The Pharmacokinetics of Milrinone in Pediatric Patients after Cardiac Surgery 

The study protocol was approved by the Human Investigations Committee of Emory University School of Medicine. After we obtained informed parental consent, we evaluated 20 children after they underwent primary surgical repair of congenital heart defects. Table 1shows the patient demographics.

Patients were evaluated after surgical repair of the presenting defect, separation from cardiopulmonary bypass, and administration of protamine. All patients were anesthetized with fentanyl (>50 [micro sign]g/kg) and midazolam (>0.1 mg/kg) after halothane inductions (if an intravenous catheter was available, anesthesia was induced with fentanyl and midazolam), supplemented with isoflurane during the period before cardiopulmonary bypass. No patient in the study had a residual systemic-pulmonary shunt as determined by either transesophageal echocardiography or by measurement of hemoglobin oxygen saturation of samples taken from the superior vena cava, right atrium, and pulmonary artery. After the surgical repair was completed, the patients were weaned from cardiopulmonary bypass using inotropes chosen at the discretion of the attending anesthesiologist. After hemodynamic and hemostatic stability was achieved after separation from cardiopulmonary bypass, a set of baseline hemodynamic measurements was recorded (heart rate and rhythm, systemic blood pressure, left atrial pressure, central venous pressure, and cardiac output). Cardiac output was measured by thermodilution using a 2.5-French thermistor placed in the main pulmonary artery by the surgical team and injection of 3 or 5 ml cold (4 [degree sign]C) saline into the distal port of a double-lumen central venous catheter placed via the right internal vein. A loading dose (50 [micro sign]g/kg) of milrinone was administered progressively in 5 min using an infusion pump. Left atrial pressure was kept constant during milrinone loading by administration of a 50:50 autologous blood-albumin mixture. Immediately after the loading-dose infusion was complete, an arterial sample was drawn to analyze the milrinone plasma concentration, and a second set of hemodynamic measurements was recorded. Hemodynamic variables before and after the loading dose were compared using paired t tests.

The original protocol stipulated that the 50 [micro sign]g/kg dose would be administered to 10 patients and a 50 [micro sign]g/kg loading dose plus a continuous infusion (via an infusion pump) of 0.5 [micro sign]g [middle dot] kg^-1[middle dot] min^-1would be given to another 10 patients. Two patients enrolled to receive only the 50 [micro sign]g/kg loading dose also received the 0.5 [micro sign]g [middle dot] kg^-1[middle dot] min^-1continuous infusion because the attending anesthesiologist deemed it clinically necessary. Finally, the infusion rate was increased to 0.7 [micro sign]g [middle dot] kg^-1[middle dot] min (^-1) before completion of the study for three patients at the request of the attending intensivist. For all patients, additional arterial samples were taken at 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 360, 600, and 960 min for analyses of milrinone plasma concentrations. All infusions were continued until we drew the last plasma sample, and then the infusion was discontinued at the discretion of the attending intensivist.

Milrinone plasma concentrations were measured by high-performance liquid chromatography as described in a previous study of adult patients from this laboratory [6]except that the sample size was 2 ml.

The pharmacokinetics of milrinone were analyzed using NONMEM, a nonlinear extended least-squares regression program that accounts for interpatient variability. [13]We used the first-order conditional estimation technique because we encountered systematic bias in our initial analysis using the more basic first-order method. Implementation of NONMEM for pharmacokinetic analysis requires a subroutine to predict drug plasma concentrations given pharmacokinetic parameters. We used NMVCLDRG, a Fortran program written and distributed by Dr. Steven Shafer of the Palo Alto Veteran's Medical Center and the Department of Anesthesiology of the Stanford University School of Medicine (available on the World Wide Web at http://pkpd.icon.palo-alto.med.va-.gov). We evaluated two- and three-compartment models, the parameters of which were compartment volumes (V1, V2, and V3), elimination, or metabolic clearance (Cl1) and intercompartment clearances from the central compartment of the second compartment (Cl2) and from the central compartment to the third compartment (Cl3). These parameters allow us to compare the results with those of our previous study of adult patients. NMVCLDRG assumes that the compartment volumes and clearances have a log-normal distribution; i.e., the parameter of individual I, Pⁱ, is equal to P^TVexp(Greek small letter eta]ⁱ) where [Greek small letter eta]ⁱis normally distributed around zero and P^TVis the typical value for the population. We also assumed that the pharmacokinetic parameters were not correlated. The effect of body mass on the pharmacokinetics of milrinone was evaluated by modeling each parameter as a linear function of either weight or body surface area; i.e., we considered models in which the clearances and volumes were assumed to be proportional to weight or body surface area. The effects of age and dopamine dose were initially considered by plotting the [Greek small letter eta] values for individual patients versus age. Values for [Greek small letter eta] are returned by the NONMEM post hoc step and represent the variation between the individual patient and the typical patient. Age and dopamine dose were evaluated more formally as covariates by assuming that each parameter is proportional to age or some power of age. These models were compared with a basic model in which it was assumed that the parameter was independent of age. The ability of our model to predict the observed data was measured in terms of performance error, defined as (C^measured- C^predicted)/C (^predicted). Values of the square root of the mean squared performance error and median absolute performance error were calculated for the final model. The optimal model was selected based on the objective function (-2 x logarithm of the likelihood of the results) and the median absolute performance error. [13,14] 

