Choi L, et al.
Fentanyl Pharmacokinetics during Critical Illness
Population Pharmacokinetics of Fentanyl in the Critically Ill
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Leena Choi, PhD;1 Benjamin A Ferrell, MD;2 Eduard E Vasilevskis, MD, MPH,3,8,11 Pratik P
Pandharipande, MD, MSCI;6,10 Rebecca Heltsley, PhD;9 E Wesley Ely, MD, MPH;2,7,8,11 C
Michael Stein, MB, ChB;4,5 Timothy D Girard, MD, MSCI2,7,8,11
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Choi L, et al.
Fentanyl Pharmacokinetics during Critical Illness
MATERIALS AND METHODS
Fentanyl Plasma Concentration Measurement
Plasma concentrations of fentanyl were measured at Aegis Sciences Corporation
(Nashville, TN) using validated liquid chromatography-tandem mass spectrometry (LC-MS-MS)
procedures. Specimens (0.5 mL) were extracted using a liquid-liquid extraction (LLE) with
isopropanol and toluene (10:90). Prior to extraction, each specimen was fortified with deuterium
labeled internal standards and pH adjusted using sodium hydroxide. Solvent was evaporated, and
the samples were reconstituted in 10 mM ammonium acetate, 0.1% formic acid highperformance liquid chromatography (HPLC) water (mobile phase).
LC-MS-MS analysis was performed with an API 3200 tandem mass spectrometer
operating in positive electrospray mode (ESI) (MDS SCIEX, Toronto, Canada) interfaced with a
Shimadzu LC-20AD HPLC (Columbia, Maryland). The mobile phase was 10 mM ammonium
acetate, 0.1% formic acid HPLC water, and 0.1% formic acid acetonitrile. The HPLC column
was a Restek Pinnacle DB C18 3 m, 100 x 2.1 mm. Transitions were as follows: (precursor ion,
quantitative, qualitative) fentanyl (337.2, 105.2, 188.3) and fentanyl-d5 (342.2, 105.2). Quality
controls (high positive, low positive, and negative) were acquired with each batch of samples.
According to batch acceptance criteria, positive controls must be within 20% of the measured
target concentration (previously determined in the validation). The imprecision (percent
coefficient of variation [%CV]) of the assay was evaluated by replicate analysis of the control
material (inter-variability) and was determined to be less than 7.5%. Criteria for identification
and measurement of analytes have been previously reported (1, 2). The limit of quantitation
(LOQ) was determined by diluting samples fortified with known drug concentrations with
negative matrix. The LOQ for fentanyl was 0.1 ng/mL. All quantitative data for fentanyl
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Fentanyl Pharmacokinetics during Critical Illness
included in this report were within the linear dynamic range and met identification and
quantitation (≥LOQ) criteria.
Population Pharmacokinetic Analysis
We chose the base model by comparing one-, two-, and three-compartment
pharmacokinetic models without covariates, assuming a combined additive and proportional
residual error model and lognormal distribution for the random effects. A two-compartment
model described the fentanyl pharmacokinetics substantially better than a one-compartment
model. The parameters for a three-compartment model were not identified due to sparseness of
samples. Allowing intercompartmental clearance (Q) to be random did not improve the fit, so
random-effects were assumed only for clearance (CL), volume of distribution for the central
compartment (V1), and volume of distribution for the peripheral compartment (V2) in the final
model. A two-compartment model described the fentanyl pharmacokinetics substantially better
than a one-compartment model. The parameters for a three-compartment model were not
identified due to sparseness of samples. Allowing intercompartmental clearance (Q) to be
random did not improve the fit, so random-effects were assumed only for clearance (CL),
volume of distribution for the central compartment (V1), and volume of distribution for the
peripheral compartment (V2) in the final model.
Statistical Analysis
Model selection was performed based on the objective function (-2 log likelihood) along
with the number of parameters, which approximately follows 2 distribution. The 2 statistics of
3.84 and 6.64 with the degree of freedom 1 correspond to p values of 0.05 and 0.01, respectively.
Thus, we considered the objective function value decrease of ~10 to be significant model
improvement. The first-order conditional estimation (FOCE) method with interaction was used
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Fentanyl Pharmacokinetics during Critical Illness
for the estimation. Lastly, we examined goodness-of-fit plots using population and individual
predicted fentanyl plasma concentrations as well as conditional weighted residuals. Since the
range of measured concentrations was very wide whereas the majority were less than 3 ng/mL,
plots of fentanyl plasma concentrations are presented in log axes. We used the programming
language R version 3.1.0 (3) for statistical analyses, the covariate building, model checking,
model validation, and other statistical analyses.
Model Validation
We used 10-fold cross-validation to internally validate the model’s prediction of fentanyl
plasma concentrations (4, 5). Briefly, we randomly divided the dataset containing 337 patients
into ten approximately equal groups. Holding one randomly selected group out as a validation
set, we used data from the remaining nine groups (i.e., 90% of the data) as a training set to
develop a model. We then used the estimated parameters from the developed model to predict
fentanyl plasma concentrations in the held-out validation set. We repeated this process ten times
so that all ten groups were used once as the held-out validation set with the remaining nine
groups serving as the training set. Thus, fentanyl plasma concentrations were predicted for 100%
of patients but never based on a model developed using their own data. We then repeated this
entire 10-fold cross-validation process a total of 50 times to minimize sensitivity of the results to
how the data were randomly divided and to allow many different sets of patients to be used as
training sets.
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Fentanyl Pharmacokinetics during Critical Illness
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