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      A General Shear-Dependent Model for Thrombus Formation

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          Abstract

          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. We propose a shear-dependent platelet adhesive model based on the Morse potential that is calibrated by existing in vivo and in vitro experimental data and can be used over a wide range of flow shear rates (

          ). We introduce an Eulerian-Lagrangian model where hemodynamics is solved on a fixed Eulerian grid, while platelets are tracked using a Lagrangian framework. A force coupling method is introduced for bidirectional coupling of platelet motion with blood flow. 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. The range of shear rates covered by the proposed model encompass venous and arterial thrombosis, ranging from low-shear-rate conditions in abdominal aortic aneurysms and thoracic aortic dissections to thrombosis in stenotic arteries following plaque rupture, where local shear rates are extremely high.

          Author Summary

          Hemostasis (thrombus formation) is the normal physiological response that prevents significant blood loss after vascular injury. The resulting clots can form under different flow conditions in the veins as well as the arteries. The excessive and undesirable formation of clots (i.e., thrombosis) in our circulatory system may lead to significant morbidity and mortality. Some of these pathologies are deep vein thrombosis and pulmonary embolism and atherothrombosis (thrombosis triggered by plaque rupture) in coronary arteries, to name a few. 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. Numerical models for blood clotting normally focus on one of the processes under a specific flow condition. 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. Further, we include the biochemistry of coagulation cascade, which is essential to modeling thrombus formation, and couple that to our platelet aggregation model. The simulation results—tested against three different experiments—demonstrate that the proposed model is effective in capturing the in vivo and in vitro experimental observations.

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          Most cited references37

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          Specific synergy of multiple substrate-receptor interactions in platelet thrombus formation under flow.

          We have used confocal videomicroscopy in real time to delineate the adhesive interactions supporting platelet thrombus formation on biologically relevant surfaces. Type I collagen fibrils exposed to flowing blood adsorb von Willebrand factor (vWF), to which platelets become initially tethered with continuous surface translocation mediated by the membrane glycoprotein Ib alpha. This step is essential at high wall shear rates to allow subsequent irreversible adhesion and thrombus growth mediated by the integrins alpha2beta1 and alpha(IIb)beta3. On subendothelial matrix, endogenous vWF and adsorbed plasma vWF synergistically initiate platelet recruitment, and alpha2beta1 remains key along with alpha(IIb)beta3 for normal thrombus development at all but low shear rates. Thus, hemodynamic forces and substrate characteristics define the platelet adhesion pathways leading to thrombogenesis.
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            Thrombus formation in vivo.

            To examine thrombus formation in a living mouse, new technologies involving intravital videomicroscopy have been applied to the analysis of vascular windows to directly visualize arterioles and venules. After vessel wall injury in the microcirculation, thrombus development can be imaged in real time. These systems have been used to explore the role of platelets, blood coagulation proteins, endothelium, and the vessel wall during thrombus formation. The study of biochemistry and cell biology in a living animal offers new understanding of physiology and pathology in complex biologic systems.
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              Platelet glycoprotein Ibalpha forms catch bonds with human WT vWF but not with type 2B von Willebrand disease vWF.

              Arterial blood flow enhances glycoprotein Ibalpha (GPIbalpha) binding to vWF, which initiates platelet adhesion to injured vessels. Mutations in the vWF A1 domain that cause type 2B von Willebrand disease (vWD) reduce the flow requirement for adhesion. Here we show that increasing force on GPIbalpha/vWF bonds first prolonged ("catch") and then shortened ("slip") bond lifetimes. Two type 2B vWD A1 domain mutants, R1306Q and R1450E, converted catch bonds to slip bonds by prolonging bond lifetimes at low forces. Steered molecular dynamics simulations of GPIbalpha dissociating from the A1 domain suggested mechanisms for catch bonds and their conversion by the A1 domain mutations. Catch bonds caused platelets and GPIbalpha-coated microspheres to roll more slowly on WT vWF and WT A1 domains as flow increased from suboptimal levels, explaining flow-enhanced rolling. Longer bond lifetimes at low forces eliminated the flow requirement for rolling on R1306Q and R1450E mutant A1 domains. Flowing platelets agglutinated with microspheres bearing R1306Q or R1450E mutant A1 domains, but not WT A1 domains. Therefore, catch bonds may prevent vWF multimers from agglutinating platelets. A disintegrin and metalloproteinase with a thrombospondin type 1 motif-13 (ADAMTS-13) reduced platelet agglutination with microspheres bearing a tridomain A1A2A3 vWF fragment with the R1450E mutation in a shear-dependent manner. We conclude that in type 2B vWD, prolonged lifetimes of vWF bonds with GPIbalpha on circulating platelets may allow ADAMTS-13 to deplete large vWF multimers, causing bleeding.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                January 2017
                17 January 2017
                : 13
                : 1
                : e1005291
                Affiliations
                [1 ]Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
                [2 ]Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America
                University of Pennsylvania, UNITED STATES
                Author notes

                The authors have declared that no competing interests exist.

                • Conceived and designed the experiments: AY JDH GEK.

                • Performed the experiments: HL AY.

                • Analyzed the data: HL AY.

                • Contributed reagents/materials/analysis tools: HL AY.

                • Wrote the paper: HL AY.

                Author information
                http://orcid.org/0000-0002-0139-2080
                http://orcid.org/0000-0002-9713-7120
                Article
                PCOMPBIOL-D-16-01057
                10.1371/journal.pcbi.1005291
                5240924
                28095402
                f96b7294-8ad4-4b6b-9b44-62e2455ae3c7
                © 2017 Yazdani et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 1 July 2016
                : 7 December 2016
                Page count
                Figures: 10, Tables: 0, Pages: 24
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/100000050, National Heart, Lung, and Blood Institute;
                Award ID: U01HL116323
                Award Recipient :
                This work was supported by National Institute of Health Grant No. U01HL116323. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Anatomy
                Body Fluids
                Blood
                Platelets
                Medicine and Health Sciences
                Anatomy
                Body Fluids
                Blood
                Platelets
                Biology and Life Sciences
                Physiology
                Body Fluids
                Blood
                Platelets
                Medicine and Health Sciences
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                Biology and Life Sciences
                Cell Biology
                Cellular Types
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                Medicine and Health Sciences
                Hematology
                Blood Coagulation
                Platelet Aggregation
                Medicine and Health Sciences
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                Platelet Activation
                Physical Sciences
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                Physical Sciences
                Materials Science
                Materials by Attribute
                Adhesives
                Custom metadata
                All relevant data are within the paper.

                Quantitative & Systems biology
                Quantitative & Systems biology

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