ABSTRACT
Purpose
To develop a population pharmacokinetic (PK) model which allowed the simultaneous modeling of trans-resveratrol and its glucuronide and sulfate conjugates.
Methods
Male Sprague–Dawley rats were administered i.v. and p.o. with 2, 10 and 20 mg·kg−1 of trans-resveratrol. Blood was collected at different times during 24 h. An integrated PK model was developed using a sequential analysis, with non-linear mixed effect modeling (NONMEM). A prediction-corrected visual predictive check (pcVPC) was used to assess model performance. The model predictive capability was also evaluated with simulations after the i.v. administration of 15 mg·kg−1 that were compared with an external data set.
Results
Disposition PK of trans-resveratrol and its metabolites was best described by a three-linked two-compartment model. Clearance of trans-resveratrol by conversion to its conjugates occurred by a first-order process, whereas both metabolites were eliminated by parallel first-order and Michaelis-Menten kinetics. The pcVPC confirmed the model stability and precision. The final model was successfully applied to the external data set showing its robustness.
Conclusions
A robust population PK model has been built for trans-resveratrol and its glucuronide and sulfate conjugates that adequately predict plasmatic concentrations.
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Abbreviations
- ABC:
-
ATP-binding cassette
- AIC:
-
Akaike information criterion
- AUC:
-
area under the curve
- BCRP:
-
breast cancer resistance protein
- DV:
-
observed concentrations
- IAV:
-
inter-animal variability
- IPRED:
-
individual model predicted concentrations
- MRP:
-
multidrug resistance protein
- OFV:
-
objective function value
- pcVPC:
-
prediction corrected visual predictive check
- PD:
-
pharmacodynamic
- PK:
-
pharmacokinetic
- PRED:
-
population model predicted concentrations
- RSE:
-
relative standard error
- UGT:
-
UDP-glucuronosyltransferase
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ACKNOWLEDGMENTS
This study was supported by the Ministerio de Ciencia y Tecnología grants AGL2005-05728 and AGL2009-12866 and the Generalitat de Catalunya grants 2005-SGR-00632 and 2009-SGR-00471.
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APPENDIX
APPENDIX
The NONMEM code used in the final model
Modeling of Intravenous Data
$PROBLEM trans-resveratrol and its conjugates plasmatic concentrations
$INPUT ID TIME AMT DV MDV EVID CMT WGT ROUT DOSA;DOSA=ACTUAL DOSE
$DATA data.csv IGNORE=#
IGNORE (ROUT.EQ.2)
$SUBROUTINES ADVAN6 TOL=3
$MODEL
COMP = (CENTRALRESV,DEFOBS) | ||
COMP = (PERIPHRESV) | ||
COMP = (CENTRALGLUC) | ||
COMP = (PERIPHGLUC) | ||
COMP = (CENTRALSULF) | ||
COMP = (PERIPHSULF) | ||
$PK | ||
;DISPOSITION PARAMETERS | ||
;trans-Resveratrol | ||