(Table 2) presents the hemodynamic effects of the 50-[micro sign]g/kg loading dose of milrinone. These are expressed as the mean percentage change in heart rate, mean blood pressure, left atrial pressure, central venous pressure, and cardiac index. Also shown are the standard errors of the means. This Table showsthat the 50-[micro sign]g/kg loading dose resulted in a 12% decrease in mean blood pressure (significant at the P < 0.05 level) and an 18% increase in cardiac output (significant at the P < 0.05 level). There were insignificant changes in heart rate, left atrial pressure (this was part of the study design), and central venous pressure. The mean milrinone plasma concentration when these hemodynamic effects were observed was 235 ng/ml (with a standard deviation of 104).

The basic three-compartment model, in which all volumes and clearances were equal for all patients (not a function of covariates), had a significantly lower (by 93 units) objective function than did the comparable two-compartment model. Modeling each parameter as a linear function of weight (P =[Greek small letter theta] x weight) improved the objective function of the three-compartment model by 300 units and decreased the median absolute performance error from 54.3% to 24.5%. After weight correction, the NONMEM post hoc step was used to generate values of [Greek small letter eta] for individual patients. Figure 1presents [Greek small letter eta] for Cl1 versus age. This Figure suggeststhat CL1 increases with age. Subsequently, we modeled weight-normalized CL1 as a linear function of age; i.e., we assumed that Cl1 =[Greek small letter theta](1)[middle dot] weight [middle dot](1 +[Greek small letter theta](2)[middle dot] age). This improved the objective function by an additional 44 units, with a decrease in median absolute performance error to 23.2%. Inclusion of body surface area or dopamine dose did not improve the objective function or the median absolute performance error compared with the model with all parameters normalized to weight and weight-normalized CL1, which is a linear function of age (our optimal model). Table 3shows model parameters and standard errors of the parameter estimates and estimates of interindividual variation. The parameters reported in Table 3correspond to a unit disposition function of C = 0.69 [middle dot] exp(-0.1352 [middle dot] t)+ 0.15 [middle dot] exp(-0.0161 [middle dot] t)+ 0.16 [middle dot] exp(-0.0016 [middle dot] t) for a patient with the median age (6.5 months) in this study. This Equation predictsthe concentration (normalized to unity at time zero) that would result from a instantaneous bolus dose.

The covariance matrix generated by NONMEM allows interindividual variation of parameter estimates to be determined, and these are shown in Table 3. The highest Interindividual variation (more than 100%) was observed for Cl3, whereas the lowest was close to zero (V2 and CL2), with intermediate values for the other parameters.

For the optimal model, the square root of the mean squared performance error was 42%, and the median absolute performance error was 23.2%. Figure 2shows the ratio of predicted to measured concentrations as a function of time. Figure 3is a plot of measured versus predicted concentration.

Our optimal pharmacokinetic model adjusted the compartment volumes and distribution clearances for weight and elimination clearance for weight and age. The most obvious difference we noted between the pharmacokinetics of pediatric and adult patients is the increase in elimination clearance with increasing age in the pediatric model. In general, we can expect that elimination clearance will be a function of body mass; i.e., it is intuitive that larger patients will clear more milrinone per unit of time than will smaller patients. However, after we included weight as a covariate, it appeared that elimination clearance also increased with increasing age (Figure 1). In our optimal model, weight-normalized elimination clearance was expressed as a linear function of age. The youngest patients in this study were aged 3 months. The predicted elimination clearance for these patients is 2.6 ml [middle dot] min^-1[middle dot] kg^-1. The oldest patient was aged 22 months, so the predicted elimination clearance is 5.6 ml [middle dot] min^-1[middle dot] kg^-1. Of course, it is important not to extrapolate this conclusion beyond the range of ages (3-22 months) and weights (3.2-12 kg) found in this study.

The elimination clearances predicted by our optimal model are slightly smaller than those reported by Ramamoorthy et al., [15]who report elimination clearances of 3.8 ml [middle dot] kg^-1[middle dot] min^-1for infants (younger than 1 yr) and 5.9 ml [middle dot] kg^-1[middle dot] min^-1for children (older than 1 yr). It is possible that the use of a two-compartment model by Ramamoorthy et al. led to a higher apparent elimination clearance than we found, with distribution processes contributing to the terminal phase of the biexponential unit disposition function of the two-compartment model. We found that a three compartment model significantly improved the log likelihood of the results compared with a two-compartment model. These authors predict a lower elimination clearance for infants than for children. Ramamoorthy et al. included age as a covariate in their analysis but concluded that because weight correlated highly with age in their study, deletion of age from the model did not alter the goodness of fit. The value of volume of distribution at steady state found by Ramamoorthy et al. was 900 ml/kg for infants and 700 ml/kg for children, which is comparable to the value of 851 ml/kg we found. Otherwise, it is difficult to compare the results of our study with theirs because they used a two-compartment model. The pharmacokinetic parameters reported in the current study should be considered with the realization that the need for inotropic support was not a criterion for entry into our study. If one accepts the premise that pharmacokinetics will be influenced by patient hemodynamics, then the kinetics of patients requiring inotropic support may differ from those of “healthy” patients.

