Physiology and Development

Growth and maturation are seminal features of pediatric development, and it is important to understand that they vary independently (Anderson and Holford, 2008; Rhodin et al., 2009; Sumpter and Anderson, 2009). Growth is an increase in size, often characterized by changes in weight. Maturation is a time-dependent phenomenon, often characterized by age. Traditionally, the common metric of maturation was postnatal age (PNA), the time since birth. With the superiority of neonatal intensive care and the survival of neonates as small as 500 g and 24 weeks’ gestation, who have clearly immature and widely variant degrees of development at birth, it is now well established that PNA is an inadequate metric of organ maturation, which actually begins before birth. Postconceptual age (PCA), the sum of gestational age (the period between conception and birth) and PNA, is a superior metric. Because of the inexactitude in determining the date of conception, the alternate metric of postmenstrual age (PMA) is often used instead. Particularly for infants and very small children, use of PCA or PMA rather than PNA is important in pediatric pharmacology and therapeutics.

Body composition changes dramatically during growth and development (Anderson and Holford, 2008). Simply stated, compared with adults, infants have big heads, large torsos, and short, stumpy legs. Figure 7-1 depicts developmental changes in pediatric physiology that can affect drug disposition. Table 7-1 describes the changes in organ weight that occur during growth. The most significant changes with age are in total body water, the intracellular vs. extracellular distribution of body water, and muscle and fat mass (Tables 7-2 and 7-3). Total body water content constitutes 75% of body weight in the full-term newborn and 80% to 85% of body weight in the preterm neonate. This decreases to about 60% at 5 months and remains relatively constant until puberty. Extracellular water redistributes intracellularly during the first year of life. Extracellular fluid is 45% to 50% of body weight in premature and newborn infants, decreasing to 26% at 1 year and 18% in adults. In contrast, body fat increases with age, from 3% in premature neonates and 12% in full-term newborns, to 30% at 1 year of age. “Baby fat” is shed when toddlers start walking and drops to adult levels of about 18%, concomitant with an increase in muscle mass. A major consequence of body-composition changes may be differences in drug volume of distribution, with neonates and infants having larger volumes of water-soluble drugs, as described below.

FIGURE 7-1 Developmental changes in physiologic factors that influence drug disposition in infants, children, and adolescents. A, Activity of many cytochrome P450 (CYP) isoforms and a specific UGT isoform is markedly diminished during the first two months of life. Increases to adult activity over time are enzyme- and isoform-specific. B, Age-dependent changes in body composition, which influence the apparent volume of distribution for drugs. Infants in the first 6 months of life have markedly expanded total body water and extracellular water as compared with older infants and adults. This is expressed as a percentage of total body weight. C, Age-dependent changes in both the structure and function of the gastrointestinal tract. As with hepatic drug-metabolizing enzymes (A), the activity of cytochrome CYP1A1 in the intestine is low during early life. D, Effect of postnatal development on the processes of active tubular secretion—represented by the clearance of para-aminohippuric acid and the GFR, both of which approximate adult activity by 6 to 12 months of age. E, Age dependence in the thickness, extent of perfusion, and extent of hydration of the skin and the relative size of the skin surface area (reflected by the ratio of body surface area to body weight). Although skin thickness is similar in infants and adults, the extent of perfusion and hydration diminishes from infancy to adulthood.

(From Kearns GL et al: Developmental pharmacology: drug disposition, action, and therapy in infants and children, N Engl J Med 349:1157, 2003.)

TABLE 7-1 Changes in Organ Weights with Age (Percentage of Body Weight)

TABLE 7-2 Body Composition during Growth

TABLE 7-3 Age-Related Estimates of Gas and Tissue Volumes and Blood Flow

The relative lack of dosing data for many drugs used in pediatrics has necessitated the use of extrapolations from adult dosing. Considerable effort has been expended to provide a scientific basis for such extrapolations, such as of volumes of distribution, clearance, renal function, and dose. Basic models for predicting physiologic function and drug dose based on size include the linear per-kilogram model, the surface-area model, and the allometric model. It is now increasingly evident and accepted that allometric scaling provides the most accurate information. Throughout nature, many body-size relationships are of the form:

where Y is the biological characteristic, W is the body mass, and a and b are empirically derived constants. For physiologic functions such as cardiac output, metabolic rate, oxygen consumption, glomerular filtration rate (GFR), and pharmacologic functions such as drug clearance, the power exponent b is 0.75. For physiologic volumes such as blood volume, lung volume, tidal volume, and stroke volume, and pharmacologic volumes such as the volume of distribution, the power exponent is 1. For time-based physiologic functions such as circulation time, heart rate, and respiratory rate, and pharmacologic functions such as drug elimination half-life, the exponent is 0.25 (Johnson and Thomson, 2008). This allometric model may then be used to scale metabolic processes across size:

where W_i is the weight of any individual and W_std is the weight of a standardized individual (such as a mythical 70-kg adult). The applicability of scaling will subsequently become apparent.

Pharmacokinetic Parameters

Pharmacokinetics refers to the time course of drug disposition in the body and the processes that affect it. These processes include absorption, distribution, metabolism and transport, and excretion. Conceptually, pharmacokinetics is characterized by the fundamental primary parameters of volume of distribution and clearance and by the secondary parameter of half-life (which is proportional to volume of distribution and inversely proportional to clearance).

Volume of Distribution

Volume of distribution (V_d) is a theoretic concept that relates the amount of drug in the body (dose) to the concentration (C) of drug that is measured (in blood, plasma, and unbound in tissue water). Volume of distribution is the volume of fluid “apparently” required to contain the total-body amount of drug homogeneously at a concentration equal to that in plasma (or blood) (Fig. 7-2):

FIGURE 7-2 Apparent volume of distribution. The real volume of the beaker is 5 L (V_d = 50 mg/10 mcg/mL = 5 L). However, based on measured concentrations in fluid and calculated according to the equation for V_d on p. 180, the volume of distribution may vary (thus apparent volume). It depends on significant tissue or plasma protein binding. Significant tissue binding (i.e., significant digoxin binding to myocardial Na⁺, K⁺-ATPase) increases volume of distribution (V_d = 10 L; see the text for explanation). Because routinely measured fluid concentration includes both free unbound and plasma protein bound drug, the increased protein binding reduces volume of distribution (V_d = 2.5 L).

The volume of distribution does not necessarily correspond to any specific physiologic volume or space. Drugs such as highly water-soluble compounds, which are confined intravascularly, have a small volume of distribution (approximately equal to intravascular volume), whereas lipophilic drugs that distribute to tissues have a large volume of distribution (that may be so large as to exceed total body water). For example, in adults the volume of distribution of gentamicin is 0.2 to 0.3 L/kg, whereas that of digoxin is 8 to 10 L/kg. Plasma protein binding of drugs decreases the apparent volume of distribution, and tissue binding increases the apparent volume of distribution. The major practical value of volume of distribution lies in the calculation of initial drug dosing (loading):

A major consequence of growth and maturational changes in body composition may be differences in volume of distribution. In general, neonates and infants have larger distribution volumes for water-soluble drugs and smaller volumes for lipophilic drugs. For example, the volume of distribution of gentamicin is 0.5 to 1.2 L/kg in neonates and infants compared with 0.2 to 0.3 L/kg in adults (Echeverrisa).

