# Pharmacokinetics and Pharmacology of Drugs Used in Children

6 Pharmacokinetics and Pharmacology of Drugs Used in Children

THE PHARMACOKINETICS AND PHARMACODYNAMICS of most medications, when used in children, especially neonates, differ from those in adults.111 Children exhibit different pharmacokinetics (PK) and pharmacodynamics (PD) from adults because of their immature renal and hepatic function, different body composition, altered protein binding, distinct disease spectrum, diverse behavior, and dissimilar receptor patterns.1,3,1219 PK differences necessitate modification of the dose and the interval between doses to achieve the desired clinical response and to avoid toxicity.7,2022 In addition, some medications may displace bilirubin from its protein binding sites and possibly predispose an infant to kernicterus.2328 The capacity of the end organ, such as the heart or bronchial smooth muscle, to respond to medications may also differ in children compared with adults (PD effects). In this chapter we discuss basic pharmacologic principles as they relate to drugs commonly used by anesthesiologists.

# Pharmacokinetic Principles and Calculations

Changes in drug concentrations within the body over time are referred to as pharmacokinetics. The principles and equations that describe these changes can be used to adjust drug doses rationally to achieve more effective drug concentrations at the site of action.2933 The equations in this section are intended for general and practical use, whereas the more rigorous mathematical intricacies of PK are covered elsewhere.3437

Within the body, a drug may diffuse between several body fluids and tissues at different rates, yet the consistent change in its circulating concentration may be used to characterize its kinetics and to guide dosages. The rate of removal of drug from the circulation is usually described using either first-order or zero-order exponential equations. The difference between these two types of rates has important implications for drug treatment.

## Apparent Volume of Distribution

If concentration is expressed with the unconventional units of milligrams per liter rather than micrograms per milliliter (which is equivalent), it is easier to balance the equation. This equation serves as the basis for most of the PK calculations because it is easily rearranged to solve for Vd and dose. It is also important to note that this equation represents the change in concentration after a rapidly administered IV dose of a drug whose elimination is great compared with its time for distribution. After a mini-infusion (e.g., of vancomycin or gentamicin), a more complex exponential equation may be required to account for drug elimination during the time of infusion.40 For neonates in whom drug elimination is relatively slow, only a small fraction of drug is eliminated during the time of infusion, and such adjustments can be omitted, whereas more complex equations may be needed in older children.

Knowledge of the apparent Vd is essential for dosage adjustments. Vd may be calculated by rearranging Equation 7.

### Pharmacokinetic Example

Step 2: At steady-state, peak and trough concentrations reach the same levels after each dose. The time between the peak and trough concentrations is 10 hours, that is, 12 hours minus 1 hour infusion minus 1 hour to peak concentration. Half-life may be solved by rearranging Equation 2 to solve for k (elimination rate constant) and substituting the calculated k into Equation 3. In this case, the calculated elimination rate constant is 0.098 hour−1 and the corresponding half-life is 7.1 hours. However, a practical and clinically applicable “bedside” approach may be used without need for logarithmic calculations. For example, the plasma concentration decreased from 32 to 16 mg/L in one half-life and then from 16 to 12 mg/L in a fraction of the second half-life. At the end of the second half-life, the concentration would have decreased to 8 mg/L. Because 12 mg/L is the midpoint between the first and second half-lives, 1.5 half-lives have elapsed during the 10 hours between the peak and trough. Thus, if one assumes a linear decline, the half-life may be estimated as 6.67 hours (10 hours ÷ 1.5 half-lives). Note that the error between the actual half-life of 7.1 hours and the estimated half-life (6.67 hours) is a result of the linear assumptions of this calculation between half-lives. In fact, first-order elimination is a nonlinear process and concentration will actually decline from 32 mg/L to 22.6 mg/L during the first 50% of the first half-life rather than from 32 mg/L to 24 mg/L using this linear approach. The same occurs during subsequent half-lives. However, the small error associated with this method is often acceptable for rapid bedside estimates of PK parameters.

