Population pharmacokinetic model
Based on the goodness-of-fit and obtained OFV and AIC, a
four-compartment chain model with first-order elimination adequately
described the PCr and Cr data. The schematic diagram is shown inFigure 1 . The disposition of PCr in blood was characterized by
a two-compartment model (compartment 1 and 2) which includes central
volume of distribution (VcPCr), peripheral volume of
distribution (VpPCr), central clearance
(CLPCr) and inter-compartmental clearance
(QPCr). The parent PCr was converted into metabolite Cr.
The disposition of Cr in blood was described using another
two-compartment model (compartment 3 and 4) including central volume of
distribution (VcCr), peripheral volume of distribution
(VpCr), central clearance (CLCr) and
inter-compartmental clearance (QCr). The fraction
(Fm) of PCr metabolized to Cr was fixed to 0.75 and it
was assumed that 75 percent PCr was eliminated via metabolic conversion
to Cr. Besides, another parameter of the baseline endogenic Cr (baseCr)
was incorporated into the model to describe this basal value. The
following are the differential functions to describe the process:
\(\frac{\text{dA}_{1}}{\text{dt}}=A_{0}-\frac{\text{CL}_{\text{PCr}}}{V_{\text{cPCr}}}\times A_{1}+\frac{Q_{\text{PCr}}}{V_{\text{pPCr}}}\times A_{2}-\frac{Q_{\text{PCr}}}{V_{\text{cPCr}}}\times A_{1}\)(8)
\(\frac{\text{dA}_{2}}{\text{dt}}=-\frac{Q_{\text{PC}r}}{V_{p\text{PC}r}}\times A_{2}+\frac{Q_{\text{PC}r}}{V_{c\text{PC}r}}\times A_{1}\)(9)
\(\frac{\text{dA}_{3}}{\text{dt}}=\frac{\text{CL}_{\text{PC}r}}{V_{c\text{PC}r}}\times A_{1}\times F_{m}-\frac{\text{CL}_{Cr}}{V_{cCr}}\times A_{3}+\frac{Q_{Cr}}{V_{pCr}}\times A_{4}-\frac{Q_{Cr}}{V_{cCr}}\times A_{3}\)(10)
\(\frac{\text{dA}_{4}}{\text{dt}}=-\frac{Q_{Cr}}{V_{pCr}}\times A_{4}+\frac{Q_{Cr}}{V_{cCr}}\times A_{3}\)(11)
\(CobsPCr=\frac{A_{1}}{V_{\text{cPCr}}}\) (12)
\(CobsCr=\frac{A_{3}}{V_{\text{cCr}}}+baseCr\) (13)
A1 and A2 are the PCr amount in the
central and peripheral compartments, respectively. A3and A4 are the Cr amount in the central and peripheral
compartments, respectively. A0 represents the
administration rate of creatine phosphate sodium in blood.
Fm represents the
fraction of PCr metabolized to Cr. CobsPCr and CobsCr are the observed
drug concentration of PCr and Cr in the central compartment (plasma
concentration), respectively. The definition of the other parameters
(VcPCr, VpPCr, CLPCr,
QPCr, VcCr, VpCr,
CLCr, QCr, baseCr) can be found inFigure1 .
The interindividual variability was estimated for CLPCr,
VcCr, VpCr, CLCr, and
baseCr. The proportional error accounted for the residual error model of
both PCr and Cr observations. Finally, the OFV of the base model was
6785.535. According to the criteria of forward inclusion and backward
exclusion, covariate GFR was
identified and included in the
final population pharmacokinetic model. The incorporation of covariate
markedly decreased the OFV from 6785.535 to 6773.0502 (△OFV = -12.4848).
In the final model, GFR had a positive significant influence on
CLCr and their relationship was described by the
following equation:
\(\mathrm{\text{CL}}_{\text{Cr}}\mathrm{\ (L/min)\ =\ 0.0825\ \times\ }({BW/20)}^{0.75}\mathrm{\ \times\ }({GFR/127.78)}^{0.311}\mathrm{\ \times}\ e^{\eta\mathrm{\text{CL}}_{\text{Cr}}}\)(14)
In
equation
(14), 0.0825 L/min is the typical value of CLCr, 20 kg
is the median value of BW, 127.78 mL/min/1.73m2 is the
median value of GFR and 0.311 is the correlation coefficient between BW
and CLCr. The estimated values of the parameters of the
final model, their relative standard error (RSE) and interindividual
variability are summarized in Table 2 . All parameters were
estimated with acceptable precision with RSE of estimates <
30%. The shrinkage in random IIV estimates for CLPCr,
VcCr, VpCr, CLCr, and
baseCr were 3.93%, 10.3%, 22.6%, 5.22% and 1.04% respectively.