Clearance

Clearance is the fundamental parameter describing the ability to eliminate a drug. Clearance may refer to elimination from the body (systemic or total clearance) or by a specific organ (renal or hepatic clearance). Clearance is not the amount of drug actually eliminated, but rather represents the theoretic amount of biologic fluid (blood or plasma) from which the drug is completely removed per unit time (mL/min, L/hr). Systemic clearance represents the sum of hepatic clearance; renal clearance; and for some drugs, other routes of clearance (e.g., pulmonary elimination of volatile anesthetics, hydrolysis in blood, or dialysis).

where CL indicates clearance. Clearance is achieved through the processes of metabolism and excretion. A major practical value of understanding clearance is that at steady-state, total clearance is a primary determinant of dose and dosing interval (dose rate) when the desired steady-state plasma concentration (C_ss) is known:

Renal Clearance

The kidney is the most important organ for elimination of water-soluble drugs and metabolites. This is particularly true for infants and small children, in whom hepatic metabolism is underdeveloped, and in whom age-dependent renal clearance is a major determinant of age-appropriate drug dosing (Kearns et al., 2003). Maturation of renal function, which occurs independently of PNA, is a dynamic process. Nephrogenesis begins between about weeks 5 and 9 of gestation and is complete by week 36, after which there are changes in renal blood flow (Kearns et al., 2003; Rhodin et al., 2009). GFR is approximately 5 mL/min in full-term neonates, but about one fifth that in preterm neonates. GFR increases with PMA, at a rate described as a maturation function (MF), based on the sigmoidal hyperbolic Hill equation, where PMA₅₀^γ is the maturation half-time, and γ is the Hill coefficient:

The rate of GFR maturation is nonlinear and maximum at about 48 weeks’ PMA. It varies with prematurity, with preterm neonates (33 to 34 weeks’ PMA) having a slower increase (14 mL/min per 1.73 m² per week PMA) in the first few weeks of life than full-term neonates (39 to 41 weeks’ PMA; 94 mL/min per 1.73 m² per week PMA). In general, healthy newborns’ GFR is about 30% of adult GFR and reaches adult values at about 8 to 12 months of age. Renal tubular function matures more slowly, reaching adult levels at about 12 to 18 months of age. For example, the dosing interval for tobramycin, which is eliminated renally, is 24 hours in full-term newborns but 36 to 48 hours in preterm newborns (Kearns et al., 2003).

Renal drug clearance depends on glomerular filtration, active tubular secretion, and active and passive tubular reabsorption. In addition to both the growth and the maturational aspects of renal function, disease and concomitant drug administration (either directly or by altering rates of renal maturation) can also affect renal function.

Hepatic Clearance

For many drugs, including several used in anesthesia (e.g., sedative hypnotics, benzodiazepines, opioids, and neuromuscular blockers), hepatic clearance (CL_H in the following formulas) is a major route of elimination (Wilkinson, 1987). Hepatic clearance is the product of liver blood flow (Q_H) and the hepatic extraction ratio (E_H) of a drug.

E_H is defined as the fraction of drug entering the liver that is eliminated in one pass through the liver.

E_H depends on liver blood flow and the intrinsic clearance of the drug (CL_int), defined as the total capacity of the liver to eliminate drug in the absence of limitations from blood flow.

CL_int functionally represents drug biotransformation (the total activity of enzymes and transporters involved in metabolism and biliary secretion). Thus, combining the previous equation with the equation for hepatic clearance:

Since only an unbound drug is considered diffusible into liver cells (although in reality a simplification), E_H also depends on the fraction of unbound drug in the blood (f_u) (Baker and Parton, 2007). Therefore the three theoretic primary determinants of hepatic drug clearance are liver blood flow, intrinsic clearance (biotransformation), and plasma protein binding.

In reality, the important determinants of hepatic clearance are liver blood flow and the extraction ratio (Fig. 7-3). For drugs with a high extraction ratio (e.g., lidocaine, fentanyl, sufentanil, and propofol), hepatic clearance depends primarily on hepatic blood flow (because intrinsic clearance is so efficient, drug delivery to the liver becomes rate limiting). For low-extraction drugs (e.g., methadone, diazepam, and alfentanil), hepatic clearance is independent of hepatic blood flow and depends primarily on intrinsic clearance (metabolism).

FIGURE 7-3 Effect of increasing liver blood flow on the hepatic clearance of drugs with varying extraction ratios. Each curve represents a drug whose extraction ratio at 1.5 L/min is shown above that flow. For drugs with a low extraction ratio, an increase in liver blood flow within the physiologic range (arrow) produces very little change in hepatic clearance. For a drug with a high extraction ratio, however, increases in liver blood flow produce an almost proportional increase in hepatic clearance.

(From Wilkinson GR, Shank DG: Commentary: a physiological approach to hepatic drug clearance, Clin Pharmacol Ther 18:377, 1975.)

Metabolism

Metabolism of a drug can result in bioactivation of an inactive prodrug, formation of an active or inactive metabolite, or occasionally a toxic metabolite. The liver is the primary site of drug metabolism, although the intestine can metabolize oral drugs before they reach the systemic circulation and extrahepatic metabolism (e.g., renal, blood, and other tissues) may be important for certain drugs (i.e., remifentanil and propofol). Phase I reactions (oxidation, reduction, and hydrolysis) chemically modify the drug structure to add, form, or uncover a functional group and render the molecule more water soluble. Phase II reactions (glucuronidation, sulphation, and glutathione conjugation) add an endogenous molecule to the drug or metabolite to render it even more water soluble for elimination. Typical pathways of drug metabolism are provided in Table 7-4.

TABLE 7-4 Pathways in Drug Metabolism

Reaction	Examples
Phase I
Oxidation reactions	Thiopental, methohexital
Aliphatic hydroxylation	Pentazocine, meperidine, glutethimide, doxapram, ketamine, chlorpromazine, fentanyl, propranolol
Aromatic	Lidocaine, bupivacaine, mepivacaine
Expoxidation	Phenytoin
O-Dealkylation	Pancuronium, vecuronium, codeine, phenacetin, methoxyflurane
N-Dealkylation	Morphine, meperidine, fentanyl, diazepam, amide local anesthetics, ketamine, codeine, atropine, methadone
N-Oxidation	Meperidine, normeperidine, morphine, tetracaine
S-Oxidation	Chlorpromazine
Oxidative deamination	Amphetamine, epinephrine
Desulfuration	Thiopental
Dehalogenation	Halogenated anesthetics
Dehydrogenation	Ethanol
Reduction Reactions
Axo reduction	Fazadinium
Nitroreduction	Nitrazepam, dantrolene
Carbonyl reduction	Prednisolone
Alcohol dehydrogenation	Ethanol, chloral hydrate
Hydrolysis Reactions
Ester hydrolysis	Ester local anesthetics, succinylcholine, acetylsalicyclic acid, propanidid amide local anesthetics
Phase II: Conjugation Reactions
Glucuronamide	Oxazepam, lorazepam, morphine, nalorphine, codeine, fentanyl, naloxone
Sulfate	Acetaminophen, morphine, isoproterenol, cimetidine
Methylation	Norepinephrine
Acetylation	Procainamide
Amino acid	Salicyclic acid
Mercapturic acid	Sulfobromophthalein
Glutathione	Acetaminophen

Modified from Tucker GT: Drug metabolism, Br J Anaesth 51:603, 1979.

