Fluid Mechanics of Blood Clot Formation.

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

[1]  Warwick S Nesbitt,et al.  Identification of a 2-stage platelet aggregation process mediating shear-dependent thrombus formation. , 2007, Blood.

[2]  A Alexander-Katz,et al.  Shear-induced unfolding triggers adhesion of von Willebrand factor fibers , 2007, Proceedings of the National Academy of Sciences.

[3]  Aaron L. Fogelson,et al.  Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions , 2011, Journal of Fluid Mechanics.

[4]  S. Diamond,et al.  Platelet‐targeting sensor reveals thrombin gradients within blood clots forming in microfluidic assays and in mouse , 2012, Journal of thrombosis and haemostasis : JTH.

[5]  S. Diamond,et al.  Thrombin flux and wall shear rate regulate fibrin fiber deposition state during polymerization under flow. , 2010, Biophysical journal.

[6]  A. Federici,et al.  Activation-independent platelet adhesion and aggregation under elevated shear stress. , 2005, Blood.

[7]  Aaron L Fogelson,et al.  Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. , 2011, Mathematical medicine and biology : a journal of the IMA.

[8]  J. R. Abbott,et al.  A constitutive equation for concentrated suspensions that accounts for shear‐induced particle migration , 1992 .

[9]  H. Weiss,et al.  Red blood cells: their dual role in thrombus formation. , 1980, Science.

[10]  A Alexander-Katz,et al.  Shear-flow-induced unfolding of polymeric globules. , 2006, Physical review letters.

[11]  Y. Ikeda,et al.  Characterization of the Unique Mechanism Mediating the Shear-dependent Binding of Soluble von Willebrand Factor to Platelets (*) , 1995, The Journal of Biological Chemistry.

[12]  M. Berndt,et al.  Platelet physiology and thrombosis. , 2004, Thrombosis research.

[13]  M. Wardell,et al.  Interaction of von Willebrand factor domain A1 with platelet glycoprotein Ibalpha-(1-289). Slow intrinsic binding kinetics mediate rapid platelet adhesion. , 2000, The Journal of biological chemistry.

[14]  M. King,et al.  Platelet adhesive dynamics. Part II: high shear-induced transient aggregation via GPIbalpha-vWF-GPIbalpha bridging. , 2008, Biophysical journal.

[15]  A. Alexander-Katz,et al.  Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows. , 2011, The Journal of chemical physics.

[16]  V. Turitto,et al.  Platelet deposition on subendothelium exposed to flowing blood: mathematical analysis of physical parameters. , 1975, Transactions - American Society for Artificial Internal Organs.

[17]  J. Antaki,et al.  Investigation of platelet margination phenomena at elevated shear stress. , 2007, Biorheology.

[18]  S. Jackson,et al.  Signaling events underlying thrombus formation , 2003, Journal of thrombosis and haemostasis : JTH.

[19]  G. Karniadakis,et al.  Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi , 2006, Proceedings of the National Academy of Sciences.

[20]  A. Tilles,et al.  The near-wall excess of platelet-sized particles in blood flow: its dependence on hematocrit and wall shear rate. , 1987, Microvascular research.

[21]  Todd D. Giorgio,et al.  Shear-induced platelet aggregation requires von Willebrand factor and platelet membrane glycoproteins Ib and IIb-IIIa. , 1987 .

[22]  J. Moake,et al.  Generation and Breakdown of Soluble Ultralarge von Willebrand Factor Multimers , 2012, Seminars in Thrombosis & Hemostasis.

[23]  Aaron L. Fogelson,et al.  Immersed-boundary-type models of intravascular platelet aggregation☆ , 2008 .

[24]  Aaron L. Fogelson,et al.  Coagulation under Flow: The Influence of Flow-Mediated Transport on the Initiation and Inhibition of Coagulation , 2006, Pathophysiology of Haemostasis and Thrombosis.

[25]  Z. Ruggeri,et al.  HEMOSTASIS , THROMBOSIS , AND VASCULAR BIOLOGY Contribution of Distinct Adhesive Interactions to Platelet Aggregation in Flowing Blood , 1999 .

[26]  Tomohiro Mizuno,et al.  Distinct and concerted functions of von Willebrand factor and fibrinogen in mural thrombus growth under high shear flow. , 2002, Blood.

[27]  Aaron L Fogelson,et al.  The Influence of Hindered Transport on the Development of Platelet Thrombi Under Flow , 2013, Bulletin of mathematical biology.

[28]  S. Diamond,et al.  Multiscale Systems Biology and Physics of Thrombosis Under Flow , 2012, Annals of Biomedical Engineering.

