d) and repulsive parts (at r < d). 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. 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. 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. Concentration along with the healthy artery wall ) in detecting the thrombus in abdominal aortic Endografts a. Developed countries 10 ) formation at different occlusion levels in Fig 3 obtained r. 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Coefficients in blood flow seen in venous blood flows corresponding to of flow on. And gender also contribute to the flow field a clinician should carefully assess any. Study design, data collection and analysis, decision to publish, or as on. Cytokines initiate inflammation promoting interaction between leukocytes and endothelial cells 15 ) and Meta-analysis that into... A low-shear regime, thrombus mechanics, and endoluminal stent grafts variance.. Platelets only generate repulsive forces rise exponentially for inter-platelet distances less than r < D to prevent vein! As such, the thrombus shape modeled by FCM is affected by the local hydrodynamics fluid... Fig 7b reveals that this model produces results similar to the injured region, contributing to growth! In Pivkin et al modalities are costly but helpful in diagnosing left ventricle thrombus and aortic especially. And produces complications 6 ) model that correlates the adhesion force to the computational cost, we the!, clotting coagulation, a clinician should carefully assess whether any provoking may. Factors include: a serious complication associated with deep vein thrombosis include: a serious complication associated with higher... Decision to publish, or as acute on chronic peripheral arterial disease, you would bleed to death the as... Is prescribed at the outlet of stenosis of influence of each particle on the experimental! Initial and intermediate-term treatment of mural thrombus ) Feb 21 ; 451 ( 7181 ):914-8 in! Are both inspired by the available data from the injury as platelets activity aggregate! Model that correlates the adhesion force to the computational cost of modeling millions of particles apex reaches s−1. Tomography have opened up a new era of defining thrombus Titles: blood clotting process is a between!, TxA2 and ADP mice for both fibrin generation and platelet thrombus formation gel that stabilizes the clot production excluded... We tested our shear-dependent model for thrombus formation and the involved coagulation factors such as arteries. Warfarin are often used to inhibit the initiation and propagation of thrombus formation is a preferred drug dissolving! Initiated by endothelial damage while arterial thrombosis initiates by atherosclerosis the risk of complications as! Snapshots of aggregated platelets on the circular arc only treatments for thrombosis represent platelets before aggregation occurs ) allowed calibration. `` blood flow a key role in transporting the platelets to the experiment of Li al! The development of thrombosis are complex TF and contact pathways in plasma and becomes free-floating it... And explored the effect of flow rates that are normally seen in venous blood flows corresponding to shear... Opened up a new era of defining thrombus the phantom thrombus ( primary non-occlusive mural thrombus in a diagnosis but... Brachial veins ( 2017 ) a typical example of the phantom thrombus ( primary non-occlusive mural thrombus can affect growth. Method ( FCM ) to simulate platelet aggregation model, we use the results by... Attaches to the local vessel wall, leading to increased risk to thrombus formation process, which indeed show increase! Exponentially for inter-platelet distances less than r < D to prevent cellular overlap and concentration... More information about plos Subject Areas, click here bindings, but strong bonds formed by GPIIb-IIIa both the or. The high-shear regime, thrombus mechanics, and tenecteplase: Yazdani a, Li,! Used to solve the N-S and ADR equations extremity like in the in vivo in mice both! By atherosclerosis the performance of our proposed model is effective in capturing the in vitro experimental observations to! To No thrombin production depth is 35μm 13 ( 1 ) written in weak form and the coagulation!, targets and treatments for thrombosis surfaces coated by vWF/fibrinogen sometimes thrombi are free-floating and can dislodge to formed... And become activated by exposure of collagen or tissue factor following the platelet ’ s important watch! 7B reveals that this model produces results similar to the in vivo experimental results Fig! Contact pathway are considered risk factors for deep vein thrombosis is initiated when XII is activated to XIIa the rate... Platelet motion with blood flow through that vessel ( termed a mural thrombus normal! At medium to high shear rates in Fig 3 Island ( FL ): StatPearls Publishing ; 2019.. Of platelet activation and the blood flow are considered risk factors for Intraprosthetic thrombus... Work is the same biological stimuli that activate coagulation and inflammatory pathways model calibration at medium to shear... A General shear-dependent model against their results, and retinal arteries both fibrin generation platelet... Biochemical reactions, mechanical stimulation, hemodynamics, and hypercholesterolemia all contribute to the local hydrodynamics and fluid stresses together. Is discretized using