Comprehensive reviews of human drug metabolism are available, but a generalized overview is instructive for understanding developmental changes in biotransformation (Kramer and Testa, 2008; Pelkonen et al., 2008; Zanger et al., 2008). Cytochrome P450 (CYP) is the main oxidative (phase I) metabolizing enzyme system, and more than 50 human P450s have been identified, although only a small fraction are responsible for the majority of drug metabolism (Fig. 7-4) (Paine et al., 2006; Zanger et al., 2008). Individual CYPs are classified by their sequence evolution and amino-acid similarities (Ingelman-Sundberg et al., 2007; Zanger et al., 2008). Those with greater than 40% sequence homology are grouped in a family (designated by an Arabic number, e.g., CYP3); those with more than 55% homology are in a subfamily (designated by a letter, e.g., CYP3A), and individual CYPs are identified by a third number (e.g., CYP3A4). The majority of drugs in humans are metabolized by CYPs 1, 2, and 3 (particularly CYPs 1A2, 2B6, 2C8, 2C9, 2C19, 2D6 and 3A4, 3A5, and 3A7). CYPs can have numerous genetic variants, and there are several highly polymorphic CYPs. Allelic CYP variants are designated by an asterisk and number (e.g., CYP3A5*3, where the “wild-type” is always *1) (Ingelman-Sundberg et al., 2007; Zanger et al., 2008). CYPs can have varying degrees of substrate specificity, and some are very accommodating, like CYP3A, which metabolizes approximately one third to one half of all therapeutically used drugs.

FIGURE 7-4 Cytochrome P450 isoform content in human liver and intestine.

(Data from Rowland-Yeo K et al.: Abundance of cytochromes P450 in human liver: a metaanalysis, Br J Clin Pharmacol 57:687, 2004; Paine et al.: The human intestinal cytochrome P450 “pie,” Drug Metab Dispos 34:880, 2006.)

The developmental pattern of biotransformation activity generally follows a hyperbolic curve with age that begins in fetal development, with hepatic drug metabolism and very low clearance before and during the first month. It reaches near adult levels at approximately 1 year, becomes maximum before puberty, and declines slightly into adulthood (Johnson and Thomson, 2008). There are, however, enzyme and isoform-specific patterns of developmental maturation of drug-metabolizing enzymes (Blake et al., 2005; Hines, 2008). Several pertinent examples are in the following paragraphs.

The CYP3A family is the most important drug-metabolizing enzyme. The important isoforms are CYP3A4 (the major CYP present in the adult liver and the intestine), CYP3A5 (which metabolizes very many of the CYP3A4 substrates with equal or diminished activity and is polymorphically expressed), and CYP3A7 (a fetal form that is usually less active than 3A4 or 3A5). CYP3A undergoes a “developmental switch” with CYP3A7, the predominant CYP3A expressed in fetal liver (Stevens, 2006; Hines, 2008). Indeed it is the most abundant of any CYP and is thought to be important in fetal steroid metabolism and homeostasis (Fig. 7-5, A). CYP3A7 expression decreases during gestation, declines further after birth, and is typically undetectable after the first year. CYP3A4 expression is low during development and then increases after the first 6 months of age. CYP3A metabolizes many drugs of importance in anesthesiology, including all of the fentanyl series opioids (except remifentanil), most benzodiazepines, and local anesthetics. Although high in abundance, CYP3A7 has low activity toward many drugs (1% to 3% of the activity of CYP3A4 towards midazolam and alfentanil) (Björkman, 2006). Therefore, CYP3A-catalyzed drug metabolism and clearance increases with age. For example, the hepatic extraction of midazolam is only 0.04 in neonates, compared with 0.38 in adults (Björkman, 2006). Midazolam clearance is similarly very low in neonates, particularly in preterm infants. The age-dependent maturation of midazolam clearance is shown in Figure 7-5, B.

FIGURE 7-5 Developmental aspects of hepatic CYP3A expression and activity. A, Content of hepatic CYP3A4, CYP3A5, and CYP3A7 proteins as a function of age. B, Clearance of the CYP3A substrate midazolam. EGA, Estimated gestational age; PNA, postnatal age.

(A From Stevens JC: New perspectives on the impact of cytochrome P450 3A expression for pediatric pharmacology, Drug Discov Today 11:440, 2006; B, Redrawn from de Wildt SN et al.: Cytochrome P450 3A: ontogeny and drug disposition, Clin Pharmacokinet 37:485, 1999.)

Other hepatic CYP isoforms also demonstrate maturation of expression. CYPs 1A2, 2C9, 2C19, 2D6, and 2E1 are expressed minimally or not at all in the fetus, but substantial increases occur after birth. CYP2D6 metabolizes about one fourth of all drugs, including antidepressants, antipsychotics, β-blockers, and numerous orally administered opioids, most notably catalyzing bioactivation of the inactive prodrugs codeine and tramadol (to the pharmacologically active metabolites morphine and O-desmethyltramadol, respectively) (Ingelman-Sundberg et al., 2007; Madadi and Koren, 2008). Isoform-dependent maturation of CYP enzymes in infants is exemplified by the development of tramadol metabolism and disposition, which shows that CYP2D6-catalyzed O-demethylation matures faster than CYP3A-catalyzed N-demethylation (Fig. 7-6). CYP1A2 metabolizes caffeine and theophylline, two methylxanthines that are commonly used in pediatrics. CYP1A2 is essentially absent in fetal liver and minimally active in neonates, such that 85% of caffeine is eliminated unchanged renally in neonates (Cazeneuve et al., 1994). CYP1A2 activity matures rapidly thereafter, reaching adult values by age 6 months, and caffeine clearance in these children reflects primarily hepatic demethylation (Kearns et al., 2003).

FIGURE 7-6 Age-dependent and cytochrome P450 (CYP) isoform-dependent development of tramadol metabolism and disposition. Tramadol is a relatively inactive prodrug. Tramadol undergoes CYP2D6-catalyzed O-demethylation to the active analgesic metabolite O-desmethyltramadol, and CYP3A4-catalyzed N-demethylation to the inactive metabolite N-desmethyltramadol. The O-desmethyltramadol/tramadol concentration ratio represents a bioactivation pathway and reflects CYP2D6 activity. The N-desmethyltramadol/tramadol concentration ratio represents an inactivation pathway, and reflects CYP3A4 activity. The figure shows the influence of age on metabolite/tramadol concentration ratios in 24-hour urine collections in neonates and infants after administration of intravenous tramadol. Maturation of CYP2D6 activity is faster than that of CYP3A4.

