Wilhelmus E. A. de Witte (1), Alexander Kulesza (1), Stephan Schaller (1)
(1) ESQlabs GmbH, Saterland, Germany
Introduction:
The development and application of pharmacometric models to describe and predict preclinical and clinical studies has become a routine exercise for an ever-growing community of pharmacometricians. However, in-depth analysis to gain insight into the developed models and the biological systems they represent is often lacking or minimal. The main tools applied to explore the applied models are individual simulations for smaller models and a (global) sensitivity analysis for larger (QSP or PBPK) models[1]. Occasionally, small (semi-)mechanistic models are thoroughly analyzed mathematically with tools such as a bifurcation analysis[2] or singular perturbation theory[3]. While this mathematical analysis provides a comprehensive insight, it requires a specific skillset and is often difficult to scale to large QSP or PBPK models and it is therefore not part of the standard pharmacometrics workflow. The current limitations in model analysis tools limits our understanding of the applied models. This decreases the efficiency of model development, the clarity of model communications and the quality/reproducibility of models, since model specification errors are more likely to pass undetected with a limited understanding of model behavior.
Objectives:
In this study, we aim to bridge the gap between generic numerical high-level model analysis tools for large models and analytical in-depth model analysis tools for small models, by developing a numerical in-depth model analysis toolbox that can be applied to large models.
Methods:
The analysis toolbox presented here utilizes the standard sensitivity analysis spider plots as present in the esqlabsR package (v5.1.3) and the ospsuite package (v12.0.0) in R (v4.3.1). Simulation models were created using a whole-body Physiologically-Based Pharmacokinetic model (PK-Sim® v11.2) and extended in MoBi® (v11.2) to include TMDD or PD models. The created models were saved as .pkml files and analyzed in R using dedicated R code for the developed analysis toolbox.
Results:
The starting point for this analysis was the first extension of a single local sensitivity analysis: a repeated local sensitivity analysis with the impact of a change in parameter value evaluated for the change in summary PK parameters such as AUC, Cmax or half-life. The impact of parameter changes can be visualized by plotting the summary PK parameters versus the change in parameter values in a so-called spider plot. Here we developed a “repeated spider plot”, a first extension of a single spider plot, by repeating the same analysis for various combinations of two other parameters that define relevant scenarios. The next step towards a comprehensive understanding of model behavior was the normalization of the sensitivity for the sensitivity of the previous step in the causal change, which can be used to identify where the observed sensitivity originates. Finally, we applied the repeated spider plot to a modified model with continuous infusion in multiple compartments to identify rate-limiting steps and conditions as well as the compartment in steady-state. The developed analysis tools were applied to several whole-body PBPK model elements including a combined tissue TMDD-PBPK model and to a simple two-compartment model for comparison.
Conclusion:
Our study demonstrates how variations on the local sensitivity analysis can provide a comprehensive insight into model behavior of large-scale mechanistic models, for which analytical model analysis is unfeasible. The studied examples demonstrate how these analysis tools can reveal rate-limiting steps and in which conditions the potential rate-limiting steps become relevant. The provided numerical analysis tools resolve the limited insight provided by other numerical tools like the global sensitivity analysis, while still being applicable to large-scale models.
References:
[1] D. Lee, S. Nayak, S.W. Martin, A.C. Heatherington, P. Vicini, F. Hua, A quantitative systems pharmacology model of blood coagulation network describes in vivo biomarker changes in non-bleeding subjects, J. Thromb. Haemost. 14 (2016) 2430–2445. https://doi.org/10.1111/jth.13515.
[2] S. Bakshi, E. de Lange, P. van der Graaf, M. Danhof, L. Peletier, Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study, CPT Pharmacomet. Syst. Pharmacol. 5 (2016) 339–351. https://doi.org/10.1002/psp4.12098.
[3] L.A. Peletier, J. Gabrielsson, Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification, J. Pharmacokinet. Pharmacodyn. 39 (2012) 429–451. https://doi.org/10.1007/s10928-012-9260-6.
Reference: PAGE 32 (2024) Abstr 11252 [www.page-meeting.org/?abstract=11252]
Poster: Methodology - New Modelling Approaches