Key words: Anesthesia: pediatric. Neuromuscular relaxants: rocuronium. Pharmacokinetics: rocuronium.

ROCURONIUM, a new nondepolarizing muscle relaxant, has a rapid onset and an intermediate duration of action in infants, [1 ] children aged 1–5 yr, [2 ] and adults. [3 ] These characteristics suggest that rocuronium will be useful during clinical anesthesia for older children. Although the pharmacokinetic characteristics of rocuronium have been reported in adults and the elderly, similar data have not been reported in children. In the current study, we examine the pharmacokinetics of rocuronium in children aged 4–11 yr undergoing anesthesia with nitrous oxide and halothane.

After obtaining approval from the Institutional Review Board of the Baylor College of Medicine and the Texas Children's Hospital and written informed consent from parents, we studied 20 children aged 4–11 yr, with ASA physical status 1–2, undergoing elective surgery requiring tracheal intubation. Patients were excluded if they had metabolic disorders or neuromuscular disease or took medications known to alter neuromuscular function or cause histamine release. Two patients received midazolam; the remainder received no premedication. Anesthesia was induced with nitrous oxide and halothane (< 3% inspired concentration) and maintained with 70% nitrous oxide and less or equal to 1% inspired halothane. Some patients received morphine, fentanyl, or sufentanil intravenously or bupivacaine to provide regional analgesia before surgical incision. Ventilation was controlled to normocapnia, and body temperature was kept normal. Arterial blood pressure (oscillometry) and heart rate were monitored. Rocuronium (600 micro gram/kg) was given as a bolus into a rapidly flowing peripheral intravenous.

Five venous plasma samples (5 ml each) were obtained from each subject, one before administration of rocuronium (“blank” sample), and four at predetermined intervals after administration of rocuronium (Table 1). The first sample was obtained at 2, 6, 10, or 15 min after rocuronium administration; the second at 20, 30, 40, or 50 min; the third at 60, 75, 90, or 120 min; and the final at 150, 180, 210, or 240 min. No two subjects had identical sampling regimens.

Samples were iced immediately, then plasma was stored at -20 degrees Celsius until analysis. Plasma concentrations of rocuronium were measured using capillary gas chromatography with nitrogen phosphorous detection using ORG 9273 as the internal standard (Pharmaco LSR, Richmond, VA). The assay requires 1.0 ml plasma, is linear over a concentration range of 25–2,500 ng/ml (r²> 0.99), and is sensitive to 25 ng/ml with inter- and intraday coefficients of variation < 6%. Drugs commonly used during anesthesia do not interfere with the desired chromatographic peaks.

A population-based pharmacokinetic analysis was performed using the NONMEM statistical package.* The parameters for each two- compartment model were volume of the central compartment (V¹), volume of the second compartment (V²), clearance (Cl, elimination clearance equal to V¹*symbol* kappa¹⁰), and distribution clearance (Cl^distribution, equal to V¹*symbol* kappa¹²); volume of distribution at steady-state (V^ss) was equal to V¹plus V². Three-compartment models had an additional distribution clearance (equal to V¹*symbol* kappa¹³) and volume of the third compartment (V³).

The pharmacokinetic analysis was performed using two different approaches, mixed-effects modeling and naive pooled data analysis. The mixed-effects approach permits individuals to differ from each other as a function of random interindividual variability. Variability for clearance was modeled as:Equation 1where Cl is the value for an individual, Cl^typicalis the typical value for the population, and eta is a normally distributed variable with mean zero. Interindividual variation in the other structural pharmacokinetic parameters was modeled in a similar manner. Most models had four parameters for interindividual variability: for two compartment models, one for each of the clearances and volumes. For three compartment models, the two distributional clearances and the two noncentral compartments had the same interindividual variability. The post hoc step of NONMEM was used to determine eta values for each individual. i.e., to estimate the differences remaining between the pharmacokinetic valtics for each individual and a “typical” member of the population. Differences (residual errors) between the observed measurements of plasma concentration values and the predicted values were allowed to have two components, one proportional to the predicted plasma concentration (constant coefficient of variation) and a second that is constant. The naive pooled data approach differs from mixed-effects modeling by not accounting for random variability between individuals. This is accomplished by excluding the eta terms described for the mixed- effects approach.

