Sample assay
An improved HPLC-MS/MS method based previous literature [15] was
used to measure plasma concentrations of PCr and Cr, using salidroside
and creatine-(methly-d3) (Cr-d3) as internal standards, respectively. 50
μL of plasma and 10 μL of internal standard solution (20 μg/mL
salidroside and 100 μg/mL Cr-d3 for PCr and Cr determination,
respectively) were prepared by protein precipitation with
acetonitrile/water (1000 μL, 1:1, v/v). After vortex and centrifugation,
100 μL of the supernatant fluid was diluted with 500 μL of solvent, and
10 μL was injected into the HPLC-MS/MS system for the determination of
PCr. While, for the Cr determination, 20 μL of the supernatant fluid was
diluted with 1000 μL of solvent, and 5 μL was injected into the
HPLC-MS/MS system.
A Hypersil Gold C18 column (150×2.1 mm, 5 μm, Thermo
Scientific, USA) was used for separation of PCr. The mobile phase was
solution A: 2 mM ammonium acetate in water (pH 10, adjusted with
ammonia), and solution B: methanol. Chromatography separation was
obtained with gradient elution solvent, the gradient elution program
was: 0-1.5 min, 98-20% A; 1.5-4 min, 20% A; 4-4.01 min, 20-98% A;
4.01-10 min, 98% A. Monitored ion pairs were m/z 210 → 79 and m/z 299 →
119 for PCr and salidroside in negative ionization mode.
For the separation of Cr, a Hypersil Gold C18 column
(150×4.6 mm, 5 μm, Thermo Scientific, USA) was applied. The mobile phase
was solution A: 2 mM ammonium acetate in water (0.4‰ formic acid), and
solution B: acetonitrile. Isocratic elution with 30% A was obtained.
Monitored ion pairs were m/z 132 → 90 and m/z 135 → 93 for Cr and Cr-d3
in positive ionization mode.
This method was accurate with the intra-day and inter-day precision less
than 6%. The lower limit of quantification (LLOQ) for PCr and Cr were
0.5 μg/mL and 4 μg/mL, respectively. Measured concentrations below LLOQ
were reported in the dataset.
Population
pharmacokinetic model development
A sequential two-step analysis approach to model building was
implemented [16]. First, a population pharmacokinetic model of PCr
was developed and then parent parameters were fixed to develop the
population pharmacokinetic model for Cr. The nonlinear mixed-effects
modeling method was applied to establish the population pharmacokinetic
model. The PCr and Cr concentrations were fitted using the Phoenix NLME
software (version 8.2, Certara, St. Louis, MO) with the first-order
conditional estimation-extended least squares (FOCE-ELS) method
throughout the model building process. Pharmacokinetic data which were
below LLOQ were handled using the M3 method [17]. Model selection
criteria were based on goodness-of-fit plots, objective function value
(OFV, equal to -2 log likelihood), akaike information criteria (AIC) and
precision of parameter estimates. The complex parent-metabolite joint
population pharmacokinetic model was established in a stepwise fashion.
First, the base model including PCr and Cr was developed with residual
error model and interindividual variability model. After that, covariate
effects on base model were investigated to construct the covariate
model.
For PCr, structural model was tested either one-compartment or
two-compartment PK models. The one-compartment model parameters included
volume of distribution (V) and central clearance (CL). For the
two-compartment structural model,
inter-compartmental clearance (Q) and
volume of the second compartment (V2) were included. The structural
model for Cr was also tested. The fraction (Fm) of PCr
metabolized to Cr was fixed so as to avoid identifiability problem and
the volumes of the compartment for Cr was estimated. A published
literature reported that a large amount of PCr was metabolized as Cr in
animals after intravenous injection of exogenous PCr, and the conversion
rate was about three-quarters [10]. In this study, according to the
references and the characteristics of drug concentration-time curves of
PCr and Cr, the Fm of PCr converted to Cr was assumed to
be 0.75. Because of the existence of endogenous Cr which was detected at
each of the pre-dose sample, a parameter of the
baseline
of endogenous Cr levels was added.
Allometric
scaling based on bodyweight (BW) was applied to the PK parameters. An
allometric power model was used with power exponents fixed at 0.75 for
clearances and 1.0 for volumes of distribution, as described in the
following equations [18, 19]:
\(\text{CL}_{i}\ =\ \theta_{\text{CL}}\ \times\left(\text{BW}_{i}/20\right)^{0.75}\)(1)
\(V_{i}\ =\ \theta_{V}\ \times\left(\text{BW}_{i}/20\right)^{1}\)(2)
In this expression, CLi and Vi are the
typical clearance and central volume of distribution for an individual i
with bodyweight BWi while θCL and
θV are the respective parameter values for a subject
with a bodyweight of 20 kilogram.
The inter-individual variability (η) of pharmacokinetic parameters was
assumed to follow a log-normal distribution with a mean of 0 and a
variance of ω2. Exponential formula was applied to
account for IIV (Equation 3).
\({P_{\text{ij}}\ =\ P_{j}\ \times e}^{\eta_{\text{ij}}}\) (3)
where Pj and Pij represent the typical
value of j th population parameter and i th individual’j th parameter.
Proportional error model (Equation 4), additive error model (Equation
5), additive and proportional error model (Equation 6), and power error
model (Equation 7) were evaluated to describe the residual error.
\(C_{\text{ij}}\ =\ \text{IPRED}_{\text{ij}}\ \times(1+\ \varepsilon_{\text{ij}})\)(4)
\(C_{\text{ij}}\ =\ \text{IPRED}_{\text{ij}}\ +\ \varepsilon_{\text{ij}}\)(5)
\(C_{\text{ij}}\ =\ \text{IPRED}_{\text{ij}}\ \times\left(1+\ \varepsilon_{ij,1}\right)+\ \varepsilon_{ij,2}\)(6)
\(C_{\text{ij}}\ =\ \text{IPRED}_{\text{ij}}\ +\ {{\text{IPRED}_{\text{ij}}}^{0.5}\times\varepsilon}_{\text{ij}}\)(7)
where Cij was the observation concentration ofi th individual at the j th sampling point and
IPREDij was the individual prediction value. The
residual error (ε) is normally distributed with a mean of 0 and a
variance of σ2.
The impact of covariates on
pharmacokinetic parameters was
evaluated. The relationship between covariates and IIV for
pharmacokinetic parameters were investigated graphically ahead of
covariate assessment. In this
dataset, both categorical variables (gender) and continuous variables
(height, BW, age, disease
duration, WBC, RBC, hemoglobin, PLT, NEUT, LYMPH, MONO, EO, BASO, TP,
ALB, ALP, AST, ALT, TBIL, DBIL, urea, creatinine, UA, CK, CK-MB, LDH,
HBDH, HSTN-I, GFR) were tested. Categorical covariates were included in
the population model with the use of indicator variables and the impact
of the categorical covariates on each parameter was tested using power
function. Continuous covariates were centered at their median values,
and the impacts of each covariate on parameters were evaluated using
power functions. The stepwise forward addition and backward elimination
were applied to develop the covariate model. In the forward addition, a
covariate was retained if it resulting in a reduction the OFV
> 6.64 (P < 0.01, df = 1). In the backward
elimination, each covariate was left out of the full model built by
forward addition one at a time. A covariate was retained if the
elimination of the covariate lead to an increase of OFV >
10.83 (P < 0.001, df = 1).