Population Pharmacokinetic Modeling in Very Premature Infants Receiving Midazolam during Mechanical Ventilation : Midazolam Neonatal Pharmacokinetics

The study was performed in the Neonatal Intensive Care Unit of the Mater Mothers' Hospital (Brisbane, Australia). Selection of the infants was dependent on one of the investigators obtaining informed parental consent. The study received previous written approval from the ethics committees of the Mater Mothers' Hospital and The University of Queensland. Mechanically ventilated, preterm infants with birth weights less than 1,500 g requiring midazolam for sedation were eligible for enrollment. The indication for sedation was determined according to the clinical opinion of the attending physician and nurse who were not otherwise associated with the study. Infants were ineligible if they were younger than 24 h of age, had cardiovascular instability (use of an inotrope or volume expander for blood pressure support in the previous 4 h) or neurologic instability (abnormal clinical signs, suspicion of seizure activity, abnormality on cranial ultrasonography), or had hepatic or renal dysfunction. Characteristics of the study infants are presented in Table 1.

Midazolam (HCl salt) was administered intravenously (100 [micro sign]g/kg) over 2 min as a single dose as a multiple doses every 4 - 6 h when necessary. The frequency of administration of midazolam was determined according to the clinical opinion of a physician and nurse who were not otherwise associated with the study.

Blood (0.25 ml) was collected via heel prick (arterial) or umbilical catheter (venous) as follows: one sample before administration of midazolam; three samples drawn randomly at predetermined times within each of the postdose intervals 5-15 min, 20-60 min, and 60-120 min; and one sample drawn randomly at a predetermined time after 2 h. Samples were collected either during the first dose interval or during subsequent intermittent administration. Sera were collected and stored at -75 [degree sign]C before analysis.

Midazolam was assayed by a published high-performance liquid chromatographic method. [16]Serum (100 [micro sign]l) was extracted with 10% vol/vol isopropyl alcohol in dichloromethane containing 25 ng/ml climazolam (internal standard) followed by back extraction into phosphoric acid (0.02 M). A mobile phase of acetonitrile:tetrahydrofuran:phosphate buffer (0.01 M, pH 6.7, 350:50:600 vol/vol/vol) was pumped at 1 ml/min through a C⁸Symmetry [trade mark sign](150 x 3.9-mm) column (Waters, Milford, MA). The eluent was monitored at 220 nm. Midazolam and climazolam were eluted at 7.4 and 8.4 min, respectively. Recoveries were more than 70%. Calibration plots in drug-free serum were linear (r > 0.999) from 12.5-800.0 ng/ml. Within-day and between-day imprecisions (percent coefficient of variation [CV%]) were 1.8-6.5% and 4.1-8.8%, respectively. Inaccuracy, defined as the difference between target and measured concentrations expressed as a percentage of target concentration, was 12.3% or less. The lowest quantifiable concentration was 12.5 ng/ml.

Fixed Effects. All modeling was performed with NONMEM (version 4.2)** using a two-compartment linear pharmacokinetic model. [11-13]The parameters of this model are the total systemic clearance (C1^T), intercompartmental clearance (Cl^Q), and volumes of distribution of the central (V¹) and peripheral (V²) compartments. Model building was conducted as described previously. [17-19]A baseline model (Cl^T=[small theta, Greek]¹; V¹=[small theta, Greek]²; Cl^Q=[small theta, Greek]³; V²=[small theta, Greek]⁴) was obtained using all 60 patients; then candidate covariates were screened statistically by adding these, in turn, according to a slope-intercept model (e.g., Cl^T=[small theta, Greek]¹+[small theta, Greek]²[middle dot] WT, where WT = total body weight) or using indicator variables (e.g., Cl^T=[small theta, Greek]¹[middle dot] GEN +[small theta, Greek]²[middle dot][1 - GEN], where GEN [gender]= 1 for male and 0 for female). Thus, for example, in the slope-intercept model, the typical Cl^Tin the population of infants might be described by a baseline component ([small theta, Greek]¹) plus the product of current weight (WT) multiplied by a coefficient ([small theta, Greek]²). The covariates screened were current weight, birth weight, birth of a single/multiple pregnancy, and sex of the infant. The difference in the objective function (OF; a NONMEM-calculated global goodness-of-fit indicator equal to -2 log likelihood value of the data) between a full:reduced pair (e.g., Cl^T=[small theta, Greek]¹+[small theta, Greek]²[middle dot] WT:Cl^T=[small theta, Greek]¹) approximates the [chi squared] value with one degree of freedom.** The level of significance ([small alpha, Greek]) was set to 0.01, which corresponds to a required change in the OF value of 6.6.** Changes in the OF value and plots of residuals and weighted residuals (weighted in NONMEM by the standard deviation) versus predicted concentration of midazolam in serum were recorded.

