A mathematical model for warfarin reversal using vitamin K

Introduction: Vitamin K is indicated for warfarin reversal when active bleeding is present or when there is a high risk of bleeding (INR > 5). However, choosing an appropriate dose of vitamin K is challenging due to our limited understanding of the dose-response relationship and the interactions between warfarin and the vitamin K cycle. For instance, an unexpectedly prolonged resistance to warfarin has been reported with the use of vitamin K for warfarin reversal. The aim of this study was to develop a mechanistic mathematical model to describe the interactions between warfarin and vitamin K cycle, and to use the model to explore the underpinning enzyme kinetics that are consistent with pharmacodynamic outcomes observed during warfarin initiation, warfarin overdose, and warfarin reversal with vitamin K.

Methods: The model structure was derived based on individual mechanistic components identified from the literature. The system was described by a set of 18 ordinary differential equations, with 11 reactions/fluxes and 43 parameters. Simulations from the model were conducted in MATLAB Version R2017a (The MathWorks, Inc., Natick, Massachusetts, United States). Initial estimates of the parameters were set to values derived from the published literature or arbitrary values if such values were unavailable. Parameter values were then calibrated heuristically to achieve reported steady-state amounts for five moieties of interest: vitamin K epoxide, vitamin K quinone, vitamin K hydroquinone, coagulation proteins, and the international normalised ratio for three scenarios: (1) physiological condition, (2) warfarin maintenance therapy, and (3) warfarin reversal with vitamin K.

Results: The model developed performed acceptably in simulating the five states of interest for all the three different scenarios. In the initial stage, the model, which specified that vitamin K reduction can only occur via the vitamin K epoxide reductase (VKOR), was not able to replicate the effect of vitamin K on reversing warfarin overdose. However, when an alternative (putative non-VKOR pathway) for vitamin K reduction was introduced, the rapid reversal effect of vitamin K on warfarin was able to be captured adequately. This finding is significant because it highlights the importance of the alternative pathway in reversing warfarin overdose which has not been well explored in previous studies.

Discussion: This model serves as a starting point to improve our current understanding of warfarin and the vitamin K system. Further work is required to refine the model. The model may be applied to explore various clinical scenarios and to determine suitable dose and frequency to administer vitamin K for effective warfarin reversal.