Elimination of drugs
Most drugs are eliminated from the body by metabolism in the liver and/or by excretion of the drug and its metabolites by the kidneys. Other mechanisms for drug metabolism and excretion also apply for some drugs and poisons. For example, volatile substances are partially removed by expiration, although other mechanisms (e.g. via faeces and sweat) also apply. Two terms, clearance and half-life, are frequently used to quantify the rate and extent of drug removal from the body.
Clearance is the sum of the elimination process of metabolism, renal excretion and other minor processes. Overall, the efficiency of elimination by an organ can be expressed as the proportion of drug entering the organ that is eliminated from the plasma in a single passage; this is called the extraction ratio. The other major factor that controls the overall ability of an organ to remove drug from the body is the rate of delivery of the drug (i.e. blood flow) to the organ. Drug elimination can be represented as the product of this rate of delivery and the extraction ratio. This product gives the volume of plasma from which drug is completely removed per unit time and is given the name clearance (Cl). Clearances by different organs are additive. Although the reference fluid normally used is plasma, whole blood may also be used. The concept of clearance has found particular application in clinical work as it offers a simple relationship between dose rate (dose divided by the time interval between doses, D/s), and the average plasma concentration (Cav) of the drug:
Renal clearance is often measured with creatinine. Creatinine is a metabolic by-product of protein metabolism that is neither reabsorbed nor secreted by the tubules. Its concentration can therefore be used to measure the degree of concentration of urine from the glomerular filtrate. The efficiency of an eliminating organ in removing a drug from plasma depends on the health of the organ. Thus, diseased kidneys operate less efficiently, and the net change in clearance is proportional to the extent of renal impairment. Despite its clinical utility, the concept of clearance has certain limitations for the forensic toxicologist because it does not give an immediate indication of the persistence of a drug in the body. For example, although gentamicin and digoxin have similar clearances (about 100 mL/min), digoxin stays in the body much longer than gentamicin. This is because the volume of distribution of digoxin is several times that of gentamicin, and there is therefore a much greater volume of fluid from which the drug must be cleared before it is all eliminated. It is therefore of some advantage to the toxicologist to be able to relate clearance to the persistence of a drug in the body. This can be done by expressing clearance as a fractional clearance; that is clearance divided by the volume of distribution. Fractional clearance (Cl/Vd) has the dimensions of reciprocal time and represents the proportion of drug removed from the body per unit time, so it is a first-order rate constant for drug elimination (kel). This rate constant is given by the gradient of the terminal part of the concentration–time curve shown in Figure 1.
Half-life The elimination half-life of a drug (t1/2) is the time required for plasma concentrations to decline by 50%, provided that elimination occurs by a first-order process (Fig. 1). It is related to the elimination rate constant (kel) by the equation:
The half-life of a drug provides a measure of the rate of drug loss from the blood. If the dose is known, the half-life of a drug can be used together with information on the volume of distribution and bioavailability, where necessary, to estimate the time elapsed since administration. Conversely, if the elapsed time is known, the half-life can be used to estimate the drug dose, subject to the limitations discussed earlier. The half-life is a function of volume of distribution, clearance and the proportion of drug elimination in unit time. This last term depends on both the extent of its distribution and on the efficiency of its elimination. Thus, the half-life of a drug may differ between children and adults because of size and weight, even though the clearances are equivalent. Zero-order processes are best described as a loss of drug per unit time. For example, ethanol elimination is often assumed to be zero order for concentrations over 0.02 g/100 mL and the rate of elimination is expressed as a loss of ethanol per unit time, that is 0.10–0.25 g/L/h (mean 0.18 g/L/h).
Figure 1 Plot of the natural logarithm of plasma drug concentration (ln C) versus time(t) after intravenous admin istration. The gradient of the linear part of the curve is equal to the elimination rate constant (-kel).
Excretion Drugs and metabolites are excreted mainly by the kidneys into urine (Fig. 2). Renal clearance can result either from glomerular filtration or through tubular secretion. In some cases, reabsorption occurs, which reverses the secretion process. The drug or metabolite is brought to the kidneys with a total plasma flow for both kidneys of approximately 1400 mL/min. Plasma is filtered at the rate of 125 mL/min in the glomeruli, which are the principal sites of excretion. Filtration is passive and only the nonprotein-bound drug in the plasma is eliminated by this pathway. A considerable amount of filtered drug may be reabsorbed into the plasma by diffusion back across the tubule wall (which is permeable to non-ionised, lipid-soluble species). The filtrate (125 mL/min) is gradually concentrated as it passes down the tubule to give a final production of urine of about 1 mL/min. About 575 mL/min of plasma circulates in intimate contact with the proximal and distal renal tubules. The renal tubule may contribute to elimination by active secretion (tubular secretion), and in such cases protein-bound drug may also be eliminated from the plasma. The extent of elimination by the kidneys can be extremely variable depending on which of the three processes of filtration, secretion or reabsorption predominates for the drug in question. Thus, procainamide is eliminated partly by metabolism and partly as unchanged drug through the kidney. Its renal clearance is of the order of 450 mL/min, which indicates a major involvement of tubular secretion. By contrast, digoxin has a renal clearance of about 120 mL/min, which could be explained by either filtration alone, or because secretion is balanced by reabsorption. In practice, it is known that filtration accounts for almost all of the renal clearance of digoxin. A further example is methaqualone, which has a renal clearance of about 1 mL/min, indicating extensive reabsorption of filtered drug. One of the major physiological factors that determines the variability in the rate of drug excretion into the urine is the pH of the urine. Only non-ionised species are available for reabsorption by the tubules along the concentration gradient. Thus, acidic drugs (e.g. barbiturates, salicylates) are excreted more rapidly at high pH than basic drugs (e.g. amfetamines). Conversely, basic drugs are excreted more rapidly at low pH. For example, about 85% of a dose of aspirin is excreted as free salicylic acid in alkaline urine, but only about 5% is excreted when the urine is acidic. Conversely, about 75% of a dose of amfetamine is excreted unchanged in acidic urine, but less than 5% if the urine is alkaline. The effect of varying urinary pH has been used in the treatment of drug overdose by applying alkaline diuresis as an adjunct to the treatment of salicylate or phenobarbital poisoning. The success of the treatment is limited by the extent to which these drugs are distributed, and by the presence of alternative pathways of elimination. Unfortunately, a drug with a high volume of distribution has a relatively long half-life; hence, any increase in clearance does not make much difference to its pharmacological or toxicological effect. Persons who abuse amfetamines have used the effect of urinary pH on excretion to advantage by simultaneously ingesting bicarbonate. This produces alkaline urine, which delays elimination of the amfetamine and therefore prolongs its stimulant effect. Conversely, substances that acidify urine have been taken to enhance the elimination of amfetamine-like stimulants in the hope of avoiding detection in routine dope screening procedures. Exercise in itself can also decrease urinary pH and thus increase the renal clearance of basic drugs. While the quantity of drug in a urine sample is the product of the renal clearance of the drug, the average plasma concentration of the drug during the interval that the urine was produced, and the duration of that interval, the calculation of a likely plasma concentration or even dose from urinary data is not advised, since urinary flow rate and the degree of metabolism must also be considered. Many drugs also show nonlinear pharmacokinetics, that is their excretion rate and degree of metabolism are dose dependent.
Figure 2 Drug elimination by the kidneys. Schematic diagram of a nephron to illustrate the sites of filtration, diffusion and active secretion of drugs.