Step 3: A new dosage regimen must be calculated if the concentrations are unsatisfactory. Accordingly, one must decide on a desired peak and trough concentration. If, for example, the desired vancomycin peak and trough concentrations were 32 mg/L (20 to 40 mg/L) and 8 mg/L (5 to 10 mg/L), respectively, then Equation 8 may be rearranged to solve for the new dose.

## Repetitive Dosing and Drug Accumulation

(Eq. 10)

In Equations 10 and 11, f is the fraction of the dose that is absorbed, D is the dose, τ is the dosing interval in the same units of time as the elimination half-life, k is the elimination rate constant, and 1.44 equals the reciprocal of 0.693 (see Equation 3). The magnitude of the average Css is directly proportional to the ratio of T1/2/τ and D.32

Steady state occurs when the amount of drug removed from the body between doses equals the amount of the dose.33,37 Five half-lives are usually required for drug elimination and distribution among tissue and fluid compartments to reach equilibrium. When all tissues are at equilibrium (i.e., steady state), the peak and trough concentrations are the same after each dose. However, before this time, constant peak and trough concentrations after intermittent doses, or constant concentrations during drug infusions, do not prove that a steady state has been achieved because drug may still be entering and leaving deep tissue compartments. During continuous infusion, the fraction of steady-state concentration that has been reached can be calculated in terms of multiples of the drug’s half-life.32 After three half-lives, the concentration is 88% of that at steady state. When changing doses during chronic drug therapy, the concentration should usually not be rechecked until several half-lives have elapsed, unless elimination is impaired or signs of toxicity occur. Drug concentrations may not need to be checked if symptoms improve.

If the time to reach a constant concentration by continuous or intermittent dosing is excessive, a loading dose may be used to reach plateau in the concentration more rapidly. This frequently is applied to initial treatment with digoxin, which has a 35- to 69-hour half-life in term neonates and an even longer half-life in preterm infants.44 Use of a loading dose increases the circulating concentration of drug earlier in the therapeutic course, but for the equilibration to reach a true steady-state still requires treatment for five or more half-lives. Loading doses must be used cautiously, because they increase the likelihood of drug toxicity, as has been observed with loading doses of digoxin.3,16,17,44

Dose calculations using a 1-compartment model (Eq. 9) may not be applicable to many anesthetic drugs that are characterized using multi-compartment models. The use of V1 results in a loading dose too high, while the use of Vdss results in a loading dose too low. Too high a dose may cause transient toxicity, although slowing the rate of administration may prevent excessive concentrations during the distributive phase.

The time to peak effect (Tpeak) is dependent on clearance and effect-site equilibration half-time (T1/2keo). At a submaximal dose, Tpeak is independent of dose. At supramaximal doses, maximal effect will occur earlier than Tpeak and persist for longer duration because of the shape of the response curve (see later discussion). The Tpeak concept has been used to calculate optimal initial bolus doses,45 because V1 and Vdss poorly reflect the required scaling factor. A new parameter, the volume of distribution at the time of peak effect-site concentration (Vpe) is used and is calculated.

(Eq. 12)

# Pediatric Pharmacokinetic Considerations

## Size

Support for a value of comes from investigations that show the log of BMR plotted against the log of body weight produces a straight line with a slope of in all species studied, including humans. Fractal geometry mathematically explains this phenomenon. The -power law for metabolic rates was derived from a general model that describes how essential materials are transported through space-filled fractal networks of branching tubes.50 A great many physiologic, structural, and time related variables scale predictably within and between species with weight (W) exponents (PWR) of , 1, and , respectively.51 These exponents have applicability to PK parameters, such as clearance (CL exponent of ), volume (V exponent of 1) and half-time (T1/2 exponent of ).51 The factor for size (Fsize) for total drug clearance may be expressed:

(Eq. 15)

Remifentanil clearance in children aged 1 month to 9 years is similar to adult rates when scaled using an allometric exponent of .52 Nonspecific blood esterases that metabolize remifentanil are mature at birth.53

## Maturation

Allometry alone is insufficient to predict clearance in neonates and infants from adult estimates for most drugs.54,55 The addition of a model describing maturation is required. The sigmoid hyperbolic or Hill model56 has been found useful for describing this maturation process (MF).

