Experimental results of Westein et al. Green particles represent the seeded platelets at the site of injury, whereas blue and red particles are passive and activated platelets, respectively. In the heart, macrothrombi can develop as a result of blood stasis in the ventricles or atria due to underlying valvular heart disease, cardiomyopathies or arrhythmias such as atrial fibrillation predisposing to ischemic emboli and CVA. [18]. To model these effects using the current numerical approach, we introduce a new parameter τact that delays the activation of platelets once stimulated by other activated platelets. Available from: https://www.ncbi.nlm.nih.gov/books/NBK538430, Mackman N. Triggers, targets and treatments for thrombosis. where the position vectors for all the platelets are updated at each time step using a second-order Euler forward scheme. 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. Platelet adhesion. 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. No, Is the Subject Area "Platelet aggregation" applicable to this article? However, several contributing factors are neglected, including mechanisms of thrombus formation in a low-shear regime, thrombus mechanics, and embolization. Microfluidic experimental results of Li et al. After this process is activated, it remains critical to contain thrombus formation so that it is localized to the site of injury and to modulate thrombus size to be proportionate to the injury. Other thrombosis sites include superior vena cava thrombosis, jugular vein thrombosis, cerebral venous sinus thrombosis, cavernous sinus thrombosis, retinal vein occlusion. Yes Thrombus formation starts in response to injury, activating the hemostatic process. In atherosclerotic arteries, the presence of plaques generates fluid mechanical conditions that promote high-shear platelet aggregation and thrombus formation [14, 15]. A number of cardiac conditions pose an increased risk to thrombus formation. To mimic the site of injury and initiate platelet aggregation, we place fixed activated particles (green particles in Fig 3a) uniformly at the bottom of the channel 150 − 180 μm from the inlet. Yes We consider four different occlusion levels of 20, 40, 60, and 80%. Platelets transporting through the regions with values of ω > 1 will become activated. (b) Exponential growth rates (normalized by the maximum value) computed from the simulations and plotted as a function of blood flow velocity (−□−). For example, platelets and reactants flow into an AAA and initiate intraluminal thrombus at specific locations in the aneurysm bulge [20, 21]. The main difference between thrombus and embolus is that thrombus remains attached to the vessel wall FCM provides a flexible platform for two-way coupling of platelets (treated as rigid spherical particles) with the background flow. Ann Vasc Surg. If a thrombus dislodges and becomes free-floating, it is considered an embolus. At low shear rates (), platelets adhere to the thrombogenic area through different pathways, relying on the exposed extracellular matrix (ECM) proteins [4, 5, 8]. As noted, thrombosis occurs when there is an imbalance in endogenous anticoagulation and hemostasis through a complex pathophysiologic mechanism. (4) The hexahedral elements show the structured grid used to solve the N-S and ADR equations. Additional details will be discussed in section Results. Data Availability: All relevant data are within the paper. The resulting clots can form under different flow conditions in the veins as well as the arteries. When the entire coagulation process works properly, blood holds firmly together at the site of an injury and bleeding stops. The maximum attractive forces between the two platelets can be calculated by ∂Finter/∂r = 0, which gives Fmax = βDe/2 occurring at (r/d − 1) = log(2)/βd. One important trend in the in vivo experimental results of Westein et al. 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. This is due to a combination of factors including varying degrees of maturity of the clot and results in acoustic boundaries between relatively fresh and more organized regions. This nonphysical trend necessitates the use of a shear-dependent model for adhesive forces similar to Eq (10). 2014; 34:1674–1680. With the advent of acute reperfusion strategies, there has been a decline in prevalence. We introduce an Eulerian-Lagrangian model where hemodynamics is solved on a fixed Eulerian grid, while platelets are tracked using a Lagrangian framework. The model has the advantage of predicting thrombus occlusion time with no significant computational cost using a well-trained model by data extracted from different experiments. Endoluminal stent grafting is the least invasive option, but it carries the high risk of distal embolization through wire manipulation and stent deployment 8). 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). where A′ = 3 × 10−8 nM is the ADP content for each platelet [39], and is the time at which platelet n becomes activated. https://doi.org/10.1371/journal.pcbi.1005291.s004. Subsequently, XIIa activates the zymogen XI to its active enzyme form XIa, which further activates IX to IXa in the presence of Ca2+. It’s important to watch for signs and symptoms of a pulmonary embolism and seek medical attention if they occur. In our simulations, βd is selected to be 2.5 and thus the maximum attractive force is obtained at r ≈ 1.27d. e1005291. Multiple thrombi were formed in 70% of mice lacking CD40L. Its embolization to brain induces cerebrovascular events, causes mesenteric ischemia in the gut, and causes renal infarction, coronary ischemia in heart, pulmonary infarction, among others. For calibrating our platelet aggregation model, we consider an interaction distance of 2d between platelets within which resting platelets can get activated. They also become activated by exposure to sufficiently high concentrations of thrombin, TxA2 and ADP. In this work, to reduce the computational cost, we use a slightly reduced-order model of coagulation proposed by Anand et al. Thrombosis (from Ancient Greek θρόμβωσις thrómbōsis "clotting”) is the formation of a blood clot inside a blood vessel, obstructing the flow of blood through the circulatory system. (1) (2) (3) Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America. As noted, arterial thrombosis can present as an acute stroke, myocardial infarction, or as acute on chronic peripheral arterial disease. Echocardiography. Thrombus is a blood clot that forms either in a vein or an artery even though you are not bleeding. [36]. We assume that the overall effect of interactions between receptors and ligands is incorporated into the adhesive model of Eqs (9) and (10), with the undetermined parameter. [37], , where the enhanced diffusion is considered in the lateral direction only. Kamada et al. Further, we couple the calibrated platelet aggregation model with a tissue-factor/contact pathway coagulation cascade, representing the relevant biology of thrombin generation and the subsequent fibrin deposition. Experimental measurements show that platelets release a finite quantity of ADP to the blood stream within 5 seconds following activation [40]. Thrombosis, formation of a blood clot in the heart or in a blood vessel. Clinically, stasis and low blood flow are considered risk factors for deep vein thrombosis. 