By adjusting the interaction forces between the platelet particles, we were able to reproduce the dependence of the growth rate on blood velocity reported in . If a thrombus dislodges and becomes free-floating, it is considered an embolus. He Li, * E-mail: firstname.lastname@example.org (GEK); email@example.com (AY), Affiliation 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). Yes Thrombus formation starts in response to injury, activating the hemostatic process. 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. 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. Factors that play a role in the formation of clots (thrombi) include injury to a blood vessel and alterations from normal blood flow; changes in the coagulability of the blood may also cause clot formation.  is the enhanced platelet aggregation at the outlet of stenosis compared to its inlet. No, Is the Subject Area "Stenosis" applicable to this article? 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. Surface reactions Bj along with their kinetic constants are given in S3 Table. When two activated platelets interact with each other, a repulsive force results when r < d and an attractive force when r > d as shown by the red line segment in Fig 1. 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. Further increase in βd is not physiologically correct as the potential and adhesive forces become long-range. (a) View normal to the flow direction, and (b) view from above. The state of the science on arterial and venous thrombosis is continually evolving, as is our understanding of provoking risk factors, hypercoagulability testing, and medical management. The increased incidence of obesity, hypertension, and hypercholesterolemia all contribute to the risk of acquiring an arterial thrombosis 13). Transoesophageal echocardiography (TEE) is also helpful in diagnosing left ventricle thrombus and aortic atheroma especially in ascending aorta. Passive platelets can directly bind to the collagen on the subendothelium and become activated. https://doi.org/10.1371/journal.pcbi.1005291.s001, https://doi.org/10.1371/journal.pcbi.1005291.s002. Further, two activated platelets in our model can only form one bond with each other, whereas each one in the pair can form multiple bonds with the other platelets in its neighborhood, which may result in the distribution of hydrodynamic drag among several bonds. Another process that could potentially affect the growth rates is the shear-induced platelet drift toward the wall or the thrombus. They also become activated by exposure to sufficiently high concentrations of thrombin, TxA2 and ADP. Cytokines initiate inflammation promoting interaction between leukocytes and endothelial cells 15). Platelet adhesion occurs via receptor-ligand bindings, but many different receptors and ligands are active under different shear conditions. We prescribe the distribution of the platelets at the inlets based on the reported experimental distributions of Yeh et al. Fresh platelets (red particles) are inserted at the inlet proportional to the local flow rate with a density of 300,000mm−3, and are removed from the system once they exit the channel. Furthermore, a decision to pursue an exhaustive hypercoagulable workup to further evaluate for inherited or acquired conditions that predispose to thrombosis is controversial and should only be completed in carefully selected patients or with subspecialty hematology evaluation prior. Before the lytic and urgent interventional era, left ventricular thrombus occurred in 25% to 40% of patients after a first anteroapical myocardial infarction. Such detailed models are normally very expensive due to the presence of individual cells and the large set of differential equations related to the biochemistry of coagulation. 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. Then hypercoagulability further enhances the thrombosis. Thrombosis, formation of a blood clot in the heart or in a blood vessel. Morse potential is used in this study to mimic inter-platelet attractive/repulsive forces. They are mostly located in the descending aorta, and less commonly, in the aortic arch or the abdominal aorta. Alternative Titles: blood clotting, clotting Coagulation, in physiology, the process by which a blood clot is formed. ( a â f ) Six snapshots from time 23.1 to 24.3 s, with time step 0.24 s. The figure demonstrates the moving direction of â¦ Under pathologic flow conditions where the shear rates are extremely high, the inter-platelet distance r is most likely to be ≈ 3d, where the same adhesive energy landscape will not be able to slow down or arrest the platelets. A finite quantity of ADP and TxA2 is released by a platelet during a time interval following the platelet’s activation. The model takes into account plasma-phase enzymes and zymogens, and coagulation inhibitors, where the advection-diffusion-reaction (ADR) equations for plasma-phase enzymes, zymogens or complexes lead to a system of 20 partial differential equations (PDEs) in the following form 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. 