Computational estimation of errors generated by lumping of physiologically-based pharmacokinetic (PBPK) interaction models of inhaled complex chemical mixtures

Abstract

Many cases of environmental contamination result in concurrent or sequential exposure to more than one chemical. However, limitations of available resources make it unlikely that experimental toxicology will provide health risk information about all the possible mixtures to which humans or other species may be exposed. As such, utilizing computational models in order to make toxicological predictions is a useful tool in complementing experimental efforts which examine mixtures in health risk assessment. This paper outlines a novel mathematical method which reduces the complexity of a mixtures model and increases computational efficiency via a biologically-based lumping methodology (BBLM). In contrast to previous chemical lumping methodologies, BBLM allows the computation of error as a measure of the difference between the lumped simulation based on BBLM and the full mathematical model. As a consequence, the modeler has the opportunity to find the optimal configuration in the tradeoff between simplification and accuracy in order to determine an acceptable number and composition of lumped chemicals. To demonstrate this method, lumped equations based on a typical inhalation physiologically-based pharmacokinetic (PBPK) model assuming a competitive inhibition interaction mechanism are developed for a mixture of arbitrary size. The novel methodology is further tested using literature data for a mixture of 10 volatile organic chemicals (VOCs). Through simulation of these chemicals, BBLM is shown to produce good approximations when compared to the unlumped simulation and experimental data.

Keywords::

• Inhalation PBPK model
• lumping
• order reduction
• mixtures

Acknowledgments

The authors gratefully acknowledge the comments which were provided by Rory Conolly, John Wambaugh, and Marina Evans in the process of producing this manuscript. Their thoughtful insights added to the depth at which our ideas have been expressed and the clarity with which they have been presented.

Declaration of interest

The authors report no declarations of interest.