THE PHARMACOKINETICS AND PHARMACODYNAMICS of most medications, when used in children, especially neonates, differ from those in adults.¹^–¹¹ 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,^3,¹²^–¹⁹ PK differences necessitate modification of the dose and the interval between doses to achieve the desired clinical response and to avoid toxicity.^7,²⁰^–²² In addition, some medications may displace bilirubin from its protein binding sites and possibly predispose an infant to kernicterus.²³^–²⁸ 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.²⁹^–³³ The equations in this section are intended for general and practical use, whereas the more rigorous mathematical intricacies of PK are covered elsewhere.³⁴^–³⁷

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.

First-Order Kinetics

Most drugs are cleared from the body with first-order exponential rates in which a constant fraction or constant proportion of drug is removed per unit of time. Because the proportion of drug cleared remains constant, the higher the concentration, the greater the amount of drug removed from the body. Such rates can be described by exponential equations that fit the following form:

(Eq. 1)

where C is the concentration at time t, C₀ is the starting concentration (a constant determined by the dose and distribution volume), and k is the elimination rate constant with units of time⁻¹. First-order indicates that the exponent is raised to the first power (−kt in Equation 1). Second-order equations are those that are raised to the second power, such as e^(z)2. First-order exponential equations, such as Equation 1, may be converted to the form of the equation of a straight line (y = mx + b) by taking the natural logarithm of both sides, after which they may be solved by linear regression.

(Eq. 2)

If ln C (i.e., natural logarithm of C) is graphed versus time, the slope is −k, and the intercept is ln C₀. If log C (i.e., common logarithm of C) is graphed versus time, the slope is −k/2.303, because ln x equals 2.303 log x. When graphed on linear–linear axes, exponential rates are curvilinear and on semilogarithmic axes, they produce a straight line.

Half-Life

Half-life, the time for a drug concentration to decrease by one half, is a familiar exponential term used to describe the kinetics of many drugs. Half-life is a first-order kinetic process, because the same proportion or fraction of the drug is removed during equal periods of time. As described earlier, the greater the starting concentration, the greater the amount of drug removed during each half-life.

Half-life can be determined by several methods. If concentration is converted to the natural logarithm of concentration and graphed versus time, as described in Equation 2, the slope of this graph is the elimination rate constant, k. For both accuracy and precision, at least three concentration-time points should be used to determine the slope, and they should be obtained over an interval during which the concentration decreases at least in half. In clinical practice, for infants and small children, however, k is often estimated from just two concentrations obtained during the terminal elimination phase. With multiple data points, the slope of ln C versus time may be calculated easily by least squares linear regression analysis. Half-life (T_1/2) may be calculated from the elimination rate constant, k (time⁻¹), as follows:

(Eq. 3)

Graphic techniques may be used to determine half-life from a series of timed measurements of drug concentration. The concentration-time points should be graphed on semilogarithmic axes and used to determine the best fitting line either visually or by linear regression analysis. This approach is illustrated in Figure 6-1, in which the best-fitting line has been drawn to the concentration-points and crosses a concentration of 20 μg/mL at 100 minutes and a concentration of 10 μg/mL at 200 minutes. The concentration has decreased by one half in 100 minutes, so the half-life is 100 minutes. The elimination rate constant is (0.693/100) min⁻¹ or 0.00693 min⁻¹.

FIGURE 6-1 Graphic determination of half-life. Half-life can be determined from a series of concentration time-points on a semilogarithmic graph, if the kinetics are first-order exponential. The concentrations are plotted on semilogarithmic axes; the best-fit line is drawn to the points; convenient concentrations are chosen that decrease in half, such as 20 μg/mL and 10 μg/mL, as illustrated; and the interval between those concentrations is the half-life, which is 100 minutes in the illustration.