(Redrawn from Allegaert K et al.: Determinants of drug metabolism in early neonatal life, Curr Clin Pharmacol 2:23, 2007.)

Compared with hepatic CYP enzymes, the ontogeny of CYPs in the intestine is far less understood. CYPs 3A4, 3A5, and 2C9 are the predominant intestinal isoforms, accounting for approximately 80% (3As) and 15% (2C9) of the total, respectively, with the remainder comprising CYPs 1A1, 1A2, 2C19, 2J2, and 2D6 (Paine et al., 2006). CYP3A expression declines from the proximal to distal intestine, with 75% occurring in the duodenum and jejunum (Paine et al., 1997). In the intestine, like in the liver, CYP3A4 is the predominant CYP3A isoform, and CYP3A5 is polymorphically expressed in 20% to 70% of adults (Paine et al., 1997). In otherwise histologically normal duodenal biopsies from a population of 74 children, CYP3A4 protein expression increased steadily with age (Fig. 7-7) (Johnson and Thomson, 2008). In fetal duodenum it was essentially absent, and in neonates it was expressed at about half the level seen in mature children. Intestinal CYP3A enzyme activity followed the same pattern as enzyme expression (Johnson and Thomson, 2008).

FIGURE 7-7 Developmental aspects of duodenal CYP3A4 expression and activity (mean ± SD). The number of patients in each group is given in brackets. CYP3A protein expression was measured by Western blotting. Statistically significant differences were observed between the fetus group and all of the other groups and between neonates and children older than 5 years (p < 0.05). The age-related pattern of duodenal CYP3A activity was similar to that of CYP3A protein expression (not shown).

(From Johnson TN et al.: Enterocytic CYP3A4 in a paediatric population: developmental changes and the effect of coeliac disease and cystic fibrosis, Br J Clin Pharmacol 51:451, 2001.)

Other phase I enzymes are important in drug metabolism. Ester hydrolysis is a ubiquitous reaction catalyzed by a diverse array of esterases in blood and tissue. Esterase activity is important in the hydrolysis of remifentanil to an inactive metabolite, resulting in termination of clinical effect. Remifentanil is hydrolyzed by nonspecific esterases in plasma and (more so) tissue, but not by plasma cholinesterase (Manullang and Egan, 1999). In contrast, and unlike most ester drugs, red-cell rather than plasma esterases metabolize esmolol. Whereas CYPs mostly mature in the first months to year of life, esterase activity in neonates is already at levels nearly equivalent to those in adults (Allegaert et al., 2008). For example, remifentanil clearance in children from the ages of 1 month to 9 years old resembles that in adults (Sumpter and Anderson, 2009).

Phase II drug-metabolizing enzymes include glucuronosyltransferases (UGTs), sulfotransferases (SULTs), acetyltransferases, and glutathione transferases, all catalyzing conjugation reactions with multiple isoforms of each enzyme, often with isoform-dependent ontogeny (Blake et al., 2005; Hines, 2008). The two main UGT families are UGT1 and UGT2. UGT1A1, the major enzyme responsible for bilirubin conjugation, is not detectable in fetal liver, increases immediately after birth, and reaches adult levels by 3 to 6 months of age. UGT2B7 is of particular interest, because it conjugates morphine. UGT2B7 activity in fetal liver is present at 10% to 20% of adult values and increases in neonates to reach adult values by 2 to 3 months after birth. Morphine clearance is very low in premature infants and increases substantially over the first year of life. SULT ontogeny is isoform-specific, with SULT1E1 activity highest in the fetus and declining thereafter, SULT2A1 activity is barely detectable in neonates and increases in neonates, whereas SULT1A1 activity is constant from fetal age to adulthood.

Elimination

Elimination refers to all processes that remove a drug from the body, including drug metabolism (biotransformation) and excretion. Returning to the concept of drug elimination in general, it is now appreciated that several elements affect the development of drug elimination from fetus to adult, including patient size, organ maturation, organ function, and coexisting disease. Developmental patterns of drug clearance are shown for several drugs in Figure 7-8. For drugs in which renal elimination largely determines systemic clearance, the age-dependence of such clearance approximates that of GFR. In contrast, when hepatic metabolism predominates, the pattern differs.

FIGURE 7-8 Clearance maturation, expressed as a percentage of mature clearance. Maturation profiles for acetaminophen, morphine, and dexmedetomidine, in which glucuronidation and renal excretion play a major role, resemble that for renal function (GFR). For propofol, cytochrome P450 enzymes also contribute to biotransformation and elimination, thus causing faster maturation than that predicted from renal excretion alone. The maturation half-time (TM₅₀) and Hill coefficient are shown for each drug.

(From Sumpter A, Anderson BJ: Pediatric pharmacology in the first year of life, Curr Opin Anaesthesiol 22:469, 2009.)

The complexity of developmental pharmacokinetics can be appreciated using a drug such as propacetamol. Propacetamol is an N, N-diethylglycine ester prodrug of acetaminophen (paracetamol), which is hydrolyzed by plasma esterases after intravenous administration to the active metabolite acetaminophen. Acetaminophen in turn undergoes both phase I, and more so phase II metabolism, to glucuronic acid, sulfate, cysteine, and glutathione conjugates. Figure 7-9 shows the developmental aspects of propacetamol pharmacokinetics (Anderson et al., 2005). Consistent with the relative age invariance of esterase expression, ester hydrolysis to the active metabolite, acetaminophen, was also age invariant. The central compartment volume of distribution was also age invariant, whereas the peripheral compartment volume was somewhat decreased in neonates. Clearance increased markedly with age in the first year, from 12% of adult values at 27 weeks’ PCA to 84% of its mature value by 1 year. Importantly, PCA was more important than PNA, as described above.

FIGURE 7-9 Developmental aspects of intravenous propacetamol disposition. A, Lack of effect of age on the half-life of propacetamol hydrolysis to acetaminophen. B, Influence of age on the peripheral compartment volume of distribution (V₃) of acetaminophen, standardized to a 70-kg person. The solid line represents the nonlinear relation between V₃ and age. Peripheral volume of distribution decreased from 27 weeks’ postconceptional age to reach 110% of the value in older children by 6 months. The central volume of distribution did not change with age. C, Influence of age on acetaminophen’s apparent systemic clearance, standardized to a 70-kg person. The solid line represents the nonlinear relation between clearance and age. Clearance increased from 27 weeks’ postconceptional age to reach 84% of the value in older children by 1 year. Data are from a meta-analysis, with different symbols representing different individual studies.

(From Anderson BJ et al.: Pediatric intravenous paracetamol (propacetamol) pharmacokinetics: a population analysis, Pediatr Anesth 15:282, 2005.)

