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Multiscale Systems Biology and Physics of Thrombosis Under Flow

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Abstract

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α2β1, and α2bβ3 controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture–activation–arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm2), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.

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References

  1. Aarts, P. A., S. A. van den Broek, G. W. Prins, G. D. Kuiken, J. J. Sixma, and R. M. Heethaar. Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arterioscler. Thromb. Vasc. Biol. 8:819–824, 1988.

    Article  CAS  Google Scholar 

  2. Bagchi, P. Mesoscale simulation of blood flow in small vessels. Biophys. J. 92:1858–1877, 2007.

    Article  PubMed  CAS  Google Scholar 

  3. Barg, A., R. Ossig, T. Goerge, M. F. Schneider, H. Schillers, H. Oberleithner, and S. W. Schneider. Soluble plasma-derived von Willebrand factor assembles to a halemostatically active filamentous network. Thromb. Haemost. 97:514–526, 2007.

    PubMed  CAS  Google Scholar 

  4. Bathe, M., and R. D. Kamm. A fluid–structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery. J. Biomech. Eng. 121:361–369, 1999.

    Article  PubMed  CAS  Google Scholar 

  5. Boyanova, D., S. Nilla, I. Birschmann, T. Dandekar, and M. Dittrich. PlateletWeb: a systems biologic analysis of signaling networks in human platelets. Blood 119:e22–e34, 2011.

    Article  PubMed  Google Scholar 

  6. Bungay, S. D., P. A. Gentry, and R. D. Gentry. A mathematical model of lipid-mediated thrombin generation. Math. Med. Biol. 20:105–129, 2003.

    Article  PubMed  Google Scholar 

  7. Chatterjee, M. S., W. S. Denney, H. Jing, and S. L. Diamond. Systems biology of coagulation initiation: kinetics of thrombin generation in resting and activated human blood. PLoS Comput. Biol. 6:e1000950, 2010.

    Article  PubMed  Google Scholar 

  8. Chatterjee, M. S., J. E. Purvis, L. F. Brass, and S. L. Diamond. Pairwise agonist scanning predicts cellular signaling responses to combinatorial stimuli. Nat. Biotechnol. 28:727–732, 2010.

    Article  PubMed  CAS  Google Scholar 

  9. Chen, H., and A. Alexander-Katz. Polymer-based catch-bonds. Biophys. J. 100:174–182, 2011.

    Article  PubMed  CAS  Google Scholar 

  10. Chintagumpala, M. M., R. L. Hurwitz, J. L. Moake, D. H. Mahoney, and C. P. Steuber. Chronic relapsing thrombotic thrombocytopenic purpura in infants with large von Willebrand factor multimers during remission. J. Pediatr. 120:49–53, 1992.

    Article  PubMed  CAS  Google Scholar 

  11. Colace, T., E. Falls, X. Zheng, and S. Diamond. Analysis of morphology of platelet aggregates formed on collagen under laminar blood flow. Ann. Biomed. Eng. 39:922–929, 2011.

    Article  PubMed  CAS  Google Scholar 

  12. Crowl, L. M., and A. L. Fogelson. Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Int. J. Numer. Methods Biomed. Eng. 26:471–487, 2010.

    Article  Google Scholar 

  13. Delfino, A., N. Stergiopulos, J. E. Moore, Jr., and J. J. Meister. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J. Biomech. 30:777–786, 1997.

    Article  PubMed  CAS  Google Scholar 

  14. Diamond, S. L. Reaction complexity of flowing human blood. Biophys. J. 80:1031–1032, 2001.

    Article  PubMed  CAS  Google Scholar 

  15. Doddi, S. K., and P. Bagchi. Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys. Rev. E 79:046318, 2009.

    Article  Google Scholar 

  16. Doggett, T. A., G. Girdhar, A. Lawshe, D. W. Schmidtke, I. J. Laurenzi, S. L. Diamond, and T. G. Diacovo. Selectin-like kinetics and biomechanics promote rapid platelet adhesion in flow: the GPIbα-vWF tether bond. Biophys. J. 83:194–205, 2002.

