Review article Pediatric models for adult target-controlled infusion pumps

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1 Pediatric Anesthesia : doi: /j x Review article Pediatric models for adult target-controlled infusion pumps BRIAN J. ANDERSON PhD FANZCA FJFICM Department of Anaesthesiology, University of Auckland, Auckland, New Zealand Summary Target-controlled infusion (TCI) pumps currently do not satisfactorily cater for the pediatric population, particularly for those under 5 years. Growth and development are two major aspects of children not readily apparent in adults, and these two aspects influence clearance (CL) and volume of distribution (V). In simple terms, V determines initial dose, and CL determines infusion rate at steady state. Three major covariates (size, age, and organ function) contribute to parameter variability in children. Size can be standardized for clearance in a 70-kg person using the allometric ¾ power model. Remifentanil, a drug cleared by hydrolysis, can be modeled in all age groups by simple application of this model using a standardized clearance of 2790 mlæmin )1 for a 70-kg person. Allometry alone is insufficient to predict clearance in neonates and infants from adult parameters for most drugs used in anesthesia. The addition of a model describing maturation is required. The sigmoid Emax or Hill model has been found useful for describing this maturation process. Propofol maturation has been described with a mature clearance of 1.83 læmin )1 Æ70kg )1, a maturation half-time (TM 50 ) of 44 weeks and a Hill coefficient of 4.9. Organ function also affects clearance, and propofol clearance is reduced in neonates and infants after cardiac surgery. Although pharmacokinetics (PK) in children is receiving increasing attention and is eminently programmable into a TCI device, pharmacodynamic (PD) measures in children remain poorly defined, partly because the depth of anesthesia monitoring are inadequate. Both PK and PD are necessary for safe use of TCI pumps. Keywords: modeling; anesthesia; pharmacokinetics; pharmacodynamics; target concentration; pediatrics Introduction Correspondence to: Assoc Prof Brian Anderson, C - PICU, Auckland Children s Hospital, Park Road, Auckland, New Zealand ( briana@adhb.govt.nz). Propofol and remifentanil are two drugs that are gaining increasing use for intravenous anesthesia in children. Infusion devices that deliver a constant infusion are unable to maintain a steady-state Ó 2009 Blackwell Publishing Ltd 223

2 224 B.J. ANDERSON plasma concentration, because many of the drugs commonly used in anesthesia are described using multiple mamillary compartment models. Redistribution of drug from the central to peripheral compartments does not allow a propofol target concentration of 3 mcgæml )1 to be maintained by a fixed infusion rate, at least during early infusion. A simple manual infusion regimen consisting a bolus 1 mgækg )1 followed by an infusion of 10 mgækg )1 Æh )1 (0 10 min), 8 mgækg )1 Æh )1 (10 20 min), and 6 mgækg )1 Æh )1 thereafter was suggested (the rule ) for adults to maintain this steady-state target concentration (1). Extrapolation of this rule to children was unsuitable because of pediatric pharmacokinetics (PK) differences, but alternative rules for children have been calculated (2,3). Computerized pumps, known as target-controlled infusion (TCI) systems, have replaced manual systems and deliver drug at a rate that achieves and maintains the desired target concentration in either blood or effect site. A syringe pump, a computer with a serial communication port, and a computer program to control the pump are required. Infusion rate changes occur every 10 s compared to the 10 min used in the rule. These devices maintain a steady-state concentration that can then be altered according to the desired effect. There will be differences in the target concentration achieved between individuals because of unexplained pharmacokinetic variability. Even if these devices achieved the same target concentration in all individuals, there would be differences in response attributable to unexplained pharmacodynamic (PD) variability. TCI pumps do not cater for the pediatric population, particularly for those in infancy. Early investigations into propofol TCI device performance showed plasma concentrations in children of 1 12 years were less than that predicted by the adult delivery system algorithm based on a 3- compartment pharmacokinetic (PK) model (4). Adult parameter estimates required redefinition for target concentration