Elimination half-life is of no value in characterizing disposition of many intravenous (IV) anesthetic drugs during dosing periods relevant to anesthesia. A more useful concept is that of the context-sensitive half-time (CSHT) where “context” refers to the duration of the infusion. This is the time required for the plasma drug concentration to decrease by 50% after terminating the infusion.³⁸ The CSHT is the same as the elimination half-life for a one-compartment model and does not change with the duration of the infusion. However, most drugs in anesthesia conform to multiple compartment models and the CSHTs are markedly different from their respective elimination half-lives.

CSHT may be independent of the duration of the infusion (e.g., remifentanil, 2.5 minutes); moderately affected (propofol, 12 minutes at 1 hour, 38 minutes at 8 hours); or display marked prolongation (e.g., fentanyl, 1 hour at 24 minutes, 8 hours at 280 minutes). This is a result of return of drug to plasma from peripheral compartments after stopping the infusion. Peripheral compartment sizes and clearances differ in children from adults and at termination of the infusion such that more or less drug remains in the body in children for any given plasma concentration compared with adults. The CSHT for propofol in children, for example, is greater than that in adults.³⁹ The CSHT gives insight into the PK of a drug, but the parameter may not be clinically relevant; the percentage decrease in concentration required for recovery from the drug effect is not necessarily 50%.

First-Order Single-Compartment Kinetics

The number of exponential equations required to describe the change in concentration determines the number of compartments. Although a drug may diffuse among several tissues and body fluids, its clearance often fits first-order, single-compartment kinetics if it quickly distributes homogeneously within the circulation and is removed rapidly from the circulation through metabolism or excretion. This may be judged visually, if a semilogarithmic graph of the change in drug concentration fits a single straight line. Kinetics may appear to be single-compartment, when they are really multiple compartments, if drug concentrations are not measured soon enough after IV administration to detect the initial distribution phase (α phase).

First-Order Multiple-Compartment Kinetics

If drug concentrations are measured several times within the first 15 to 30 minutes after IV administration as well as during a more prolonged period, more than one rate of clearance is often present. This can be observed as a marked change in slope of a semilogarithmic graph of concentration versus time (Fig. 6-2). The number and nature of the compartments required to describe the clearance of a drug do not necessarily represent specific body fluids or tissues. When two first-order exponential equations are required to describe the clearance of drug from the circulation, the kinetics are described as first-order, two-compartment (e.g., central and peripheral compartments) that fit the following equation (Fig. 6-2)³¹:

FIGURE 6-2 Two compartment kinetics in a semilogarithmic graph. The initial rapid decrease in serum concentration reflects distribution and elimination followed by a slower decrease because of elimination. A is the concentration at time 0 for the distribution rate. Subtraction of the initial decrease in concentration resulting from elimination, using the concentrations from the elimination line extrapolated back to time 0 at B, produces the lower line with a steep slope = α(distribution rate constant)/2.303. The terminal elimination phase has a slope = β(elimination rate constant)/2.303.

(Eq. 4)

where concentration is C, t is time after the dose, A is the concentration at time 0 for the distribution rate represented by the purple line graph with the steepest slope, α is the rate constant for distribution, B is the concentration at time 0 for the terminal elimination rate, and β is the rate constant for terminal elimination. Rate constants indicate the rates of change in concentration and each corresponds to the slope of the respective line divided by 2.303 for logarithm concentration versus time.

Such two-compartment or biphasic kinetics are frequently observed after IV administration of drugs that rapidly distribute out of the central compartment of the circulation to a peripheral compartment.³¹ In such situations, the initial rapid decrease in concentration is referred to as the α or distribution phase and represents distribution to the peripheral (tissue) compartments in addition to drug elimination. The terminal (β) phase begins after the inflection point in the line when elimination starts to account for most of the change in drug concentration. To determine the initial change in concentration as a result of distribution (Fig. 6-2), the change in concentration that results from elimination must be subtracted from the total change in concentration. The slope of the line representing the difference between these two rates is the rate constant for distribution.