[29]  D. Slaaf,et al.  Concentration profile of blood platelets differs in arterioles and venules. , 1992, The American journal of physiology.

[30]  Aaron L Fogelson,et al.  Fibrin gel formation in a shear flow. , 2007, Mathematical medicine and biology : a journal of the IMA.

[31]  Kenneth G. Mann,et al.  Surface-dependent reactions of the vitamin K-dependent enzyme complexes , 1990 .

[32]  D. Slaaf,et al.  Distribution of blood platelets flowing in arterioles. , 1985, The American journal of physiology.

[33]  J. Moake,et al.  Measurement of the binding forces between von Willebrand factor and variants of platelet glycoprotein Ibα using optical tweezers , 2002 .

[34]  A Tokarev,et al.  Modelling of thrombus growth in flow with a DPD-PDE method. , 2013, Journal of theoretical biology.

[35]  Aaron L Fogelson,et al.  Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution. , 2004, Mathematical medicine and biology : a journal of the IMA.

[36]  Hiroshi Uji-i,et al.  Local Elongation of Endothelial Cell-anchored von Willebrand Factor Strings Precedes ADAMTS13 Protein-mediated Proteolysis* , 2011, The Journal of Biological Chemistry.

[37]  A. Acrivos,et al.  The shear-induced migration of particles in concentrated suspensions , 1987, Journal of Fluid Mechanics.

[38]  Aleksander S Popel,et al.  Microcirculation and Hemorheology. , 2005, Annual review of fluid mechanics.

[39]  A. Pries,et al.  Blood viscosity in tube flow: dependence on diameter and hematocrit. , 1992, The American journal of physiology.

[40]  J. R. Smart,et al.  Measurement of the drift of a droplet due to the presence of a plane , 1991 .

[41]  Jeffrey W. Smith,et al.  Platelet Mimetic Particles for Targeting Thrombi in Flowing Blood , 2012, Advanced materials.

[42]  K. Shim,et al.  Platelet-VWF complexes are preferred substrates of ADAMTS13 under fluid shear stress. , 2008, Blood.

[43]  E. Eckstein,et al.  Model of platelet transport in flowing blood with drift and diffusion terms. , 1991, Biophysical journal.

[44]  R M Heethaar,et al.  Fluid shear as a possible mechanism for platelet diffusivity in flowing blood. , 1986, Journal of biomechanics.

[45]  A. Chauhan,et al.  Systemic antithrombotic effects of ADAMTS13 , 2006, The Journal of experimental medicine.

[46]  Z. Ruggeri,et al.  Platelet Adhesion under Flow , 2009, Microcirculation.

[47]  M. Kahn,et al.  Platelet integrins and immunoreceptors , 2007, Immunological reviews.

[48]  S. Diamond,et al.  Hierarchical organization in the hemostatic response and its relationship to the platelet-signaling network. , 2013, Blood.

[49]  Aaron L Fogelson,et al.  Platelet motion near a vessel wall or thrombus surface in two-dimensional whole blood simulations. , 2013, Biophysical journal.

[50]  K. Neeves,et al.  The hydraulic permeability of blood clots as a function of fibrin and platelet density. , 2013, Biophysical journal.

[51]  Scott L Diamond,et al.  Determination of surface tissue factor thresholds that trigger coagulation at venous and arterial shear rates: amplification of 100 fM circulating tissue factor requires flow. , 2008, Blood.

[52]  S. Diamond,et al.  Simulation of aggregating particles in complex flows by the lattice kinetic Monte Carlo method. , 2011, The Journal of chemical physics.

[53]  T. Nguyen,et al.  Von Willebrand factor, ADAMTS-13, and thrombotic thrombocytopenic purpura. , 2010, Seminars in thrombosis and hemostasis.

[54]  Jonathan B. Freund,et al.  Simulation of Platelet, Thrombus and Erythrocyte Hydrodynamic Interactions in a 3D Arteriole with In Vivo Comparison , 2013, PloS one.

[55]  Hong Zhao,et al.  Shear-induced particle migration and margination in a cellular suspension , 2012 .

[56]  N. Filipovic,et al.  Modelling thrombosis using dissipative particle dynamics method , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[57]  Weiwei Wang,et al.  Multiscale Modeling of Platelet Adhesion and Thrombus Growth , 2012, Annals of Biomedical Engineering.

[58]  F. Millero,et al.  Conditions for the occurrence of large near-wall excesses of small particles during blood flow. , 1988, Microvascular research.

[59]  Aaron L. Fogelson,et al.  Computational Methods for Continuum Models of Platelet Aggregation , 1999 .

