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.