gms | German Medical Science

Background: Comprehensive knowledge about pharmacologically relevant processes is comprised in large-scale systems biology models. While these models thus contain important biological information, their complexity renders them unsuitable for parameter estimation, e.g. when analysing clinical data. It would therefore be desirable to leverage these models to derive simple, mechanism-based drug effect models suitable for the analysis of clinical trial data. The anticoagulant effect of the drug warfarin on blood coagulation is a prototypical example where knowledge from a systems biology model can be exploited to derive a mechanism-based drug effect model. In the clinics, the effect of warfarin is quantified by the international normalised ratio (INR), which describes the time until blood clots in vitro. Our objective was to derive a simple algebraic formula for the INR from a systems biology blood coagulation model.

Methods: We started from the published blood coagulation model [1] to simulate the anticoagulant effect of warfarin on the INR. Warfarin influences the blood coagulation system by lowering the concentrations of specific coagulation factors. For the calculation of the INR, the concentration-time course of Fibrin is of special interest. Fibrin is a coagulation factor that can cross-link the blood cells, thus, strengthening the blood clot. To derive a simple algebraic formula for the INR, we first reduced the blood coagulation model by using the model order reduction approach presented in [2], which is based on the novel concept of input-response index. A close examination of the reduced model allowed us to further reduce the model such that we were able to solve the final model analytically.

Results: The model reduction yielded a simplified blood coagulation model, which depends on the warfarin concentration only via three coagulation factor concentrations (factors II, VII and X). We obtained the approximate analytic solution for Fibrin concentration:

(F(t)=II VIIX(p(t)+q(t)(-ct))),

where c is constant and p(t) and q(t) are polynomials of third and first order, respectively. It can be seen that Fibrin and consequently the INR depend on warfarin only via the product of the three factor concentrations. From this, an algebraic equation for the INR can be derived. This algebraic representation greatly simplifies the computation of the INR since it eliminates the need to solve the differential equations in the blood coagulation model numerically. Our mechanistic derivation of the warfarin effect model also sheds light on empirically determined warfarin effect models, e.g. [3], [4]. These models can be derived by further approximations to our INR equation, thus providing them with mechanistic interpretation.

Conclusion: We presented a model order reduction approach that allowed us to derive a mechanism-based drug effect model for warfarin action on INR from a blood coagulation model. This approach can also be used to derive simple mechanism-based effect models from other complex systems biology models, thereby making them accessible for statistical analysis of clinical data.

WH has received research funding from an industry consortium (AbbVie Deutschland GmbH & Co. KG, AstraZeneca, Boehringer Ingelheim Pharma GmbH & Co. KG, Grünenthal GmbH, F. Hoffmann-La Roche Ltd, Merck KGaA and SANOFI) to support the PharMetrX PhD program.

The authors declare that an ethics committee vote is not required.