[60]  Karen Vanhoorelbeke,et al.  Platelets at work in primary hemostasis. , 2011, Blood reviews.

[61]  Edward F. Leonard,et al.  Effects of Shear Rate on the Diffusion and Adhesion of Blood Platelets to a Foreign Surface , 1972 .

[62]  Takuji Ishikawa,et al.  Simulation of platelet adhesion and aggregation regulated by fibrinogen and von Willebrand factor , 2007, Thrombosis and Haemostasis.

[63]  Andrew T. Irish,et al.  Sources of Variability in Platelet Accumulation on Type 1 Fibrillar Collagen in Microfluidic Flow Assays , 2013, PloS one.

[64]  J. Sixma,et al.  Functional self-association of von Willebrand factor during platelet adhesion under flow , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[65]  D. Hittel,et al.  Myostatin-induced inhibition of the long noncoding RNA Malat1 is associated with decreased myogenesis. , 2013, American journal of physiology. Cell physiology.

[66]  Andrew R. Fisher,et al.  Dissociation of bimolecular αIIbβ3-fibrinogen complex under a constant tensile force. , 2011, Biophysical journal.

[67]  Brian Savage,et al.  Initiation of Platelet Adhesion by Arrest onto Fibrinogen or Translocation on von Willebrand Factor , 1996, Cell.

[68]  X. Zheng,et al.  von Willebrand factor cleaved from endothelial cells by ADAMTS13 remains ultralarge in size , 2009, Journal of thrombosis and haemostasis : JTH.

[69]  Aaron L. Fogelson,et al.  Continuum models of platelet aggregation: formulation and mechanical properties , 1992 .

[70]  Zhiliang Xu,et al.  A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade. , 2010, Biophysical journal.

[71]  A. Guha,et al.  Hemophilia as a defect of the tissue factor pathway of blood coagulation: effect of factors VIII and IX on factor X activation in a continuous-flow reactor. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[72]  P. Richardson,et al.  Effect of red blood cells on platelet aggregation , 2009, IEEE Engineering in Medicine and Biology Magazine.

[73]  Shaun P Jackson,et al.  The growing complexity of platelet aggregation. , 2007, Blood.

[74]  S. Diamond,et al.  Selectin-like kinetics and biomechanics promote rapid platelet adhesion in flow: the GPIb/spl alpha/-vWF tether bond , 2002, Proceedings of the Second Joint 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society] [Engineering in Medicine and Biology.

[75]  Sriram Neelamegham,et al.  von Willebrand factor self-association on platelet GpIbalpha under hydrodynamic shear: effect on shear-induced platelet activation. , 2010, Blood.

[76]  Chun Xu,et al.  Platelet near-wall excess in porcine whole blood in artery-sized tubes under steady and pulsatile flow conditions. , 2004, Biorheology.

[77]  T. Orfeo,et al.  Dilutional control of prothrombin activation at physiologically relevant shear rates. , 2011, Biophysical journal.

[78]  H. Shankaran,et al.  Aspects of hydrodynamic shear regulating shear-induced platelet activation and self-association of von Willebrand factor in suspension. , 2003, Blood.

[79]  A. Alexander-Katz,et al.  Dynamics and Instabilities of Collapsed Polymers in Shear Flow , 2008 .

[80]  Hong Zhao,et al.  Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded Couette flow at zero Reynolds number , 2013 .

[81]  A. Fogelson A MATHEMATICAL MODEL AND NUMERICAL METHOD FOR STUDYING PLATELET ADHESION AND AGGREGATION DURING BLOOD CLOTTING , 1984 .

[82]  M. Barigou,et al.  Comparative rheology of the adhesion of platelets and leukocytes from flowing blood: why are platelets so small? , 2013, American journal of physiology. Heart and circulatory physiology.

[83]  Bahman Anvari,et al.  Ultralarge multimers of von Willebrand factor form spontaneous high-strength bonds with the platelet glycoprotein Ib-IX complex: studies using optical tweezers. , 2002, Blood.

[84]  A. Yoshioka,et al.  Visual evaluation of blood coagulation during mural thrombogenesis under high shear blood flow. , 2008, Thrombosis research.

[85]  Sriram Neelamegham,et al.  Hydrodynamic forces applied on intercellular bonds, soluble molecules, and cell-surface receptors. , 2004, Biophysical journal.

[86]  B. Furie,et al.  Thrombus formation in vivo. , 2005, The Journal of clinical investigation.

[87]  Scott L. Diamond,et al.  Thrombus Growth and Embolism on Tissue Factor-Bearing Collagen Surfaces Under Flow: Role of Thrombin With and Without Fibrin , 2012, Arteriosclerosis, thrombosis, and vascular biology.

