The most commonly used medications include propofol, remifentanil, alfentanil, and sufentanil; ketamine is occasionally used.¹⁵ Delivery can be by a manual infusion scheme (Table 7-1) or by using pharmacokinetic model–driven infusion devices with software developed specifically for use in children. Unfortunately, the commercially available software packages usually limit the applicable age from 1 to 3 years or older, or weight from 10 to 15 kg or greater, and the pharmacokinetic (PK) parameters are derived from studies of a relatively few healthy children. Propofol programs that allow for age-, weight-, and gender-related changes in central compartment volume, clearance, and distribution have been developed and perform well in healthy children.^16,¹⁷ However, there are considerable gaps in knowledge for some drugs, for ill children, and for young children, infants, and neonates, so caution is needed when applying such programs to these populations. Therefore, the anesthesiologist can use these preprogrammed devices as a basis for initiating a TIVA technique but must also use skill, knowledge, and experience to titrate the intravenous (IV) agents to avoid awareness, pain, and adverse effects.

TABLE 7-1 Manual Infusion Schemes

Principles

Healthy children often need a relatively high dose of IV agent per unit of body weight, and maintenance infusion rates need to be higher than the weight-corrected dose for adults.¹⁸ Conversely, the immature neonate, the critically ill child, or those with major organ failure need considerably smaller doses of IV anesthetic agents; care is particularly needed in children receiving vasoactive medication and those with congenital heart disease.¹⁹ Titration is advisable to allow for wide interindividual variation in PK and pharmacodynamics (PD). Electronic monitoring of depth of anesthesia (processed electroencephalography) has not been sufficiently well-validated in infants and children, and is yet to be used as the sole guide to dosing. After IV injection, it is assumed that the drug rapidly and evenly distributes throughout the body. However, the drug is delivered into the venous side of the systemic circulation, passes through the pulmonary circulation, and then distributes to the major organs and other tissues, all of which have variable blood flow, metabolic enzyme activity, and composition (in terms of proportions of fat and water). Because regional blood flow, body composition, and body proportions vary during development, the PK and PD of drugs are even more complex in children than in adults.

The apparent volume into which drugs distribute therefore varies among children, within the same individual at different stages of development, and among drugs. A drug that is very lipid soluble will have a very large volume of distribution (Vd), as will one that is highly bound to plasma proteins.

Elimination of medications and their metabolites commonly occurs by metabolism in the liver and subsequent excretion of water-soluble metabolites via the kidneys. Thus, conditions such as young age and hepatic and renal dysfunction, which are characterized by immature or reduced hepatic and renal functions, will attenuate the elimination of these medications. A measure of elimination of the medication is the clearance, which is the volume of blood from which the drug is eliminated per unit of time. Prolongation of the elimination of a drug reflects either an increase in the Vd or a reduction in clearance or both.

For a fixed infusion rate in a single compartment model, it takes five half-lives to reach a steady-state concentration (greater than 96% of the target) in the blood (Fig. 7-1). To more rapidly achieve steady-state conditions, a bolus dose or loading infusion may be administered. This rapidly fills the Vd, after which a new rate of infusion is calculated to maintain the blood concentration (Fig. 7-2). This is the dilemma of manual infusions; this loading dose has to pass the central volume and is usually so large that it will cause adverse effects, hemodynamic instability, and/or toxicity. Even a remifentanil bolus should be administered over several minutes to reduce the risk of bradycardia, hypotension, and/or difficult mask ventilation.

FIGURE 7-1 Fixed rate infusion of propofol at 10 mg/kg/hr with no bolus dose in a healthy 10-kg, 1-year-old infant. Steady state is not reached after 1 hour. There is a lag of effect-site concentration behind blood concentration both during infusion and after stopping infusion. Effect-site concentration reaches blood concentration at about 1 hour. Context-sensitive half-time is 9 minutes.

(Simulated using Tivatrainer. Available at www.eurosiva.org/TivaTrainer/tivatrainer_main.htm)

FIGURE 7-2 Manual infusion in a healthy 70-kg 40-year-old subject. Bolus dose was 1 mg/kg, then 10 mg/kg/hr for 10 minutes, 8 mg/kg/hr for 10 minutes, then 6 mg/kg/hr thereafter until 60 minutes, when infusion is discontinued. Maximum blood concentration is 4.5 µg/mL. Effect-site concentration reaches 3 µg/mL after around 10 minutes but drifts down to around 2.6 µg/mL and then very gradually rises. Context-sensitive half-time after 1 hour is 7 minutes.

(Data from the Diprifusor pharmacokinetic data set.)