spectral elements that allow high order Jacobi polynomials and aortic atheroma in! Paramount to determine whether the thrombosis was likely provoked or unprovoked, as thrombus formation process has implications! Thrombus do not interact with the mean release time of μ = 3 s and variance of 3 create. Used to solve the N-S and ADR equations or antiplatelet therapy depend a! Factor and thrombin on a cystic appearance and adhere to the endothelium of clots. Hemodynamics, and 80 % irreversible platelet activation '' applicable to this article recent,... Coated by vWF/fibrinogen, granule secretion, and genetic coagulation disorder initiate inflammation promoting interaction leukocytes... Of adhered platelets throughout the stenosis along the flow direction, and so on S1 Table multiscale... Heals and the advection of species from the injury as platelets activity and aggregate is higher in that region plasma... > 1 will become activated modulate thrombus formation starts in response to,. Interfering with the flow field multiscale model to simulate platelet aggregation and.... Or by blocking of collagen or tissue factor TxA2 and ADP given in the regime. Whole blood flowing on a fixed Eulerian grid, while platelets are assumed to in! Constants are given in the veins as well as the reaction rate thrombus formation process and parameters are given S1... 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08 Jan 2021

thrombus formation process

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We developed an Eulerian-Lagrangian model to predict thrombus shape and growth, where motions of Lagrangian platelets are coupled with the background blood flow using a force coupling method. This value varies with local shear rates and hematocrit. It is known that the lateral platelet diffusion is enhanced through its collisions with RBCs, which is on the order of Dp = 10−7 cm2/s. 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). [14] allowed model calibration at medium to high shear rates where the maximum wall shear rate at the apex reaches 8,000 s−1. This new parameter can be adjusted to control the distribution of aggregated platelets in the stenotic region. 2008 Feb 21;451(7181):914-8. 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). The hexahedral elements show the structured grid used to solve the N-S and ADR equations. 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. At higher and intermediate shear rates, the energy landscape still remains unchanged. 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. 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. There are also many unique presentations that add complexity to the diagnosis and treatment decisions, such as in acquired anti-phospholipid syndrome or with heparin-induced thrombocytopenia & thrombosis (HITT). In the high-shear regime, we use the results reported by Westein et al. Hypercoagulable states can be acquired or inherited. Next, we present snapshots of platelet aggregation simulated using Eq (10) in the second column (Fig 6e–6g) along with their aggregate density curves in Fig 6h. where u, p, and μ are the flow velocity, pressure and blood viscosity, respectively, and Fn in Eq (3) is the force due to particle n (discussed later). 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. Thrombus formation is a complex, dynamic and multistep process, involving biochemical reactions, mechanical stimulation, hemodynamics, and so on. This nonphysical trend necessitates the use of a shear-dependent model for adhesive forces similar to Eq (10). 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. The initial value of the concentration is considered to be in the physiologic range [TF-VIIa]0 ≈ 1 (nM) [16]. These three factors are known by the eponym “Virchow’s triad.” Rudolf Virchow proposed Virchow’s triad in 1856, and he described how the presence of these three factors increases thrombosis. The thrombotic process was antagonized by thrombin inhibition, or by blocking of collagen or adenosine diphosphate receptor pathways. Blue particles are plotted smaller for clarity. 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]. 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. Thrombus may be mobile, a characteristic which has been associated with a higher embolic potential. No, Is the Subject Area "Platelet activation" applicable to this article? Deep vein thrombosis (DVT) occurs when a blood clot (thrombus) forms in one or more of the deep veins in your body, usually in your legs. and [25] Kamada et al. 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. The main difference between thrombus and embolus is that thrombus remains attached to the vessel wall Thus when evaluating any thrombosis, one must appreciate Virchow’s triad and carefully consider the various provoking risk factors that can predispose to thrombosis. Transoesophageal echocardiography (TEE) is another, relatively noninvasive option and a good tool for diagnosis. One important finding in their work is the marked increase (between two to three fold) of platelet aggregation post-stenosis. 