Undine Falkenhagen (1,2), Jane Knöchel (1,3), Charlotte Kloft (4), Wilhelm Huisinga (2)
(1) PharMetrX Graduate Research Training Program: Pharmacometrics & Computational Disease Modelling, Freie Universität Berlin/Universität Potsdam, (2) Mathematical Modelling and Systems Biology, Institut fu¨r Mathematik, Universität Potsdam, (3) Current Address: AstraZeneca R&D, Mölndal, Sweden, (4) Institut fu¨r Pharmazie, Freie Universität Berlin
Objectives: Quantitative systems pharmacology (QSP) models integrate comprehensive knowledge about pharmacologically relevant processes. QSP models, however, are usually very complex and not suitable for parameter estimation in the context of analysing clinical data. It would nevertheless be desirable to leverage this knowledge to derive simple, mechanism-based pharmacodynamic (PD) models suitable for population analysis of clinical trial data. A prototypical example is the effect of warfarin on blood coagulation and the international normalised ratio (INR) as a measure of warfarin effect on the coagulation time. Our objective was to derive a reduced model of the effect of warfarin on key coagulation factors that influence the prothrombin time (driving the INR), and a simple algebraic model of the INR that only depends on these key coagulation factors.
Methods: We used a published QSP blood coagulation model [1] to describe the action of warfarin. The same model can also be used to determine the prothrombin time (determined as the time at which the AUC of fibrin concentration-time course reaches a certain value). To compute the INR using the QSP blood coagulation model, simulations of two scenarios are needed: (i) the in vivo effect of warfarin on the concentrations of coagulation factors by indirect inhibition of the synthesis rates (warfarin model); and (ii) the in vitro effect of the relevant coagulation factor concentrations on the PT (and correspondingly the INR) after activation of the system by the addition of tissue factor (INR model). We reduced the warfarin and INR models using the model order reduction approach in [2] based on the novel concept of input-response indices. We further reduced the INR model by linearising and eliminating reactions that were not important on the relevant time scale. Subsequently we were able to solve the INR model analytically.
Results: The model reduction yielded an in vivo model describing the action of warfarin on the coagulation factors concentrations II, VII and X only, and a simplified in vitro model dependent on these factor concentrations. The simplified model also approximates the original model well under parameter variability.
Solving the simplified in vitro model analytically, we inferred that the fibrin concentration depends on the warfarin model only via the product of the concentrations of factors II, VII and X. From this, we found an approximate solution for the INR model depending only on the product of the factor concentrations II, VII and X. This algebraic representation greatly simplified the computation of the INR model (by avoiding to solve the ODEs numerically).
Our mechanistic derivation of the warfarin PD model also sheds light on empirically determined PD models like the models published in [3,4], as these could be derived as further approximations to the above INR equation. For example, our PD model indicates that the artificial quantities in the empirical model in [3] represent relative changes in coagulation factor concentrations after warfarin treatment.
Conclusion: We present a general approach to reduce complex QSP models to simple mechanistic PD models. A reduced mechanistic PD model can add interpretability to existing PD models or act as a basis for population modelling. The approach yields a suitable model in the example of warfarin effect on INR, and can be applied to other QSP models as well.
References:
[1] Wajima, Y. et al.: A comprehensive Model for the Humoral Coagulation Network in Humans. Clin Pharmacol Ther, 86, 260-298 (2009)
[2] Knöchel, J. et al.: Understanding and reducing complex systems pharmacology models based on a novel input-response index. J Pharmacokinet Pharmacodyn, 45, 139-157 (2018)
[3] Hamberg, A.-K. et al.: A PK-PD Model for Predicting the Impact of Age, CYP2C9, and VKORC1 Genotype on Individualization of Warfarin Therapy. Clin Pharmacol Ther, 81, 529-538 (2007)
[4] Ohara, M. et al.: Determinants of the Over-Anticoagulation Response during Warfarin Initiation Therapy in Asian Patients Based on Population Pharmacokinetic-Pharmacodynamic Analyses. PLoS ONE, 9 (2014)
Reference: PAGE 29 (2021) Abstr 9844 [www.page-meeting.org/?abstract=9844]
Poster: Methodology - New Modelling Approaches