Fig 1.
Diagram for the analysis workflow.
κ is the ratio of internal concentration (μM) to dose (mg/kg/day) determined using the PBTK model for an external dose of 1 mg/kg/day. ORMSE is the orthogonal root mean square error. Example chemicals are denoted by Ex1, etc. to enable demonstration of data mergers.
Fig 2.
Diagram of the PBTK model in the httk R package.
Q represents flow rates, Cl indicates hepatic clearance, k indicates absorption rate [23].
Fig 3.
Example regressions of the standardized, log10 transforms of variables.
Results are shown for forward dosimetry (CPBTK, Crandom, Dose; a-c, respectively) and reverse dosimetry (AEDPBTK, AEDrandom, AC50; d-f, respectively) from the endpoint level analysis for the in vitro assay endpoint of ATG_PXRE_CIS_up and the in vivo effect of systemic, nonneoplastic liver pathology from chronic studies. The dashed lines along y = x are the best fit lines for the standardized variables and the corresponding ORMSE (orthogonal root mean square error) are also reported; units are dimensionless.
Fig 4.
Distributions of ORMSE for the endpoint level analysis.
Results are for the assumption set of nonrestrictive clearance and mean total plasma concentration. The number of unique chemicals in the comparison are indicated by fill color. The ORMSE for the random result are median values across the ten sets of results. Figure panels show results for combinations of different ORMSE results and dosimetry: a) PBTK-Forward Dosimetry, b) Random-Forward Dosimetry, c) Dose or AC50-Forward Dosimetry, d) PBTK-Reverse Dosimetry, e) Random-Reverse Dosimetry, and f) Dose or AC50-Reverse Dosimetry.
Fig 5.
Distributions of ORMSE for the POD level analysis.
Results are for the assumption set of nonrestrictive clearance and mean total plasma concentration. The number of unique chemicals in the comparison are indicated by fill color. The ORMSE for the random result are median values across the ten sets of results. Figure panels show results for combinations of different ORMSE results and dosimetry: a) PBTK-Forward Dosimetry, b) Random-Forward Dosimetry, c) Dose or AC50-Forward Dosimetry, d) PBTK-Reverse Dosimetry, e) Random-Reverse Dosimetry, and f) Dose or AC50-Reverse Dosimetry.
Fig 6.
Allocated counts from the forward dosimetry method.
Counts compare in vitro AC50 with predicted in vivo concentration for the endpoint level analysis (top row) and POD level analysis (bottom row) as a function of the assumptions used in application of the PBTK model. Counts are from assay-effect pairs with at least 20 unique chemicals and are median values from the 10 sets of comparisons. The error bars are plus or minus two standard deviations from the 10 comparisons. Labels on the x-axis indicate assumption set: for clearance (res.–restrictive, nres.–nonrestrictive), in vivo concentration selection (tot.–total, free, vein, tis.–tissue, mean, max), and use of the Armitage disposition model to estimate the free concentration in vitro.
Fig 7.
Allocated counts from the reverse dosimetry method.
Counts compare in vivo dose with predicted AED from in vitro toxicity assay results for the endpoint level analysis (top row) and POD level analysis (bottom row) as a function of the assumptions used in application of the PBTK model. Counts are from assay-effect pairs with at least 20 unique chemicals and are median values from the 10 sets of comparisons. The error bars are plus or minus two standard deviations from the 10 comparisons. Labels on the x-axis indicate assumption set: for clearance (res.–restrictive, nres.–nonrestrictive), in vivo concentration selection (tot.–total, free, vein, tis.–tissue, mean, max), and use of the Armitage disposition model to estimate the free concentration in vitro.
Table 1.
Median of variances for log10 transforms of AC50 and dose by analysis level.
Fig 8.
Plots of the log10 transforms of the 10th percentile dose from POD level in vivo data vs the 10th percentile AED using the PBTK model, determined with a time scale of the corresponding lowest dose.
Each point corresponds to a particular chemical. Results are for the assumption set of total mean concentration, and are otherwise indicated by the panel labels: a) restrictive clearance with in vivo mean total venous plasma concentration, b) restrictive clearance with in vivo mean free venous plasma concentration, c) restrictive clearance with in vivo mean free venous plasma and free concentration in vitro predicted by the Armitage model, d) nonrestrictive clearance with mean tissue concentration. The dashed lines are y = x lines. Corresponding RMSE and ORMSE (the latter defined for the standardized variables) are also reported.
Fig 9.
Heatmap of correlation between residuals and input parameters.
Residuals are from comparisons of log10 POD10 and log10 AED10 for each assumption set. The absolute value of the Pearson’s correlation coefficient (|COR|) was determined between the residuals and each input parameter. Labels on the x-axis indicate assumption set: for clearance (res.–restrictive, nres.–nonrestrictive), concentration selection (tot.–total, free, vein, tis.–tissue, mean, max), use of the Armitage disposition model to estimate the free concentration in vitro, and direct comparison to 10th percentile AC50 values.
Fig 10.
Heatmap summarizing results previously shown in Figs 6 and 7.
The fraction of counts for which the PBTK model was selected is indicated by color, with brighter shades indicating a higher fraction of selection. Labels on the x-axis indicate assumption set: for clearance (res.–restrictive, nres.–nonrestrictive), concentration selection (tot.–total, free, vein, tis.–tissue, mean, max), and use of the Armitage disposition model to estimate the free concentration in vitro.