Scaling Pediatric Dosing

Ideal clinical practice would be informed by age-specific clinical pharmacokinetic data for every drug used in children. As this remains an unattained ideal, considerable effort has been expended to establish pharmacokinetic models to predict age-dependent dosing based on adult data (Anderson and Holford, 2008; Johnson, 2008 Tod et al., 2008; Sumpter and Anderson, 2009). Several principles are now apparent, some of which have been described previously in this chapter. Loading doses depend on concentration and central volume of distribution. For central volumes, allometric modeling (p. 195) suggests that the volume of distribution scales with a power of 1, such that

where W_i is the weight of any individual and V_std is the volume of a standardized 70-kg adult. Because maintenance dosing equals the product of concentration and clearance, the fidelity of clearance models is important. Historically, the linear per-kilogram model, the body-surface area model, and the allometric three-fourths power model have been used. There is a nonlinear relationship between clearance and size. The linear per-kilogram model, although widely used, is the most inaccurate of the three models, because clearance (per kg) is larger in children than in adults. It leads to underprediction by more than 10% at body weights less than 47 kg, and approaches 50% for a 3.5-kg newborn. The body-surface area model, which assumes that adults and children are geometrically similar (although they in fact are not), over-predicts clearance by more than 10% at body weights below 20 kg. The allometric model, which is based on physiologic principles and has been well-validated clinically, is the most accurate.

Figure 7-10 compares the accuracy of the linear per-kilogram, the body-surface area, and the allometric three-fourths power models.

FIGURE 7-10 Relative differences in clearance determined by the dose per surface area and the dose per kilogram of weight models when compared with the allometric ¾-power weight model.

(From Anderson BJ, Holford NH: Mechanism-based concepts of size and maturity in pharmacokinetics, Ann Rev Pharmacol Toxicol 48:303, 2008.)

Clearance, however, depends on not just growth (size), but also on maturation of organ clearance processes (i.e., PCA). It is also influenced by concomitant diseases and potentially by drug interactions, which can influence organ function. While allometry alone provides reasonable estimates of clearance in older children using adult data, it alone is insufficient to predict clearance in infants and young children (Sumpter and Anderson, 2009). Therefore, the most parsimonious model for prediction drug clearance is as follows:

where MF is the maturation function (with a value from 0 to 1), and OF is organ function (also with a value from 0 to 1). The only major exception to this rule is in neonates, where organ maturation is relatively uninitiated, and the practical relationship is best approximated by the linear per-kilogram model.

For practical purposes, size models have been simplified for clinical use. This is also influenced by regulatory considerations, which sort children into the categories of neonates (younger than 1 month), infants (1 month to 2 years), children (2 to 12 years), and adolescents (12 to 18 years). Table 7-5 presents age-specific dose adjustments. An even simpler method suggests 1 month, 1 year, 7 years, and 12 years, respectively for doses that are one eighth, one fourth, one half, and three fourths of the adult doses (Anderson and Holford, 2008). It is important to remember that these dose adjustments are for drug disposition only, and they do not take into account any age-dependent differences in pharmacodynamic response.

TABLE 7-5 Pediatric Maintenance Doses of Drugs Expressed as a Percentage of Adult Dose Using an Allometric ¾ Power Model*

Pharmacodynamics

Pharmacodynamics refers to the biological effect of a drug, specifically the concentration (usually plasma)-effect relationship (or more precisely, the effect site concentration-effect relationship, although the effect-site concentration is rarely actually measured). Far less is known about the developmental aspects of pharmacodynamics than of pharmacokinetics. The concentration-effect relationship defining drug pharmacodynamics is characterized by potency and efficacy. Potency (drug concentration, or less correctly drug dose, that produces a specific effect) is characterized by the ED₅₀, defined as the concentration producing half-maximal effect in a graded dose-response (from zero to maximal response) curve in a single experiment, cell, animal, or individual. Potency can also be characterized by the ED₅₀, or as the concentration producing an all-or-nothing (quantal) response in a quantal dose-response curve in 50% of a population of cells, animals, or individuals. Efficacy is the maximum possible response at the highest possible drug concentration. The developmental aspects of drug pharmacodynamics are therefore best described by age-dependent changes in potency and efficacy. Often, however, the only information available is age dependence of clinical drug response, which may reflect both pharmacokinetic and pharmacodynamic changes.

True age-related pharmacodynamic changes may be qualitative or quantitative, and they may apply to both therapeutic and adverse effects (Stephenson, 2005). One example of quantitative differences in therapeutic response is the effect of warfarin in prepubertal, pubertal, and adult patients. Despite equivalent plasma drug concentrations, warfarin effects on prothrombin fragments 1 and 2 and on the international normalized ratio (INR) were higher in prepubertal patients than in adults. Similarly, augmented response was observed with cyclosporine, in which peripheral blood monocytes from infants had twofold lower proliferation and sevenfold lower interleukin-2 expression compared with older subjects. Examples of age-dependent adverse effects occurring only in children include chloramphenicol toxicity (“gray baby syndrome”), limb deformation from thalidomide during embryogenesis, tetracycline staining of dental enamel, and valproic acid hepatotoxicity, which is increased in young children. Generalized factors leading to age-dependent drug responses include physiology, pathology, host response to disease, and adverse drug reactions, as well as pharmacodynamics (Stephenson, 2005).

For drugs used in anesthesia, the best information on developmental pharmacodynamics has been obtained for inhaled anesthetics, and to a lesser extent, certain intravenous anesthetics. The potency of inhaled anesthetics is significantly affected by developmental age. The principal metric of inhaled anesthetic potency (the median effective concentration, or EC₅₀), has been called the minimum alveolar concentration (MAC) and defined as the “minimum alveolar concentration of anesthetic at 1 atmosphere that produces immobility in 50% of those patients or animals exposed to a noxious stimulus,” where the stimulus is usually an incision (Mapleson, 1996). Other endpoints have been analogously defined, such as MAC_AWAKE endpoint, which defines loss (or return) of consciousness. The quantal EC₅₀ of all inhaled anesthetics is similarly influenced by age, with a common log-linear negative slope (for age older than 1 year) (Mapleson, 1996). For decreasing ages younger than 40 years, EC₅₀ (MAC) increases 6% per decade. Thus, the MAC for sevoflurane is conceptually 20% greater at age 10 and 27% greater at age 1 (i.e., 2.16% and 2.29% at ages 10 and 1, respectively, for a MAC of 1.8% at age 40 (Mapleson, 1996). A clinical study found the MAC of sevoflurane to be 2.5% in children between 1 and 12 years old and 3.2% in infants 6 to 12 months old, compared with 2% at age 40 (Lerman et al., 1994; Mapleson, 1996). The MAC_AWAKE endpoint for sevoflurane was 0.43%, 0.45%, and 0.66% in children 8 to 12 years old, 5 to younger than 8 years, and 2 to younger than 5 years, respectively (Davidson et al., 2008c). The ratio between the MAC_AWAKE endpoint and MAC did not differ with age.