The “goodness of fit” of each pharmacokinetic model was determined by several measures. First, the pattern of residual differences between measured concentrations and those predicted by the model was examined for systemic errors. Second, values of the objective function (equivalent to the residual sum of squares in a traditional pharmacokinetic analysis) were compared; a decrease of 7.6 (P < 0.01) was considered significant. For the mixed-effects approach, interindividual variability (the square root of the variance of eta) was examined: In that eta represents the remaining differences between the pharmacokinetic parameters of the individual and those of the “typical” member of the population, smaller interindividual variability suggests an improved model. In addition, values for eta were plotted against covariates (age, weight, height) and the lowess smoother, (a local nonlinear regression), was drawn. Systematic deviations of this smoother from a slope of zero suggested the need to incorporate additional covariates into the model.

The first model tested (the reduced model) was a two- compartment mamillary model in which all volumes and clearances were assumed to be the same for all subjects (e.g., not weight- proportional). The second model (the full model) was one in which each of the clearances and volumes included two components, a constant and a value proportional to a covariate (e.g., Cl = theta (1)+ theta (2)*symbol* weight). Each of the second models (i.e., one each for the covariates weight, height, and age) was compared to the reduced model. The third model tested was a three-compartment model. Additional models represented intermediate steps of the models described above.

“Typical” values for distribution and elimination half-lives (t^1/2alpha and t^1/2beta, respectively) for patients of representative weights were determined using standard formulas. [4 ].

Plasma samples to determine rocuronium concentrations were obtained at the predetermined times with three exceptions. In one subject (aged 5 yr), the 210-min sample was obtained at 180 min; in a second (aged 8 yr), the 10-min sample was obtained at 11 min; and in a third (aged 7 yr), the 210-min sample was obtained at 213 min. In two instances, the “blank” sample was reported as having a high concentration of rocuronium, and the initial postrocuronium sample was reported as showing no detectable rocuronium; we assumed that these samples were mislabeled. Two samples, both the terminal samples for the respective subjects, failed to detect rocuronium. Rather than omit these values from the analysis (thereby ignoring the valuable information that these concentrations were less than the limit of detection of the assay), these samples were assigned the concentration value zero.

Using the mixed-effects approach, the reduced two- compartment model in which all volumes and clearances were equal for all subjects (not a function of the covariates) suggested an influence of the covariates on (at least) clearance. Three full models were tested, one for each of the height, age, and weight covariates. Each of these showed an improved objective function compared to the reduced model; however, the objective function was better with the covariate weight than with either age or height (Table 2). A new two-compartment reduced model was tested in which all pharmakokinetic parameters were only weight-proportional. Although the objective function increased only 13 (insignificant in light of four fewer theta s), plots suggest a systematic error: eta for clearance against weight shows a significant downward slope (Figure 1). Another model in which clearance had both a constant and weight proportional component no longer suggested a systematic error. In addition, the objective function was similar to that for the full model, and interindividual variability was small. Two additional two-compartment models were tested. First, noting that interindividual variability for V¹approached zero, we tested a model with only three eta s; one for each of V², Cl, and Cl^distribution. Second, we tested a model with the parameters V¹and V^ss(instead of V¹and V²) and three eta s (one for each of V^ss, Cl, and Cl^distribution). Both of these models had the same value for the objective function as the model in which clearance has both a constant and weight-proportional component.

Three-compartment models demonstrated an improved objective function, but the appearance of the fits and residuals was not improved. In addition, values for eta (which were small for the optimal two- compartment model, ranging from 11% to 18%) increased markedly (to 14- 525%), suggesting that the three-compartmental model offers little advantage.

Thus, the final (“optimal”) model (Figure 2) had two compartments and the parameters V¹, V^ss, Cl, and Cl^distributionand allowed for interindividual variation in V^ss, Cl, and Cl^distribution. With this model, weight-normalized Cl decreased with increasing weight; weight-normalized Cl^distribution, V¹, and V^sswere constant (Table 3).

The results from the naive pooled approach were similar to those from the mixed-effects approach. Of the three full models, the objective function was better with the covariate weight than with either age or height (Table 2). A reduced two-compartment model with all pharmacokinetic parameters being only weight-proportional was tested: Its objective function increased 44. Another model in which clearance had both a constant and weight-proportional component no longer suggested a systematic error. In addition, the objective function was similar to that for the full model, and interindividual variability was small. With the three compartment model, neither the objective function nor the appearance of the fits and residuals was significantly improved compared to the two-compartment model. Thus, the final (“optimal”) model had two compartments and was identical to that determined from the mixed-effects approach except for the absence of interindividual variation in V^ss, Cl, and Cl^distribution.

With both the mixed-effects approach and naive pooled data analysis, distribution and elimination half-lives increased with weight (Table 4), a result of maturational changes in weight-normalized clearance in the absence of maturational changes in weight-normalized volume of distribution.