A primary reason for pharmacokinetic analysis is determination of an effective dosing regimen. To accomplish this goal, a therapeutic plasma concentration must be identified. We found that administration of a 50-[micro sign]g/kg loading dose of milrinone progressively in 5 min resulted in a mean percentage increase in cardiac index of 18% and a mean percentage decrease in mean blood pressure of 12%. Changes in heart rate, central venous pressure, and left atrial pressure (by study design) were insignificant. From a clinical perspective, cardiac output probably cannot be measured to more than 15% accuracy. The 50-[micro sign]g/kg loading dose resulted in an increase in cardiac index in excess of this threshold and was associated with a mean peak plasma concentration of 235 ng/ml. The magnitude of therapeutic effect was probably underestimated in this study because the need for inotropic support was not an inclusion criterion. Studies of amrinone in children and of milrinone in adults suggest a greater therapeutic effect in patients who need inotropic support to maintain an adequate cardiac index. [9-11]Chang et al. [11]reported an average increase in cardiac index of 42.3% in neonates receiving a 50-[micro sign]g/kg loading dose progressively in 15 min. Using the pharmacokinetic parameters derived in this study, we estimate that this loading dose would have resulted in a mean peak plasma concentration of 140 ng/ml. The pharmacokinetics of milrinone may be somewhat different in neonates than in our study population. Nevertheless, the observation of statistically and clinically significant increases in cardiac index at a simulated plasma concentration of 140 ng/ml in the study by Chang et al. [11]and at an average measured concentration of 235 ng/ml in this study suggests that an approximate therapeutic target would be 200 ng/ml. In short, the 50-[micro sign]g/kg loading dose achieves the desired therapeutic effect (in this study and that of Chang et al.). If we accept the assumption that drug effect correlates with plasma concentration, then a reasonable goal for the dosing regimen would be to maintain the plasma levels achieved by this loading dose. However, our data were not adequate to provide a model of the entire concentration-effect relation. Thus, we cannot comment on the effects of lower or higher plasma concentrations. We also should emphasize that assuming that drug effect is proportional to plasma concentration is a major assumption. If there were significant plasma-"effect" site hysteresis, the 200 ng/ml target at steady state could be unnecessarily high. It is our clinical experience that the peak hemodynamic effects of milrinone are noted soon after bolus injection, and this is consistent with presumed effect sites (myocardium and vascular endothelium), which would equilibrate rapidly with plasma.

(Figure 4) shows the concentrations one would predict after a loading dose of 50 [micro sign]g/kg, given as a bolus dose, with the concomitant institution of an infusion of 0.7 [micro sign]g [middle dot] kg (^-1)[middle dot] min^-1to a 6.5-month-old infant (the median in this study). It can be seen that the loading dose of 50 [micro sign]g/kg produces therapeutic levels (> 200 ng/ml), but these levels decrease rapidly. Figure 5shows the levels predicted for a 50-[micro sign]g/kg loading dose followed by an infusion of 3.5 [micro sign]g [middle dot] kg^-1[middle dot] min (^-1), which is reduced at 30 min to 0.5 [micro sign]g [middle dot] kg^-1[middle dot] min^-1. This dosing regimen was derived from the parameters in Table 3using an approximate technique to maintain constant plasma concentrations [16]and consistently maintains therapeutic levels at more than 200 ng/ml. Thus, this dosing regimen is predicted to be effective for the median patient in our study. The kinetic parameters reported in Table 3may be used to derive dosing regimens for patients of other ages and weights. [16]Obviously, because there is significant inter-patient variability, dosing guidelines are only approximate. Because the parameters determining distribution kinetics are linear with weight, we can anticipate that a rational dosing regimen would consist of a 50-[micro sign]g/kg loading dose (because this results in a statistically and clinically significant increase in cardiac index) and a rapid infusion of approximately 3 [micro sign]g [middle dot] kg^-1[middle dot] min^-1for the first 30 min for all patients, to maintain the therapeutic levels achieved by the loading dose during drug redistribution. This should be followed by a maintenance infusion of approximately 0.5 [micro sign]g [middle dot] kg^-1[middle dot] min^-1, with the realization that elimination clearance, and thus the necessary maintenance infusion rate, may be lower in infants.

In conclusion, we have found that milrinone significantly increases the cardiac index in children after cardiac surgery in association with plasma levels of 235 ng/ml. The pharmacokinetics of milrinone in this patient population were best described by a three-compartment model with all parameters corrected for weight and with weight-normalized elimination clearance also proportional to age.