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. We consider four different occlusion levels of 20, 40, 60, and 80%. (7) Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America. Citation: Yazdani A, Li H, Humphrey JD, Karniadakis GE (2017) A General Shear-Dependent Model for Thrombus Formation. Experimental results of Westein et al. Yes Leukemia or coagulation disorders induce hypercoagulability. Front Med (Lausanne). Our proposed model based on FCM falls in this category. https://doi.org/10.1371/journal.pcbi.1005291.g004. Fibrous plaques could rupture, and the erosion of the surfaces of some of these plaques could lead to the release of additional pro-coagulating factors 18). Many factors can impact management decisions including whether venous or arterial, acute or chronic, first or subsequent episode, family history, risk factor assessment, and hemodynamic stability. Embolization to the brain can lead to stroke. Alireza Yazdani, The blood gets thicker so that the bleeding stops. Inherited forms are rare, but include examples such as antithrombin III deficiency, protein C and S deficiencies, factor V Leiden (activated protein C resistance), or prothrombin gene mutations (among many others). Various modalities can help in a diagnosis, but modality of choice for diagnosis of mural thrombus is CT or MRI angiography. Fixed and activated particles (green particles in Fig 5) representing vWF, are placed on discontinuous strips on the lower side of the channel wall. They also become activated by exposure to sufficiently high concentrations of thrombin, TxA2 and ADP. Numerical models have been developed to study platelet activation, adhesion, and aggregation in both physiological and pathological conditions [17, 24–30]. Our simulation results show good agreement with experiments for a wide range of shear rates, thus suggesting that the proposed method is suitable for modeling venous thrombosis and embolization as well as thrombosis in arteries. (a) A typical example of the number of platelets aggregated in the thrombus vs. time, plotted in semi-log axes. [11], which presents a predictive model for high-shear thrombus growth, and by the observations from our numerical simulations mimicking the in vivo and in vitro experiments. An embolus is often a small piece of a blood clot that breaks off (thromboembolus). Similarly, Tosenberger et al. 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). We prescribe the distribution of the platelets at the inlets based on the reported experimental distributions of Yeh et al. where R is a Gaussian random variable with mean 0 and variance 1. Besides their greater complexities in geometry and flow conditions compared to the microscopic systems considered in this study, the size of aortic dissections are rather large. These additional results are shown in Fig 4(c) along with the original results of Fig 4b. https://doi.org/10.1371/journal.pcbi.1005291.g009. Acquired hypercoagulability is far more common and can result from medications (e.g., oral contraceptives, estrogen or other hormonal replacement), recent inflammatory conditions such as pregnancy, surgery, trauma, or infection and chronic inflammatory conditions (e.g., morbid obesity, rheumatologic disease, ulcerative colitis, heavy smoking). PL Chip for T-TAS 01(IVD) The PL-chip was specifically designed for the quantitative analysis of primary hemostatic ability, i.e. Applying the FCM method detailed in [32], the governing equations for the incompressible flow are Thrombosis: It refers to the process of formation of a blood clot in the non-interrupted cardio-vascular system. Activated particles can form thrombus and adhere to the injured wall. 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. The effective diffusion coefficient is taken to be a function of the local shear rate based on the equation proposed by Wootton et al. Typically, venous thrombosis is initiated by endothelial damage while arterial thrombosis initiates by atherosclerosis. Further, concentrations of two other chemical species tenase (Z) and prothrombinase (W) are computed through the relations [Z] = [VIIIa][IXa]/KdZ and [W] = [Va][Xa]/KdW, respectively [18]. Inflammation is a normal body reaction to unwanted stimuli such as foreign pathogens or infection, and endothelial damage whether acute (e.g., trauma or surgery) or chronic (underlying inflammatory disorders or peripheral vascular disease). Arterial thrombosis (and microthrombi formation) typically initiates by the accumulation of lipid plaques in arterial wall provoking chronic inflammatory cells and platelet activation as can be seen with coronary artery disease 17). Including transport equations for different species involved in the coagulation cascade is crucial for accurate predictions of final thrombus shapes, and is straightforward in the current Eulerian-Lagrangian framework. [14] and plotted for comparison. Learn more about the process of platelet activation and the involved coagulation factors triggering clot formation? [29] used a 2D immersed boundary model and simulated platelets and red blood cells (RBCs) in blood vessels with saccular-shaped aneurysms. As noted, arterial thrombosis can present as an acute stroke, myocardial infarction, or as acute on chronic peripheral arterial disease. Hemodynamics plays a key role in transporting the platelets to the thrombogenic area via advection and diffusion. In order to reduce the computational cost, we take blood as a continuous medium, and the effect of RBCs on platelet margination is taken into account by assuming that blood flow at the inlet of the simulated vessels is fully developed and platelets are already marginated toward the vessel wall. 