Our pharmacokinetic analysis suggests that rocuronium's weight- normalized Cl decreased with weight and therefore, presumably, with age. These values for weight normalized Cl in children can be compared to those for adults with normal hepatic and renal function given a single bolus dose of rocuronium during anesthesia with a potent inhaled anesthetic [5 ](isoflurane, in contrast to halothane in the current study), 2.89 plus/minus 0.25 ml *symbol* kg sup -1 *symbol* min sup -1 (mean plus/minus SE). Weight-normalized Cl is greater in children than in adults, similar to the finding for atracurium [6 ] but different from the findings for d-tubucurarine [7 ] and vecuronium. [8 ]Figure 3shows “typical” plasma concentration versus time curves for a 20-, 30-, or 50-kg child (other values are omitted for clarity); for comparison, “typical” values for an adult with normal renal and hepatic function are shown. [5 ] The greater weight-normalized Cl in smaller patients is associated with a more rapid decrease in the plasma concentration versus time. Assuming that the typical adult weighs more than 60 kg, this suggests that the physiologic changes of maturation continue into the adult period.

Volume of the central compartment in the current study is slightly larger than in adults [5 ] and exceeds the expected value of plasma volume. Exceeding plasma volume is likely the result of our obtaining relatively few early samples, such that any rapid decrease in plasma concentrations during the first minutes (which would reflect a higher initial concentration and a lower V¹) might be missed. In addition, samples are venous rather than arterial: In that the difference between venous and arterial samples is greatest immediately after drug administration, projected concentrations at time 0 will be underpredicted and V¹overestimated. That the value is larger in these children compared to adults is likely the result of the larger plasma volume in children. V^ssin the current study is similar to that in adults. [5 ] This is expected because muscle relaxants, being polar, distribute to extracellular fluid, a physiologic parameter whose volume changes little beyond the first year of life. [9 ].

We do not report onset or duration of action of rocuronium nor did we perform a pharmacodynamic analysis of rocuronium, similar to those that have been performed for other nondepolarizing muscle relaxants in children. [6–8 ] Although twitch tension was measured in the current study, neither twitch tension nor anesthetic concentrations were stable for a sufficient period before rocuronium administration to permit such an analysis. Despite our lacking pharmacodynamic data, the results of the pharmacokinetic study should permit speculation regarding the implications of the current study. The maturational decrease in weight-normalized clearance and increase in elimination half-life should result in younger children requiring more frequent dosing and experiencing more rapid recovery from comparable degrees of paralysis compared to older children.

We obtained only five plasma rocuronium samples per subject (including a “blank” sample before rocuronium administration), a result of ethical limitations on the amount of blood that can be sampled from pediatric patients. The small number of samples obtained from each subject would have prevented us from determining the pharmacokinetics of rocuronium in each individual subject. Similar to the manner in which Kataria et al. [10 ] determined the pharmacokinetics of propoful in pediatric patients, we used two population-based approaches designed to work with small numbers of samples per individual to determine the pharmacokinetics of rocuronium in children. As did Kataria et al., we ensured that our sampling regimen was balanced (identical numbers of samples were obtained from each subject, and the timing of samples was not influenced by covariates). [11 ] Therefore, despite the small number of samples per individual, we were able to determine the pharmacokinetic parameters in this sample and to identify the influence of weight on one parameter, clearance.

We determined rocuronium's pharmacokinetics using two different population approaches, mixed-effects modeling and the naive pooled data approach. As with Kataria et al., we found similar results using the two modeling approaches. Although recent investigations have suggested certain situations in which the mixed-effects approach method provides biased pharmacokinetic estimates, such bias has been demonstrated only when large numbers of samples are obtained from each individual.** In contrast, the current study and that of Kataria et al. demonstrate little difference in the pharmacokinetic parameters between the two approaches. Each of these two approaches offers an advantage. The naive pooled approach is mathematically less cumbersome and can be implemented with various software programs Mixed-effects modeling estimates variability of the pharmacokinetic parameters, a feature not available with the naive pooled approach.

In summary, in children aged 4–11 yr anesthetized with nitrous oxide and halothane, rocuronium's weight-normalized plasma clearance decreases with weight, and there are no maturational changes in weight-normalized distributional clearance or volumes of distribution In turn, distribution and elimination half-lives increase with weight and, presumably, with age.

*Beal SL, Sheiner LB: NONMEM Users Guides. San Francisco. NONMEM Project Group, University of California, San Francisco, 1992.

**Youngs E, Sharer S: Personal communication 1995.