Measures of the age-dependent change in apparent anesthetic potency may be influenced by the clinical drug effect used as the index of response. For example, various electroencephalogram (EEG)-derived parameters (e.g., spectral edge frequency, bispectrum, and bispectral index [BIS]) have been used to measure volatile anesthetic effects in children (Wodey et al., 2005; Tirel et al., 2006; Davidson et al., 2008b). Although there were age-dependent effects of volatile anesthetics on various EEG parameters, the EEG itself was found to be highly age-dependent. Specifically, EEG was fundamentally different in infants between 0 and 6 months old, and caution was suggested in the use of BIS to determine volatile anesthetic pharmacodynamics in children (Wodey et al., 2005; Davidson et al., 2008b). Similar results were obtained when EEG-derived parameters were used to evaluate age and propofol effects, and EEG results in children younger than 1 year old were considered inaccurate (Jeleazcov et al., 2007).

Compared with inhaled anesthetics, much less is known about developmental aspects of intravenous drug pharmacodynamics. In part, this reflects the ease, lack of expense, ubiquity, and real-time availability of measuring end-tidal inhaled anesthetic concentrations, compared with measuring plasma concentrations of intravenous anesthetics. Limited data are available for propofol, which suggests slightly lower sensitivity (diminished potency) in children. Plasma propofol concentration-effect (BIS) curves analyzed in children (mean age of 10 years, range of 6 to 13 years) and adults (mean age of 18 years, range of 14 to 32 years) found graded EC₅₀ means values of 4 vs. 3.3 mcg/mL, respectively. When propofol infusions were targeted to maintain a steady-state BIS of 50, measured mean plasma concentrations were 4.3 ± 1.1 and 3.4 ± 1.2 mcg/mL, respectively (Rigouzzo et al., 2008). Somewhat lower propofol potency was also reported by others (Jeleazcov et al., 2008). In contrast, one study found no difference in propofol EC₅₀ in adults and children, however, predicted rather than measured plasma concentrations were used in the analysis, which is a limitation of such studies (Munoz et al., 2006). Increased propofol EC₅₀ in children is consistent with diminished EC₅₀ in older adults (Schnider et al., 1999). No data are available regarding propofol pharmacodynamics in neonates.

In summary, available data suggest some developmental age-dependence of inhaled and intravenous anesthetic pharmacodynamics, with somewhat lower potency in young children. Nonetheless, developmental changes in drug pharmacodynamics, in general, appear to be much smaller and of less clinical significance than developmental changes in drug pharmacokinetics.

Nonlinear Pharmacokinetics

For some drugs, an increase in dose is not followed by proportional increases in plasma C_ss and area-under-the-plasma-concentration curve (AUC). Instead, the C_ss and AUC increase more than expected. The explanation for this nonlinear pharmacokinetics is that the enzymes responsible for metabolism and elimination of the drug may be saturated. The nonlinear pharmacokinetics, also called Michaelis-Menten kinetics, occur when the maximum rate of metabolism (V_max) for the drug is approached. Michaelis-Menten pharmacokinetics describes the rate of production of molecules (drug metabolites) produced by enzymatic chemical reactions. Enzymes can perform up to several million catalytic reactions per second. To determine the maximum rate of an enzymatic reaction, the substrate (plasma drug) concentration should be increased until a constant rate of product (drug metabolite) formation is achieved. This is the maximum velocity (V_max) of the enzyme. At this point, the active sites of the enzymes are saturated with drug, and a constant amount of drug begins to be eliminated per unit of time (“zero-order” kinetics). Because the substrate (drug plasma) concentration at V_max cannot be measured exactly, the metabolism of drug can be characterized by Michaelis-Menten constant (K_m), or the drug plasma concentration at which the rate of metabolism is half of its maximum (K_m = V_max/2). For practical purposes, the K_m is the plasma concentration at which, when the dose is increased, the nonproportional increase in C_ss and AUC start to occur.

For most of drugs that are metabolized by hepatic enzymes and eliminated by the liver, the K_m is above the required therapeutic range and the drugs follow linear kinetics. However, when the therapeutic range is above the K_m, nonlinear kinetics occurs. For example, the average K_m and therapeutic range for phenytoin are 4 mg/L and 10 to 20 mg/L, respectively, and many patients on phenytoin experience nonlinear pharmacokinetics.

The nonlinear pharmacokinetics may also be seen in low-clearance drugs for which elimination is significantly influenced by the binding of the drug to plasma proteins. In this scenario, after increasing the dose of the drug, a less-than-expected increase in C_ss and AUC occurs. This would suggest that the plasma protein-binding sites have been saturated and that the free fraction of low-clearance drug has increased. The latter would result with increased clearance and a less-than-expected increase C_ss occurs. However, if measured, the free fraction of the low-clearance drug increases proportionally. Both valproic acid and disopyramide follow this type of nonlinear pharmacokinetics (Bowdle et al., 1980; Lima et al., 1991).

Compartment Models

For many drugs, after intravenous administration, the process of distribution throughout plasma and tissues occurs rapidly and simultaneously, and the whole body could be thought of as a single compartment. In this single-compartment model, after bolus intravenous administration of the drug, there is a monoexponential decrease in plasma concentration. The latter is the result of the elimination process that allows a constant portion of the drug (not amount) in the body to be eliminated per unit of time. In this case, the drug follows the first-order kinetic. The first order elimination of a drug from the body or plasma (C_p ) is defined as follows:

A_B⁰ is the initial amount in the body and C_p⁰ is plasma concentration immediately after the bolus; t is the time since bolus, and K_d is the rate constant of elimination. The e^−Kdt represents the fraction of the A_B⁰ remaining at time t. The K_d is an index of the body’s capacity to remove the drug. The elimination rate constant K_d is the fraction of the total amount of drug in the body that is removed per unit of time. It is a function of clearance and volume of distribution:

The elimination rate constant (K_d) can be also thought of as the fraction of the volume of distribution that is effectively cleared of drug per unit of time. Because the drug plasma concentration diminishes monoexponentially, a graph plot of the logarithm of the plasma concentrations vs. time yields a straight line. The elimination rate constant defines the slope of this curve, and two plasma concentrations measured during the decay or elimination phase can be used to calculate the K_d (Fig. 7-11):

FIGURE 7-11 Single-compartment model. The initial plasma (body) drug concentration (C_p⁰) produced by single loading dose diminishes monoexponentially (left). The semilogarithmic graph of concentration vs. time yields a straight line (right).

The K_d is often expressed in terms of a time required for one half of the total amount of drug in the body to be eliminated, or the plasma concentrations to decrease by one half, that is, by the half-life of the drug (t_½). If plasma concentrations decrease by 50% and C_p1 = 2C_p2, then in the previous equation, t₂–t₁ = t_½ and:

The half-life, like K_d, is dependent on volume of distribution and clearance, and this relationship is shown in the next equation:

The half-life is a variable that determines the following factors:

FIGURE 7-12 Changes in plasma concentration and steady-state level after intravenous infusion are in the function of half-life.