prediction in children (4). Popular pediatric programs used for propofol infusion targeting either a plasma or an effect site concentration are based on data from Marsh (4) and Kataria (3). Unfortunately, these data sets only investigate PK in children out of infancy and do not provide a rate constant to link effect site compartment dynamics. Weight and size are the two major PK covariates in children. The use of weight as a covariate was noted to decrease PK variability in the analysis by Kataria (3) while age had little impact. In contrast to propofol where an attempt is often made to account for pediatric PK differences in adults, remifentanil is commonly used with PK parameter estimates derived from adults (5). The safety of this technique may be attributable to its unique short context-sensitive half-life and rapid clearance by plasma hydrolyses. Between patient variability There is a considerable variability in any measured plasma concentration when identical doses are given to individuals. Typical values for population PK parameter variability are 50% for compliance with medication regimens, 30% for absorption, 10% for tissue distribution, 50% for metabolic elimination, and 20% for renal elimination (6). The use of concentration rather than dose to link to effect allows PK variability to be separated from PD variability. The reduction in total variability produced by the removal of the PK component has been estimated to be 50% or greater. The contribution of PD variability because of the distribution from the blood to the site of action will depend largely on changes in perfusion of target tissue (5 60%). Receptor sensitivity variability (5 50%) and efficacy variability (30%) also exist. The observed response may not be a direct consequence of drug receptor binding, but rather through intermediate physiological mechanisms (e.g. antipyretics, angiotensin-converting enzyme inhibitors). A typical value for this variability is 30% (6). The introduction of covariate models to describe PK or PD reduces this variability. Most developmental PK, PD, and pharmacogenomic (PG) changes occur within the first year of life. Growth and development are two major aspects of children not readily apparent in adults, and these two aspects influence clearance (CL) and volume of distribution (V). In simple terms for a one-compartment model, V determines initial dose, and CL determines infusion rate at steady state.

3 MODELS FOR PEDIATRIC TCI 225 Pharmacokinetic covariate models Growth and development interact in ways that are not necessarily easy to determine from observations, because they are quite highly correlated. Drug elimination clearance, for example, may increase with weight, height, age, body surface area, and creatinine clearance (7). Tod has identified three major covariates (size, age, organ function) for pediatric PK and suggested standardization for size before incorporating factors for maturation and organ function (8). These three covariates can be explained by mathematical equations that can be incorporated into electronic infusion pumps. Size Size is usually defined in terms of weight, and we refer to clearance typically as lækg )1. Infusion regimens for TCI are usually referenced as mgækg )1 Æh )1. This reference system, while quite adequate, can lead to confusion when interpreting dose or clearance. Morphine infusion dose, for example, that achieves a target concentration of 10 mgæl )1 is highest in infants (Table 1) (9). Infusion rate at each age is based on clearance for that age. Clearance changes with age. The clearance of paracetamol, a drug that, like morphine, is metabolized by glucuronide conjugation shows a similar trend (Figure 1). Clearance might be expected to be reduced in infants because of immaturity of conjugating systems, but why should clearance in a 4-month infant be the same as a teenager with mature clearance? Explanations for the increased clearance in a 1-year-old have been attributable to the increased relative liver size (10,11), but an alternative explanation is the method of scaling. The per kilogram model may Table 1 Morphine infusion rate required to achieve a target plasma concentration of 10 mgæl )1. The highest rate occurs at 1 year of age Age Infusion rate (mcgækg )1 Æh )1 ) Birth 5 1 month months year 18 2 years 16 5 years years 11 Clearance (l h 1 kg 1 ) Term neonate 0.14 l h 1 kg 1 1 year l h 1 kg 4 months 16 years 0.24 l h 1 kg l h 1 kg Postmenstrual age (weeks) Figure 1 The maturation profile of paracetamol expressed using the per kilogram model. We might