A Workflow for Global Sensitivity Analysis of PBPK Models

Abstract

Physiologically based pharmacokinetic (PBPK) models have a potentially significant role in the development of a reliable predictive toxicity testing strategy. The structure of PBPK models are ideal frameworks into which disparate in vitro and in vivo data can be integrated and utilized to translate information generated, using alternative to animal measures of toxicity and human biological monitoring data, into plausible corresponding exposures. However, these models invariably include the description of well known non-linear biological processes such as, enzyme saturation and interactions between parameters such as, organ mass and body mass. Therefore, an appropriate sensitivity analysis (SA) technique is required which can quantify the influences associated with individual parameters, interactions between parameters and any non-linear processes. In this report we have defined the elements of a workflow for SA of PBPK models that is computationally feasible, accounts for interactions between parameters, and can be displayed in the form of a bar chart and cumulative sum line (Lowry plot), which we believe is intuitive and appropriate for toxicologists, risk assessors, and regulators.

Keywords: Lowry plot; PBPK; alternatives; global sensitivity analysis.

Figure 1

Schematic of the PBPK model for m-xylene.

Figure 2

Simulation of venous blood m-xylene and urinary excretion of methylhippuric acid (expressed against creatinine). The symbols are typical measured values from two volunteers and the solid lines are model predictions using mean point values for anatomical, physiological and biochemical parameters for, (A) CV and (B) C_urine. In panel (A) the lower broken line shows the region of approximate total variance. The upper broken line is the approximate total variance multiplied by 25 in order to show more clearly the relationship to model prediction. The short broken lines at 3 and 5 h in panel (A) and 5 and 8 h in panel (B) show the time slices chosen for eFAST analysis.

Figure 3

The Morris Screening exercise. Results of the Morris Screening exercise for, (A) the concentration of m-xylene in venous blood (CV) and, (B) the urinary excretion of methylhippuric acid (expressed against creatinine) (C_urine).

Figure 4

Lowry plot of the eFAST quantitative measure. The total effect of a parameter ($S_{T_i}$), is comprised the main effect S_i (black bar) and any interactions with other parameters (grey 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) CV at 3 h, (B) CV at 5 h, (C) C_urine at 5 h and (D) C_urine at 8 h.

Figure 5

Selected latticed Lowry plots showing concentration and time-dependent changes in parameter interactions and ordering.