A Computational Workflow for Probabilistic Quantitative in Vitro to in Vivo Extrapolation

Abstract

A computational workflow was developed to facilitate the process of quantitative in vitro to in vivo extrapolation (QIVIVE), specifically the translation of in vitro concentration-response to in vivo dose-response relationships and subsequent derivation of a benchmark dose value (BMD). The workflow integrates physiologically based pharmacokinetic (PBPK) modeling; global sensitivity analysis (GSA), Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) simulation. For a given set of in vitro concentration and response data the algorithm returns the posterior distribution of the corresponding in vivo, population-based dose-response values, for a given route of exposure. The novel aspect of the workflow is a rigorous statistical framework for accommodating uncertainty in both the parameters of the PBPK model (both parameter uncertainty and population variability) and in the structure of the PBPK model itself recognizing that the model is an approximation to reality. Both these sources of uncertainty propagate through the workflow and are quantified within the posterior distribution of in vivo dose for a fixed representative in vitro concentration. To demonstrate this process and for comparative purposes a similar exercise to previously published work describing the kinetics of ethylene glycol monoethyl ether (EGME) and its embryotoxic metabolite methoxyacetic acid (MAA) in rats was undertaken. The computational algorithm can be used to extrapolate from in vitro data to any organism, including human. Ultimately, this process will be incorporated into a user-friendly, freely available modeling platform, currently under development, that will simplify the process of QIVIVE.

Keywords: PBPK; benchmark dose; computational; extrapolation; in vitro; in vivo; workflow.

Figure 1

(A) Comparison of PBPK model predictions of MAA in venous blood against the experimental data of Hays et al. (2000) (upper panel); (B) a comparison of 10 alternative parameter sets against the experimental data of Hays et al. (2000) following an oral dose of 3.3 mmol/kg bodyweight EGME (lower panel).

Figure 2

Lowry plots of the eFAST quantitative measure of the most sensitive parameters identified by Morris screening. The total effect of a parameter S_Ti comprised the main effect S_i (purple bar) and any interactions with other parameters (gray bar) given as a proportion of variance. The ribbon, representing variance due to parameter interactions, is bounded by the cumulative sum of main effects (lower bold line) and the minimum of the cumulative sum of the total effects (upper bold line) (A) for venous blood MAA concentrations following, (A) inhalation exposure (upper panel), and (B) oral exposure (lower panel).

Figure 3

Posterior mode and a 95% credible interval for the exposure-time concentration of MAA following a 5 day inhalation exposure to 10 ppm (A) and 50 pmm (B) EGME.

Figure 4

Posterior mode and a 95% credible interval for the exposure-time concentration of MAA following and oral dose of 3.3 mmol/kg bodyweight EGME.

Figure 5

Comparisons of the 200 concentration response profiles simulated in the rejection phase for a target concentration of 0.28 mM: (A) 200 exposure-time concentrations of MAA following a 5 day inhalation exposure (upper left panel); (B) retained samples within a relative error of 7.5% (upper right panel); (C) 200 exposure-time concentrations of MAA following an oral dose (lower left panel); (D) retained samples within a relative error of 7.5% (lower right panel).

Figure 6

Comparison of 95% credible intervals for concentration-responses within a relative error of 5% (lighter interval) and based on only those samples with parameters within the calibrated limits (darker interval): (A) exposure-time concentrations of MAA following a 5 day inhalation exposure (upper panel); (B) exposure-time concentrations of MAA following an oral dose (lower panel).

Figure 7

Predicted in vivo dose response curves for developmental toxicity of EGME after, (A) inhalation (upper panel), and (B) oral exposure (lower panel) showing the median, 2.5 and 97.5% percentiles.