These parameters (A, B, α, β) have little connection with underlying physiology and an alternative parameterization is to use a central volume and three rate constants (k₁₀, k₁₂, k₂₁) that describe drug distribution between compartments. Another common method is to use two volumes (central, V1; peripheral, V2) and two clearances (CL, Q). Q is the intercompartment clearance and the volume of distribution at steady state (Vdss) is the sum of V1 and V2. A more detailed mathematical discussion may be found elsewhere.^31,⁴⁰

Although many drugs demonstrate multiple-compartment kinetics, traditional studies of kinetics in neonates did not include enough samples immediately after dosing to determine more than one compartment. For clinical estimates of dose and dosing intervals, it is often not necessary to use multiple-compartment kinetics. To minimize cost, limit blood loss, and simplify PK calculations, dose adjustments are often based on only two plasma concentrations (peak and trough), and linear, single-compartment kinetics (such as that of gentamicin and vancomycin) is assumed. Because the elimination rate constant should be determined from the terminal elimination phase, it is important that peak concentrations of multiple-compartment drugs not be drawn prematurely, that is, during the initial distribution phase. If drawn too early, the concentrations will be greater than those during the terminal elimination phase (Fig. 6-2), which will overestimate the slope and the terminal elimination rate constant. Population modeling has improved analysis and interpretation of such data.^41,⁴²

Zero-Order Kinetics

The elimination of some drugs occurs with loss of a constant amount per time, rather than a constant fraction per time. Such rates are termed zero-order, and because e⁰ = 1, the change in the amount of drug in the body fits the following equation ⁴⁰:

(Eq. 5)

where dA is the change in the amount of drug in the body (in milligrams), dt is the change in time, and k₀ is the elimination rate constant with units of amount per unit time. After solving this equation, it has the following form:

(Eq. 6)

where A₀ is the initial amount of drug in the body and A is the amount of drug in the body (in milligrams) at time t.

Zero-order (also known as Michaelis-Menten) kinetics may be designated saturation kinetics, because such processes occur when excess amounts of drug saturate the capacity of metabolic enzymes or transport systems. In this situation, only a constant amount of drug is metabolized or transported per unit of time. If kinetics are zero order, a graph of serum concentration versus time is linear on linear-linear axes and is curved when graphed on linear-logarithmic (i.e., semilogarithmic) axes. Clinically, first-order elimination may become zero order after administration of excessive doses or prolonged infusions or during dysfunction of the organ of elimination. Certain drugs administered to neonates exhibit zero-order kinetics at therapeutic doses and may accumulate to excessive concentrations, including thiopental, theophylline, caffeine, diazepam, furosemide, and phenytoin.⁴³ Some drugs (e.g., phenytoin, ethyl alcohol) may exhibit mixed-order kinetics (i.e., first order at low concentrations and zero order after enzymes are saturated at higher concentrations). For these drugs, a small increment in dose may cause disproportionately large increments in serum concentrations (Fig. 6-3).

FIGURE 6-3 Transition from exponential to saturation kinetics. During every-6-hour dosing, concentrations during the first 24 hours reflect exponential kinetics with a half-life of 3 hours (k = 0.231/hr) followed by a change to saturation kinetics at 24 hours with elimination of 1 mg/hr, leading to drug accumulation to toxic concentrations.

Apparent Volume of Distribution

The apparent volume of distribution (Vd) is a mathematical term that relates the dose to the circulating concentration observed immediately after administration. It might be viewed as the volume of dilution that can be used to predict the change in concentration after a dose is diluted within the body (i.e., a scaling factor). Vd does not necessarily correspond to a physiologic body fluid or tissue volume, hence the designation “apparent.” For drugs that distribute out of the circulation or bind to tissues, such as digoxin, Vd may reach 10 L/kg, a physical impossibility for a fluid compartment in the body. This illustrates the mathematical nature of Vd. The units used to express concentration are amount per unit volume, and it may help to remind the reader of the following equation that expresses the relation between dose in amount per kilogram and the Vd in volume per kilogram that dilutes the dose to produce the concentration:

(Eq. 7)

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.