expect clearance to be reduced in the neonate because glucuronide conjugation is immature. The observation that clearance in a 4-month-child is similar to that in a 16-year-old teenager is unexpected. Clearance is maximal at the age of 1 year. muddy understanding of clearance development. Alternative scaling systems allow mechanistic approach to clearance maturation (12,13). Allometry is a term used to describe the nonlinear relationship between size and function. This nonlinear relationship is expressed as y ¼ a BodyMass PWR where y is the variable of interest [e.g. basal metabolic rate (BMR)], a is the allometric coefficient, 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 2 3 (i.e. body surface area) are at odds with those advocating a value of ¾. While body surface area is reasonably satisfactory in humans out of infancy, the ¾ exponent has wider applicability. In all species studied, including humans, the log of BMR plotted against the log of body weight produces a straight line with a slope of ¾. Fractal geometry is used to mathematically explain this phenomenon (14). The ¾ 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. A great many physiological, structural, and time-related variables scale predictably within and between species with weight (W) exponents (PWR) of 3 4, 1 and 1 4 respectively (12). These exponents have applicability to pharmacokinetic parameters such as CL, volume (V), and

4 226 B.J. ANDERSON half-time (12). The factor for size (Fsize) for total drug clearance may be expected to scale to a 70-kg person with a power of ¾: F size ¼ W 3=4 = 70 Weight remains the commonest measure of size used. This measure may be inappropriate in the presence of obesity, and other measures of size such as lean body mass (15), fat free mass (16), or normal fat mass (17) may prove superior to weight. Lean body mass has proved a useful covariate for propofol clearance (15) while normal fat mass has been used to describe glomerular filtration rate (18). This latter mass descriptor acknowledges that fat is not an inert substance and may make a limited contribution to PK parameter estimates. Application to remifentanil Remifentanil can be modeled in all age groups by simple application of this allometric model (19). For a typical child who had undergone cardiac surgery with a body weight of 10.5 kg, clearance was 68.3 mlækg )1 Æmin )1, intercompartmental clearance (Q) was 80 mlækg )1 Æmin )1, the central compartment volume (V1) was 91.7 mlækg )1, and the peripheral compartment volume (V2) was 141 mlækg )1. Owing to enhanced clearance rates, smaller (younger) children will require higher remifentanil infusion rates than larger (older) children and adults to achieve equivalent blood concentrations. Standardized clearance was 2790 mlæmin )1 Æ70 kg )1, similar to that reported by others in children (20,21) and adults (5,22). The effect of age on the dose of remifentanil tolerated during spontaneous ventilation under anesthesia has been investigated in children undergoing strabismus surgery (n = 45, age 6 months 9 years). The propofol infusion was titrated using state entropy as a PD endpoint and remifentanil infused, using a modified up-and-down method, with respiratory rate depression as a PD endpoint. A respiratory rate of just greater than 10, stable for 10 min, determined the final remifentanil infusion rate (23). This influence of age on the remifentanil infusion requirement is shown in Figure 2. Superimposed on this figure are clearance estimates for age using an allometric model with a standardized clearance of 2790 mlæmin )1 for a 70-kg person. Clearance mirrors infusion rate in children over the age of 1 year. There is a divergence between clearance estimate and infusion rate in those children in infancy. The higher infusion rates recorded in those infants can be attributed to greater suppression of respiratory drive in this age group than the older children during the study; a respiratory rate of 10 breaths per minute in an infant is disproportionately slow compared to the same rate in a 7-year-old child, suggesting excessive dose Remifentanil (mcg kg 1 min 1 ) Remifentanil clearance Clearance (ml min 1 kg 1 ) Age (months) Figure 2 The effect of age on the dose of remifentanil tolerated during spontaneous ventilation under anesthesia in children undergoing strabismus surgery.(23) Superimposed on this plot is estimated remifentanil clearance determined using an allometric model (19). There is a mismatch between clearance and infusion rate for those individuals still in infancy.