    Article  PubMed  CAS  Google Scholar 

  17. Dong, J.-f., J. L. Moake, L. Nolasco, A. Bernardo, W. Arceneaux, C. N. Shrimpton, A. J. Schade, L. V. McIntire, K. Fujikawa, and J. A. Lopez. ADAMTS-13 rapidly cleaves newly secreted ultralarge von Willebrand factor multimers on the endothelial surface under flowing conditions. Blood 100:4033–4039, 2002.

    Article  PubMed  CAS  Google Scholar 

  18. Dopheide, S. M., M. J. Maxwell, and S. P. Jackson. Shear-dependent tether formation during platelet translocation on von Willebrand factor. Blood 99:159–167, 2002.

    Article  PubMed  CAS  Google Scholar 

  19. Dumont, K., J. Vierendeels, R. Kaminsky, G. van Nooten, P. Verdonck, and D. Bluestein. Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a CFD/FSI model. J. Biomech. Eng. 129:558–565, 2007.

    Article  PubMed  Google Scholar 

  20. Eckstein, E. C., and F. Belgacem. Model of platelet transport in flowing blood with drift and diffusion terms. Biophys. J. 60:53–69, 1991.

    Article  PubMed  CAS  Google Scholar 

  21. Fedosov, D. A., B. Caswell, and G. E. Karniadakis. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys. J. 98:2215–2225, 2010.

    Article  PubMed  CAS  Google Scholar 

  22. Fedosov, D. A., W. Pan, B. Caswell, G. Gompper, and G. E. Karniadakis. Predicting human blood viscosity in silico. Proc. Nat. Acad. Sci. 108:11772–11777, 2011.

    Article  PubMed  CAS  Google Scholar 

  23. Flamm, M. H., T. Colace, M. S. Chatterjee, H. Jing, S. Zhou, D. Jaegar, L. F. Brass, T. Sinno, and S. L. Diamond. Multiscale prediction of patient-specific platelet function under flow. Blood 2012 (in press).

  24. Flamm, M. H., S. L. Diamond, and T. Sinno. Lattice kinetic Monte Carlo simulations of convective-diffusive systems. J. Chem. Phys. 130:094904, 2009.

    Article  PubMed  Google Scholar 

  25. Flamm, M. H., T. Sinno, and S. L. Diamond. Simulation of aggregating particles in complex flows by the lattice kinetic Monte Carlo method. J. Chem. Phys. 134:034905, 2011.

    Article  PubMed  Google Scholar 

  26. Fogelson, A. L., Y. H. Hussain, and K. Leiderman. Blood clot formation under flow: the importance of Factor XI depends strongly on platelet count. Biophys. J. 102:10–18, 2012.

    Article  PubMed  CAS  Google Scholar 

  27. Folie, B. J., and L. V. McIntire. Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow. Biophys. J. 56:1121–1141, 1989.

    Article  PubMed  CAS  Google Scholar 

  28. Guo, Z., K. M. Bussard, K. Chatterjee, R. Miller, E. A. Vogler, and C. A. Siedlecki. Mathematical modeling of material-induced blood plasma coagulation. Biomaterials 27:796–806, 2006.

    Article  PubMed  CAS  Google Scholar 

  29. Haynes, L. M., Y. C. Dubief, and K. G. Mann. Membrane binding events in the initiation and propagation phases of tissue factor initiated zymogen activation under flow. J. Biol. Chem. 287:5225–5234, 2012.

    Article  PubMed  CAS  Google Scholar 

  30. Haynes, L. M., Y. C. Dubief, T. Orfeo, and K. G. Mann. Dilutional control of prothrombin activation at physiologically relevant shear rates. Biophys. J. 100:765–773, 2011.

    Article  PubMed  CAS  Google Scholar 

  31. Hockin, M. F., K. C. Jones, S. J. Everse, and K. G. Mann. A model for the stoichiometric regulation of blood coagulation. J. Biol. Chem. 277:18322–18333, 2002.