(Eq. 16)

The TM50 describes the maturation half-time, while the Hill coefficient relates to the slope of this maturation profile. Maturation of clearance begins before birth, suggesting that postmenstrual age (PMA) would be a better predictor of drug elimination than postnatal age.51 Figure 6-4 shows the maturation profile for dexmedetomidine, expressed as both the standard per-kilogram model and by using allometry. Clearance is immature in infancy. Clearance, expressed as per kilogram, is greatest at 2 years of age, decreasing subsequently with age. This “artifact of size” disappears with use of the allometric model.

## Organ Function

Changes associated with normal growth and development can be distinguished from pathologic changes describing organ function.49 Morphine clearance is reduced in neonates because of immature glucuronide conjugation, but clearance was lower in critically ill neonates than healthier cohorts,5759 possibly attributable to reduced hepatic function. The impact of organ function alteration may be concealed by another covariate. For example, positive pressure ventilation may be associated with reduced clearance. This effect may be attributable to a consequent reduced hepatic blood flow with a drug that has perfusion limited clearance (e.g., propofol, morphine).

(Eq. 17)

# Pharmacodynamic Models

## Quantal Effect Model

The potency of anesthetic vapors may be expressed by minimum alveolar concentration (MAC), and this is the concentration at which 50% of subjects move in response to a standard surgical stimulus. MAC appears, at first sight, to be similar to EC50, but is an expression of quantal response rather than magnitude of effect. There are two methods of estimating MAC. Responses can be recorded over the clinical dose range in a large number of subjects and logistic regression applied to estimate the relationship between dose and quantal effect; the MAC can then be interpolated. Large numbers of subjects may not be available, so an alternative is often used. The “up and down” method described by Dixon63,64 estimates only the MAC rather than the entire sigmoid curve. It usually involves a study of only one concentration in each subject and, in a sequence of subjects, each receives a concentration depending on the response of the previous subject; the concentration is either decreased if the previous subject did not respond or increased if they did. The MAC is calculated either as the mean concentration of equal numbers of responses and no-responses or is the mean concentration of pairs of “response–no response.”

There may also be a delay as a result of transfer of the drug to the effect site (e.g., neuromuscular blockers), a lag time (e.g., diuretics), physiologic response (e.g., antipyresis), active metabolite (e.g., propacetamol), or synthesis of physiologic substances (e.g., warfarin). A plasma concentration-effect plot can form a hysteresis loop because of this delay in effect. Hull and Sheiner introduced the effect compartment concept for neuromuscular blockers.66,67 A single first-order parameter (T1/2keo) describes the equilibration half-time. This mathematical trick assumes that the concentration in the central compartment is the same as that in the effect compartment at equilibration, but that a time delay exists before drug reaches the effect compartment. The concentration in the effect compartment is used to describe the concentration-effect relationship.68

The T1/2keo for propofol in children has been described. As expected, a shorter T1/2keo with decreasing age based on size models has been described.67,69 Similar results have been demonstrated for sevoflurane and changes in the EEG.70 If the effect-site is targeted and peak effect (Tpeak) is anticipated to be later than it actually is because it was determined in a teenager or adult, this will result in excessive dose in a young child.

