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

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

An adjoint-based methodology is proposed to compute the gradient of the outcomes of mathematical models for the coagulation cascade. The method is first exposed and validated by considering a simple, analytically tractable case involving only 3 species. Its potential is further illustrated by considering a detailed model for the extrinsic pathway involving 34 chemical species interacting through 45 chemical reactions and for which the gradient of Endogeneous Thrombin Potential, clotting time, maximum rate and peak value of thrombin with respect to the initial concentrations and reactions rates are computed. It is shown that the method produces gradients estimates that are fully consistent with the finite differences approximation used so far in the literature, but at a much lower computational cost.

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

Thrombin is an enzyme produced during blood coagulation that is crucial to the formation of a stable clot. Thrombin cleaves soluble fibrinogen into fibrin, which polymerizes and forms an insoluble, stabilizing gel around the growing clot. A small fraction of circulating fibrinogen is the variant γA/γ′, which has been associated with high-affinity thrombin binding and implicated as a risk factor for myocardial infarctions, deep vein thrombosis, and coronary artery disease. Thrombin is also known to be strongly sequestered by polymerized fibrin for extended periods of time in a way that is partially regulated by γA/γ′. However, the role of γA/γ′-thrombin interactions during fibrin polymerization is not fully understood. Here, we present a mathematical model of fibrin polymerization that considered the interactions between thrombin, fibrinogen, and fibrin, including those with γA/γ′. In our model, bivalent thrombin-fibrin binding greatly increased thrombin residency times and allowed for thrombin-trapping during fibrin polymerization. Results from the model showed that early in fibrin polymerization, γ′ binding to thrombin served to localize the thrombin to the fibrin(ogen), which effectively enhanced the enzymatic conversion of fibrinogen to fibrin. When all the fibrin was fully generated, however, the fibrin-thrombin binding persisted but the effect of fibrin on thrombin switched quickly to serve as a sink, essentially removing all free thrombin from the system. This dual role for γ′-thrombin binding during polymerization led to a paradoxical decrease in trapped thrombin as the amount of γ′ was increased. The model highlighted biochemical and biophysical roles for fibrin-thrombin interactions during polymerization and agreed well with experimental observations.