    Article  PubMed  CAS  Google Scholar 

  32. Hubbell, J. A., and L. V. McIntire. Platelet active concentration profiles near growing thrombi. A mathematical consideration. Biophys. J. 50:937–945, 1986.

    Article  PubMed  CAS  Google Scholar 

  33. Hund, S. J., and J. F. Antaki. An extended convection diffusion model for red blood cell-enhanced transport of thrombocytes and leukocytes. Phys. Med. Biol. 54:6415–6435, 2009.

    Article  PubMed  CAS  Google Scholar 

  34. Jadhav, S., C. D. Eggleton, and K. Konstantopoulos. A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling. Biophys. J. 88:96–104, 2005.

    Article  PubMed  CAS  Google Scholar 

  35. Jesty, J., and E. Beltrami. Positive feedbacks of coagulation. Arterioscler. Thromb. Vasc. Biol. 25:2463–2469, 2005.

    Article  PubMed  CAS  Google Scholar 

  36. Kadash, K. E., M. B. Lawrence, and S. L. Diamond. Neutrophil string formation: hydrodynamic thresholding and cellular deformation during cell collisions. Biophys. J. 86:4030–4039, 2004.

    Article  PubMed  CAS  Google Scholar 

  37. Kim, J., C.-Z. Zhang, X. Zhang, and T. A. Springer. A mechanically stabilized receptor–ligand flex-bond important in the vasculature. Nature 466:992–995, 2010.

    Article  PubMed  CAS  Google Scholar 

  38. Konstantopoulos, K., T. W. Chow, N. A. Turner, J. D. Hellums, and J. L. Moake. Shear stress-induced binding of von Willebrand factor to platelets. Biorheology 34:57–71, 1997.

    Article  PubMed  CAS  Google Scholar 

  39. Kuharsky, A. L., and A. L. Fogelson. Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J. 80:1050–1074, 2001.

    Article  PubMed  CAS  Google Scholar 

  40. Leiderman, K., and A. L. Fogelson. Grow with the flow: a spatial temporal model of platelet deposition and blood coagulation under flow. Math. Med. Biol. 28:47–84, 2011.

    Article  PubMed  Google Scholar 

  41. Lenoci, L., M. Duvernay, S. Satchell, E. DiBenedetto, and H. E. Hamm. Mathematical model of PAR1-mediated activation of human platelets. Mol. BioSyst. 7:1129–1137, 2010.

    Article  Google Scholar 

  42. Levy, G. G., W. C. Nichols, E. C. Lian, T. Foroud, J. N. McClintick, B. M. McGee, A. Y. Yang, D. R. Siemieniak, K. R. Stark, R. Gruppo, R. Sarode, S. B. Shurin, V. Chandrasekaran, S. P. Stabler, H. Sabio, E. E. Bouhassira, J. D. Upshaw, D. Ginsburg, and H.-M. Tsai. Mutations in a member of the ADAMTS gene family cause thrombotic thrombocytopenic purpura. Nature 413:488–494, 2001.

    Article  PubMed  CAS  Google Scholar 

  43. Li, M. X., J. J. Beech-Brandt, L. R. John, P. R. Hoskins, and W. J. Easson. Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses. J. Biomech. 40:3715–3724, 2007.

    Article  PubMed  CAS  Google Scholar 

  44. Li, Z., M. K. Delaney, K. A. O’Brien, and X. Du. Signaling during platelet adhesion and activation. Arterioscler. Thromb. Vasc. Biol. 30:2341–2349, 2010.

    Article  PubMed  CAS  Google Scholar 

  45. Litvinov, R. I., V. Barsegov, A. J. Schissler, A. R. Fisher, J. S. Bennett, J. W. Weisel, and H. Shuman. Dissociation of bimolecular aIIb–b3–fibrinogen complex under a constant tensile force. Biophys. J. 100:165–173, 2011.

    Article  PubMed  CAS  Google Scholar 

  46. Liu, J., N. J. Agrawal, A. Calderon, P. S. Ayyaswamy, D. M. Eckmann, and R. Radhakrishnan. Multivalent binding of nanocarrier to endothelial cells under shear flow. Biophys. J. 101:319–326, 2011.