# Drug Distribution

## Protein Binding

Acidic drugs (e.g., diazepam, barbiturates) tend to bind mainly to albumin while basic drugs (e.g., amide local anesthetic agents) bind to globulins, lipoproteins and glycoproteins. In general, plasma protein binding of many drugs is decreased in the neonate relative to the adult in part because of reduced total protein and albumin concentrations (Fig. 6-6).71 Many drugs that are highly protein bound in adults have less of an affinity for protein in neonates (E-Fig. 6-1).7175 Reduced protein binding increases the free fraction of medications, thus providing more free medication and greater pharmacologic effect.1,3,12,14,17 This effect is particularly important for medications that are highly protein bound, because the reduced protein binding increases the free fraction of the medication to a greater extent than for low protein bound drugs. For example, phenytoin is 85% protein bound in healthy infants but only 80% in those who are jaundiced. This equates to a 33% increase in the free fraction of phenytoin when jaundice occurs (E-Fig. 6-2). Differences in protein binding may have considerable influence on the response to medications that are acidic and are, therefore, highly protein bound (e.g., phenytoin, salicylate, bupivacaine, barbiturates, antibiotics, theophylline, and diazepam).17 In addition, some medications, such as phenytoin, salicylate, sulfisoxazole, caffeine, ceftriaxone, diatrizoate (Hypaque), and sodium benzoate, compete with bilirubin for binding to albumin (see E-Fig. 6-2). If large amounts of bilirubin are displaced, particularly in the presence of hypoxemia and acidosis, which open the blood-brain barrier, kernicterus may result.24,25,72,7577 Because these metabolic derangements often occur in sick neonates coming to surgery, special care must be taken when selecting medications for the anesthetic.77 Medications that are basic (e.g., lidocaine or alfentanil) are generally bound to plasma α1-acid glycoprotein; α1-acid glycoprotein concentrations in preterm and term infants are less than in older children and adults. Therefore, for a given dose, the free fraction of a drug is greater in preterm and term infants.7880 Protein binding changes are important for the relatively unusual case of a drug that is more than 95% protein bound, with a high extraction ratio and a narrow therapeutic index, that is given parenterally (e.g., lidocaine administered IV), or a drug with a narrow therapeutic index that is given orally and has a very rapid T1/2keo (e.g., antiarrhythmic drugs; propafenone, verapamil).81

## Body Composition

Preterm and term infants have a much greater proportion of body weight in the form of water than do older children and adults (Fig. 6-7).19 The net effect on water-soluble medications is a greater Vd in infants, which in turn increases the initial (loading) dose, based on weight, to achieve the desired target serum concentration and clinical response.1,3,14,83,84 Term neonates often require a greater loading dose (milligrams per kilogram) for some medications (e.g., digoxin, succinylcholine, and aminoglycoside antibiotics) than older children.8387 However, neonates also tend to be sensitive to the respiratory, neurologic, and circulatory effects of many medications and therefore tend to be more responsive to these effects at reduced blood concentrations than are children and adults. Preterm infants are usually more sensitive than term neonates and in general require even smaller blood concentrations.1 On the other hand, dopamine may increase blood pressure and urine output in term neonates only at doses as large as 50 μg/kg/min. This dose, which would induce intense vasoconstriction in adults, suggests that neonates are less sensitive in their cardiovascular responsiveness.3,85,8891 It is important to carefully titrate the doses of all medications that are administered to preterm and term infants to the desired response.

Compared with children and adolescents, preterm and term neonates have a smaller proportion of body weight in the form of fat and muscle mass; with growth, the proportion of body weight composed of these tissues increases (Fig. 6-8).* Therefore, medications that depend on their redistribution into muscle and fat for termination of their clinical effects likely have a larger initial peak blood concentration. These medications may also have a more sustained blood concentration because neonates have less tissue for redistribution of these medications. An incorrect dose may result in prolonged undesirable clinical effects (e.g., barbiturates and opioids may cause prolonged sedation and respiratory depression). The possible influence of small muscle mass on the response to muscle relaxants is exemplified by achieving neuromuscular blockade at smaller serum concentrations in infants.85

# Absorption

Adult enteral absorption rates may not be reached until 6 to 8 months after birth.94,95 Congenital malformations (e.g., duodenal atresia), co-administration of drugs (e.g., opioids), or disease characteristics (e.g., necrotizing enterocolitis) may further affect the variability in absorption. Delayed gastric emptying and reduced clearance may dictate reduced doses and frequency of repeated drug administration. For example, a mean steady state target paracetamol concentration greater than 10 mg/L at trough can be achieved by an oral dose of 25 mg/kg/day in preterm neonates at 30 weeks, 45 mg/kg/day at 34 weeks, and 60 mg/kg/day at 40 weeks PMA.96 Because gastric emptying is slow in preterm neonates, dosing may only be required twice a day.96 In contrast, the rectal administration of some drugs (e.g., thiopental, methohexital) is more rapid in neonates than adults. However, the interindividual absorption and relative bioavailability variability after rectal administration may be more extensive compared to oral administration, making rectal administration less suitable for repeated administration.97

