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Reconstructing exposures from small samples using physiologically based pharmacokinetic models and multiple biomarkers

Journal of Exposure Science & Environmental Epidemiology volume 19, pages 284–297 (2009)Cite this article

Abstract

This study examines the use of physiologically based pharmacokinetic (PBPK) models for inferring exposure when the number of biomarker observations per individual is limited, as commonly occurs in population exposure surveys. The trade-off between sampling multiple biomarkers at a specific time versus fewer biomarkers at multiple time points was investigated, using a simulation-based approach based on a revised and updated chlorpyrifos PBPK model originally published. Two routes of exposure, oral and dermal, were studied as were varying levels of analytic measurement error. It is found that adding an additional biomarker at a given time point adds substantial additional information to the analysis, although not as much as the addition of another sampling time. Furthermore, the precision of the estimates of exposed dose scaled approximately with the analytic precision of the biomarker measurement. For acute exposure scenarios such as those considered here, the results of this study suggest that the number of biomarkers can be balanced against the number of sampling times to obtain the most efficient estimator after consideration of cost, intrusiveness, and other relevant factors.

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Acknowledgements

We thank Dr. Charles Timchalk for generously providing his SIMUSOLV® (a registered trademark of the Dow Chemical Co., Midland, MI) code and output files, and Dr. Joel Mattsson and the Dow Chemical Company for provision of the human volunteer CPF exposure data described in Nolan et al. (1984). We also thank Dr. Sydney Gordon of Battelle, and Mr. Andy Clayton, Dr. Cary Eaton, Ms. Amy Etheridge, Dr. Timothy Fennell, Dr. James Raymer, Ms. Carol Sloan and Dr. Roy Whitmore of RTI for their review and administrative support of this study.

Author information

Authors and Affiliations

  1. RTI International, Research Triangle Park, North Carolina, USA

    Paul L Mosquin, Amy Collins Licata, Bing Liu & Susan C J Sumner

  2. National Exposure Research Laboratory, US EPA, Office of Research and Development, Las Vegas, Nevada, USA

    Miles S Okino

Authors
  1. Paul L Mosquin
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  2. Amy Collins Licata
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  3. Bing Liu
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  4. Susan C J Sumner
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  5. Miles S Okino
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Corresponding author

Correspondence to Miles S Okino.

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Disclaimer

The United States Environmental Protection Agency through its Office of Research and Development funded and collaborated in the research described here under contract EP-D04-068 to Battelle with a subcontract to the RTI International. It has been subjected to Agency review and approved for publication.

Appendix

Appendix

PBPK model equations, both ordinary differential and algebraic, that are different from Timchalk et al. (2002b), as well as the definitions of terms used in the model, are presented here:

Liver Compartment CPF Model

Liver Compartment CPF-oxon Model

Blood Compartment CPF-oxon Model

One-Compartment TCP

One-Compartment DEP

One-Compartment DETP

Definition of terms used in the model

d=change (unitless)

AH=amount (μmol) of CPF in the liver

t=time (h)

QH=blood flow (h) to the liver

CAHf=free CPF concentration (μmol/l) in arterial blood entering the liver

CVHf=free CPF concentration (μmol/l) in venous blood leaving the liver

dOral/dH=rate of uptake (μmol/h) into the liver compartment from the GI tract

CH=CPF concentration (μmol/l) in the liver

Vmax1=maximum rate (μmol/h) for metabolism (CPF to CPF-oxon)

Km1=Michaelis–Menten constant (μmol/l) for metabolism (CPF to CPF-oxon)

Vmax2=maximum rate (μmol/h) for metabolism (CPF to TCP; CPF to DETP)

Km2=Michaelis–Menten constant (μmol/l) for metabolism (CPF to TCP; CPF to DETP)

AHo=amount (μmol) of CPF-oxon in liver

Vmax3=maximum rate (μmol/h) for metabolism (CPF-oxon to TCP (liver), CPF-oxon to DEP (liver))

Km3=Michaelis–Menten constant (μmol/l) for metabolism (CPF-oxon to TCP (liver); CPF-oxon to DEP (liver))

CAHof=free CPF-oxon concentration (μmol/l) in arterial blood entering the liver

CVHof=free CPF-oxon concentration (μmol/l) in venous blood leaving the liver

ABL=amount (μmol) of CPF-oxon in mixed blood compartment

QC=cardiac output (l/h)

CVmof=free CPF-oxon concentration (μmol/l) in mixed blood compartment

CVeof=free CPF-oxon concentration (μmol/l) in venous blood

Vmax4=maximum rate (μmol/h) for metabolism (CPF-oxon to TCP (blood); CPF-oxon to DEP (blood))

Km4=Michaelis–Menten constant (μmol/l) for metabolism (CPF-oxon to TCP (blood); CPF-oxon to DEP (blood))

ATCP=amount (μmol) of TCP

KeTCP=urinary elimination rate (h−1) for TCP

VdTCP=volume of distribution (l) for TCP

cbTCP=TCP concentration (μmol/l) in blood

ADEP=amount (μmol) of DEP

KeDEP=urinary elimination rate (h−1) for DEP

VdDEP=volume of distribution (l) for DEP

cbDEP=DEP concentration (μmol/l) in blood

ADETP=amount (μmol) of DETP

KeDETP=urinary elimination rate (h−1) for DETP

VdDETP=volume of distribution (l) for DETP

cbDETP=DETP concentration (μmol/l) in blood

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Mosquin, P., Licata, A., Liu, B. et al. Reconstructing exposures from small samples using physiologically based pharmacokinetic models and multiple biomarkers. J Expo Sci Environ Epidemiol 19, 284–297 (2009). https://doi.org/10.1038/jes.2008.17

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