Random Effects. Deviations of Cl^Tj, V^1j, Cl^Qjand V (^2j) of the jth individual from the estimated population average values were estimated according to an exponential interpatient error model, [18]**Equation 1where PK^jis the required pharmacokinetic parameter in the jth infant, EXP is the exponentiation operator, and [Greek small letter eta]^j,PK is a random variable distributed with zero mean and variance [small omega, Greek]²PK about the average value (TVPK) in the population. NONMEM also estimates the residual variance among pairs of observed and model-predicted data. For pharmacokinetic data, these differences, [small epsilon, Greek]^ij, are attributable to intrapatient variability introduced, for example, in the timing of blood collections, dose times, drug assay, and by misspecification of the pharmacokinetic model. The following additive intrapatient error model was used:Equation 2where C^ijis the ith observed concentration for the jth individual, C^pred,ij is the concentration of midazolam in serum predicted by the pharmacokinetic model, and [small epsilon, Greek]^ij(the difference between C^ijand C^pred,ij) is a randomly distributed variable with zero mean and variance of [small sigma, Greek]². [20]**

Using the fixed and random effects parameter values of the final population model, Monte Carlo simulations were performed in NONMEM** to obtain the estimated concentrations of midazolam in serum that might be expected in 40 infants (in each of the two birth-weight categories) up to 132 h after the introduction of midazolam.

Unpaired t tests of boys versus girls and birth of a single-birth pregnancy versus a multiple-birth pregnancy were performed using birth weight as the dependent variable. The level of significance was 0.05. A normal probability plot for the analysis of weighted residuals was constructed. These statistical analyses were obtained using the STATISTICA software package (version 5.1H; StatSoft, Tulsa, OK).

A scatterplot of concentrations of midazolam in serum versus postdose sampling time is shown in Figure 1. There were 199 serum concentrations ranging from 0.0-583.0 ng/ml; the lowest quantifiable concentration was 19 ng/ml. The data also were fitted to a one-compartment model, but the results were inferior to the two-compartment model in that they showed larger errors of estimation of the parameters and lack of random scatter in the plots of residuals. The inclusion of a birth-weight category (> 1,000 g, <or= to 1,000 g) reduced the OF value by a significant amount ([chi squared]¹,0.01 > 6.6) for all kinetic parameters. Birth from a single-/multiple-birth pregnancy and male/female gender were identified as significant categoric factors modifying Cl^T. Table 2contains examples of factors that caused the largest decrease in the OF value of the baseline model. Attempts to combine the effect of each of these factors, in turn, into a combined model was unsuccessful. For example, incorporation of single-/multiple-birth pregnancy (model 3, Table 2) with gender (model 2, Table 2) resulted in an increase in the OF value of 490.

Plots of observed concentrations in serum versus predicted concentrations in serum and weighted residual versus predicted concentrations in serum are shown in Figure 2A and Figure 2B, respectively. The latter plot shows that most weighted residuals lay within two units of the zero ordinate of perfect agreement. Furthermore, the weighted residuals were normally distributed as shown by the linear normal probability plot (Figure 2C).