(Eq. 8)

The concentration after a drug infusion, C (postdose), must be measured after the distribution phase to avoid overestimating the peak concentration that would, in turn, lead to an erroneously low Vd. For the first dose, the predose concentration is 0.

Pharmacokinetic Example

The following example illustrates the application of these PK principles using a four-step approach: (1) calculate Vd; (2) calculate half-life; (3) calculate a new dose and dosing interval based on a desired peak and trough; and (4) check the peak and trough of the new dosage regimen.

For example, vancomycin was administered in a dose of 15 mg/kg IV over 60 minutes every 12 hours. The following plasma concentrations were measured on the third day of treatment (presumed steady-state). The predose or trough concentration was 12 mg/L; the peak concentration, measured 60 minutes after the end of the infusion, was 32 mg/L.

Step 1: Substituting the data into Equation 8, we calculate Vd.

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.

(Eq. 9)

The current dose produces a peak of 32 mg/L that is in the recommended therapeutic range, and lengthening the dosing interval to 2 half-lives ( hours) after the peak is reached (2 hours after beginning the dose infusion) will produce a trough concentration of 8 mg/L. The dose interval should be increased to 16 hours and the dose increased to 18 mg/kg.

Step 4: Estimating peak and trough concentrations with the new regimen provides a good double check against a mathematical error. Sixteen hours after the 15 mg/kg dose is administered (or approximately 2 half-lives after the measured peak), the trough should be approximately 8 mg/L. At this time, administration of 18 mg/kg will raise the concentration by 24 mg/L (assuming a Vd of 0.75 L/kg) to a peak concentration of 32 mg/L.

Repetitive Dosing and Drug Accumulation

When multiple doses are administered, the dose is usually repeated before complete elimination of the previous one. In this situation, peak and trough concentrations increase until a steady-state concentration (C_ss) is reached (Fig. 6-3). The average C_ss (AvgC_ss) can be calculated as follows³²:

(Eq. 10)

(Eq. 11)

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 C_ss is directly proportional to the ratio of T_1/2/τ and D.³²

Steady State

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.

Loading Dose

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 (T_1/2keo). 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)

where C₀ is the theoretical plasma concentration at t = 0 after the bolus dose, and Cpeak is the predicted effect-site concentration at the time of peak effect-site concentration. Loading dose (LD) can then be calculated as

(Eq. 13)

Population Modeling

Pediatric anesthesiologists have embraced the population approach for investigating PK and PD. This approach, achieved through nonlinear mixed effects models, provides a means to study variability in drug responses among individuals representative of those in whom the drug will be used clinically. Traditional approaches to interpretation of time-concentration profiles relied on “rich” data from a small group of subjects. In contrast, mixed effects models can be used to analyze “sparse” (2 to 3 samples) data from a large number of subjects. Sampling times are not crucial for population methods and can be fit around clinical procedures or outpatient appointments. Sampling time-bands rather than exact times is equally effective and allows flexibility in children.^45,⁴⁶ Interpretation of truncated individual sets of data or missing data is also possible with this type of analysis, rendering it particularly useful for pediatric studies. Population modeling also allows pooling of data across studies to provide a single robust PK analysis rather than comparing separate smaller studies that are complicated by different methods and analyses.