TVCL1 | = THETA(1) | |
CL1 | = TVCL1*EXP(ETA(1)) | ;Plasmatic CL of resveratrol |
V1 | = THETA(2) | ;Central compartment V of resveratrol |
Q | = THETA(3)*EXP(ETA(2)) | ;Distributional CL of resveratrol |
V2 | = THETA(4) | ;Peripheral compartment V of resveratrol |
;Glucuronide | ||
V3 | = 0.05 | ;Central compartment V of the glucuronide |
QM1 | = THETA(5) | ;Distributional CL of the glucuronide |
V4 | = THETA(6) *EXP(ETA(3)) | ;Peripheral compartment V of the glucuronide |
;Linear elimination process | ||
CL2 | = THETA(7) | ;Plasmatic CL of the glucuronide |
;Non-linear elimination process | ||
VMG | = THETA(8) | ;Maximal elimination rate of the glucuronide |
KMG | = THETA(9) | ;Concentration of the glucuronide at which the elimination is half maximal |
FM | = THETA(10) | ;Fraction of resveratrol converted to its glucuronide |
;Sulfate | ||
V5 | = THETA(11) | ;Central compartment V of the sulfate |
V6 | = THETA(12) | ;Peripheral compartment V of the sulfate |
QM2 | = THETA(13) | ;Distributional CL of the sulfate |
;Linear elimination process | ||
CL3 | = THETA(14) | ;Plasmatic CL of the sulfate |
;Non-linear elimination process | ||
VMS | = THETA(15) | ;Maximal elimination rate of the sulfate |
KMS | = THETA(16) | ;Concentration of the sulfate at which the elimination is half maximal |
S1 = V1 |
S3 = V3 |
S5 = V5 |
;RATE CONSTANTS
K12 = Q/V1 |
K21 = Q/V2 |
K30 = CL2/V3 |
K34 = QM1/V3 |
K43 = QM1/V4 |
K56 = QM2/V5 |
K65 = QM2/V6 |
K50 = CL3/V5 |
;DIFFERENTIAL EQUATIONS
$DES
DADT(1) | = −K12*A(1)+K21*A(2)-(CL1/V1)*FM*A(1)-(CL1/V1)*(1-FM)*A(1) |
DADT(2) | = K12*A(1)-K21*A(2) |
DADT(3) | = (CL1/V1)*FM*A(1)-K30*A(3) + K43*A(4)-K34*A(3)-(VMG*A(3))/(KMG + A(3)) |
DADT(4) | = K34*A(3)-K43*A(4) |
DADT(5) | = (CL1/V1)*(1-FM)*A(1)-K56*A(5) + K65*A(6)-K50*A(5))-(VMS*A(5))/(KMS + A(5)) |
DADT(6) | = K56*A(5)-K65*A(6) |
;RESIDUAL ERROR FOR LOG-TRANSFORMED DATA
$ERROR
IPRED | = −5 |
IF(F.GT.0) | IPRED= LOG(F) |
IF(CMT.EQ.2) | Y= IPRED + EPS(1) |
IF(CMT.EQ.4) | Y= IPRED + EPS(2) |
IF(CMT.EQ.6) | Y= IPRED + EPS(3) |
IWRES | = (DV-IPRED) |
;INITIAL ESTIMATES
$THETA
$OMEGA
$SIGMA
$ESTIMATION
$COVARIANCE
Modeling of Oral Data
$PROBLEM trans-resveratrol and its conjugates plasmatic concentrations
$INPUT ID TIME AMT DV MDV EVID CMT WGT ROUT DOSA;DOSA=ACTUAL DOSE
$DATA data.csv IGNORE=#
IGNORE (ROUT.EQ.1)
$SUBROUTINES ADVAN6 TOL=3
$MODEL
COMP = (DEPOT) |
COMP = (CENTRALRESV,DEFOBS) |
COMP = (PERIPHRESV) |
COMP = (CENTRALGLUC) |
COMP = (PERIPHGLUC) |
COMP = (CENTRALSULF) |
COMP = (PERIPHSULF) |
$PK
“FIRST
“ COMMON/PRCOMG/IDUM1,IDUM2,IMAX,IDUM4,IDUM5
“ INTEGER IDUM1,IDUM2,IMAX,IDUM4,IDUM5
“ IMAX=70000000
;DISPOSITION PARAMETERS
;trans-Resveratrol | ||
TVCL1 | = THETA(1) | |
CL1 | = TVCL1*EXP(ETA(1)) | ;Plasmatic CL of resveratrol |