    Article  PubMed  CAS  Google Scholar 

  47. Lo, K., W. S. Denney, and S. L. Diamond. Stochastic modeling of blood coagulation initiation. Pathophysiol. Haemost. Thromb. 34:80–90, 2005.

    Article  PubMed  CAS  Google Scholar 

  48. Loth, F., P. F. Fischer, and H. S. Bassiouny. Blood flow in end-to-side anastomoses. Annu. Rev. Fluid Mech. 40:367–393, 2008.

    Article  Google Scholar 

  49. Luan, D., M. Zai, and J. D. Varner. Computationally derived points of fragility of a human cascade are consistent with current therapeutic strategies. PLoS Comput. Biol. 3:e142, 2007.

    Article  PubMed  Google Scholar 

  50. Maloney, S. F., L. F. Brass, and S. L. Diamond. P2Y12 or P2Y1 inhibitors reduce platelet deposition in a microfluidic model of thrombosis while apyrase lacks efficacy under flow conditions. Integr. Biol. 2:183–192, 2010.

    Article  CAS  Google Scholar 

  51. Moake, J. L., N. A. Turner, N. A. Stathopoulos, L. Nolasco, and J. D. Hellums. 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. Blood 71:1366–1374, 1988.

    PubMed  CAS  Google Scholar 

  52. Moake, J. L., N. A. Turner, N. A. Stathopoulos, L. H. Nolasco, and J. D. Hellums. Involvement of large plasma von Willebrand factor (vWF) multimers and unusually large vWF forms derived from endothelial cells in shear stress-induced platelet aggregation. J. Clin. Investig. 78:1456–1461, 1986.

    Article  PubMed  CAS  Google Scholar 

  53. Mody, N. A., and M. R. King. Platelet adhesive dynamics. Part I: Characterization of platelet hydrodynamic collisions and wall effects. Biophys. J. 95:2539–2555, 2008.

    Article  PubMed  CAS  Google Scholar 

  54. Nesbitt, W. S., E. Westein, F. J. Tovar-Lopez, E. Tolouei, A. Mitchell, J. Fu, J. Carberry, A. Fouras, and S. P. Jackson. A shear gradient-dependent platelet aggregation mechanism drives thrombus formation. Nat. Med. 15:665–673, 2009.

    Article  PubMed  CAS  Google Scholar 

  55. Okorie, U. M., W. S. Denney, M. S. Chatterjee, K. B. Neeves, and S. L. Diamond. Determination of surface tissue factor thresholds that trigger coagulation at venous and arterial shear rates: amplification of 100 fM circulating tissue factor requires flow. Blood 111:3507–3513, 2008.

    Article  PubMed  CAS  Google Scholar 

  56. Perktold, K., and D. Hilbert. Numerical simulation of pulsatile flow in a carotid bifurcation model. J. Biomed. Eng. 8:193–199, 1986.

    Article  PubMed  CAS  Google Scholar 

  57. Purvis, J. E., M. S. Chatterjee, L. F. Brass, and S. L. Diamond. A molecular signaling model of platelet phosphoinositide and calcium regulation during homeostasis and P2Y1 activation. Blood 112:4069–4079, 2008.

    Article  PubMed  CAS  Google Scholar 

  58. Purvis, J. E., R. Radhakrishnan, and S. L. Diamond. Steady-state kinetic modeling constrains cellular resting states and dynamic behavior. PLoS Comput. Biol. 5:e1000298, 2009.

    Article  PubMed  Google Scholar 

  59. Ruggeri, Z. M., J. N. Orje, R. Habermann, A. B. Federici, and A. J. Reininger. Activation-independent platelet adhesion and aggregation under elevated shear stress. Blood 108:1903–1910, 2006.

    Article  PubMed  CAS  Google Scholar 

  60. Schneider, S. W., S. Nuschele, A. Wixforth, C. Gorzelanny, A. Alexander-Katz, R. R. Netz, and M. F. Schneider. Shear-induced unfolding triggers adhesion of von Willebrand factor fibers. Proc. Nat. Acad. Sci. 104:7899–7903, 2007.

