Abstract
The fibrin clot is gelatinous matter formed upon injury to stop blood loss and is later destroyed by fibrinolysis, an enzymatic cascade with feedback. Pharmacological fibrinolysis stimulation is also used to destroy pathological, life-threatening clots and thrombi (thrombolysis). The regulation of the nonlinear spatially nonuniform fibrinolytic process in thrombolysis is not currently well understood. We developed a reaction-diffusion-advection model of thrombolysis by tissue plasminogen activator (TPA) in an occluded vessel with a pressure gradient. Sensitivity-analysis-based model reduction was used to reveal the critical processes controlling different steps of thrombolysis. The propagation of thrombolysis in the system without flow was predominantly controlled by TPA diffusion, whereas transport of other active components was rendered nonessential either by their high fibrin-binding parameters and short lifetimes or their initial uniform distribution. The concentration of the main TPA inhibitor plasminogen activator inhibitor 1 (PAI-1) controlled both the extent of lysis propagation and the shape of fibrin spatial distribution during lysis. Interestingly, PAI-1 remained important even when its concentration was an order of magnitude below that of TPA because of its role at the edge of the diffusing TPA front. The system was robust to reaction rate constant perturbations. Using these data, a reduced model of thrombolysis was proposed. In the presence of flow, convection of TPA was the critical controlling process; although the role of PAI-1 concentration was much less in the presence of flow, its influence became greater in the presence of collateral bypassing vessels, which sufficiently reduced TPA flux through the thrombus. Flow bypass through the collateral vessel caused a decrease in TPA flux in the clotted vessel, which increased the PAI-1/TPA ratio, thus making PAI-1-induced inhibition relevant for the regulation of spatial lysis up to its arrest.