Sensitivity analysis of a reduced model of thrombosis under flow: Roles of Factor IX, Factor XI, and γ‘-Fibrin

Abstract

A highly reduced extrinsic pathway coagulation model (8 ODEs) under flow considered a thin 15-micron platelet layer where transport limitations were largely negligible (except for fibrinogen) and where cofactors (FVIIa, FV, FVIII) were not rate-limiting. By including thrombin feedback activation of FXI and the antithrombin-I activities of fibrin, the model accurately simulated measured fibrin formation and thrombin fluxes. Using this reduced model, we conducted 10,000 Monte Carlo (MC) simulations for ±50% variation of 5 plasma zymogens and 2 fibrin binding sites for thrombin. A sensitivity analysis of zymogen concentrations indicated that FIX activity most influenced thrombin generation, a result expected from hemophilia A and B. Averaging all MC simulations confirmed both the mean and standard deviation of measured fibrin generation on 1 tissue factor (TF) molecule per μm2. Across all simulations, free thrombin in the layer ranged from 20 to 300 nM (mean: 50 nM). The top 2% of simulations that produced maximal fibrin were dominated by conditions with low antithrombin-I activity (decreased weak and strong sites) and high FIX concentration. In contrast, the bottom 2% of simulations that produced minimal fibrin were dominated by low FIX and FX. The percent reduction of fibrin by an ideal FXIa inhibitor (FXI = 0) ranged from 71% fibrin reduction in the top 2% of MC simulations to only 34% fibrin reduction in the bottom 2% of MC simulations. Thus, the antithrombotic potency of FXIa inhibitors may vary depending on normal ranges of zymogen concentrations. This reduced model allowed efficient multivariable sensitivity analysis.

An adjoint‐based method for the computation of gradients in coagulation schemes

“…The Monte Carlo approach, where about 10 4 À 10 5 simulations are performed with randomly selected input values, was followed by a few groups in the past. 17,18,[20][21][22] This methodology is accurate but time consuming and hardly tractable for complex models. Several parametric studies were also performed, where the outcome of the model is analysed for different deficiencies in coagulation factors.…”

“…Making the models useful in the current efforts towards a better understanding of coagulation requires knowing how thrombin production depends on the uncertain inputs. The Monte Carlo approach, where about simulations are performed with randomly selected input values, was followed by a few groups in the past 17,18,20–22 . This methodology is accurate but time consuming and hardly tractable for complex models.…”

Mathematical modeling to understand the role of bivalent thrombin-fibrin binding during polymerization

“…The interactions between thrombin and γ ′ fibrinogen may also provide possible avenues to develop targeted, thrombin-exosite peptides that exploit thrombin allostery [ 15 , 19 , 20 ]. Low levels of γ ′ fibrin(ogen) are associated with increased fibrin generation and increased thrombin generation [ 21 ]. Additionally, it has been suggested that fibrin-trapped thrombin, or the disruption thereof, could play a role in the observed fibrinolytic breakdown as a result of COVID-19 infection that leads to unintended bleeding and clotting.…”