Elimination of drugs and other xenobiotics terminates their effects. Elimination involves various excretory pathways with or without a preceding chemical alteration of the drug molecule, enzymatically or nonenzymatically. The elimination processes may be seen as part of the body’s defense mechanism. Without these processes, drug accumulation and toxicity would ensue. The sum of all elimination processes is equal to the total-body intravenous (IV) clearance (Cl_IV) of the drug. This, by definition, is the volume of blood or plasma that is irreversibly cleared of drug per unit time. If an IV dose D of the drug is administered to the patient and the area under the plasma concentration-versus-time curve (AUC_IV) is assessed, the Cl_IV can be calculated from

The Cl_IV reflects the sum of the different elimination routes. Thus, Cl_IV may be the sum of hepatic (Cl_H) and renal (Cl_R) clearance as well as other clearance mechanisms. If the drug is administered orally, the apparent oral clearance
(Cl_O) (consider the fraction F of the oral dose that reaches the systemic circulation) is:

It follows that 1 – F is the fraction of the oral dose that is metabolized or otherwise eliminated in the liver and/or gut wall during passage from the gut to the systemic circulation. This phenomenon is called first-pass elimination. If all the drug in the gut reaches the portal vein, then

where E is the hepatic extraction ratio. This is the proportion of the dose that is eliminated during one passage through the liver. The endothelial cells lining the villi harbor drug-metabolizing enzymes that may contribute to the first-pass elimination. In addition, many drugs are acted on by ATP-binding cassette (ABC) transporter proteins or organic anion-transporting polypeptides (OATP) in the endothelial cells and pumped out of the cells back into the gut lumen. If only part of the oral dose reaches the portal vein, the deficient absorption or uptake must be corrected for in the calculations of E and F.

The relationship between Cl_H, the liver blood flow Q, and the total intrinsic hepatic clearance Cl_i is defined by the perfusion-limited clearance model (3), (4) for drug clearance in the liver. This relation is defined as

The intrinsic clearance is defined as the maximum capacity of the liver (or any other organ) to remove drug from the blood in the absence of flow limitations. From Equation (4) it is obvious that changes in liver blood flow will preferentially affect the clearance of drugs with high values of Cl_i, which may be observed as changes in plasma half-life t_1/2. In contrast, changes in enzyme activity will affect the t_1/2 only of drugs with low values of Cl_i. In addition, such changes will affect the AUC both after oral and IV administration such that the AUC is decreased when the enzyme activity is enhanced.

The drug clearance from an organ is also dependent on drug binding in the blood by modification of Equation (4):

where f_B denotes the unbound fraction in blood and Cl_i′ is the intrinsic hepatic clearance of unbound drug. If Cl_i′ is high, drug binding in blood has little importance for the Cl_H. In contrast, drug binding has a limiting (restrictive) influence on Cl_H if the value of Cl_i′ is low (5). As a corollary, hepatic drug extraction from the blood is denoted as nonrestrictive or restrictive, respectively. The derivation of the hepatic clearance is important since the determinants are subject to age-dependent development.

Estimation of metabolic clearance is of interest in pediatric pharmacology since many enzymatic fractions develop slowly in neonatal life. As the hepatic blood flow varies, in vitro estimates such as intrinsic clearance (Cl_i = V_max/K_m) are not very useful. Therefore, in vivo methods for estimating Cl_i are preferred. By definition, Cl_O is equivalent to the intrinsic hepatic clearance Cl_i of the drug, provided the drug is eliminated only by liver metabolism and is completely bioavailable to the portal vein. However, very few drugs fulfill these criteria, and in children, no data on the apparent oral clearance of such drugs seem to exist.

The plasma half-life t_1/2 may serve as an estimate of the hepatic drug-metabolizing activity only under certain criteria. The t_1/2 gives no information about the efficiency of drug elimination processes even though it provides a rough estimation of duration of effect. If the drug is solely eliminated by hepatic metabolism, that is, if systemic clearance Cl_s is equal to Cl_H, then

This relationship demonstrates that t_1/2 depends on Cl_H as well as on the apparent volume of distribution V_d of the drug.

As is evident from Equation (5), hepatic clearance Cl_H is a function not only of enzyme activity (Cl_i) and drug binding in blood (f_B) but also of blood flow (Q). Therefore, to interpret kinetics data from systemic administration of drugs at different stages of development, it is important to differentiate between low-extraction and high-extraction drugs. A number of drugs have been classified according to this system on the basis of adult human pharmacokinetic data (Table 4.1).

