A Quantitative Systems Pharmacology Model to Predict the Effects of Warfarin, Rivaroxaban and Enoxaparin on the Human Coagulation Network

Aims: Warfarin is the anticoagulant of choice for venous thromboembolism treatment. However, its suppression of the endogenous clot dissolution components PC and PS, and consequently of the APC:PS complex, ultimately leads to longer time-to-clot dissolution profiles, resulting in an increased re-thrombotic risk. (1,2) Other anti-coagulants, such as enoxaparin or the direct oral anti-coagulants such as rivaroxaban, might constitute an alternative to warfarin as they act via different pathways, therefore hypothesized to not stimulate the suppression of the endogenous clot dissolution components. The objective was to develop a quantitative systems pharmacology (QSP) model describing the coagulation network to monitor coagulation factor levels under warfarin, enoxaparin, and rivaroxaban treatment.

Methods: Individual steady-state coagulation factor concentrations from therapeutic drug monitoring of 312 subjects on enoxaparin (dose levels: 40, 60, 80, 120 mg), rivaroxaban (dose levels: 15, 20, 30 mg) and warfarin/phenprocoumon (Vitamin K antagonists (VKA)) (dose levels: 2.5, 5, 7.5 mg) treatment (observed coagulation factor level concentrations for rivaroxaban: factor II (FII), FV, FVII, FIX, FX, FXI, FXII, FXIII, protein S (PS), protein C (PC); for VKA: PC, PS, plasminogen, for enoxaparin: PC, PS, plasminogen) were used to develop and to externally evaluate a QSP model of the coagulation network build in MATLAB® using Wajima et al. (3) as a starting point. Additional coagulation factor level concentrations of PC and PS were available from subjects (n=20) being switched from VKA to enoxaparin or rivaroxaban treatment. Parameter values for all factor rate constants (Vmax, Km) as well as production rates in the QSP model were estimated using global optimization. Inter-individual variability of ±20% was added on the production rates of FII, FV, FVII, FIX, FX, FXI, FXII, FXIII, PC, PS, plasminogen, and fibrinogen. Drug effects of rivaroxaban, enoxaparin and VKA were incorporated into the model via separate dosing compartments and pathways according to their specific mechanisms of action. Sobol sensitivity analysis4 was performed to identify key parameters having the greatest impact on clot dissolution. External model evaluation using data not utilized for model development was performed using MatVPC5.

Results: The developed QSP model allowed for estimation of the individual coagulation factor rate constants and production rates based on the available individual subject coagulation factor level concentrations. The coagulation factor activation reactions were computed using Michaelis-Menten kinetics. Predictions of individual coagulation factor time courses under steady-state VKA, enoxaparin, and rivaroxaban treatment were well described by the developed model and reflected the suppression of PC and PS under VKA treatment compared to rivaroxaban and enoxaparin. Treatment switch from VKA to either enoxaparin or rivaroxaban was simulated using the developed QSP model and evaluated by overlaying the simulations with the observed data. The simulations described the observed 50% increase in PC and PS factor levels adequately well after subjects were switched from VKA to rivaroxaban or enoxaparin treatment. Additionally, the model was able to estimate the duration of level recovery to be 9 and 11 days for PC and PS levels, respectively. Concordantly, treatment switch from enoxaparin to VKA lead to a 50% decrease in PC and PS factor levels and the estimated duration of level suppression was 8 and 10 days, respectively. Sobol sensitivity analysis (4) identified the production rate for vitamin K being the most influential parameter to stimulate clot-dissolution. External model evaluation using the Monte Carlo simulation tool in MatVPC (5), resulted in adequately well predictions of all coagulation factor level concentrations for dosing regimens and subjects not used during model development.

Conclusion: A QSP model was developed to describe the human coagulation network and time courses of several clotting factors under different treatment regimens. The model may be used as a tool during clinical practice or regulatory decision making to predict the effects of different anti-coagulant therapies on individual clotting factor time-courses to optimize anti-thrombotic therapy regimens.

References: 1. Haran MZ, et al. Unbalanced protein s deficiency due to warfarin treatment as a possible cause for thrombosis. Br. J. Haematol. 139, 310–1 (2007) 2. Hackeng TM, et al. Protein s stimulates inhibition of the tissue factor pathway by tissue factor pathway inhibitor. Proc. Natl. Acad. Sci. U. S. A. 103, 3106–11 (2006) 3. Wajima T, et al. A comprehensive model for the humoral coagulation network in humans. Clin. Pharmacol. Ther. 86, 290–8 (2009) 4. Zhang, X., et al. Sobol Sensitivity Analysis : A Tool to Guide the Development and Evaluation of Systems Pharmacology Models. CPT Pharmacometrics Syst. Pharmacol. 4, 1–4 (2015) 5. Biliouris K, et al. MatVPC: A user-friendly MATLAB-based tool for the simulation and evaluation of systems pharmacology models. CPT Pharmacometrics Syst. Pharmacol. 4, 547–557 (2015)