5 MODELS FOR PEDIATRIC TCI 227 Maturation Allometry alone is usually insufficient to predict clearance in neonates and infants from adult estimates for most drugs used in anesthesia (24,25). Allometry alone is satisfactory for remifentanil where clearance is determined by plasma esterases that appear mature at birth, but the addition of a model describing maturation is required for renal and hepatic clearance pathways. The sigmoid Emax or Hill model (26), well known to anesthesiologists through the oxygen dissociation curve, has been found useful for describing this maturation process (MF). MF ¼ PMA Hill TM Hill 50 þ PMA Hill The TM 50 describes the maturation half-time, while the Hill coefficient relates to the slope of this maturation profile. It is possible that there is asymmetry about the point of inflection, and the addition of an extra parameter describing this asymmetry can be used to provide extra flexibility for this empirical function (27). Maturation of clearance begins before birth, suggesting that postmenstrual age (PMA) would be a better predictor of drug elimination than postnatal age (PNA). The fetus is capable of metabolizing drugs. There are distinct patterns associated with isoform-specific developmental expression of the cytochrome P450 (CYP) enzymes. CYP2D6 has been detected in premature neonates as young as 25 weeks PMA (28). The fetus is capable of metabolizing morphine (hepatic enzyme uridine 5 diphosphate glucuronosyl transferase-2b7, UGT2B7) from 15 weeks gestation (29,30). The neonate can use sulfate conjugation as an alternative route for substrates such as morphine or paracetamol before glucuronidation matures. Neonates are not a homogenous population. Although the term encompasses those in their first 6 weeks of life, individual may range from those born very prematurely at 22 weeks PMA through to those born after term and aged 50 weeks PMA. There are vast differences in both weight and maturity of physiological processes determining pharmacology during this 28-week interval. Although PMA is commonly used to reference neonatal clearance development, PNA may also have an effect. The impact of PMA above that of PNA has been poorly studied to date. Application to propofol Propofol PK in children has been investigated in numerous publications (3,31,32) with different estimates in each study. Both the administration method (intravenous bolus or infusion) (15) and the collection of venous blood for assay rather than arterial blood will have influence on PK parameter estimates. Schuttler (33) pooled data from adults and children to investigate covariate effects using allometry. The allometric exponent for clearance was estimated as 0.75 (33). This pooled analysis did not include neonates or infants. A recent study has attempted to link neonatal data with those from children (34). That analysis suggested a more rapid maturation of propofol than that of morphine or paracetamol (35). Although glucuronidation is the major metabolic pathway of propofol metabolism and this pathway is immature in neonates, multiple CYP isoenzymes, including CYP2B6, CYP2C9, or CYP2A6, also contribute to its metabolism and cause a faster maturation profile than expected from glucuronide conjugation alone (36). An extension of that analysis is shown in Figure 3. Neonatal data (36) were combined with pediatric data (3,31) and CL (l min 1 70 kg 1 ) ? PNA effect Data lacking Post-menstrual age (weeks) Figure 3 Maturation of propofol clearance using an allometric ¾ size model and a sigmoid Emax maturation model. It is possible that postnatal age may have an effect above that attributable to PMA. Vital data from infants out of the neonatal period that could refine the maturation profile are missing. There is a slight decrease in clearance at old age.

6 228 B.J. ANDERSON adult data (37 39) ( Results are similar to those reported by Allegaert (34) with a mature clearance of 1.83 læmin )1 Æ70 kg )1, a TM 50 of 44 weeks, and a Hill coefficient of 4.9. It is possible that PNA may also have an additional effect on maturation of propofol clearance above that predicted by PMA (36). Figure 3 shows a group of neonates who are at or greater than 10-day PNA and have a clearance greater than the population mean. Further longitudinal data that examine individual neonates as they grow are required to clarify this aspect of maturation. In addition, there is a large area in this graph where data are missing; the infant group that lie between neonates and the 1-year-old child. This missing cohort requires investigation before the maturation profile can be fully elucidated. Organ function Changes associated with normal growth and development need to be explicitly distinguished from pathological changes describing organ function (OF) (8). The impact of reduced glomerular filtration rate on drugs excreted by the renal system is well recognized and commonly introduced into the equations calculating dose of such drugs (e.g. gentamicin). Temperature changes during cooling for head injury management or pediatric cardiac surgery are associated with reduced clearance while hyperthermia is associated with increased clearance. Morphine clearance was reduced in infants undergoing cardiac surgery compared with those undergoing noncardiac surgery (40), and clearance was lower in critically ill neonates than healthier cohorts (41 43). Preliminary exploration of propofol PK in neonates and children after cardiac surgery also suggests reduced clearance (44). A reduced metabolic clearance and increased peripheral distribution volume following surgery caused prolonged elimination. A follow-up pooled analysis of that authors pediatric intensive care patients (44) and from healthy children (45) as well as data from others (33) confirmed this reduced clearance. At its simplest, this factor for OF could be simply adding a