Mathematical Framework for Platelet Plug Coagulation
Fig 1 : Schematic of mathematical framework depicting (1) the discrete platelet plug, the (2) reduced coagulation model of thrombin generation on the surfaces of platelets in the plug, and (3) the fibrin polymerization model which assumes species larger than monomer are not transported. We envision that the variables of the reduced model of coagulation roughly represent actual coagulation species E 0 E_{0} (TF:fVIIa), S 1 S_{1} (fX), E 1 E_{1} (fXa), S 2 S_{2} (prothrombin), E 2 E_{2} (thrombin), C 2 b = S 1 b : E 2 b C_{2}^{b}=S_{1}^{b}:E_{2}^{b} (platelet-bound tenase fVIIIa:fIXa), and C 1 b
Paper context
Paper title: Platelet plug microstructure and flow modulate fibrin gelation dynamics: Insights from computational simulations Abstract: During the formation of a thrombus, the architecture of the growing platelet aggregate is heterogeneous, with areas of dense and loosely packed platelets. The surface of activated platelets facilitate biochemical coagulation reactions that ultimately result in the formation of a fibrin network which stabilizes the thrombus. How platelet-plug microstructure and flow jointly govern the onset and development of fibrin is incompletely understood. We developed a novel 2D computational framework that integrates (1) a pre-adhered, discrete platelet aggregate, (2) a reduced coagulation model that generates thrombin, and (3) a fibrin polymerization model. Three platelet-plug configurations were constructed with prescribed interplatelet gaps and simulations were performed with various wall shear rates. We quantified spatiotemporal clotting metrics, including coagulation factor concentrations, fibrin evolution, and gelation onset. Across geometries, gelation initiation accelerated with increasing plug density. For more dense geometries, gelation emerged first near the plug periphery. As the platelet density increased, intraplug transport was increasingly restricted and the thrombin concentrations in between platelets increased. In contrast, the loose plug supported fibrinogen replenishment deeper into the plug core. Despite slower coagulation initiation due to reduced platelet surface area, monomer generation persisted in the interior, causing gelation to begin at the vessel wall. These Passages referencing this figure: levant shear conditions. This study systematically explores how platelet microstructure and shear rate together modulate thrombin generation and fibrin polymerization. By quantifying the temporal and spatial metrics of clot initiation, such as thrombin concentration, fibrin development, and gelation onset, we aim to provide deeper mechanistic insights into the initial steps of thrombus formation. Fig 1 : Schematic of mathematical framework depicting (1) the discrete platelet plug, the (2) reduced coagulation model of thrombin generation on the surfaces of platelets in the plug, and (3) the fibrin polymerization model which assumes species larger than monomer are not transported. We envision that the variables of the reduced model of coagulation roughly represent actual coagulation species