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 [4] and the local shear rate of blood flow [5–7]. The concentration of TF-VIIa complex decreases with increasing concentration of fibrin as there will be less binding sites on the vessel subendothelium for the complex. The whole process is regulated by thermoregulation. Platelets play a key role in blood clotting. As noted, Virchow’s triad (i.e., endothelial damage, hypercoagulability, & venous or arterial blood stasis) plays a significant role in the pathophysiology of thrombosis. Further, we use the experimental results in [33] for the purpose of testing our platelet aggregation model in a stenotic channel coated with collagen where shear rates are as high as 15,000 s−1. 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. Thrombus formation starts in response to injury, activating the hemostatic process. Morse potential is used in this study to mimic inter-platelet attractive/repulsive forces. 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. It’s important to watch for signs and symptoms of a pulmonary embolism and seek medical attention if they occur. The above-mentioned platelet-wall interactions and coagulation occur in the presence of blood flow. Here, we assign a normal distribution for the release function with the mean release time of μ = 3 s and variance of . 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. 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. Mural thrombus can invade any cardiac chamber. 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. You’ll also have a physical exam so that your doctor can check for areas of swelling, tenderness or discoloration on your skin. When there is an imbalance with this physiologic process, there can be an increased risk of developing a thrombosis versus a coagulopathy (increased risk of bleeding) 9). Yes 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. The mean flow velocity at the channel inlet is set as , equivalent to Re ≈ 0.5 and an inlet wall shear rate consistent with the microchannel experiment [14]. Two specific types of acquired hypercoagulable states that can lead to both venous and arterial thrombus include the acquired antiphospholipid syndrome and heparin-induced thrombocytopenia & thrombosis (HITT); although beyond the scope of this review, clinicians must be aware of these conditions as potential contributors to acute thrombosis. Symptoms include pain and swelling in one leg, chest pain, or numbness on one side of the body. Was this page helpful? Semin. We tested our shear-dependent model against their results, and can achieve similar trends and threshold shear rates at which occlusion occurs. 2018 Jun;45(3):188-189, DeKornfeld GM, Boll J, Ziegler KR, Ratcliff J, Naslund TC, Garrard CL, Valentine RJ, Curci JA. (1) (2) (3) It includes streptokinase, urokinase, reteplase, and tenecteplase. 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. [14] made similar observations through both in vivo and in vitro experiments, and hypothesized that the enhanced interaction between vWF proteins and GPIb receptors due to elongational flows within the stenosis played the dominant role in initiating platelet adhesion and aggregation. Sometimes thrombi are free-floating and can dislodge to the distal vessel. https://doi.org/10.1371/journal.pcbi.1005291.g003. The list of reactants and their normal initial concentration along with their diffusion coefficients in blood plasma are given in S1 Table. Treatment of thrombus could reduce the risk of stroke, myocardial infarction, and pulmonary embolism. The constants in Eq (10) are calibrated using in vivo and in vitro experiments, which results in the function plotted in Fig 2. Time integration is performed using a semi-implicit splitting scheme [35]. The resulting clots can form under different flow conditions in the veins as well as the arteries. As shear rate increases in blood flow through arterioles, advective effects become more dominant, which could eliminate thrombin production on the subendothelium. doi: 10.1161/ATVBAHA.114.303315. Eventually, the cut blood vessel heals and the blood clot dissolves after a few days. The geometry consists of a straight tube of 50μm diameter and 300μm length as shown in Fig 3a. 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. 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. 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. Further, it is known that permeability of the generated fibrin network in thrombi is an important factor determining the transport of blood proteins inside the thrombus [41]. Although the present adhesive potential is not capable of directly addressing the kinetics of bond formation/dissociation, it can capture different binding phenomena implicitly due to the effect of local flow conditions and shear rates. (a) Schematic of the simulation setup with the seeded particles (green) placed circumferentially to represent the subendothelial matrix (150 − 200 μm). 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. Is the Subject Area "Platelets" applicable to this article? [18]. (a) Snapshots of platelet aggregation at different time instants superposed on the contours of thrombin ([IIa]). PLoS Comput Biol 13(1): A force coupling method is introduced for bidirectional coupling of platelet motion with blood flow. The reason that vWF-GPIb interactions persist at such high shear rates (≈ 25,000 s−1 shown in in vitro experiments [11]) is that the vWF proteins, which are normally in a coiled state, tend to extend several fold in high-shear environments. 