Wilhelmus E.A. de Witte, PhD: No financial relationships to disclose
Background: Whole-body PBPK and QSP models are increasingly popular in predicting preclinical and clinical studies in all stages of drug development. However, the size of these models often leaves both the developers and the reviewers of these models and their applications uncertain about the driving factors in the model behavior. 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], which often lack generalizability (local sensitivity) or granularity (global sensitivity). Occasionally, small (semi-)mechanistic models are thoroughly analyzed mathematically with tools such as a bifurcation analysis[2] or singular perturbation theory[3]. This mathematical analysis is often difficult to scale to large QSP or PBPK models.
Objectives: We aimed to increase our understanding of large-scale models and to develop efficient tools that can be applied to large-scale models without losing insight into mechanistic details. We aimed to develop a numerical model analysis toolbox that utilizes continuous infusion simulations to provide a numerical steady-state analysis.
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: 3 types of continuous infusion analyses were developed for various applications: firstly, if a long terminal half-life is observed in a single simulation, comparing that same simulation with a continuous infusion in plasma gives the relative concentrations in different organs in steady-state and reveals which concentration is not in steady-state and causing the long terminal half-life in the original simulation. Secondly, a repeated local sensitivity analysis combined with a continuous infusion in different compartments and for various molecular species provided a comprehensive steady-state analysis and the predominant parameters of various elements of large-scale models. These model elements included the partition coefficient calculation methods in the small-molecule whole-body PBPK model, FcRn-mediated endosomal uptake and recycling in the large-molecule whole-body PBPK model, the two-pore model in the large-molecule whole-body PBPK model and a tissue TMDD-PBPK model. Finally, applying the continuous infusion repeated sensitivity analysis with infusion in both compartments of a two-compartment model provided a comprehensive insight into this model with a clear distinction between two possible steady states, depending on the rate-limiting step.
Conclusion: Our study demonstrates how continuous infusion simulations can provide numerical model analysis tools that greatly enhance our understanding of large-scale models. This understanding will improve efficiency in developing and communicating these models and their applications.
Citations: [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.
