2.1 Study Design

This was a prospective, observational study conducted at Starship Children’s Hospital, Auckland, New Zealand, from August 2011 to October 2012. Patients aged between 1 day and 18 years old undergoing cardiac surgery supported by CPB and receiving milrinone after surgery were eligible for inclusion. Written informed consent was obtained from the parents or legal guardians for all children who participated in the study. Ethical approval for this study was given by the Health and Disability Ethics Committee, reference CEN/09/04/016 with locality approval from Auckland District Health Board, reference A+4373.

2.2 Drug Administration and Blood Sampling

Milrinone (Primacor, Sanofi-Aventis, Auckland, New Zealand) was prescribed at a dose rate between 0.25 and 1.25 µg/kg/min, administered intravenously and initiated after the end of the CPB procedure (but during surgery). The maintenance dose rate was titrated empirically depending on haemodynamic and clinical response. Serial blood samples (up to 1 mL) were taken from an indwelling catheter starting in the operating room after surgery and then in the Paediatric Intensive Care Unit. Sampling occurred around clinical care and after any dose changes. The median time for the first blood sample to be taken after milrinone initiation was 5.17 h (95%ile interval 39 min to 34 h). Whole blood samples were kept on ice and then transferred to the laboratory where they were centrifuged at 3000×g for 15 min. Separated plasma samples were stored at − 80 °C until analysis.

2.3 Bioanalysis

Quantitation of total milrinone in human plasma in the Starship Hospital Clinical Study was performed using liquid chromatography coupled mass spectrometry (LC-MS). The assay was linear across the concentration range of 5–500 µg/L and the inter-day assay variability of < 15% coefficient of variation across all quality controls. The patient samples were analysed in two batches (batch 1 and batch 2) and the lower limit of quantitation for both batches was 5 µg/L.

2.4 Pooled Data

Data from another published study was available to conduct a pooled pharmacokinetic analysis [5]. The Paradisis et al. [5] study was a prospective, open-labelled, dose-escalation study conducted in 29 very premature neonates (< 28 weeks postmenstrual age [PMA]) administered milrinone for prophylaxis of low systemic blood flow following birth. Patients received an infusion of either 0.25 µg/kg/min, 0.5 µg/kg/min or 0.75 µg/kg/min for 3 h followed by 0.2 µg/kg/min. Blood samples were taken during and after the milrinone infusion and stored at − 30 °C until analysis. Quantitation of total milrinone in human serum in the Paradisis et al. [5] study used high performance liquid chromatography with ultraviolet detection (HPLC-UV), based on an assay reported by Edelson et al. [14]. The assay was linear across the concentration range of 20–1500 µg/L and the inter-day assay variability was < 10% coefficient of variation across all quality controls. The lower limit of quantitation was 20 µg/L.

2.5 Pharmacokinetics Analysis

One- two- and three-compartment models were investigated to describe milrinone distribution. Population parameters were a priori scaled for size using theory-based allometry [15, 16]. Normal fat mass (NFM) was used as a measure of size [17] (Eq. 1).

$$_}}=}}_}}}_}}}\right)}^$$

(1)

$$}}_=}}_+F_}\times (}}_-}}_)$$

(2)

$$}}_}}=56.1+F_} \times (70-56.1)$$

(3)

NFMi (Eq. 2) is the individual NFM calculated from total body mass (TBM) and fat free mass (FFM) predicted from neonates to adults [18]. An additional parameter, Ffat, describes both the mass and body composition effects on PK parameters. NFMstd (Eq. 3) is the standard value for NFM which may be calculated for a male with a TBM of 70 kg, an FFM of 56.1 kg, a height of 1.76 m and the drug and parameter specific value of Ffat.

Maturation of elimination process occurs over the first 2 years of life and so a maturation model was used to describe changes in CL (Eq. 4). This model was included a priori during model development.

$$_}}=\frac}}}}_}\right)}^}$$

(4)

PMA is postmenstrual age in weeks, TM50 is the maturation half-time and HILL is the exponent that describes the steepness of the maturation curve. Fmat approaches a value of 1 during infancy signalling completion of maturational processes.

Changes in body composition correlated with ageing may impact drug volume of distribution (V). An empirical exponential maturation function was investigated to describe changes in V with age, above what can be predicted by size alone (Eq. 5).

$$_}}=_}}\times F_}\times \left(1+FV\times ^}\left(2\right)\times }}}}}\right)$$

(5)

Vgrp is the group value of V after accounting for the fixed effects from covariates, Vpop is the population parameter value of V and Fsize is described in Eq. (1). The y-intercept of the function is determined by 1 + FV and describes the fractional difference in V at time = 0. TVOL is the maturation half-time when V is 50% of the mature value. Postnatal age (PNA) and PMA were explored as age descriptors to describe changes in V associated with the birth effect (PNA) or more gradual changes (PMA).

Renal function is a metric for kidney function that accounts for size, maturation and body composition. It is calculated from the ratio of estimated glomerular filtration rate (eGFR) to normal GFR (nGFR) [18] (Eq. 6).

Normal GFR is calculated using Eq. (7).

$$}=}}_}}\times _}}\times _},}}\times _},}}$$

(7)

GFRstd is the standard GFR for a 70-kg TBM male, height of 176 cm, reported in Rhodin et al. [19] but updated using the models for FFR and nGFR described in O’Hanlon et al. [18]. Fsize is a factor for size using normal fat mass (Eq. 1), Fmat,PMA is a factor for maturation based on PMA and Fmat,PNA is a factor for maturation based on PNA, and describes the impact of the birth effect on maturation. Estimated GFR can be calculated under the assumption that creatinine clearance (CLcr) equals eGFR (Eq. 8).