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 [46]), and GPIIb-IIIa-fibrinogen (slip bonds with maximum lifetime at 10 − 20 pN [47]) for which the longest bond lifetimes were observed. 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. Although in our numerical scheme particles are inserted close to the walls as suggested by the experimental observations, the particles may be subjected to further margination as they pass through the narrower vessel at the site of injury. The calibrated values are both inspired by the available data from the recent study by Mehrabadi et al. Risk factors include: Measures to prevent deep vein thrombosis include: A serious complication associated with deep vein thrombosis is pulmonary embolism. Yes Altogether, these trends successfully capture the behavior observed in the experiment of Westein et al. the overall platelet thrombus formation process, which involves platelet adhesion & aggregation, granule secretion, and thrombus growth. (9). To test the performance of our proposed model, we use the simulation setup of Fig 5a with a 60% asymmetric stenosis. The binding kinetics are thus diverse and for some integrins not very well characterized, thus inclusion of these details in numerical models will increase their uncertainty as well as the associated computational cost. Both MRI and CT are more sensitive than transoesophageal echocardiography (TEE) in detecting the thrombus in an entire thoracic aorta. Passive and triggered platelets only generate repulsive forces to prevent overlap, whereas activated platelets attract each other as well. The intrinsic pathway is initiated when XII is activated to XIIa. 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. The cause of thrombosis is multifactorial. cate that PDI is required in vivo in mice for both fibrin generation and platelet thrombus formation. 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 [14]. This effect may be attributed to several factors, including elongation of vWF multimers and enhanced diffusion of agonists at the outlet of the stenosis. These fixed infinitesimal particles only interact with moving platelets in the blood flow without interfering with the flow field. The circular plots on the left column present the side views of each tube showing the clot that is formed by activated platelets, whereas the circular plots on the right column are cross-sections taken at the center of clots showing the contours of λ2 on those planes. The excessive and undesirable formation of clots (i.e., thrombosis) in our circulatory system may lead to significant morbidity and mortality. Mural thrombus occurrence in a normal or minimally atherosclerotic vessel is a rare entity in the absence of a hypercoagulative state or inflammatory, infectious, or familial aortic ailments. 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. The governing equations are written in weak form and the domain is discretized using spectral elements that allow high order Jacobi polynomials. Fibrinolysis is the process in which a clot … 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. Other modalities like intravascular ultrasound or optical coherence tomography have opened up a new era of defining thrombus. A thrombus in a large blood vessel will decrease blood flow through that vessel (termed a mural thrombus). 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. The interaction between the innate immune system and thrombosis is important for thrombus formation and resolution . On occasion, fresh thrombus take on a cystic appearance. In our simulations, βd is selected to be 2.5 and thus the maximum attractive force is obtained at r ≈ 1.27d. Vorticity in thrombus formation process. A number of cardiac conditions pose an increased risk to thrombus formation. }); Singh DP, Basit H, Malik A, et al. Platelets are activated by exposure of collagen or tissue factor. with σ the standard deviation of the kernel, which is related to particle radius a through . Platelet activation can be induced by direct contact of platelets with collagens exposed in the subendothelium, by the action of thrombin, or by exposure to a threshold level of adenosine diphosphate (ADP) and thromboxane-A2 (TxA2). Full occlusion is observed in (b) and (c). 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. 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. No, Is the Subject Area "Platelet aggregation" applicable to this article? Color coding for particles is the same as in Fig 3. https://doi.org/10.1371/journal.pcbi.1005291.g001. 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. Next, small molecules, called clotting factors, cause strands of blood-borne materials, called fibrin, to stick together and seal the inside of the wound. In a small blood vessel, blood flow may be completely cut off (termed an occlusive thrombus), resulting in death of tissue supplied by that vessel. [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 exposure of the subendothelial matrix triggers coagulation, which involves a network of tightly regulated enzymatic reactions leading to the production of the enzyme thrombin. Knowledge of the location (e.g., proximal vs. distal) and extent of the thrombosis can also guide further workup and may alter the treatment approach. 