Mixed effects models are “mixed” because they describe the data using a mixture of fixed and random effects. Fixed effects predict the average influence of a covariate, such as weight, as an explanation of some of the variability between subjects in a parameter like clearance. Random effects describe the remaining variability between subjects that are not predictable from the fixed effect average. Explanatory covariates (e.g., age, size, renal function, sex, temperature) can be introduced that explain the predictable part of the between-individual variability. Nonlinear regression is performed by an iterative process to find the curve of best fit.^47,⁴⁸

Pediatric Pharmacokinetic Considerations

Growth and development are two major aspects of children not readily apparent in adults. How these factors interact is not necessarily easy to determine from observations because they are quite highly correlated. Drug clearance, for example, may increase with weight, height, age, body surface area, and creatinine clearance. One approach is to standardize for size before incorporating a factor for maturation.⁴⁹

Size

Clearance in children 1 to 2 years of age, expressed as L/hr/kg, is commonly greater than that observed in older children and adolescents. This is a size effect and is not because of bigger livers or increased hepatic blood flow in that subpopulation. This “artifact of size” disappears when allometric scaling is used. Allometry is a term used to describe the nonlinear relationship between size and function. This nonlinear relationship is expressed as

(Eq. 14)

where y is the variable of interest (e.g., basal metabolic rate [BMR]), a is a scaling parameter and PWR is the allometric exponent. The value of PWR has been the subject of much debate. BMR is the commonest variable investigated and camps advocating for a PWR value of (i.e., body surface area) are at odds with those advocating a value of .

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 (T_1/2 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.

FIGURE 6-4 The clearance (CL) maturation profile of dexmedetomidine, expressed using the per-kilogram model and the allometric -power model. This maturation pattern is typical of many drugs cleared by the liver or kidneys.

(Data extracted from Potts AL, Anderson BJ, Warman GR, et al. Dexmedetomidine pharmacokinetics in pediatric intensive care—a pooled analysis. Pediatr Anesth 2009;19:1119-29.)

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,⁵⁷^–⁵⁹ 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).

Pharmacokinetic parameters (P) can be described in an individual as the product of size (Fsize), maturation (MF) and organ function (OF) influences, where Pstd is the parameter value in a standard size adult without pathologic changes in organ function ⁴⁹:

(Eq. 17)

Pharmacodynamic Models

Pharmacokinetics is what the body does to the drug, while pharmacodynamics is what the drug does to the body. The precise boundary between these two processes is ill defined and often requires a link describing movement of drug from the plasma to the effect-site and its target. Drugs may exert effects at nonspecific membrane sites, by interference with transport mechanisms, by enzyme inhibition or induction, or by activation or inhibition of receptors.

Sigmoid Emax Model

The relation between drug concentration and effect may be described by the Hill equation or Emax model (see maturation model above)⁵⁶:

(Eq. 18)

where E0 is the baseline response, Emax is the maximum effect change, Ce is the concentration in the effect compartment, EC₅₀ is the concentration producing 50% Emax, and N is the Hill coefficient defining the steepness of the concentration-response curve (Fig. 6-5). Efficacy is the maximum response on a dose or concentration-response curve. EC₅₀ can be considered a measure of potency relative to another drug, provided N and Emax for the two drugs are the same. A concentration-response relationship for acetaminophen has been described using this model. An EC₅₀ of 9.8 mg/L, N = 1, and an Emax of 5.3 pain units (on a visual analog scale [VAS] of 0 to 10) was reported.⁶⁰ Midazolam PD in adults have been similarly defined using electroencephalographic (EEG) responses.^61,⁶²

FIGURE 6-5 The sigmoid Emax model is commonly used to describe the relationship between drug response and concentration. Changing the Hill coefficient (N) dramatically alters the shape of the curve.

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 Dixon ^63,⁶⁴ 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.”

Logistic Regression Model

When the pharmacologic effect is difficult to grade, then it may be useful to estimate the probability of achieving the effect as a function of plasma concentration. Effect measures, such as movement/no movement or rousable/nonrousable, are dichotomous. Logistic regression is commonly used to analyze such data and the interpolated EC₅₀ value refers to the probability of response. For example, an EC₅₀ of 0.52 mg/L for arousal after ketamine sedation in children has been estimated using this technique.⁶⁵

Linking Pharmacokinetics with Pharmacodynamics

A simple situation in which drug effect is directly related to concentration does not mean that drug effects parallel the time course of concentration. This occurs only when the concentration is low in relation to EC₅₀. In this situation the half-life of the drug may correlate closely with the half-life of drug effect. Observed effects may not be directly related to serum concentration. Many drugs have a short half-life but a long duration of effect. This may be attributable to induced physiologic changes (e.g., aspirin and platelet function) or may be a result of the shape of the Emax model. If the initial concentration is very high in relation to the EC₅₀, then drug concentrations five half-lives later, when we might expect a minimal concentration, may still exert considerable effect.