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. Treatment of thrombus could reduce the risk of stroke, myocardial infarction, and pulmonary embolism. 2018 Jun;45(3):188-189, DeKornfeld GM, Boll J, Ziegler KR, Ratcliff J, Naslund TC, Garrard CL, Valentine RJ, Curci JA. Treasure Island (FL): StatPearls Publishing; 2019 Jan-. Thrombus is classified into 3 major groups depending on the relative amount of platelets and red blood cell 1). A thrombus occurs when the hemostatic process, which normally occurs in response to injury, becomes activated in an uninjured or slightly injured vessel. 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). 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. Further, we include the biochemistry of coagulation cascade, which is essential to modeling thrombus formation, and couple that to our platelet aggregation model. where ci and Di are the concentration and diffusion coefficient for each reactant, respectively, and Si represents the rate of production or destruction of that reactant. Med. Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America, Affiliation (a), (b) and (c) Snapshots of platelet aggregation inside 60, 40 and 20% stenoses, respectively. Mural thrombus can be incidentally detected lying in walls of the aorta in an asymptomatic patient. 12) speculated that these two types of thrombosis are triggered by the same biological stimuli that activate coagulation and inflammatory pathways. Competing interests: The authors have declared that no competing interests exist. To test the performance of our proposed model, we use the simulation setup of Fig 5a with a 60% asymmetric stenosis. Mural Thrombi. Simulations with fully resolved RBC and platelet suspensions in blood are challenging due to the computational cost of modeling millions of particles. Such intraluminal thrombus can affect the mechanical properties of the local vessel wall, leading to increased risk of aneurysm rupture [22]. Virchow’s triad describes the pathogenesis of thrombus formation. Long trips with limited mobility can also become a relative risk factor for thrombosis, especially if concurrent additional risk factors are present (as above). The exponential growth rate is computed by fitting the data (red line). The use and duration of anticoagulation or antiplatelet therapy depend on a careful assessment of these factors. https://doi.org/10.1371/journal.pcbi.1005291, Editor: Scott L. Diamond, Nesbitt et al. Full occlusion is observed in (b) and (c). 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. Platelet motion within a flow field and adhesion to a damaged surface are solved together by coupling a spectral/hp element method (SEM) [35] with a FCM [32]. Leukemia or coagulation disorders induce hypercoagulability. Vasc Med. Either no or very short delay times will lead to aggregation at the inlet toward the middle parts of stenosis, whereas platelets with properly adjusted activation delays do not become adhesive until they pass the apex of the stenosis. [14] and plotted for comparison. A pulmonary embolism can be life-threatening. The magnitude of the interaction forces resulting from this Morse potential can be obtained by taking the variation of the potential with respect to interparticle distance r, which gives Signs and symptoms of a pulmonary embolism include: A common complication that can occur after deep vein thrombosis is known as postphlebitic syndrome, also called postthrombotic syndrome. In addition to acute management (not reviewed here), secondary prevention focuses on reducing cardiovascular risk factors such as obesity, high cholesterol, diabetes, high blood pressure and encouraging lifestyle modification such as smoking cessation. Results from (b) replotted here for comparison (−□−). Similar non-monotonic trends can be observed in the experimental data of Begent and Born, which are extracted from their article and plotted in Fig 4b for comparison. First, we consider venous thrombus formation and growth similar to the in vivo experiment of Begent and Born [19]. Lowe GD. The repulsive forces rise exponentially for inter-platelet distances less than r < d to prevent cellular overlap. Introduction Evidence is mounting that important steps in the process of thrombus formation may be regulated by the oxidation states of labile disulfide bonds in critical hemostatic proteins (1). [24] used spring models for a variety of ligand-receptor interactions between platelets to investigate effects of ligand-receptor deficiencies on thrombus formation at different shear rates. As mentioned in section Materials and Methods, we set the interaction range of the Morse potential βd = 2.5 so that the potential strength De is the only parameter left to be tuned. Damage to the vessel wall leads to the production of proinflammatory (and prothrombotic) cytokines, increase in available tissue factor, the proliferation of adhesion molecules and enhanced platelet activation. The second term accounts for the interaction forces between platelets with each other and the wall, which represent overall effects of different ligand-receptor interactions. Further, it is possible to introduce porosity to the formed thrombus by adjusting the radius of influence of each particle on the fluid. 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). [15] observed that platelet aggregation was predominately in the post-stenosis region and proposed that the aggregation of platelets was resulted from platelet tethering. The resulting clots can form under different flow conditions in the veins as well as the arteries. No, Is the Subject Area "Fibrin" applicable to this article? (c) Normalized density of adhered platelets throughout the stenosis along the flow direction vs. normalized axial location. Int Urol Nephrol. [14]. The kinetic reactions of the coagulation cascade leading to the generation of thrombin and fibrin can be resolved by solving the related advection-diffusion-reaction (ADR) equations. In a recent work, Mehrabadi et al. The correlation has to be able to cover different flow conditions (e.g., clotting in venules vs. arteries) and adhesive mechanisms (e.g., adhesion at low vs. high shear rates). The platelet undergoes a … Here, we propose a general numerical model that encompass a wide range of hemodynamic conditions in the veins and arteries, with individual platelets and their adhesive dynamics included explicitly in the models. 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