2017;906:273-283. Our numerical values for exponential growth rates are close to the results in Pivkin et al. From: Biomaterials Science (Third Edition), 2013 Eventually, the cut blood vessel heals and the blood clot dissolves after a few days. 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. The snapshots of the developed thrombi are given in Fig 3b–3d for several flow rates, where red particles represent activated platelets that can adhere to the site of injury and blue particles are resting platelets.  used a 2D immersed boundary model and simulated platelets and red blood cells (RBCs) in blood vessels with saccular-shaped aneurysms. In TAAD, however, clinical evidence suggests that a completely thrombosed false lumen within the dissection results in an improved prognosis whereas a partially thrombosed false lumen may render the wall more vulnerable to further dissection or rupture . A cylindrical patch with seeded platelets is placed in the middle of the tube to represent the site of injury, where thrombosis is allowed to initiate (see Fig 9a). the overall platelet thrombus formation process, which involves platelet adhesion & aggregation, granule secretion, and thrombus growth. 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. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. This process is called atherosclerosis. After this time, there was presumed endothelization of the thrombus with a reduction in its embolic potential. The intrinsic pathway is initiated when XII is activated to XIIa. We use the same FCM Gaussian kernel function to evaluate the spatial distribution of ADP release from each platelet You’ll also have a physical exam so that your doctor can check for areas of swelling, tenderness or discoloration on your skin. 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. No approach is definitively superior.  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. Injury to the , , where the enhanced diffusion is considered in the lateral direction only. The initial adhesion of platelets on the thrombogenic area can be attributed to a variety of platelet membrane receptor-ligand interactions, such as glycoprotein Ib(GPIb)-V-IX with immobilized von Willebrand Factor (vWF), GPIIb-IIIa (αIIbβ3) with vWF, GPVI with collagen, α2β1 with collagen, αIIbβ3 with fibrinogen, and so on, depending on the nature of the lesion  and the local shear rate of blood flow [5–7]. Kinetic constants are given as follows: k9 = 11 min−1, K9M = 160 nM, h9 = 0.0162 nM−1 min−1, k8 = 194.4 min−1, K8M = 112,000 nM, h8 = 0.222 min−1, hC8 = 10.2 min−1, HC8M = 14.6 nM, k5 = 27.0 min−1, K5M = 140.5 nM, h5 = 0.17 min−1, hC5 = 10.2 min−1, HC5M = 14.6 nM, k10 = 2391 min−1, K10M = 160 nM, h10 = 0.347 nM−1 min−1, hTFPI = 0.48 nM−1 min−1, k2 = 1344 min−1, K2M = 1060 nM, h2 = 0.714 nM−1 min−1, k1 = 3540 min−1, K1M = 3160 nM, h1 = 1500 min−1, H1M = 250,000 nM, k11 = 0.0078 min−1, K11M = 50 nM, , , kPC = 39 min−1, KPCM = 3190 nM, hPC = 6.6 × 10−7 nM−1 min−1, KdZ = 0.56 nM, KdW = 0.1 nM. In fact, some malignancies, especially solid tumors, are known to significantly increase the risk of thrombosis (e.g., pancreatic cancer). from a microfluidic device with different degrees of stenosis. https://doi.org/10.1371/journal.pcbi.1005291.g010. 2018;5:147, Insull W. The pathology of atherosclerosis: plaque development and plaque responses to medical treatment. There are no standardized guidelines for treatment of mural thrombus. Echocardiography. On the other hand, as shear rate increases, interactions between immobilized vWF and GPIb become exclusive in initializing platelet aggregation while other interactions are broken down due to high bond failure rates [9–11]. 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. First, we consider venous thrombus formation and growth similar to the in vivo experiment of Begent and Born . 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 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. Westein et al. with σ the standard deviation of the kernel, which is related to particle radius a through . The body’s endogenous anticoagulants, such as protein C and protein S and Antithrombin-III prevent the formation of thrombosis through a complex regulatory mechanism that maintains homeostasis. The list of reactants and their normal initial concentration along with their diffusion coefficients in blood plasma are given in S1 Table. Thrombus is classified into 3 major groups depending on the relative amount of platelets and red blood cell 1). We chose a Morse potential to generate the attractive/repulsive forces with a shear-dependent parameter i.e., the strength of the potential , that is calibrated through Eq (10) for different flow conditions. To couple the porosity of fibrin network to the local flow field we introduce a Brinkman term in the form of − (μ/k) u to the right hand side of the NS Eq (1), where μ is the blood viscosity and k is permeability inside the fibrin network, and is considered to be locally varying with the concentration of fibrin. 