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 (T_1/2keo) 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

Adult T_1/2keo values are well described (e.g., morphine, 16 minutes; fentanyl, 5 minutes; alfentanil, 1 minute; propofol, 3 minutes). This T_1/2keo parameter is commonly incorporated into target controlled infusion pumps in order to achieve a rapid effect-site concentration. The adult midazolam T_1/2keo of 5 minutes may be prolonged in the elderly, resulting in overdose if this is not recognized during dose titration.⁶⁶

The T_1/2keo for propofol in children has been described. As expected, a shorter T_1/2keo 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).⁷¹^–⁷⁵ 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,^72,⁷⁵^–⁷⁷ 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.⁷⁸^–⁸⁰ 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 T_1/2keo (e.g., antiarrhythmic drugs; propafenone, verapamil).⁸¹

FIGURE 6-6 Changes in total serum protein and albumin values that occur with maturation. Note that total protein and albumin are less in fetuses than in neonates and less in neonates than in adults. The result may be altered pharmacokinetics and pharmacodynamics for drugs with a high degree of protein binding, because less drug is protein bound and more is available for clinical effect.

(Data from Ehrnebo M, Agurell S, Jalling B, et al. Age differences in drug binding by plasma proteins: studies on human foetuses, neonates and adults. Eur J Clin Pharmacol 1971;3:189-93.)

E-FIGURE 6-1 Altered protein binding may affect the clinical response to any medication; note the much lower protein binding of phenobarbital and penicillin in the neonate and fetus compared with the adult. This reduced protein binding may partially account for the prolonged pharmacologic effects of barbiturates in neonates, because more unbound drug is able to be pharmacologically active.

(Data from Ehrnebo M, Agurell S, Jalling B, et al. Age differences in drug binding by plasma proteins: studies on human foetuses, neonates and adults. Eur J Clin Pharmacol 1971;3:189-93.)

E-FIGURE 6-2 Note that in the presence of hyperbilirubinemia, many drugs that are protein bound compete with bilirubin for binding sites, resulting in both elevated unbound bilirubin and unbound drug. This interaction may lead to an increased propensity for the development of kernicterus as well as more drug available for clinical effect. This effect is particularly important for drugs that normally are highly protein bound (e.g., phenytoin) but would be of minimal importance for drugs that have low protein binding (e.g., ampicillin).

(Data from Ehrnebo M, Agurell S, Jalling B, et al. Age differences in drug binding by plasma proteins: studies on human foetuses, neonates and adults. Eur J Clin Pharmacol 1971;3:189-93.)

Maturational changes in tissue binding also affect drug distribution. Myocardial digoxin concentrations in infants are 6-fold greater than those in adults, despite similar serum concentrations. Erythrocyte/plasma concentration ratios of digoxin in infants are one-third smaller during loading digitalization than during maintenance digoxin therapy. These findings are consistent with a greater Vd of digoxin in infants and may explain, in part, the unusually large therapeutic doses needed in infants.⁸²

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.⁸³^–⁸⁷ 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,^85,⁸⁸^–⁹¹ It is important to carefully titrate the doses of all medications that are administered to preterm and term infants to the desired response.

FIGURE 6-7 Changes in the intracellular and extracellular compartments that occur with maturation. Note the large proportion of extracellular water in preterm and term infants. This large water compartment creates an increased volume of distribution for highly water-soluble medications (e.g., succinylcholine, gentamicin) and may account for the large (by weight) loading dose required for some medications to achieve a satisfactory clinical response.