Summary results of the population pharmacokinetics of midazolam and the interpatient variability in the parameters are presented in Table 3. Infants with birth weights more than 1,000 g had average values of Cl^T, Cl^Q, V¹, and V²that were approximately 1.5- to 2.0-fold greater than for infants weighing 1,000 g or less at birth. The interpatient variability (CV%) for these four parameters was considerable and ranged from 43-193%(Table 3). The intrapatient SD was 5.4 ng/ml, which translates to CV% values of 28%, 4.5%, and 0.93%, respectively, at the lowest (19 ng/ml), arithmetic mean (121 ng/ml), and highest (583 ng/ml) concentrations of midazolam in serum measured. The uncertainty (CV%) in estimating each population parameter value was determined by expressing the standard error of estimation (calculated in NONMEM) as a percentage of the estimated value.** As expected for a population analysis, the fixed effects parameters ([small theta, Greek] values) were estimated with better precision (11.5-31.1%) than the random effects parameters ([small omega, Greek]²= 32.8-83.9%;[small sigma, Greek]²= 59.0%).

Plots of simulated concentrations of midazolam in serum generated for a 24-h loading dose infusion (0.025 mg/h), followed by a continuous infusion (0.0125 mg/h), are shown in Figure 3A (n = 40, birth weight <or= to 1,000 g) and 3B (n = 40, birth weight > 1,000 g).

Very premature infants frequently have a range of breathing disorders that require mechanical ventilation. To facilitate intubation, the sedating agent midazolam often is prescribed, and in the current study, we aimed to investigate the pharmacokinetic disposition of this drug in 60 ventilated infants weighing less than 1,500 g at birth. The limited amount of previous kinetic data in very premature infants is attributable largely to the fact that serious ethical and logistical restrictions apply to the rate and extent of blood sampling required by traditional study designs. Population-based methods, however, have the potential to circumvent these restrictions and provide a powerful means for studying drug disposition in patients who have been largely inaccessible for pharmacokinetic inquiry. [21] 

Despite the increasing use of midazolam in neonatal pharmacotherapy, only the recent study of Burtin et al. [13]used this potentially valuable approach to obtain pharmacokinetic data for midazolam in neonates. In that study, the Cl^Twas reported to be a complex, multiplicative function of birth weight, gestational age older than 39 weeks, coadministration of sympathomimetic amines, and coadministration of aminophylline, when V¹was proportional to birth weight. In contrast, we found that a satisfactory model based on a single categoric covariate, birth weight, gave stable estimates for the two-compartment kinetic parameters Cl (^T), V¹, Cl^Q, and V²together with small, normally distributed (weighted) residuals. The differences between our results and those of the study by Burtin et al. [13]may be attributable partly to the fact that most of the patients in the latter study were much less premature than ours, and it included term infants up to a birth weight of 5,200 g. Furthermore, the influence of coadministered drugs was not considered in the current study because of the large imbalance in the numbers of infants who were receiving other drugs.

Substitution of current body weight for birth weight gave OF values that were considerably higher than for the baseline model, indicating an inferior fit to the data (particularly in estimating V¹and V²). Moreover, the application of a slope-intercept model, Cl^T=[small theta, Greek]¹+[small theta, Greek]²[middle dot] BWT (where BWT = birth weight), produced rounding errors and substantially higher OF values compared with those obtained from the baseline model. This strongly suggested that the data did not support a model in which a component of the Cl^Tcould be identified that was independent of the degree of prematurity. More than one third of the 60 study infants were born of either twin (n = 15), triplet (n = 6), or quintuplet (n = 1) pregnancies. It is noteworthy that, of the covariates screened, the greatest change (-121) in the OF value resulted when the infants were subdivided on the basis of whether they were a child from a multiple-birth or a single-birth pregnancy. The population average Cl^Tof those born of a single-birth pregnancy was greater than that from multiple-birth pregnancies (1.03 ml/min vs. 0.783 ml/min, respectively). Initially, it was assumed that multiple-birth pregnancy could be acting as a surrogate marker for the degree of prematurity (viz. birth weight). Using an unpaired t test analysis, however, the mean +/− SD birth weight of infants born of a single-birth pregnancy (937 +/− 233 g) was statistically insignificant (P > 0.05) compared with that of infants born of a multiple-birth pregnancy (1,015 +/− 255 g).