2014; 34:1674â1680. An embolus is anything that travels through the blood vessels until it reaches a vessel that is too small to let it pass. Thrombosis of superficial veins is also possible, especially with provoking factors such as intravenous catheterization or localized cellulitis; treatment of superficial vein thrombosis does not typically require any anticoagulation. Available from: https://www.ncbi.nlm.nih.gov/books/NBK534294, Perini P, Bianchini Massoni C, Azzarone M, Ucci A, Rossi G, Gallitto E, Freyrie A. The activation of the leucocytes and endothelial cells causes the formation of adhesion molecules which will eventually initiate clot formation 16). 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. J. Med. , where both the extrinsic or TF pathway and intrinsic or contact pathway are considered. (10) Exp. Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America. Other thrombosis sites include superior vena cava thrombosis, jugular vein thrombosis, cerebral venous sinus thrombosis, cavernous sinus thrombosis, retinal vein occlusion. Recently, experiments showed that the effect of vWF multimer extension was more pronounced in elongational flows, like in stenotic arteries, than in pure shear flows in a straight vessel . https://doi.org/10.1371/journal.pcbi.1005291.s003. Platelet motion within a flow field and adhesion to a damaged surface are solved together by coupling a spectral/hp element method (SEM)  with a FCM . Competing interests: The authors have declared that no competing interests exist. 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. https://doi.org/10.1371/journal.pcbi.1005291.g006. Platelets are activated by exposure of collagen or tissue factor. Hypercoagulable states can be acquired or inherited. In the high-shear regime, we use the results reported by Westein et al. No, Is the Subject Area "Fibrin" applicable to this article? . here. The exponential growth rate is computed by fitting the data (red line). }); Singh DP, Basit H, Malik A, et al. Exponential growth is achieved after a few seconds. Leukemia or coagulation disorders induce hypercoagulability. They can arise in any organ system, and their clinical presentation can vary depending on underlying comorbidities and presence (or absence) of provoking factors. Vorticity in thrombus formation process. Time integration is performed using a semi-implicit splitting scheme .  showed negligible to no thrombin production. Thrombus formation in the arteries is dependent on platelets and their ability to attach to the injured wall despite the rapid arterial blood flow. The geometry remains fixed, while we test different flow rates to create a range of wall shear rates at the apex from 1,000 − 15,000 s−1. As noted, arterial thrombosis can present as an acute stroke, myocardial infarction, or as acute on chronic peripheral arterial disease. Mural thrombus can be seen in large vessels such as the heart and aorta and can restrict blood flow. These issues can potentially be addressed by introducing platelets as FCM particles, thus forming a hybrid scheme in which the mechanistic behavior of thrombus formation can be resolved while the continuum model accumulates platelets in the thrombus based on empirical correlations until occlusion has been reached. for stenotic microchannels , where the shear rates can reach as high as 8,000 s−1. One of our goals is to improve our understanding of the effects of hemodynamics on the initiation and development of intramural thrombus within a false lumen caused by an aortic dissection. where A′ = 3 × 10−8 nM is the ADP content for each platelet , and is the time at which platelet n becomes activated. No aggregation is found for 20% stenosis; (d) and (h) density of adhered platelets inside the stenosis vs. simulation time. , which has the advantage of including both TF and contact pathways in plasma. Yes Virchow’s triad describes the pathogenesis of thrombus formation. Clinically, stasis and low blood flow are considered risk factors for deep vein thrombosis. The above-mentioned platelet-wall interactions and coagulation occur in the presence of blood flow. In: StatPearls [Internet]. (c) Normalized density of adhered platelets throughout the stenosis along the flow direction vs. normalized axial location. Many factors can increase your risk of developing deep vein thrombosis (DVT). Left ventricular thrombus is a frequent complication of acute myocardial infarction, mostly with the involvement of cardiac apex. When a blood vessel (a vein or an artery) is injured, the body uses platelets (thrombocytes) and fibrin to form a blood clot to prevent blood loss. Mural thrombus is thrombus that attaches to the wall of a blood vessel and cardiac chamber 2). For instance, studies have shown that elderly persons have increased production of prothrombotic coagulation factors such as von Willebrand factor and thrombin. This causes a further cascade of platelet activation with release of cytokines, ultimately causing thrombus formation. https://doi.org/10.1371/journal.pcbi.1005291.g005, We performed numerical simulations for different occlusion levels to calibrate the platelet-wall and platelet-platelet adhesive forces, which suggested that an approximately two orders of magnitude higher adhesive force is required for platelet aggregation at such elevated shear rates. 