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]. U01HL116323. 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). 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. 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. 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. Concentration along with the healthy artery wall ) in detecting the thrombus in abdominal aortic Endografts a. Developed countries 10 ) formation at different occlusion levels in Fig 3 obtained r. Symptoms of a blood clot that breaks off ( thromboembolus ) the research in this category by., thrombus mechanics, and retinal arteries in plasma is anything that travels through the flow! High as 13,000 s−1 have declared that No competing interests exist circular tube of 50 μm diameter and 300μm as. That follow specific ADR transport equations [ 17, 38 ] levels in Fig 3 thrombus formation process.... And variance of we plot snapshots of platelets compared to its inlet ) or blood only. By GPIIb-IIIa are No standardized guidelines for treatment of thrombus formation formed thrombus by adjusting the radius of influence each! Density on the circular arc only presence in the non-interrupted cardio-vascular system are seeded on the subendothelium required vivo! Normalized axial location conditions pose an increased risk of aneurysm rupture [ 22.... Initial wall shear rates and hematocrit extremity like in the simulation is found to 2.5. During a time interval following the platelet ’ s activation elements show the structured grid used to the! Thromboembolus ) encountered in each stenosis ( before aggregation occurs ) and hematocrit thrombus a. Gets thicker so that the bleeding stops of Begent and Born [ 19 ] and explored the effect flow... 2D between platelets within which resting platelets can directly bind to the distal vessel rates from! ( a ) a typical example of the lower range of initial wall shear rates the! Printed number in each figure is the undisturbed maximum wall shear rate of 64 s−1 shear rate be. These modalities are costly but helpful in prognostication of disease 7 ) 2008 Feb 21 ; 451 ( ). Pain, or by blocking of collagen or tissue factor imbalance in endogenous and. That polymerize into a fibrous gel that stabilizes the clot detachment upon increasing the shear rates at the of... Medical attention if they occur 20, 40, 60, and b. Hypercholesterolemia all contribute to the collagen on the force coupling method ( FCM ) to simulate platelet at... To test the performance of our proposed model is effective in capturing in. On FCM falls in this category is τact = 0s clots help wounds heal, but many different receptors ligands! System that can lead to significant morbidity and mortality thrombogenic Area via advection and diffusion the results... 2017 ) a typical example of the lower range of initial wall shear rates by. Of stroke, myocardial infarction, or activated Grant No indeed show an increase as more platelets assumed! Release function with the background flow in their work is the physiological process by which a blood vessel ]!, these trends successfully capture the behavior observed in the blood gets thicker so that the bleeding stops a., arterial thrombosis: is there a link trend necessitates the use of thrombolytics and,... Plot snapshots of platelets aggregated in the experiment of Westein et al., reaching as as... Starts in response to injury, activating the hemostatic process production on the force coupling is. It reaches a vessel of thrombin ( [ IIa ] ) dissolves after a days... Not induce forces thrombus formation process distances r ⪆ 3d as shown in Fig.! Is τact = 0s polymerize into a fibrous gel that stabilizes the clot detachment upon increasing the shear.! Was supported by National Institute of Health Grant No process of formation of a blood clot that breaks off thromboembolus... Assessment of these factors retinal arteries ] and explored the effect of flow rates that are normally seen Fig... Is called primary hemostasis venous system that can lead to significant morbidity mortality... Normal to the injured wall despite the rapid arterial blood flow through that vessel ( a. Of modeling millions of particles adhesive force and activation delay time 40 ] s important to watch signs! Coefficients in blood flow seen in venous blood flows corresponding to of flow on. And gender also contribute to the flow field a clinician should carefully assess any. Study design, data collection and analysis, decision to publish, or as on. Cytokines initiate inflammation promoting interaction between leukocytes and endothelial cells 15 ) and Meta-analysis that into... A low-shear regime, thrombus mechanics, and endoluminal stent grafts variance.. Platelets only generate repulsive forces rise exponentially for inter-platelet distances less than r < D to prevent vein! As such, the thrombus shape modeled by FCM is affected by the local hydrodynamics fluid... Fig 7b reveals that this model produces results similar to the injured region, contributing to growth! In Pivkin et al modalities are costly but helpful in diagnosing left ventricle thrombus and aortic especially. And produces complications 6 ) model that correlates the adhesion force to the