scaling factor to the TCI pump e.g. reduce clearance by 26% in children immediately after cardiac surgery. Pharmacokinetic parameters (P) can be described in an individual as the product of factors for size (Fsize), maturation (MF), and OF influences where Pstd is the value in a standard size adult without pathological changes in OF (8): P ¼ P std F size MF OF Pharmacodynamic differences It has been claimed that children s responses to drugs have common receptor, cellular, and general physiological bases to adults, irrespective of age or stage of development (46). This may be true of children, but it is not the case for neonates where numerous well-reported differences exist. The minimal alveolar concentration (MAC) is commonly used to express anesthetic vapor potency. The MAC for almost all these vapors is less in neonates than in infants (47 49). The cause of these differences is uncertain. Changes in regional blood flow may influence the amount of drug going to the brain. Gamma-aminobutyric acid (GABA A ) receptor numbers or developmental shifts in the regulation of chloride transporters in the brain may change with age, altering response. Neonates have an increased sensitivity to the effects of neuromuscular blocking drugs (50). The reason for this is unknown, but it is consistent with the observation that there is a threefold reduction in the release of acetylcholine from the infant rat phrenic nerve (51,52). Cardiac calcium stores in the endoplasmic reticulum are reduced in the neonatal heart because of immaturity. Exogenous calcium has greater impact on contractility in this age group than in older children or adults. Amide local anesthetic agents induce shorter block duration and require a larger weight-scaled dose to achieve similar dermatomal levels when given by subarachnoid block to neonates. There is an age-dependent expression of intestinal motilin receptors and the modulation of antral contractions in neonates. Prokinetic agents may not be useful in very preterm infants, partially useful in older preterm infants, and useful in fullterm infants. Similarly, bronchodilators are ineffective because of the paucity of bronchial smooth muscle that can cause bronchospasm. Catecholamine release and response to vasoactive drugs vary with age. These PD differences are based in part upon developmental changes in myocardial

7 MODELS FOR PEDIATRIC TCI 229 structure, cardiac innervation, and adrenergic receptor function. For example, the immature myocardium has fewer contractile elements and therefore a decreased ability to increase contractility (53). A major problem is our inability to monitor anesthesia depth in neonates and children. This hinders the development of integrated PK PD models for drugs such as propofol. Investigations have suggested that current PD effect measures for depth of anesthesia monitoring are inadequate. The Bispectral Index (BIS) currently seems to be superior to the Narcotrend Index (NI), but age-related processing algorithms of the raw electroencephalogram (EEG) must be implemented in both BIS and NI in order to be useful in children younger than 5 years (54). BIS values were higher in children aged younger than 1 month than in children older than 6 months during natural sleep (55). During anesthesia, the EEG in infants is fundamentally different from the EEG in older children, there remains a need for specific infant-derived algorithms if EEG-derived anesthesia depth monitors are to be used in infants (56,57). The link between PK and PD A plasma concentration effect plot can form a hysteresis loop because of a delay in effect. Hull (58) and Sheiner (59) introduced the effect compartment concept for muscle relaxants. The effect compartment concentration is not the same as the blood or serum concentration and is not a real measurable concentration. It has negligible volume and contains negligible blood. A single first-order parameter (T 1 2 keo) describes the equilibration half-time between the central and effect compartments (Figure 4). We might anticipate that this delay is size dependent. An adult T 1 2 keo of 17 min is reported for morphine to equilibrate between plasma and brain (60), and we might expect this T 1 2 keo to be 8 min in a term neonate and 10 min in a 1-year-old infant. The concentration in the effect compartment is used to describe the concentration effect relationship, usually with the sigmoid Emax model. An accurate estimate of this delay is therefore a key issue for controlling depth of anesthesia in nonsteady-state conditions such as induction, titration to needs during maintenance of anesthesia or recovery (61). It allows TCI systems to directly target the effect site concentration and optimize drug delivery by achieving a chosen level of effect as fast as possible without overshoot (61). The T 1 2 keo for propofol in children has not been described. Minto proposed a novel way to get around this common difficulty in clinical pharmacology simulation and control problems, where there is usually a wide choice of pharmacokinetic models Drug in Peripheral V2 (L) Q (l min 1 ) K21 (min 1 ) Central V1 (L) K1e (min 1 ) Keo (min 1 ) Effect K12 (min 1 ) K10 (min 1 ) CL (l min 1 ) Figure 4 A diagram of a two-compartment mamillary model with an effect compartment. The central compartment has a volume V1, while that in the peripheral compartment is labeled V2. Rate constants describe drug transfer between the compartments (K12, K21) and loss from the central compartment (K10) per unit time. Alternatively, elimination from the central compartment can be described in terms of clearance and between compartment movement as Q. Because the volume of the effect compartment is so small, the rate constant K1e is inconsequential compared with Keo. Consequently, Keo alone influences the rate of equilibration between the central and effect compartments.