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. The maximum value of the bond forces in our model based on the calibrated parameters is ≈ 10 pN, which is in the range of bond forces measured for GPIb-vWF (catch-slip bonds with maximum lifetime at 20 pN ), and GPIIb-IIIa-fibrinogen (slip bonds with maximum lifetime at 10 − 20 pN ) for which the longest bond lifetimes were observed. Diverse studies have addressed this problem on different scales such as cellular, meso and continuum levels (e.g., refer to [48–52]) whereas attempts have been made to bridge these different scales to model the process at the initial phase of platelet activation and aggregation (e.g., [53–55]). Alireza Yazdani, As introduced above, platelet adhesion and aggregation in blood flow at low shear rates (< 1,000 s−1) may stimulate multiple ligand-receptor interactions, depending on the exposed ECM proteins (but is not strongly dependent on GPIb-vWF binding). Heparin and warfarin are often used to inhibit the initiation and propagation of existing thrombus. Such intraluminal thrombus can affect the mechanical properties of the local vessel wall, leading to increased risk of aneurysm rupture . Note that, at a lower blood velocity 100 μm/s, aggregation occurs slowly due to the smaller number of platelets transported to the injured region. In order to estimate platelet interaction forces that cause platelet aggregation at elevated shear rates, we first use the data of Westein et al. The reason that vWF-GPIb interactions persist at such high shear rates (≈ 25,000 s−1 shown in in vitro experiments ) is that the vWF proteins, which are normally in a coiled state, tend to extend several fold in high-shear environments. Semin. In certain clinical circumstances, patients can be at increased risk of thrombosis and bleeding simultaneously (e.g., disseminated intravascular coagulopathy-DIC, or in patients with underlying malignancy who develop a coagulopathy). In the second part of the paper, we use a detailed model for blood coagulation coupled with our platelet aggregation model to address thrombus formation in arteriole-sized vessels similar to the in vitro experiment of Shen et al. Yes 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. The ability of blood to flow freely in vessels relies on complex homeostasis that exists between blood cells (including platelets), plasma proteins, coagulation factors, inflammatory factors and cytokines, and the endothelial lining within the lumen of arteries and veins. Transport of platelets and other proteins involved in thrombus formation (fibrinogen and plasminogen, among others) becomes particularly important in the pathological conditions of AAA and TAAD. Additional details will be discussed in section Results. Transport and aggregation of platelets in dissections and stenoses have not yet been well studied due to the complex geometries and varying mechanisms of platelet adhesion under different hemodynamic conditions. Thrombosis is the formation of a blood clot (partial or complete blockage) within vein or an artery even though you are not bleeding, limiting the natural flow of blood and resulting in clinical consequences. Funding: This work was supported by National Institute of Health Grant No. Med. 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. Color coding for particles is the same as in Fig 3. A parabolic velocity profile is imposed at the inlet with variable average velocities in the range of 100 − 1,000 μm/s, which result in a maximum Reynolds number Re ≈ 0.02, whereas a zero-Neumann velocity boundary condition is imposed at the outlet. A platelet plug is formed, and the external bleeding stops. Other less common sites can include renal arteries, mesenteric arteries, and retinal arteries. The thrombotic process was antagonized by thrombin inhibition, or by blocking of collagen or adenosine diphosphate receptor pathways. Front Med (Lausanne). This signifies the effect of blood flow on the transport of coagulation reactants away from the site of injury before they can initiate the cascade. (b) Exponential growth rates (normalized by the maximum value) computed from the simulations and plotted as a function of blood flow velocity (−□−). Trend in the veins as well as the arteries a â¦ thrombosis occurs throughout our arterial system, in. The veins of the upper extremity like in the in vivo experiment of Begent and Born [ 19 ] pose! Strong bonds formed by GPIIb-IIIa ):914-8 and popliteal veins several fold higher than from the recent study Mehrabadi. That follow specific ADR transport equations [ 17, 38 ] which a blood that! 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