# Metabolism and Excretion

## Hepatic Metabolism

The liver is one of the most important organs involved in drug metabolism. Hepatic enzymatic drug metabolism usually converts the medication from a less polar state (lipid soluble) to a more polar, water-soluble compound (see later discussion). Although no categorical statement applies to all drugs and enzymes, the activities of most of these enzymes are reduced in neonates.3,4,16,20,22,87,99104 Another important factor that influences hepatic degradation is hepatic blood flow. As the infant matures, a greater proportion of the cardiac output is delivered to the liver, therefore increasing drug delivery and potentially increasing drug metabolism. Some medications are extensively metabolized by the liver or other organs (e.g., the intestines or lungs) and are referred to as having high extraction ratios. This extensive metabolism produces a “first pass” effect in which a large proportion of an enteral dose is inactivated as it passes through the organ before reaching the systemic circulation. Metabolism via cytochrome P-450 in the intestinal wall may occur during drug absorption.105107 Certain foods may induce or inhibit intestinal cytochromes, resulting in food–drug interactions.108 The concentrations of these enzymes in neonates are less than in older children. These enzymes may also be affected by diseases such as cystic fibrosis or celiac disease.109,110 Further metabolism may occur as the portal venous circulation from the small intestine passes through the liver before returning to the heart.105,107 In contrast, IV administration circulates drug to the liver or intestine for metabolism in proportion to the organ blood flow. Some of the drugs that exhibit extensive first-pass metabolism include propranolol, morphine, and midazolam.111118

The opening or closing of a patent ductus may have profound effects on drug delivery to metabolizing organs in preterm infants.119,120 The ability to metabolize and conjugate medications improves considerably with age as a result of both increased enzyme activity and increased delivery of drug to the liver. Other factors influence the rate of hepatic maturation and metabolism (e.g., sepsis and malnutrition may slow maturation, whereas previous exposure to anticonvulsants, such as phenytoin or phenobarbital, may hasten maturation).3,89,99,100,104,121125 The elimination half-lives of diazepam, thiopental, and phenobarbital are markedly increased in neonates compared with adults (i.e., the elimination half-life for thiopental in the neonate (17.9 hours) is almost three times that in children (6.1 hours) and 50% greater than that in adults (12 hours) (E-Fig. 6-3).12,74,126,127 In general, the half-lives of medications that are eliminated by the liver are prolonged in neonates, decreased in children 4 to 10 years of age, and reach adult values in adolescents, mirroring clearance changes with age (see Fig. 6-4).

Metabolism through biotransformation to more polar forms is required for many drugs before they can be eliminated. Two types of drug biotransformation can occur: Phase I and Phase II reactions. Phase I reactions transform the drug via oxidation, reduction, or hydrolysis. Phase II reactions transform the drug via conjugation reactions, such as glucuronidation, sulfation, and acetylation, into more polar forms.29,30 Although the liver is the primary site for biotransformation, other organs are also involved, including the lungs and kidneys. Hepatic drug metabolism activity appears as early as 9 to 22 weeks gestation, when fetal liver enzyme activity may vary from 2% to 36% of adult activity.128 It is inaccurate to generalize that the preterm neonate cannot metabolize drugs. Rather, the specific pathway(s) of drug metabolism must be considered.