The average population Cl^Tin boys (0.642 ml/min) was less than in girls (0.808 ml/min), but this also could not be explained by the degree of prematurity because the mean +/− SD birth weights of boys and girls were 989 +/− 220 g and 949 +/− 258 g, respectively (P > 0.05). It is difficult to account for this result in such premature infants on the basis of the gender-related difference in drug disposition reported in adults [2,22]; this aspect may need to be explored further in studies involving a larger population of premature infants.

The population mean Cl^Tof 0.938 ml [middle dot] min^-1[middle dot] kg^-1calculated over all patients was markedly lower than the average value of 12.0 ml [middle dot] min^-1[middle dot] kg^-1reported in children from 0.25-8.00 yr old [23]and in young, healthy adults (4.05-7.80 ml [middle dot] min^-1[middle dot] kg^-1). [2,24]This trend is almost certainly attributable to the markedly compromised hepatic and renal function in very premature neonates. [15]The total V (i.e., V¹+ V²) calculated over all patients averaged 1.15 l/kg, which agreed closely with the mean V of 1.10 l/kg in term and preterm infants [13]but which was smaller than the 1.3-2.0 l/kg determined in adults. [2]Exploration of interpatient variability is an important aspect of population modeling, and in this study we determined that infants varied considerably among each other regarding each of the pharmacokinetic parameters of midazolam. This finding agreed with the general conclusion of Burtin et al. [13]and is consistent with our own studies of the population pharmacokinetics of other drugs in very premature infants, including theophylline, [17]caffeine, [18]and amoxicillin. [19]Variation in Cl^Tis attributable to either variable hepatic or renal elimination, but, unlike the situation in adults, the renal clearance of midazolam in very premature infants probably makes a significant contribution to the variability in Cl^Tbecause of deficient hepatic mixed-function oxidase activity. [15]Furthermore, the glomerular filtration rate of unmetabolized drug in the premature newborn may be affected by hemodynamic instability [25]and several other factors, notably mechanical ventilation, [26]a procedure received by all infants in the current study. Unfortunately, the renal clearance of midazolam could not be measured because of logistical problems and concerns about the risk of infection with catheterization of the urinary tract.

In adults, concentrations in serum of approximately 50-300 ng/ml in healthy volunteers [27]and approximately 75-175 ng/ml in mechanically ventilated patients undergoing surgery [28]reportedly produce sedation (with arousability), whereas in children (aged 0.50-8.75 yr), sedation during artificial ventilation required 250-500 ng/ml. [4]Simulations obtained using the final population model parameter values indicated that an initial 24-h infusion of 0.025 mg/h followed by 0.0125 mg/h continuously up to 132 h theoretically should produce average steady state concentrations in serum of 265 ng/ml and 170 ng/ml in infants with birth weights of 500-1,000 g and 1,001-1,500 g, respectively. The interpatient variability in the population kinetic parameters was reflected in the considerable spread of the simulated concentrations in serum. Nonetheless, most infants should have concentrations between 50 ng/ml and 500 ng/ml within 6 h of starting the loading infusion, although we emphasize that the dose recommendations mentioned have not been tested prospectively. More studies using objective outcome measures are necessary to establish therapeutic windows for midazolam when prescribed alone or in combination with other drugs (e.g., fentanyl, morphine).

The results of this study confirm and extend the small amount of pharmacokinetic data of midazolam that exists for very premature neonates. Our results and those of Burtin et al. [13]established the feasibility of using a population approach in which only a limited amount of data is contributed by each patient, using a two-compartment population pharmacokinetic model in NONMEM. The Cl^T, Cl^Q, V¹, and V²values were lower in infants with birth weights of 500-1,000 g compared with those with birth weights of 1,001-1,500 g. There was marked interpatient variability in all pharmacokinetic parameters.

** Boeckmann A, Sheiner L, Beal S: Nonmem Users' Guide. San Francisco, NONMEM Project Group, 1992.