Drug distribution is affected by a variety of physiologic factors, including vascular tissue perfusion, body composition, plasma protein binding, and tissue binding. Because the V_d may be subject to developmental changes, caution must be exercised in the interpretation of data on t_1/2 in infants and children. However, if we make a reasonable assumption that V_d is constant, then t_1/2 after an IV administration of the drug is virtually proportional to the hepatic enzyme activity (for low-extraction drugs), the hepatic blood flow (for high-extraction drugs), or both (for drugs with intermediate values of Cl_i).

The steady-state concentration C_ss of a drug administered orally and metabolized only by the liver is given by the following equation:

where Δ denotes the dosing interval and F is the drug bioavailability. Rearranging this equation gives

This relationship shows that the only biologic determinants of C_ss of a drug that is given orally and solely metabolized
by the liver are the Cl_i′ and the binding, irrespective of the extraction ratio (3), (6). In this context, any discussion about blood flow is superfluous.

Most pharmacokinetic data in children were obtained through classical studies requiring “rich” data from the individual patient. Modern therapeutic drug monitoring, improvements in drug assay methodology, and large-scale therapeutic drug monitoring in children have promoted the introduction of population pharmacokinetic modeling methods to achieve optimization and safety of pediatric drug treatment. Population pharmacokinetics is particularly useful in pediatric therapy since it is possible to use and analyze sparse data from a large number of subjects. The mixed-effects model includes fixed effects as well as random effects on variability between subjects. Data capture from a large number of subjects and application of statistical programs such as nonlinear mixed-effects model have yielded a lot of clinically useful pharmacokinetic information in children (7) and been applied in studies of, for example, pantoprazol (8), levetiracetam (9), and other drugs in children. Population modeling can also be used to explore different components of the developmental variation in pharmacokinetics such as maturation of clearance pathways, receptor functions, and so forth. This approach will be increasingly used in investigations of drugs for children.

Among the drugs that belong to this group are antiepileptics and certain benzodiazepines. They are frequently used in infants, and their t_1/2 values are predominantly dependent on the drug-metabolizing enzyme activity. The C_ss of these agents is determined by the hepatic enzyme activity and by drug binding in blood according to Equation (8). Inasmuch as the values of f_B and V_d are not age dependent, the t_1/2 and C_ss may serve as rough estimates of the capacity to metabolize the drug. Some of the drugs of this group that have been studied in newborns and adults are listed in Table 4.1.

The t_1/2 of carbamazepine and phenytoin in newborn infants of epileptic mothers treated with these agents during pregnancy is similar to the t_1/2 in adults (10), (11). This is probably due to intrauterine induction of the drug metabolism. As judged from the t_1/2 values, the capacity to metabolize phenytoin in the newborn seems to be well developed at birth, as the V_d of phenytoin does not change from the neonatal to the adult stage (12).

The V_max for oxidation of phenytoin is higher in children than in adults (13), and the capacity to oxidize phenytoin decreases with age (14). The recommendation of higher weight-related doses of these antiepileptics in children compared with adults is therefore logical (see later discussion).

Theophylline and caffeine have comparatively long plasma half-lives in the neonatal period (Table 4.1), whereas in adults the corresponding values are only 3.8 to 8 (15,16) and 4 hours (17), respectively. This difference (17,18,19) is consistent with the extremely low and undeveloped fetal hepatic in vitro activity of cytochrome P4501A (20), which is the major catalyst of the oxidation of theophylline and caffeine (21), (22).

The t_1/2 of drugs belonging to this group is dependent to a large extent on hepatic blood flow, whereas variation in enzyme activity has less influence on the elimination of an IV dose. However, enzyme activity does determine the AUC and C_ss values after single and multiple oral administration, respectively. Although the use of these drugs is limited in children, some kinetic data for these agents have been published (Table 4.1).

Table 4.2 lists the half-lives of some drugs unclassified with respect to their clearance values. The general impression is
that the half-life of most drugs in the neonate is longer than in the adult patient. This strongly suggests that most investigated drugs have a lower metabolic clearance in neonates and infants than in the adult (as judged from the values of the t_1/2). The rate of maturation of this capacity varies from drug to drug. As a corollary, attempts to predict the drug-metabolizing activity in children from adult data are bound to fail.