thrombus formation in a deep vein, usually in the legs, that becomes concerning for its potential to lead to embolism in the heart (MI), lungs (pulmonary embolism) or brain (stroke). Color coding for particles is the same as in Fig 3. 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 model platelets as rigid spherical particles using the Lagrangian description within the context of FCM [32], as adopted in [25], whereas the hemodynamics and chemical transport are obtained from the solution of the Navier-Stokes (NS) equations and advection-diffusion-reaction (ADR) equations on a fixed Eulerian grid, respectively. Therefore, the role of heterogeneous coagulation reactions on the surface of adhered platelets would become more crucial to the progression of thrombosis, and must be included in future numerical models. The various quantities reported in these experiments, such as thrombus shape and growth rate as well as platelet aggregate densities, enable us to tune our model for a wide range of shear rates. No, Is the Subject Area "Blood" applicable to this article? The resulting clots can form under different flow conditions in the veins as well as the arteries. Even the computational cost for such lower-fidelity simulations in large domains could become restrictive, and may require additional modeling strategies that will be addressed in future work. This process is called atherosclerosis. The equations governing the generation and depletion of the species (Si in Eq (11)) are formulated based on experimental data for the reaction kinetics, and are listed in S2 Table. The process of clot formation and growth at a site on a blood vessel wall involves a number of simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and platelet adhesion all of which are strongly influenced by the hydrodynamic forces. Full stenosis occlusion can be achieved when shear rate is elevated above 5,400 s−1, which is comparable to the threshold shear rate 4,000 s−1 reported by Li et al. In order to estimate platelet interaction forces that cause platelet aggregation at elevated shear rates, we first use the data of Westein et al. As such, the diagnosis and management of thrombosis are complex. Other experimental studies, using both microfluidic devices [33, 42] and macroscopic-size glass stenosis devices [43, 44], similarly focused on the thrombus growth rate and occlusion time inside a stenosis. Modeling the transport, activation, and adhesion of platelets is crucial in predicting thrombus formation and growth following a thrombotic event in normal or pathological conditions. Morse potential is used in this study to mimic inter-platelet attractive/repulsive forces. As expected, the wall shear rate intensity increases by increasing the flow rate, thus leading to smaller thrombus size inside the stenosis in the case of 28,000 s−1. 2017;906:273-283. (b), (c) and (d) Concentration profiles of thrombin ([IIa]), fibrin ([Ia]) and [ADP], respectively, at three axial positions on the site of injury: x = 157 μm (−−), x = 177 μm (− ⋅ −) and x = 193 μm (—). 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. We tested our shear-dependent model against their results, and can achieve similar trends and threshold shear rates at which occlusion occurs. 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. where De is the energy depth contributing to the strength of the interaction force and β controls the width of the energy well; r is the distance between the platelets centeroids and d = 3 μm is the equilibrium distance between two platelets and is selected to be the diameter of platelet. Next, small molecules, called clotting factors, cause strands of blood-borne materials, called fibrin, to stick together and seal the inside of the wound. The exact correlation for the variation of [TF-VIIa] is not known, and thus, we assume a cubic function in the form of [TF-VIIa] = [TF-VIIa]0(1 − ([Ia]/[Ia]thr)3). The process begins whenever flowing blood comes into contact with specific substances in your skin or in blood vessel walls. showed an inverse power law permeability with respect to the fibrin volume fraction [41]. Regardless of the molecular mechanisms that can cause such enhanced aggregation at the following edge of a stenosis, we are able to produce similar trends by introducing a platelet activation delay time parameter, τact. One important finding in their work is the marked increase (between two to three fold) of platelet aggregation post-stenosis. The constants in Eq (10) are calibrated using in vivo and in vitro experiments, which results in the function plotted in Fig 2. 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