(Css). A constant rate intravenous infusion will yield a constant Css, while a drug administered orally at regular intervals will result in fluctuation between peak and trough concentrations (Figure 1.3).
Figure 1.3 Steady‐state concentration–time profile for an oral dose (—) and a constant rate intravenous infusion (‐ ‐ ‐ ‐ ‐).
Clearance depends critically on the efficiency with which the liver and/or kidneys can eliminate a drug; it will vary in disease states that affect these organs, or that affect the blood flow to these organs. In stable clinical conditions, clearance remains constant and is directly proportional to dose rate. The important implication is that if the dose rate is doubled, the Cssaverage doubles: if the dose rate is halved, the Cssaverage is halved for most drugs. In pharmacokinetic terms, this is referred to as a first‐order or linear process, and results from the fact that the rate of elimination is proportional to the amount of drug present in the body.
Single intravenous bolus dose
A number of other important pharmacokinetic principles can be appreciated by considering the concentrations that result following a single intravenous bolus dose (see Figure 1.4) and through a number of complex equations the time at which steady state will be achieved after starting a regular treatment schedule or after any change in dose can be predicted.
As a rule, in the absence of a loading dose, steady state is attained after four to five half‐lives (Figure 1.5).
Furthermore, when toxic drug levels have been inadvertently produced, it is very useful to estimate how long it will take for such levels to reach the therapeutic range, or how long it will take for the entire drug to be eliminated once the drug has been stopped. Usually, elimination is effectively complete after four to five half‐lives (Figure 1.6).
Figure 1.4 Plot of concentration versus time after a bolus intravenous injection. The intercept on the y‐ (concentration) axis, C0, is the concentration resulting from the instantaneous injection of the bolus dose.
The elimination half‐life can also be used to determine dosage intervals to achieve a target concentration–time profile. For example, in order to obtain a gentamicin peak of 8 mg/L and a trough of 0.5 mg/L in a patient with an elimination half‐life of 3 hours, the dosage interval should be 12 hours. (The concentration will fall from 8 to 4 mg/L in 3 hours, to 2 mg/L in 6 hours, to 1 mg/L in 9 hours and to 0.5 mg/L in 12 hours.) However, for many drugs, dosage regimens should be designed to maintain concentrations within a range that avoids high (potentially toxic) peaks or low, ineffective troughs. Excessive fluctuations in the concentration–time profile can be prevented by giving the drug at intervals of less than one half‐life or by using a slow‐release formulation.
Figure 1.5 Plot of concentration versus time illustrating the accumulation to steady state when a drug is administered by regular oral doses.
Figure 1.6 Semi‐logarithmic plot of concentration versus time after a bolus intravenous injection. The slope of this line is −k; the elimination rate constant and the elimination half‐life of the drug can be determined from such a plot by noting the time at which the concentration has fallen to half its original value.
Linear versus non‐linear kinetics
As previously mentioned, most drugs display first‐order kinetics where the rate of elimination is proportional to the amount of drug in the body. However, drugs such as ethanol, phenytoin and heparin have zero‐order kinetics. Here, a constant amount of drug is eliminated per unit time, independent of plasma drug concentration. This occurs when the enzymes responsible for metabolism become saturated and the rate of elimination does not increase in response to an increase in concentration (or an increase in the amount of drug in the body) but becomes constant.
The clinical relevance of non‐linear kinetics is that a small increase in dose can lead to a large increase in concentration. This is particularly important when toxic side effects are closely related to concentration, as with phenytoin.
Principles of drug elimination
Drug metabolism
Drugs are eliminated from the body by two principal mechanisms: (i) liver metabolism and (ii) renal excretion. Drugs that are already water‐soluble are generally excreted unchanged by the kidney. Lipid‐soluble drugs are not easily excreted by the kidney because, following glomerular filtration, they are largely reabsorbed from the proximal tubule. The first step in the elimination of such lipid‐soluble drugs is metabolism to more polar (water‐soluble) compounds. This is achieved mainly in the liver, but can also occur in the gut and may contribute to first‐pass elimination. Metabolism generally occurs in two phases:
Phase 1 – Mainly oxidation, but also reduction or hydrolysis to a more polar compound:Oxidation can occur in various ways at carbon, nitrogen or sulphur atoms and N‐ and O‐dealkylation. These reactions are catalysed by the cytochrome P450‐dependent system of the endoplasmic reticulum. Knowledge of P450, which exists as a superfamily of similar enzymes (isoforms), has increased greatly recently and is divided into a number of families and subfamilies. Although numerous P450 isoforms are present in human tissue, only a few of these have a major role in the metabolism of drugs. These enzymes, which display distinct but overlapping substrate specificity, include CYP1A2, CYP2C9, CYP2C19, CYP2D6, CYP2E1 and CYP3A4. Induction or inhibition of one or more of these enzymes may form the basis of clinically relevant drug interactions. Phase 1 metabolites usually have only minor structural differences from the parent drug, but may exhibit totally different pharmacological actions. For example, the metabolism of azathioprine produces the powerful antimetabolite 6‐mercaptopurine.
Phase 2 – Conjugation usually by glucoronidation or sulphation to make the compound more polar: This involves the addition of small endogenous molecules to the parent drug, or to its Phase 1 metabolite, and almost always lead to abolition of pharmacological activity. Multiple forms of conjugating enzymes are also known to exist, although these have not been
