formulation for optimal therapeutic effect. An example is provided for a hypothetical drug in Figure 2. In this case formulation A, although providing more rapid drug absorption, would not be the desirable formulation.

Consideration has also been given to the correct design of bioavailability studies from practical, economic, and statistical points of view. Notari has reviewed some aspects of the applications of pharmacokinetics and molecular modification in drug design. Various novel or abbreviated methods of evaluating drug bioavailability have also been described. These include the use of truncated urinary excretion and blood level profiles, measurement of circulating drug levels during quasi- and non-steady-state conditions, and a method for obtaining absolute bioavailability values for drugs with perturbable renal clearance. Although the use of truncated blood and urine curves may have some practical advantages, the other methods are probably either too complex or poorly reproducible for practical application. Methods have also been proposed for utilizing drug bioavailability–pharmacological response relationships in drug design. These may be of particular use when drug assays are unavailable and when pharmacological response can be measured with some accuracy. However, the increasing sophistication of drug-assay methods will probably continue to make direct drug assay the method of choice in most cases.

Although the U.S. Food and Drug Administration has recently recommended that animal models be developed in order to correlate bioavailability studies in animals and humans, evidence has been presented that interspecies variations regarding such factors as gastro-intestinal pH may complicate the selection of the correct animal model.

Drug Distribution and Elimination. — After absorption, drug distribution within the body, or within a specific organ, is the next most important determinant of the extent and time course of drug effect. The ability of a drug to penetrate physiological membranes and tissues is a function of interactions between the physicochemical properties of the drug and such physiological parameters as intracellular and extracellular pH, passive and active transport systems, drug distribution between tissue fat and water, and drug binding to proteins and various macromolecules. Perhaps one of the most important factors determining the kinetics of drug distribution is regional blood flow. Evidence has been presented that passage of highly extractable drugs from blood into tissues is essentially perfusion-limited, whereas passage of less efficiently extractable drugs is more blood-flow dependent. Pathological conditions affecting cardiac output or drug distribution may lead to decreased hepatic drug uptake and hence to reduced hepatic clearance of drugs eliminated by this route. However, the overall contribution of hepatic clearance to drug kinetic profiles has been shown to be a complex function of hepatic blood flow, intrinsic hepatic clearance, and drug binding to plasma and tissue proteins.

The distribution characteristics of one drug may be changed by the presence of another, for example by competitive binding to plasma proteins. However, although there is now an enormous literature on drug interactions, very few studies have established whether individual interactions occur during absorption, distribution, binding at receptor sites, elimination, or a combination of these. One method proposed to help elucidate these types of problem is to use whole-animal pharmacokinetics. With this procedure the fraction of drug in a particular organ or tissue may be related to the drug in the whole animal as a function of time and under a variety of situations. The method is applicable only to small animals, but it may be useful for obtaining drug distribution and drug interaction data prior to large-animal or human studies.

One aspect of drug distribution receiving considerable attention is transfer of drug from blood into breast milk. Most drugs ingested by a nursing mother are potentially capable of entering the milk and being transmitted to the infant. Although concentrations of drug in human milk and the percentage of drug actually transferred are generally low, specific problems may be encountered. These include provoked bacterial resistance to antibiotics and sulphonamides, idiosyncratic responses in infants with enzyme deficiencies, and the possibility of haemorrhage with transmitted anticoagulants. Further studies are required of this subject and of the kinetics of placental drug transfer.

For most drugs, the ultimate site of elimination of unchanged compound (or its metabolite) is the kidney, and information continues to accumulate on the influence of renal function on drug kinetics and drug effects. Various tables, nomographs, and computer programs have been described to facilitate correct drug dosage in cases of renal impairment. Other reports discuss problems associated with pharmacokinetic and protein-binding changes resulting from dialysis.

Most pharmacokinetic approaches to dose adjustment in renal failure are based on one-compartment model kinetics and generally do not consider accumulation of active metabolites. It has been suggested that, for drugs which actually obey two-compartment model kinetics, a curvilinear relationship exists between the hybrid 'beta' elimination rate constant and the intrinsic elimination rate constant 'kc1'. Assumption of a linear relationship between these parameters, and hence between beta and renal function, may lead to incorrect dosing. However, in most practical situations, and particularly in cases of severe renal impairment, the one-compartment model is a reasonable approximation permitting realistic dosage adjustment.