CPR is creatinine production rate (predicted from neonates to adults in O’Hanlon et al. [18]) and Scr is serum creatinine concentration. Two Scr measurement were available in our dataset, one prior to surgery (baseline) and one at Day 1 (post-surgery). Serum creatinine measurements available post-surgery used a last-observation-carried-forward procedure for the calculation of renal function.

Milrinone increases cardiac output and so kidney function may improve, leading to increased clearance over time. An empirical exponential function was used to describe a fractional increase in clearance relative to clearance at therapy commencement (Eq. 9).

$$}}_}}=}}_}}\times f(}, \dots )\times \left(1-}\times ^}\left(2\right)\times }}}}}\right)$$

(9)

CLGRP is the group value of clearance after accounting for the fixed effects from covariates (e.g., size, age etc.), CLPOP is the population parameter value of clearance, f(size, …) includes the other clearance covariates (e.g., size, age, renal function) and TAD is time after dose (h). FCL is the fraction of clearance at the start of dose initiation and TCL is the half-time of 50% of the maximal fraction. The time-varying clearance model was incorporated in the differential equation solver block of the NM-TRAN control stream to avoid oversimplification of the model using step functions in patients with limited samples [20].

2.6 Data Analysis

Data were analysed using NONMEM (ICON Development Solutions, Maryland, USA) version 7.5.1 and Wings for NONMEM version 744 (http://wfn.sourceforge.net/). Population parameter estimates were obtained using NONMEM’s first-order conditional estimation method with the interaction option (FOCE-I). The convergence criterion (NSIG) was 3 with tolerance SIGL = 6. Model selection was based on the minimum objective function value (OFV), calculated by NONMEM from − 2log-likelihood. For two nested models, a decrease in the OFV of 3.84 was considered significant at p = 0.05, assuming one degree of freedom.

Parameter variability was described by a mixed effect approach with fixed and random effects. Fixed effect variability was based on a population standard parameter θPOP,std with a function of covariates such as size, height, sex, PMA and PNA to obtain the group parameter θgrp (Eq. 10).

$$_}}=_},}}\times f(},},\dots )$$

(10)

θgrp is the group parameter after accounting for fixed effects due to covariates; θi is the individual parameter after accounting for random effects. Population parameter variability (PPV) was described using an exponential function of the random effect (Eq. 11), which assumes a log-normal distribution when used for simulation. The random effect, ηi, describes both between- and within-subject variability (normally distributed with mean 0 and variance ω2).

The residual unexplained variability for these models was described using a combined (additive + proportional) error model (Eq. 12).

$$_=_} i}\times \left(1+_}}\right)+_}}$$

(12)

Yi is the individual prediction of the observed value obtained from YPred i, the model prediction and the random effects εCV and εSD (proportional and additive error model components, respectively). The random effects are normally distributed with mean zero and a variance of σCV2 and σSD2.

Observations below the limit of quantitation (BLQ) were handled using the Beal [21] M3 method. The observations were modelled using maximum likelihood estimation, of which the likelihood for a BLQ observation is the likelihood that it is truly below the limit of quantitation [22]. Residual error was estimated separately for analysis of milrinone concentrations from batch 1, batch 2 (see study design) and Paradisis et al. [5].

2.7 Model Evaluation

Model evaluation was based on parameter plausibility, parameter uncertainty and visual predictive checks (VPCs). Parameter uncertainty was evaluated using non-parametric bootstrapping [23]. A total of 100 bootstrap replicates were used to describe the distribution of the parameter estimates and estimate the uncertainty of the prediction. Visual predictive checks were used to compare the 5th, 50th and 95th percentiles of the observed and predicted values from the model [24]. The 95% confidence intervals were estimated from the replicates of each of the prediction percentiles.

2.8 Simulations

Milrinone concentrations after CPB were simulated over 48 h using the final model to assess performance of dosing regimens. A total of 1000 subjects (without replacement) were sampled from the GAVamycin covariate database [25]. The sampled covariates included PMA, PNA, TBM, FFM, sex and serum creatinine. Different dosing regimens were assessed, including the dosing guidelines at Starship Children’s Hospital (0.25–0.75 μg/kg/min). The 2.5th, median and 97.5th prediction percentiles were compared to the acceptable concentration range (100–300 μg/L). The median prediction percentiles were stratified by age group (neonates, infants and children).

The following dosing regimens were assessed over 48 h with milrinone administered for 36 h.

1.

Milrinone 0.25 μg/kg/min.

2.

Milrinone 0.5 μg/kg/min.

3.

Milrinone 0.75 μg/kg/min.

4.

Milrinone 0.25 μg/kg/min for 4 h then 0.5 μg/kg/min for 32 h.

5.

LCOS prophylaxis indication from Vogt [4] presented in Supplementary Table S1 (see electronic supplementary material [ESM]).

6.

LCOS treatment indication from Vogt [4] presented in Supplementary Table S1 (see ESM).

7.

Milrinone 50 μg/kg loading dose over 1 h then 0.5 μg/kg/min.

8.

Milrinone 50 μg/kg loading dose over 1 h then 0.375 μg/kg/min (neonates) or 0.75 μg/kg/min (infants and children).

Regimens 1–3 are based on local hospital practice of milrinone 0.25–0.75 μg/kg/min.