Although analysis of in vivo pharmacokinetic data necessitates use of time-dependent physiologically-based pharmacokinetic (PBPK) models, risk assessment applications are often driven primarily by steady-state and/or integrated (e.g., AUC) dosimetry. To that end, we present an analysis of steady-state solutions to a PBPK model for a generic volatile chemical metabolized in the liver. We derive an equivalent model that is much simpler and contains many fewer parameters than the full PBPK model. The state of the system can be specified by two state variables—the rate of metabolism and the rate of clearance by exhalation. For a given oral dose rate or inhalation exposure concentration, the system state only depends on the blood-air partition coefficient, metabolic constants, and the rates of blood flow to the liver and of alveolar ventilation. At exposures where metabolism is close to linear, only the effective first-order metabolic rate is needed. Furthermore, in this case, the relationship between cumulative exposure and average internal dose (e.g., AUCs) remains the same for time-varying exposures. We apply our analysis to oral-inhalation route extrapolation, showing that for any dose metric, route equivalence only depends on the parameters that determine the system state. Even if the appropriate dose metric is unknown, bounds can be placed on the route-to-route equivalence with very limited data. We illustrate this analysis by showing that it reproduces exactly the PBPK-model-based route-to-route extrapolation in EPA's 2000 risk assessment for vinyl chloride. Overall, we find that in many cases, steady-state solutions exactly reproduce or closely approximate the solutions using the full PBPK model, while being substantially more transparent. Subsequent work will examine the utility of steady-state solutions for analyzing cross-species extrapolation and intraspecies variability.
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