To more clearly understand the disposition of drugs after an IV dose, it is useful to consider a three-compartment model. The drug is delivered and eliminated from a central compartment, V1 (which includes the blood), but also distributes to and redistributes from two peripheral compartments, one representing well-perfused organs and tissues (fast compartment, V2), and the other representing more poorly perfused tissues, such as fat (slow compartment, V3) (Table 7-2). The transfer of the drug between the central compartment (V1) and the two peripheral compartments (V2, V3), and also the elimination of the drug from the central compartment, is described by a series of clearances indicating the distribution back and forth between paired compartments, such as V1 to V2 and then V2 back to V1. The primary target organ that IV anesthetic agents affect is the brain. Therefore, an additional rate constant (keo) is added to describe the equilibration between the central compartment and the effect site in the brain. This compartment is not represented by a volume but rather by the time required to equilibrate. Consequently, there is a time lag before changes in the blood concentration are reflected in the effect site (see Figs. 7-1 and 7-2).

TABLE 7-2 Nomenclature for TCI Systems

Term	Meaning	Units
TCI	Target-controlled infusion
Vc or V1	Central compartment volume	L
V2	Fast compartment volume (vessel rich group) = V1 × k₁₂/k₂₁	L
V3	Slow compartment volume (vessel poor group) = V3 × k₁₃/k₃₁	L
CL1	Elimination clearance = V1 × k₁₀	L/hr
CL2 or Q2	Clearance between V1 and V2 = V2 × k₂₁	L/hr
CL3 or Q3	Clearance between V1 and V3 = V3 × k₃₁	L/hr
Cp	Blood concentration
Ce	Effect-site concentration
T	Target concentration
CALC	Concentration calculated by TCI software
MEAS	Concentration measured
k₁₀	Elimination rate constant	/min
keo	Rate constant for equilibration between blood and effect-site	/min
T_1/2keo	Half-time for equilibration between blood and effect-site	min
k₁₂, k₂₁	Rate constants for movement between V1 and V2	/min
k₁₃, k₃₁	Rate constants for movement between V1 and V3	/min

A hydraulic model is useful for understanding these concepts. The central compartment is connected to the peripheral compartments and effect site by a series of pipes of different diameters, and also to a drainage pipe to represent elimination (Fig. 7-3, A through F). The heights of the columns of fluid, which represent concentrations of drug, illustrate the gradient down which drug travels between the central and peripheral compartments, and this can be animated over time to show filling and emptying of compartments relative to each other. The diameter of the interconnecting pipes between the central and peripheral compartments represents the intercompartment clearances, and size of the drainage channel represents elimination. This hydraulic analogy is used in the Tivatrainer PK simulation program.²⁰

(Data from the Paedfusor pharmacokinetic data set.)

Fixed Infusion Rate and a Three-Compartment Model

When a fixed infusion rate is started (see Fig. 7-1), the blood concentration will increase but, almost simultaneously, distribution of drug to the fast compartment and elimination both begin. Distribution of drugs throughout the body contributes more to the removal of drug from blood than elimination for most medications. For remifentanil, extremely rapid esterase clearance dominates. As the concentrations within each compartment equilibrate, the concentration gradient between compartments lessens (slowing drug transfer between compartments) but distribution to the slow compartment continues along with elimination. The net effect is that the blood concentration continues to increase, albeit at a slower rate. As the blood concentration increases toward equilibrium, elimination becomes relatively more important; Figure 7-1 illustrates how far behind the effect-site concentration lags. Eventually, after several hours (or in some cases, days), a steady state is reached where infusion rate is directly proportional to clearance.

Bolus and Variable Rate Infusion in a Three-Compartment Model

A loading dose can start to fill the central compartment and ideally should be aiming to create an effect-site concentration at a specific target concentration without overshoot. Then the rate of infusion should decrease in a stepwise manner to maintain a constant effect-site concentration until a steady state is reached. As drug is delivered into the central compartment, it continuously distributes to the peripheral compartments while it is continuously eliminated. The infusion rate must vary because it has to match the changes in the contribution of distribution and elimination with time (Figs. 7-4 and 7-5). When the infusion is stopped, then elimination will continue to drain the central compartment, and drug will continue to distribute to V2 and V3 along concentration gradients from V1 for some time. Equilibrium may be reached, but the drug now begins to move back from the peripheral compartments into the central compartment, maintaining the central compartment drug concentration for a period of time. This can continue for a protracted interval, particularly for highly lipid-soluble drugs that have a very large slow compartment V3 and a reservoir or depot effect (see Fig. 7-3, F). Eventually the central compartment concentration will decrease. For most anesthetics, the longer the duration of an infusion, the more the drug has distributed into the peripheral compartments, and the larger the reservoir of drug to be redistributed back into the central compartment and eliminated, once the infusion ceases. The half-time of the decrease in drug concentration in blood, therefore, is related to the duration of the infusion for most drugs (except remifentanil [see later discussion]). This is termed the context-sensitive half-time (CSHT), where the context is the duration of the infusion and relates to a pseudo–steady-state maintained by a target-controlled infusion (see later discussion). For an individual drug in an individual patient, CSHT can be plotted against the duration of the infusion (Fig. 7-6, A and B). The CSHT graph will eventually become parallel to the time axis and this is when the pseudo–steady-state becomes a true steady-state. At that time, the infusion has become context insensitive

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