8 230 B.J. ANDERSON but only one or two published, linked PK PD models (61). The time course of propofol concentrations in the effect site as predicted by a linked PK PD model [the Schnider model (15,37)] was used to simulate a graph showing the time of peak concentration (Tpeak) in this effect site. Pediatric parameters from the Marsh model (4) were then used to estimate a T 1 2 keo (1.93 min) that would achieve the same Tpeak. The estimated T 1 2 keo is specific to the PK parameters used and cannot be indiscriminately applied to a different PK parameter set. Parameter estimates vary between investigators and predict different time-concentration profiles (62). In addition, Tpeak will be dependent on the rate at which drug is infused along with other hypnotic drug interactions and the effect desired (63,64). Anxiety and catecholamine release may further complicate this measure (64). 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 sigmoid Emax model. Integrated PK PD studies in children are lacking, partly because of a lack of consistent effect measures. The use of processed EEG signals may be associated with delay in signal processing. Clinical endpoints such as the blink reflex or arm movement are crude. The use of incorrect or poorly understood models can result in adverse effects e.g. awareness or hypotension. For example, we might expect a shorter T 1 2 keo with decreasing age, predictable through allometric scaling using an exponent of 1/4 for time related variables. This has recently been confirmed (65). This will result in excessive dose in a young child if the effect site is targeted and Tpeak is anticipated to be later than it actually is because it was determined in a teenager or an adult. Practices such as targeting the plasma concentration rather than the effect site concentration may avoid hypotension, but the sophistication of current TCI pumps could allow better control if they were programmed with improved information. Pharmacogenomics PGs is the development and discovery of new pharmacological agents based on genome information. This may influence either PK or PD. Pharmacogenetics is the genetically determined variability in metabolism of drugs. Genetic variability influencing plasma cholinesterase activity and its influence on succinylcholine is a well-known example. The impact PG will have on TCI is uncertain. The single nucleotide polymorphism A118G of the mu opioid receptor gene has been associated with decreased potency of opioids in carriers of the mutated G118 allele, necessitating a higher opioid dose in susceptible individuals (66). PK impact will be dependent on the rate of maturation of the specific enzyme system, contribution that enzyme has on total clearance or active metabolite production. Propofol is unlikely to be affected because it is cleared by multiple enzyme pathways. The nature of the CYP2D6 polymorphism (codeine, tramadol) can be related to an activity score, and differences can be observed as early as 45 weeks PMA (67). Clearance is reduced in the premature neonate, where CYP2D6 polymorphism has little impact (67). Bedside testing is possible and results easily programmable should PG become an important covariate. Conclusions Investigation into pediatric PK using models that describe size, maturation, and organ function influences is elucidating maturation changes in the first year of life, and mathematical functions describing these changes can be introduced into TCI pumps. The ability to monitor depth of consciousness in the very young and possible differences in interpretation of effect responses in the very young currently limit PD implementation. The use of PK covariate models will serve as a future guide to dose requirements. Children, as do adults, require an effect measure for depth of anesthesia to account for between-subject variability of both PK and PD parameters. There are an increasing number of sophisticated TCI pumps becoming available that should improve safety of the technique. Consideration should be given to standardization of infusion concentration used in these pumps throughout age groups to reduce human error. References 1 Roberts FL, Dixon J, Lewis GT et al. Induction and maintenance of propofol anaesthesia. A manual infusion scheme. Anaesthesia 1988; 43(Suppl.):

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