V2 | = THETA(2) | ;Central compartment V of resveratrol |
Q | = THETA(3)*EXP(ETA(2)) | ;Distributional CL of resveratrol |
V3 | = THETA(4) | ;Peripheral compartment V of resveratrol |
;Glucuronide | ||
V4 | = 0.05 | ;Central compartment V of the glucuronide |
QM1 | = THETA(5) | ;Distributional CL of the glucuronide |
V5 | = THETA(6) *EXP(ETA(3)) | ;Peripheral compartment V of the glucuronide |
FM | = THETA(7) | ;Fraction of resveratrol converted to its glucuronide |
;Linear elimination process | ||
CL2 | = THETA(8) | ;Plasmatic CL of the glucuronide |
;Non-linear elimination process | ||
VMG | = THETA(9) | ;Maximal elimination rate of the glucuronide |
KMG | = THETA(10) | ;Concentration of the glucuronide at which the elimination is half maximal |
;Sulfate | ||
V6 | = THETA(11) | ;Central compartment V of the sulfate |
V7 | = THETA(12) | ;Peripheral compartment V of the sulfate |
QM2 | = THETA(13) | ;Distributional CL of the sulfate |
;Linear elimination process | ||
CL3 | = THETA(14) | ;Plasmatic CL of the sulfate |
;Non-linear elimination process | ||
VMS | = THETA(15) | ;Maximal elimination rate of the sulfate |
KMS | = THETA(16) | ;Concentration of the sulfate at which the elimination is half maximal |
;ABSORPTION PARAMETERS
KA1 | = THETA(17) | ;Absorption rate constant |
KA2 | = THETA(18) | ;Transformation (from the parent compound to the glucuronide)/Absorption rate constant |
TVF1 | = THETA(19)*(1-THETA(20)*DOSA) | |
F1 | = TVF1*EXP(ETA(4)) | ;Bioavailability |
;SCALE FACTORS
S2 = V2 |
S4 = V4 |
S6 = V6 |
;RATE CONSTANTS
K23 = Q/V2 |
K32 = Q/V3 |
K40 = CL2/V4 |
K45 = QM1/V4 |
K54 = QM1/V5 |
K67 = QM2/V6 |
K76 = QM2/V7 |
K60 = CL3/V6 |
;DIFFERENTIAL EQUATIONS
$DES
DADT(1) | = −KA1*F1*A(1)-KA2*(1-F1)*A(1) |
DADT(2) | = KA1*F1*A(1)-K23*A(2)+K32*A(3)-(CL1/V2)*FM*A(2)-(CL1/V2)*(1-FM)*A(2) |
DADT(3) | = K23*A(2)-K32*A(3) |
DADT(4) | = KA2*(1-F1)*A(1)+(CL1/V2)*FM*A(2)-K40*A(4)+K54*A(5)-K45*A(4)-(VMG*A(4))/(KMG+A(4)) |
DADT(5) | = K45*A(4)-K54*A(5) |
DADT(6) | = (CL1/V2)*(1-FM)*A(2)-K67*A(6)+K76*A(7)-K60*A(6))-(VMS*A(6))/(KMS+A(6)) |
DADT(7) | = K67*A(6)-K76*A(7) |
;RESIDUAL ERROR FOR LOG-TRANSFORMED DATA
$ERROR
IPRED | = −5 | |
IF(F.GT.0) | IPRED | = LOG(F) |
IF(CMT.EQ.2) | Y | = IPRED+EPS(1) |
IF(CMT.EQ.4) | Y | = IPRED+EPS(2) |
IF(CMT.EQ.6) | Y | = IPRED+EPS(3) |
IWRES | = (DV-IPRED) |
;INITIAL ESTIMATES
$THETA
$OMEGA
$SIGMA
$ESTIMATION
$COVARIANCE
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Colom, H., Alfaras, I., Maijó, M. et al. Population Pharmacokinetic Modeling of trans-Resveratrol and Its Glucuronide and Sulfate Conjugates After Oral and Intravenous Administration in Rats. Pharm Res 28, 1606–1621 (2011). https://doi.org/10.1007/s11095-011-0395-8
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DOI: https://doi.org/10.1007/s11095-011-0395-8