[88]  Xiaoping Du,et al.  Signaling During Platelet Adhesion and Activation , 2010, Arteriosclerosis, thrombosis, and vascular biology.

[89]  Y. Liu,et al.  Threshold Response of Initiation of Blood Coagulation by Tissue Factor in Patterned Microfluidic Capillaries Is Controlled by Shear Rate , 2008, Arteriosclerosis, thrombosis, and vascular biology.

[90]  Jonathan B. Freund,et al.  Numerical Simulation of Flowing Blood Cells , 2014 .

[91]  Y. Nemerson,et al.  The effects of shear rate on the enzymatic activity of the tissue factor-factor VIIa complex. , 1990, Microvascular research.

[92]  M. Graham,et al.  Mechanism of margination in confined flows of blood and other multicomponent suspensions. , 2012, Physical review letters.

[93]  J. Moake,et al.  Endothelial cell ADAMTS-13 and VWF: production, release, and VWF string cleavage. , 2009, Blood.

[94]  Goldsmith Hl,et al.  Red cell motions and wall interactions in tube flow. , 1971 .

[95]  V. Turitto,et al.  Platelet interaction with subendothelium in a perfusion system: physical role of red blood cells. , 1975, Microvascular research.

[96]  Viola Vogel,et al.  Biophysics of catch bonds. , 2008, Annual review of biophysics.

[97]  A. Fogelson,et al.  The Effect of Factor VIII Deficiencies and Replacement and Bypass Therapies on Thrombus Formation under Venous Flow Conditions in Microfluidic and Computational Models , 2013, PloS one.

[98]  David N. Ku,et al.  Determination of Critical Parameters in Platelet Margination , 2012, Annals of Biomedical Engineering.

[99]  A. Fogelson,et al.  Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. , 2001, Biophysical journal.

[100]  D. Lane,et al.  Unraveling the scissile bond: how ADAMTS13 recognizes and cleaves von Willebrand factor. , 2011, Blood.

[101]  Aaron L. Fogelson,et al.  Computational Modeling of Blood Clotting: Coagulation and Three-dimensional Platelet Aggregation , 2003 .

[102]  Jizhong Lou,et al.  Platelet glycoprotein Ibalpha forms catch bonds with human WT vWF but not with type 2B von Willebrand disease vWF. , 2008, The Journal of clinical investigation.

[103]  O. Eniola-Adefeso,et al.  The margination propensity of ellipsoidal micro/nanoparticles to the endothelium in human blood flow. , 2013, Biomaterials.

[104]  Brian Savage,et al.  Specific Synergy of Multiple Substrate–Receptor Interactions in Platelet Thrombus Formation under Flow , 1998, Cell.

[105]  E. Eckstein,et al.  An estimated shape function for drift in a platelet-transport model. , 1994, Biophysical journal.

[106]  Jerrold E. Marsden,et al.  Study of blood flow impact on growth of thrombi using a multiscale model , 2009 .

[107]  Scott L. Diamond,et al.  Direct Observation of von Willebrand Factor Elongation and Fiber Formation on Collagen During Acute Whole Blood Exposure to Pathological Flow , 2012, Arteriosclerosis, thrombosis, and vascular biology.

[108]  K. Neeves,et al.  Thrombin generation and fibrin formation under flow on biomimetic tissue factor‐rich surfaces , 2014, Journal of thrombosis and haemostasis : JTH.

[109]  M. King,et al.  Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects. , 2008, Biophysical journal.

[110]  Zhiliang Xu,et al.  A multiscale model of thrombus development , 2008, Journal of The Royal Society Interface.

[111]  Valeri Barsegov,et al.  Resolving Two-dimensional Kinetics of the Integrin αIIbβ3-Fibrinogen Interactions Using Binding-Unbinding Correlation Spectroscopy* , 2012, The Journal of Biological Chemistry.

[112]  A. Alexander-Katz,et al.  Hematocrit and flow rate regulate the adhesion of platelets to von Willebrand factor. , 2013, Biomicrofluidics.

[113]  Y. Nemerson,et al.  Platelet deposition inhibits tissue factor activity: in vitro clots are impermeable to factor Xa. , 2004, Blood.

[114]  D. Monroe,et al.  A Cell-based Model of Hemostasis , 2001, Thrombosis and Haemostasis.

[115]  S. Chien Red cell deformability and its relevance to blood flow. , 1987, Annual review of physiology.

[116]  M. Crúz,et al.  Force-induced cleavage of single VWFA1A2A3 tridomains by ADAMTS-13. , 2010, Blood.

