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drug at the receptor sites. Technically, it is quite difficult to obtain a reliable measure of the concentration of drug-receptor complexes or of the free drug at those sites, but the formation and breakdown of those complexes are rapid and obey the law of mass action for drugs that bind reversibly. Hence, changes in the tissue concentration of the drug-receptor complexes would be expected to parallel changes in the concentration of free drugs in the tissue water bathing them, and because the tissue water and plasma water are in rapid equilibrium, changes in the complex concentration, and hence in response, would parallel changes in the drug concentration in plasma.

To elucidate relationships between the levels of a given drug and its characteristic effects, measurements of the drug are made of peak (or trough) levels of the drug in the plasma of individuals, of changes in the plasma levels of the drug with time expressed as the elimination half-life (t1 =2), and of plasma levels that have reached a steady state (css). Since most drugs are eliminated by the kidneys, valuable information on the pharmacokinetics is provided by rates of urinary drug elimination and by the patterns of urinary drug metabolites.

The concentration of a drug in plasma at a steady state (css) is directly related to the dose of the drug, the half-life (ii/2), the dosing interval (t), and the distribution volume (Vd) by Equation 3.1. This equation is valid for drugs that are eliminated by first-order kinetic processes and it can be derived from first principles of pharmacokinetics.*

Thus for a given drug, the css would be expected to change directly with the dose, the bioavailability (F), and the half-life (tj/2), and indirectly with the dosing interval (t) and apparent distribution volume (Vd). For a given dose and dosing interval, css depends on three parameters that are determined experimentally in individual subjects—the bioavailability, the plasma half-life, and the apparent distribution volume of the drug. The values obtained for css should reflect the interindividual variability for each of these parameters, but among these, the plasma half-life exhibits the greatest interindividual variability (see p. 62).

*The rate of change of a drug in the body = {rate of drug absorption} - {rate of drug elimination}. When the "rate in'' equals the ''rate out,'' the drug concentration approaches a plateau. This elementary principle of pharmacology is usually referred to as the plateau principle.

Under steady-state conditions css = {rate of drug in}/{rate of drug out}. The numerator equals the dose divided by the dosing interval, t(dose/t) multiplied by the bioavailability, which is the fractional rate of absorption, F, gives {F x Dose}/t. The denominator is the drug clearance, which equals the volume of blood cleared of drug per unit time, usually expressed as liters/hour. But the clearance can be substituted by its dimensional equivalent, Vd (liters) x k (hour- ), where Vd is the distribution volume and k is the first order elimination rate constant. The k, in turn, is substituted by ln 2/t1/2, from which the expression for drug clearance becomes {0.693 Vd}/ t1/2, where0.693 is the numerical value for ln 2. Substituting the expressions for the numerator and denominator of the ratio for css and rearranging terms yields the final expression for css (Equation 3.1).

Equation 3.1 applies only to drugs that are eliminated by first-order processes, but this is a technical point that does not invalidate the well-defined relationship between the rate of drug elimination and the plasma drug concentration. The elimination of many drugs exhibits saturation kinetic behavior (also called Michaelis-Menten kinetics) in human subjects, and the equation for css that applies under those circumstances is css = (RoKm)/(Vmax - Ro) (3.2)

in which RO (milligrams/day) represents the rate of drug administration and the Km (milligrams/liter) represents the steady-state plasma drug concentration at which the rate of drug elimination is one-half the maximum rate, Vmax. For drugs that exhibit such kinetics, a relatively small increase in the plasma drug dose may be accompanied by a disproportionately large increase in css. Consequently, a small change in dose at or near saturation could increase the css from the therapeutic range to the toxic range. Since the Km is a characteristic of the individual that varies remarkably in different subjects, the value of css will vary accordingly. The antiepileptic drug phenytoin, for instance, displays saturation kinetics and its Km in humans may vary at least 16-fold (1.5-25.2 mg/liter) between individuals.11 Equation 3.2 has been used primarily as a tool for optimizing drug dosage regimens, but it can also be used to assess pharmacogenetic phenotypic individuality.

The majority of xenobiotics act reversibly at receptor sites, but some xenobio-tics act nonreversibly. They attach covalently, or bind noncovalently tightly, to receptors or other macromolecules and remain fixed to those sites even after the drug is undetectable in plasma. The biological effects of these substances persist for prolonged periods and recovery depends on regeneration or repair of receptor sites. Since the effects of nonreversible xenobiotics may be cumulative in the absence of the xenobiotic, plasma levels do not serve as a guide to the responses.

Existing Pools of Pharmacokinetic Data

Extensive tabulations of human pharmacokinetic data are available that contain quantitative information about the bioavailability, binding, distribution, and clearance, renal and metabolic, for therapeutic agents, and clinical pharmacological data on the absorption, distribution, and elimination of these agents. These resources contain a vast amount of drug data, especially for preliminary design of dosage regimens, but they may not represent patients whose pharmacokinetics are different from the average. The values tabulated have usually been measured on healthy adults, or on patients with specified diseases, but they have not usually been obtained with a view toward specifying particular phenotypic differences in genetically or ethnogeographically distinct subjects. Occasionally, the effect of a particular metabolic phenotype on the disposition of a drug may be specified as it is for isoniazid in Table 3.2. The alternative is to consult recent reviews, primary

Table 3.2 Variation in Plasma Elimination Half-Life Values for Several Agents Widely Used in Medical Therapy

Half-life

Table 3.2 Variation in Plasma Elimination Half-Life Values for Several Agents Widely Used in Medical Therapy

Half-life

Drug

Variation

Fold variation

Antipyrine

5-15 hours

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