In our simulations, we assume platelets to be spheres with radius of 1.5 μm and number density of 300,000 mm−3, while blood is assumed to be an incompressible Newtonian fluid. The kinetic constants are given as k7,9 = 32.4 min−1, K7,9M = 24 nM, k7,10 = 103.0 min−1, K7,10M = 240 nM. The third aspect of Virchow’s triad includes arterial or venous stasis of the blood, which could be due to immobility, pregnancy, or impaired blood flow resulting from previous thrombosis (e.g., residual blood clot, remodeling or fibrosis of blood vessels, or atherosclerosis). We also find that upon increasing the shear rate from 15,000 to 28,000 s−1, parts of the formed aggregate mostly on the outer edge of thrombus start to detach as the shear forces increase dramatically and overcome adhesive forces (see Fig 8d–8f). In order to estimate platelet interaction forces that cause platelet aggregation at elevated shear rates, we first use the data of Westein et al. At the site of injury, we assume that the subendothelium-bound TF-VIIa complex drives the extrinsic pathway of the coagulation cascade through the subendothelium reactions that are represented by Neumann boundary conditions in the form of −Dj∂cj/∂n = Bj. If blood velocity is increased further to 800 μm/s, the higher shear stresses on the surface of the platelet aggregate limit further aggregation, and thus reduces the growth rate. The experimental measurements of Kim et al. Specifically, SEM is used to solve the flow field and the reactive transport of chemical species on a fixed Eulerian grid, whereas FCM is implemented to describe the two-way interactions between the blood flow and Lagrangian particles (i.e., platelets). Thrombus is a blood clot that forms either in a vein or an artery even though you are not bleeding. Platelets are fundamental to both hemostasis and thrombosis in many vascular diseases, including abdominal aortic aneurysm (AAA), thoracic aortic aneurysm and dissection (TAAD), and carotid atherosclerosis [1–3]. The repulsive forces rise exponentially for inter-platelet distances less than r < d to prevent cellular overlap. The occlusion of vessels due to atherosclerosis and thrombin formation in the coronary arteries of the heart may lead to ischemic heart disease and myocardial infarction. More specifically, we use the in vivo experimental data of Begent and Born for venous thrombus formation in mice [19] to calibrate our model for low-shear-rate regimes, where platelet aggregation is induced by the release of ADP in vivo causing the formation of white thrombi. 2018;5:147, Insull W. The pathology of atherosclerosis: plaque development and plaque responses to medical treatment. 2018 Nov;53:234-242, Cicenia M, Fedele F, Petronilli V, De Carlo C, Moscucci F, Schina M, Sciomer S. Hidden in the heart: A peculiar type of left ventricular remodeling after acute myocardial infarction. Historically, the likelihood of embolic events was greatest in the first 2 weeks after the acute event and tapered off over the ensuing 6 weeks. Factor XII regulates the pathological process of thrombus formation on ruptured plaques. Our main goal in this paper is to develop a phenomenological model for platelet-wall and platelet-platelet adhesion, whose strength depends on the local shear rate, to represent different adhesion mechanisms. (11) Was this page helpful? Thrombosis occurs throughout our arterial system, especially in those with predisposing cardiovascular risk factors. Results from (b) replotted here for comparison (−□−). In this study, we concentrate on its two crucial steps: (i) platelets adhered to a vessel wall, or simply platelet adhesion, and (ii) platelets clumping and arrested to the adherent platelets, named platelet aggregation. Heparin is a preferred drug for dissolving the clot. The time course of aggregate density is plotted in Fig 9b; it shows similar exponential growth after an initial transient time (≈ 5s), and in agreement with the experiments of Begent and Born [19]. The effect of the platelets on the flow field is incorporated into the body force term f (x, t) in the Navier-Stokes Eq (1). We plot the results of platelet aggregation in an 80% stenosis in Fig 7 with both numerical and experimental platelet density profiles inside the stenosis. Numerical modeling of thrombus formation and growth is a challenging problem due to multiscale and multiphysics nature of clotting process, which involves fluid mechanics, cell mechanics, and biochemistry. Printed number in each figure is the undisturbed maximum wall shear rates encountered in each stenosis (before aggregation occurs). https://doi.org/10.1371/journal.pcbi.1005291.g008. Simulation results (−□−) are based on the activation delay time τact = 6 ± 3ms, and the error bars are computed based on 5 simulations with the same τact; experimental data (−○−) are extracted from Westein et al. Heparin and warfarin are often used to inhibit the initiation and propagation of existing thrombus. As shown in Fig 1, the Morse potential is similar to a Lennard-Jones potential; it consists of both attractive (at r > d) and repulsive parts (at r < d). The conformational change of vWF exposes the repeating functional A-1 domains in multimeric vWF, leading to enhanced adhesive interactions between GPIb and vWF [12–15]. This results in a few reactions at the wall (represented by flux conditions) that form enzymes IXa and Xa that drive the TF pathway. where [Ia]thr = 5,000 nM is the threshold concentration at the core of the clot causing the lowest clot permeability k = 8(10)−12 m2. In cases of endothelial injury or exposure of extracellular matrix to blood flow, however, platelets can quickly activate and cover the injured area to stop bleeding. Available from: https://www.ncbi.nlm.nih.gov/books/NBK538430, Mackman N. Triggers, targets and treatments for thrombosis. They discovered that thrombus growth in venules with diameters of 40 − 60μm reached a maximum at a blood flow velocity around 400μm/s due to the balance between the number of platelets transported to the injured sites and the shear stress on the surface of the growing thrombus. Hypercoagulability is a general hematologic concept that merely means increased risk of thrombosis (i.e., thrombogenic) via enhanced levels of prothrombotic components in the bloodstream. Its presence in the distal part of the vessel can induce ischemia, which can result in limb loss 5). [33]. 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