Metabolism of many drugs involves the cytochrome P-450 (CYP) enzyme system. Multiple isoforms of the CYP enzyme system exist with different substrate specificities for different drugs.129131 Induction and inhibition of these enzymes by different drugs and chemicals requires a thorough understanding of both the nomenclature of the CYP system, as well as the specific isoforms responsible for metabolism of the drugs used in pediatric anesthesia. There are both genetic and ethnic polymorphisms leading to clinically important differences in the capacity to metabolize drugs; these differences can make individual drug responses in some cases unpredictable.132136 In the future it may be possible to tailor drug doses to the individual’s requirements by determining the child’s unique metabolic capacity.137,138

## Cytochromes P-450: Phase I Reactions

CYPs are heme-containing proteins that provide most of the phase I drug metabolism for lipophilic compounds in the body.129 The generally accepted nomenclature of the cytochrome P-450 isozymes begins with CYP, and groups enzymes with more than 36% DNA homology into families designated with an Arabic number, followed by letters for the subfamily of closely related proteins (greater than 77% homology), followed by a number for the specific enzyme gene, such as CYP3A4.139,140 Isozymes that are important in human drug metabolism are found in the CYP1, CYP2, and CYP3 gene families. Table 6-1 outlines the CYP isozymes and their common substrates.

For many drugs, the reduced metabolism in neonates relates to reduced total quantities of CYP enzymes in the hepatic microsomes.141 Although the concentrations of CYP enzymes increase with gestational age, they may reach only 50% of adult values at term.141 In neonates, reduced CYP decreases clearance for many drugs, including theophylline, caffeine, diazepam, phenytoin, and phenobarbital.87,127,130,131,142144 Although many isozymes are immature in the neonate, some CYP isozymes exhibit near-adult activity whereas others produce unique metabolic pathways in the neonatal period that invalidate broad generalizations about neonatal drug metabolism (see Table 6-1).

# Developmental Changes of Specific Cytochromes

Cytochrome P-450 1A2 (CYP1A2) accounts for much of the metabolism of caffeine (1, 3, 7-trimethylxanthine)145,146 and theophylline (1,3-dimethylxanthine),147,148 which are methylxanthines frequently used to treat neonatal apnea and bradycardia. CYP1A2 activity is nearly absent in the fetal liver and remains minimal in the neonate.149 This limits N-3- and N-7-demethylation of caffeine in the neonatal period that prolongs elimination in preterm and term neonates.146,150 Elimination is through the immature renal system and consequent clearance is reduced. Adult levels of activity are reached between 4 and 6 months postnatally.151,152 A similar PK pattern of reduced metabolism at birth occurs with theophylline, in which CYP1A2 catalyzes 3-demethylation and 8-hydroxylation.147,148 Theophylline clearance reaches adult levels by 4 to 5 months, coincident with changes in CYP1A2 reflected in urine metabolite patterns.153

Other CYP enzymes that are reduced or absent in the fetus include CYP2D6 and CYP2C9.121,122,154 CYP2D6, which is involved in the metabolism of β-blockers, antiarrhythmics, antidepressants, antipsychotics, and codeine, is absent in the fetal liver and is eventually expressed postnatally (see Table 6-1).122,123 In contrast to the slow maturation of CYP1A2 and CYP2D6, CYP2C9, which are responsible for the metabolism of nonsteroidal antiinflammatory drugs (NSAIDs), warfarin, and phenytoin, have minimal activity antenatally121 and then develop rapidly postnatally.119,144

CYP3A is the most important cytochrome involved in drug metabolism, because of the broad range of drugs that it metabolizes and because it comprises the majority of adult human liver CYP (see Table 6-1).155 CYP3A is detectable during embryogenesis as early as 17 weeks, primarily in the form of CYP3A7,149 and reaches 75% of adult activity by 30 weeks gestation.122 In vivo, CYP3A activity appears to be mature at birth124; however, there is a poorly understood postnatal transition from the fetal CYP3A7 to the predominant adult isoform CYP3A4.156,157

## Phase II Reactions

The other major route of drug metabolism, designated phase II reactions, involves synthetic or conjugation reactions that increase the hydrophilicity of molecules to facilitate renal elimination.29,30 The phase II enzymes include glucuronosyltransferase, sulfotransferase, N-acetyltransferase, glutathione S