The short half-life is an obvious advantage for drugs given by intravenous infusion. It allows for drug effects to be easily and dynamically titrated; it requires a relatively shorter time for C_ss’s to be achieved; and if toxicity occurs, it is easier to handle. For drugs administered intermittently (oral or parenteral) a short half-life is a disadvantage because multiple doses are needed, it is difficult to keep the plasma concentration within the therapeutic window, and a missed dose could drop plasma concentrations below the minimal therapeutic level. It should be emphasized that volume of distribution and clearance may change independently of one another and alter the half-life in the same or opposite directions. For the given clearance, drugs with smaller volume of distribution have a shorter half-life and a faster recovery after the infusion of an anesthetic agent. Reduced clearance, with no changes in volume of distribution, increases the half-life and recovery time after intravenous infusion.

Most of the drugs used in anesthesia do not follow the simple, one-compartment pharmacokinetics but rather behave like a two- or even three-compartment model. Distribution of anesthetic drugs into and out of peripheral tissues determines the pharmacokinetic profile and the time course of the anesthetic drug’s effect. For the two-compartment model, the central compartment includes the blood and organs or tissues that have high blood flow and can be thought of as a rapidly equilibrating volume. The second compartment has a volume (V_t) that equilibrates at a much slower pace. After bolus administration of a drug that follows the two-compartment model, the two distinct phases of distribution and terminal elimination can be distinguished, and the decay of plasma concentration over time is defined by the biexponential equation (Fig. 7-13). Changes in plasma and the site-of-action concentrations would depend on drug elimination and on the equilibrium between central and peripheral tissue compartments.

FIGURE 7-13 Two-compartment model. For many drugs, after an intravenous bolus, there is no “instantaneous” and even distribution of the drug throughout the body (as in the one-compartment model). Drugs distribute with different paces between the initial or central (V_c ) compartment (i.e., circulation and well-perfused organs, including the brain) and the tissue or peripheral compartment (V_t ). The changes in plasma concentrations follow the biexponential decay.

For many anesthetic drugs, three phases can be distinguished after intravenous bolus administration. This three-compartment model is composed of the central compartment and two additional compartments that include the respective rapid and slow equilibrating tissues and organs (Fig. 7-14). Likewise, the three-compartment model is characterized by the triexponential plasma concentration equation, three volumes of distribution, and five rate constants of distribution and terminal elimination (K₁₂, K₂₁, K₁₃, K₃₁, and K₁₀).

FIGURE 7-14 Three-compartment model. For many anesthetic drugs, three phases in distribution can be distinguished after intravenous administration. After immediate distribution into the central compartment (i.e., bloodstream and highly perfused organs), there is redistribution of drugs (i.e., from the brain) back into circulation (K₂₁) and to peripheral tissue with rapid equilibrium (K₁₂). The drug also diffuses at a very slow pace into and out from the poorly perfused tissues (K₁₃, K₃₁). The triexponential decay describes the changes in plasma concentrations.

After an intravenous bolus, the anesthetic or hypnotic drug dilutes almost immediately, within the single circulation time, into the central compartment (i.e., in the bloodstream and in the highly perfused organs such as the brain and spinal cord). The central volume of distribution can be used to calculate the loading dose. Subsequently, there is a redistribution of drug out from the CNS back into the blood and to the peripheral compartments with rapid equilibrium (muscles viscera; V_drapid). Finally, the drug diffuses into poorly perfused tissues (fat) that slowly equilibrate with the central compartment. The initial redistribution, rather than metabolic clearance, determines the termination of the effect of single boluses of parenteral anesthetics. If prolonged anesthesia is required, the maintenance infusion rate should compensate not only for the drug clearance but initially also for the transient loss of anesthetic by redistribution to the peripheral compartments that are governed by “intercompartmental clearance” and elimination rate constants (K₁₂, K₂₁, K₁₃, and K₃₁).

Context-Sensitive Half-Time

Traditionally, clearance, volume of distribution, and half-life are standard pharmacokinetic parameters used to characterize the drug’s offset of action. As discussed previously, they are derived from one- and two-compartment models or, through the use of computer simulation programs, from multicompartment models. These pharmacokinetic parameters can be relatively easy to apply to calculate the infusion rate and predict the offset of action of water-soluble drugs with small volumes of distribution and relatively simple patterns of disposition (i.e., muscle relaxants).

For the anesthesiologist, pharmacokinetic factors are often used for the routine selection and use of various intravenous anesthetic agents. Drugs with short elimination half-lives are commonly selected for brief procedures, whereas drugs with longer half-lives are selected for lengthier procedures. Drugs with small volumes of distribution tend to decrease the time required for recovery after intravenous infusion, and agents with decreased plasma clearances may increase the time for recovery. In general, formulas for the calculation of continuous infusions incorporate knowledge of these pharmacokinetics. For bolus administration of drug, the volume of distribution and the desired plasma concentration are needed. Table 7-6 lists plasma concentrations in adults for some of the opioids. The bolus dose is calculated as the product of the volume of distribution and the desired plasma concentration (C_p):

TABLE 7-6 Opioid Concentrations that Ablate Responsiveness to Intraoperative Noxious Stimuli and Permit Adequate Ventilation on Emergence*

The maintenance infusion rate (MIR) is calculated as the product of the desired plasma concentration and the clearance:

Although these formulas work well, Shafer and Varvel (1991) and Hughes et al. (1992) have demonstrated the complex interactions that occur with prolonged infusions, especially in drugs that are lipid soluble.

The offset of drug effect depends on reduction of the plasma concentrations and the withdrawal of drug from the site of action; that is, for anesthetic from the receptor site in the CNS. If steady state is achieved and all compartments are saturated, then the half-life of elimination phase, which is a function of the first-order processes of elimination, correlates with a decrease in the site-of-action drug concentrations and with the offset of drug action. However, after infusion of a highly lipophilic anesthetic agent, when steady state is not achieved and not all compartments are saturated, the decline in concentrations (i.e., the offset of action and recovery from anesthesia) depends on complex interactions between the duration of the infusion and initial distribution, redistribution, and metabolic and elimination first-order processes. The classic descriptors of a drug’s pharmacokinetics and offset of action (terminal half-time) are of little help to anesthesiologists in predicting the offset of action and recovery from anesthesia for the intravenous anesthetic drugs. Fortunately, with the help of pharmacokinetic and pharmacodynamic simulation models, new predictors of offset of drug effects have evolved (Shafer and Varvel, 1991; Hughes et al., 1992; Youngs and Shafer, 1994).

Using pharmacokinetic and pharmacodynamic models and basic pharmacokinetic profiles of commonly used synthetic opioid analogs, Shafer and Varvel (1991) were the first to construct the offset of action (recovery) curves as a function of the duration of infusion for fentanyl, alfentanil, and sufentanil (Fig. 7-15). Hughes et al. (1992) introduced the term context- sensitive half-time (context refers to the duration of infusion) as a time required for a drug concentration to decrease to half of its value after drug infusion of a given duration. Of importance is that for any given drug, its context-sensitive half-time varies with the duration of the drug infusion. Because for most intravenous anesthetic drugs the 50% fall in concentration is not sufficient for recovery from anesthesia, other decrement times have been introduced (Youngs and Shafer, 1994), for example, 80% and 90% decrements.