(Data from Friis-Hansen B. Body composition during growth: in-vivo measurements and biochemical data correlated to differential anatomical growth. Pediatrics 1971;47:264-74.)

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

FIGURE 6-8 Changes in body content for fat, muscle, and water that occur with maturation. Note the small percentage of fat and muscle mass in preterm and term infants. These factors may greatly influence the pharmacokinetics and pharmacodynamics of medications that redistribute into fat (e.g., barbiturates) and muscle (e.g., fentanyl) because there is less tissue mass into which the drug may redistribute.

(Data from Friis-Hansen B. Body composition during growth: in-vivo measurements and biochemical data correlated to differential anatomical growth. Pediatrics 1971;47:264-74.)

Absorption

Anesthetic drugs are mainly administered through the IV and inhalational routes, although premedication and postoperative pain relief is commonly administered enterally. Drug absorption after oral administration is slower in neonates than in children because of delayed gastric emptying (Fig. 6-9).

FIGURE 6-9 Simulated mean predicted time-concentration profiles for a term neonate, a 1-year-old infant, and a 5-year-old child given paracetamol elixir. The time to peak concentration is delayed in neonates because of slow gastric emptying and reduced clearance.

(Reproduced with permission from Anderson BJ, van Lingen RA, Hansen TG, Lin YC, Holford NH. Acetaminophen developmental pharmacokinetics in premature neonates and infants: a pooled population analysis. Anesthesiology 2002;96:1336-45.)

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

The larger relative skin surface area, increased cutaneous perfusion, and thinner stratum corneum in neonates increase systemic exposure of topical drugs (e.g., corticosteroids, local anesthetic creams, antiseptics). Neonates have a greater tendency to form methemoglobin because of reduced methemoglobin reductase activity compared with older children. Furthermore, fetal hemoglobin is more readily oxidized compared with adult hemoglobin. Combined with an increased transcutaneous absorption, these have resulted in reluctance to apply repeat topical local anesthetics, such as EMLA (lidocaine-prilocaine) cream, in this age group.⁹⁸ Similarly, cutaneous application of iodine antiseptics in neonates may result in transient hypothyroidism.

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,^87,⁹⁹^–¹⁰⁴ 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.¹⁰⁵^–¹⁰⁷ 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.¹¹¹^–¹¹⁸

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,^104,¹²¹^–¹²⁵ 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).

E-FIGURE 6-3 Effects of hepatic maturity on thiopental metabolism. Note the markedly prolonged β-elimination half-life for thiopental in neonates compared with children or adults. Also note that children have a shorter β-elimination half-life compared with adults. This effect may in part be related to immature hepatic metabolic pathways in the neonate; a similar effect is observed with most medications metabolized by the liver. This phenomenon may also reflect a smaller proportion of the cardiac output delivered to the liver of a neonate. In the child, this likely reflects a relatively large liver in proportion to body size and a greater proportion of the cardiac output delivered to the liver.

(Data from Christensen JH, Andreasen F, Jansen JA. Pharmacokinetics of thiopental in caesarian section. Acta Anaesthesiol Scand 1981;25:174-9; Ghoneim MM, Van Hamme MJ. Pharmacokinetics of thiopentone: effects of enflurane and nitrous oxide anaesthesia and surgery. Br J Anaesth 1978;50:1237-42; and Sorbo S, Hudson RJ, Loomis JC. The pharmacokinetics of thiopental in pediatric surgical patients. Anesthesiology 1984;61:666-70.)

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.¹²⁹^–¹³¹ 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.¹³²^–¹³⁶ 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.

TABLE 6-1 Developmental Patterns and Activities for Important Cytochrome P-450 Enzymes (Phase I Reactions) in the Neonate

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,^131,¹⁴²^–¹⁴⁴ 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