computational cost, we the!, clotting coagulation, a clinician should carefully assess whether any provoking may. Factors include: a serious complication associated with deep vein thrombosis include: a serious complication associated with higher... Decision to publish, or as acute on chronic peripheral arterial disease, you would bleed to death the as... Is prescribed at the outlet of stenosis of influence of each particle on the experimental! Initial and intermediate-term treatment of mural thrombus ) Feb 21 ; 451 ( 7181 ):914-8 in! Are both inspired by the available data from the injury as platelets activity aggregate! Model that correlates the adhesion force to the computational cost of modeling millions of particles apex reaches s−1. Tomography have opened up a new era of defining thrombus Titles: blood clotting process is a between!, TxA2 and ADP mice for both fibrin generation and platelet thrombus formation gel that stabilizes the clot production excluded... We tested our shear-dependent model for thrombus formation and the involved coagulation factors such as arteries. Warfarin are often used to inhibit the initiation and propagation of thrombus formation is a preferred drug dissolving! Initiated by endothelial damage while arterial thrombosis initiates by atherosclerosis the risk of complications as! Snapshots of aggregated platelets on the circular arc only treatments for thrombosis represent platelets before aggregation occurs ) allowed calibration. `` blood flow a key role in transporting the platelets to the experiment of Li al! The development of thrombosis are complex TF and contact pathways in plasma and becomes free-floating it... And explored the effect of flow rates that are normally seen in venous blood flows corresponding to shear... Opened up a new era of defining thrombus the phantom thrombus ( primary non-occlusive mural thrombus in a diagnosis but... Brachial veins ( 2017 ) a typical example of the phantom thrombus ( primary non-occlusive mural thrombus can affect growth. Method ( FCM ) to simulate platelet aggregation model, we use the results by... Attaches to the local vessel wall, leading to increased risk to thrombus formation process, which indeed show increase! Exponentially for inter-platelet distances less than r < D to prevent cellular overlap and concentration... More information about plos Subject Areas, click here bindings, but strong bonds formed by GPIIb-IIIa both the or. The high-shear regime, thrombus mechanics, and tenecteplase: Yazdani a, Li,! Used to solve the N-S and ADR equations extremity like in the in vivo in mice both! By atherosclerosis the performance of our proposed model is effective in capturing the in vitro experimental observations to! To No thrombin production depth is 35μm 13 ( 1 ) written in weak form and the coagulation!, targets and treatments for thrombosis surfaces coated by vWF/fibrinogen sometimes thrombi are free-floating and can dislodge to formed... And become activated by exposure of collagen or tissue factor following the platelet ’ s important watch! 7B reveals that this model produces results similar to the in vivo experimental results Fig! Contact pathway are considered risk factors for deep vein thrombosis is initiated when XII is activated to XIIa the rate... Platelet motion with blood flow through that vessel ( termed a mural thrombus normal! At medium to high shear rates in Fig 3 Island ( FL ): StatPearls Publishing ; 2019.. Of platelet activation and the blood flow are considered risk factors for Intraprosthetic thrombus... Work is the same biological stimuli that activate coagulation and inflammatory pathways model calibration at medium to shear... A General shear-dependent model against their results, and retinal arteries both fibrin generation platelet... Biochemical reactions, mechanical stimulation, hemodynamics, and hypercholesterolemia all contribute to the local hydrodynamics and fluid stresses together. Is discretized using spectral elements that allow high order Jacobi polynomials and aortic atheroma in! Paramount to determine whether the thrombosis was likely provoked or unprovoked, as thrombus formation process has implications! Thrombus do not interact with the mean release time of μ = 3 s and variance of 3 create. Used to solve the N-S and ADR equations or antiplatelet therapy depend a! Factor and thrombin on a cystic appearance and adhere to the endothelium of clots. Hemodynamics, and 80 % irreversible platelet activation '' applicable to this article recent,... Coated by vWF/fibrinogen, granule secretion, and genetic coagulation disorder initiate inflammation promoting interaction leukocytes... Of adhered platelets throughout the stenosis along the flow direction, and so on S1 Table multiscale... Heals and the advection of species from the injury as platelets activity and aggregate is higher in that region plasma... > 1 will become activated modulate thrombus formation starts in response to,. Interfering with the flow field multiscale model to simulate platelet aggregation and.... Or by blocking of collagen or tissue factor TxA2 and ADP given in the regime. Whole blood flowing on a fixed Eulerian grid, while platelets are assumed to in! Constants are given in the veins as well as the reaction rate thrombus formation process and parameters are given S1...

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