FIGURE 7-15 Context-sensitive half-time: the time required for drug concentration to decrease by half of its value (Y axis) after cessation of infusion of given duration (X axis) for fentanyl and its congeners, sufentanil, alfentanil, and remifentanil (see the text for explanation).

(Modified from Shafer SL, Varvel MD: Pharmacokinetics, pharmacodynamics, and rational opioid selection, Anesthesiology 74:53, 1991; Egan TD: Clin Pharmacokinet 29:80, 1995.)

After a short intravenous infusion (0 to 15 minutes), fentanyl and other synthetic opioid analogs have similar context-sensitive half-times (Fig. 7-15). However, after prolonged infusion (longer than 1 hour), there is a marked difference among four synthetic opioid analogs (fentanyl, sufentanil, alfentanil, and remifentanil), and these differences do not correlate with their classic pharmacokinetic parameters (Table 7-7). In contrast to its older congeners, remifentanil has a short and steady context-sensitive half-life of 3 minutes, which does not change with the increasing duration of infusion (Egan et al., 1996). This contrasts with alfentanil, which has a context-sensitive half-time that increases to 1 hour after a 4-hour infusion (Ebling et al., 1990; Scholz et al., 1996). This difference is because of the unique pharmacokinetic profile of remifentanil. It is a highly liposoluble (volume of distribution at steady state [V_dss] of 30 L) opioid analog that undergoes widespread metabolism (deesterification), including metabolism in the circulation. Unlike other opioids, the termination of action of remifentanil does not depend on redistribution but rather on extremely rapid metabolic clearance. Kapila et al. (1995) demonstrated that the context-sensitive half-times of remifentanil (3 minutes) and alfentanil (50 to 55 minutes) derived from computer modeling are similar to measured context-sensitive half-times (3.2 and 47 minutes for remifentanil and alfentanil, respectively), and both correlate with measured pharmacodynamic offset (recovery of minute ventilation). The latter confirms the value and clinical applicability of this new pharmacokinetic-pharmacodynamic parameter in predicting the offset of anesthetic drugs.

TABLE 7-7 Pharmacokinetic Parameters of Synthetic Opioids after Single Intravenous Bolus Administration

The context-sensitive half-time curves provide a better, clinically more relevant comparison of the pharmacokinetic profiles of anesthetic drugs than the traditional pharmacokinetic parameters (Fig. 7-16). After a single intravenous dose, commonly used anesthetic and hypnotic drugs have a short duration of action. However, after prolonged infusions the context-sensitive half-times and duration of action increase. For some drugs (e.g., propofol and ketamine), this increase is modest, whereas for others (e.g., diazepam and thiopental), it is quite dramatic. In the case of midazolam, the rapid increase in its context-sensitive half-time with prolonged duration of infusion occurs in the presence of a relatively short elimination half-life (t_½β), and this is most likely because of the low clearance of midazolam.

FIGURE 7-16 Context-sensitive half-time for commonly used general anesthetics.

(From Reves JG et al.: Nonbarbiturate intravenous anesthetics. In Miller RD, editor: Anesthesia, ed 5, New York, 2000, Churchill Livingstone.)

The data regarding the context-sensitive half-times and other decrement times of anesthetic agents in the pediatric population are limited, at best. In children aged 3 to 11 years, longer context-sensitive half-times than in adults were reported for propofol. After a 1-hour infusion in children and adults, the context-sensitive half-times for propofol are 10.4 and 6.6 minutes, respectively, and after a 4-hour infusion, they are 19.6 and 9.5 minutes, respectively (McFarlan et al., 1999). This is probably due to the altered compartment volumes and may lead to slower recovery from a propofol infusion in children than in adults (Short et al., 1994). In contrast, the shorter context-sensitive half-time of fentanyl was determined in pediatric population (2 to 11 years old) compared with published data in adults (Ginsberg et al., 1996).

Population Pharmacokinetics

Pharmacokinetics and pharmacodynamics of drugs in the pediatric population and in adults are different. Furthermore, neonates, infants, children, and adolescents have distinct differences in physiologic development, and the pediatric population is quite heterogeneous with regard to pharmacokinetics and pharmacodynamics of drugs across different age groups. These differences justify studying pharmacokinetics and pharmacodynamics in children of various ages. However, the testing of medications in children presents a dilemma: while society wants to spare children from the potential risk involved in research, children may be harmed if they are given medications that have been inadequately studied (Steinbrook, 2002).

Classical nontherapeutic pharmacokinetics studies involve administering either single or multiple doses of a drug to a relatively small group of subjects and require multiple sampling to characterize the concentration and time profile of the drug. Conducting standard nontherapeutic pharmacokinetic studies with frequent sampling in children imposes many ethical and practical issues, and an alternative and preferable approach in many pediatric situations is the population pharmacokinetics (PPK) approach. This approach, in addition to dense data and frequent sampling, deal with sparse data and infrequent sampling of blood from a larger population, and it allows many obstacles related to classical nontherapeutic pharmacokinetic studies in children to be overcome.

PPK is an area of clinical pharmacology that studies the sources and the correlates of variability in drug-plasma concentration parameters among individuals in the target population of patients who are receiving clinically effective doses of a drug (Shen and Lu, 2007). PPK is focused on the quantitative assessment of the typical pharmacokinetic parameters, as well as the within- and between-individual and residual variability in drug absorption, distribution, metabolism, and excretion (Steiner, 1992; Ette and Williams, 2004). The population approaches use mathematic and statistic modeling to investigate the dose-concentration-effect relationship and to quantitatively and qualitatively assess factors that may explain interindividual variability (Sheiner et al., 1979). In the early 1980s, Sheiner and Beal introduced the new PPK data analysis approach (i.e., the population approach) and demonstrated that estimates of PPK parameters could be obtained even if only two or three samples are collected per patient (Sheiner and Beal, 1980, 1981, 1982). They also introduced a new software program (the Nonlinear Mixed Effects Model, or NONMEM) that was capable of performing the new type of analysis, and this is now the most commonly used population modeling program (Sheiner and Beal, 1980; Sheiner et al., 1979).

The PPK approach allows not only major contributions to variability of key pharmacokinetic parameters to be established, but it also goes one step further and allows the relative contributions of different factors to be determined. In this regard, size, age, and renal function are major contributors to vancomycin clearance variability in neonates. Using the PPK and NONMEM modeling, Anderson and colleagues (2002a) have shown that size explains 49.8%, age accounts for 18.2%, and renal function explains 14.1% of clearance variability of vancomycin in neonates. The small unexplained percentage (18%) is residual variability in clearance and suggests that target concentration intervention is unnecessary if size, age, and renal function are used to predict the dose (Anderson et al., 2002a).

Body Size and Maturation Adjustments

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