[117]  T. Ishikawa,et al.  Computational study on thrombus formation regulated by platelet glycoprotein and blood flow shear. , 2013, Microvascular research.

[118]  T. Ishikawa,et al.  A three‐dimensional particle simulation of the formation and collapse of a primary thrombus , 2010 .

[119]  J. Moake,et al.  Involvement of large plasma von Willebrand factor (vWF) multimers and unusually large vWF forms derived from endothelial cells in shear stress-induced platelet aggregation. , 1986, The Journal of clinical investigation.

[120]  G. Remuzzi,et al.  Fluid shear stress modulates von Willebrand factor release from human vascular endothelium. , 1997, Blood.

[121]  J. Moake,et al.  Shear-induced platelet aggregation can be mediated by vWF released from platelets, as well as by exogenous large or unusually large vWF multimers, requires adenosine diphosphate, and is resistant to aspirin , 1988 .

[122]  Scott L Diamond,et al.  Multiscale prediction of patient-specific platelet function under flow. , 2012, Blood.

[123]  B. Savage,et al.  Mechanisms of platelet aggregation. , 2001, Current opinion in hematology.

[124]  B. Jilma,et al.  Von Willebrand Factor in Cardiovascular Disease: Focus on Acute Coronary Syndromes , 2008, Circulation.

[125]  R M Heethaar,et al.  Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. , 1988, Arteriosclerosis.

[126]  D. Slaaf,et al.  Localization within a thin optical section of fluorescent blood platelets flowing in a microvessel. , 1982, Microvascular research.

[127]  Eugene C. Eckstein,et al.  Self-diffusion of particles in shear flow of a suspension , 1977, Journal of Fluid Mechanics.

[128]  Scott L. Diamond,et al.  Selectin-Like Kinetics and Biomechanics Promote Rapid Platelet Adhesion in Flow: The GPIbα-vWF Tether Bond , 2002 .

[129]  Weiwei Wang,et al.  Multiscale model of platelet translocation and collision , 2013, J. Comput. Phys..

[130]  A. M. Benis,et al.  Platelet Diffusion in Flowing Blood , 1972 .

[131]  J. Weisel Fibrinogen and fibrin. , 2005, Advances in protein chemistry.

[132]  Alfredo Alexander-Katz,et al.  Elongational flow induces the unfolding of von Willebrand factor at physiological flow rates. , 2010, Biophysical journal.

[133]  H. C. Hemker,et al.  The pathways of blood coagulation , 1967 .

[134]  Phapanin Charoenphol,et al.  Potential role of size and hemodynamics in the efficacy of vascular-targeted spherical drug carriers. , 2010, Biomaterials.

[135]  H. Weiss,et al.  Role of shear rate and platelets in promoting fibrin formation on rabbit subendothelium. Studies utilizing patients with quantitative and qualitative platelet defects. , 1986, The Journal of clinical investigation.

[136]  Zhiliang Xu,et al.  Fibrin Networks Regulate Protein Transport during Thrombus Development , 2013, PLoS Comput. Biol..

[137]  J. Shao,et al.  Unfolding the A2 domain of von Willebrand factor with the optical trap. , 2010, Biophysical journal.

[138]  Rustem F Ismagilov,et al.  Characterization of the threshold response of initiation of blood clotting to stimulus patch size. , 2007, Biophysical journal.

[139]  Albert van den Berg,et al.  Atherosclerotic geometries exacerbate pathological thrombus formation poststenosis in a von Willebrand factor-dependent manner , 2013, Proceedings of the National Academy of Sciences.

[140]  Nigel Mackman,et al.  New insights into the mechanisms of venous thrombosis. , 2012, The Journal of clinical investigation.

[141]  S. Jackson,et al.  Dynamics of platelet thrombus formation , 2009, Journal of thrombosis and haemostasis : JTH.

[142]  Zhiliang Xu,et al.  Computational Approaches to Studying Thrombus Development , 2011, Arteriosclerosis, thrombosis, and vascular biology.

[143]  Cheng-Zhong Zhang,et al.  Mechanoenzymatic Cleavage of the Ultralarge Vascular Protein von Willebrand Factor , 2009, Science.

[144]  J. Dong Cleavage of ultra‐large von Willebrand factor by ADAMTS‐13 under flow conditions , 2005, Journal of thrombosis and haemostasis : JTH.

[145]  Jeremy E Purvis,et al.  Pairwise agonist scanning predicts cellular signaling responses to combinatorial stimuli , 2010, Nature Biotechnology.

[146]  Jongseong Kim,et al.  A mechanically stabilized receptor–ligand flex-bond important in the vasculature , 2010, Nature.