    Article  PubMed  CAS  Google Scholar 

  61. Shankaran, H., P. Alexandridis, and S. Neelamegham. Aspects of hydrodynamic shear regulating shear-induced platelet activation and self-association of von Willebrand factor in suspension. Blood 101:2637–2645, 2003.

    Article  PubMed  CAS  Google Scholar 

  62. Shim, K., P. J. Anderson, E. A. Tuley, E. Wiswall, and J. Evan Sadler. Platelet–VWF complexes are preferred substrates of ADAMTS13 under fluid shear stress. Blood 111:651–657, 2008.

    Article  PubMed  CAS  Google Scholar 

  63. Sorensen, E. N., G. W. Burgreen, W. R. Wagner, and J. F. Antaki. Computational simulation of platelet deposition and activation: I. Model development and properties. Ann. Biomed. Eng. 27:436–448, 1999.

    Article  PubMed  CAS  Google Scholar 

  64. Sorensen, E. N., G. W. Burgreen, W. R. Wagner, and J. F. Antaki. Computational simulation of platelet deposition and activation: II. Results for Poiseuille flow over collagen. Ann. Biomed. Eng. 27:449–458, 1999.

    Article  PubMed  CAS  Google Scholar 

  65. Steppich, D. M., J. I. Angerer, K. Sritharan, S. W. Schneider, S. Thalhammer, A. Wixforth, A. Alexander-Katz, and M. F. Schneider. Relaxation of ultralarge VWF bundles in a microfluidic–AFM hybrid reactor. Biochem. Biophys. Res. Commun. 369:507–512, 2008.

    Article  PubMed  CAS  Google Scholar 

  66. Stuhne, G. R., and D. A. Steinman. Finite-element modeling of the hemodynamics of stented aneurysms. J. Biomech. Eng. 126:382–387, 2004.

    Article  PubMed  Google Scholar 

  67. Taylor, C. A., T. J. R. Hughes, and C. K. Zarins. Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis. Ann. Biomed. Eng. 26:975–987, 1998.

    Article  PubMed  CAS  Google Scholar 

  68. Turitto, V. T., A. M. Benis, and E. F. Leonard. Platelet diffusion in flowing blood. Ind. Eng. Chem. Fundam. 11:216–223, 1972.

    Article  CAS  Google Scholar 

  69. Vincentelli, A., S. Susen, T. Le Tourneau, I. Six, O. Fabre, F. Juthier, A. Bauters, C. Decoene, J. Goudemand, A. Prat, and B. Jude. Acquired von Willebrand syndrome in aortic stenosis. N. Engl. J. Med. 349:343–349, 2003.

    Article  PubMed  Google Scholar 

  70. Xu, Z., N. Chen, M. M. Kamocka, E. D. Rosen, and M. Alber. A multiscale model of thrombus development. J. R. Soc. Interface 5:705–722, 2008.

    Article  PubMed  Google Scholar 

  71. Xu, Z., N. Chen, S. C. Shadden, J. E. Marsden, M. M. Kamocka, E. D. Rosen, and M. Alber. Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 5:769–779, 2009.

    Article  CAS  Google Scholar 

  72. Xu, Z., J. Lioi, J. Mu, M. M. Kamocka, X. Liu, D. Z. Chen, E. D. Rosen, and M. Alber. A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade. Biophys. J. 98:1723–1732, 2010.

    Article  PubMed  CAS  Google Scholar 

  73. Yago, T., J. H. Wu, C. D. Wey, A. G. Klopocki, C. Zhu, and R. P. McEver. Catch bonds govern adhesion through L-selectin at threshold shear. J. Cell Biol. 166:913–923, 2004.

    Article  PubMed  CAS  Google Scholar 

  74. Yeh, C., and E. C. Eckstein. Transient lateral transport of platelet-sized particles in flowing blood suspensions. Biophys. J. 66:1706–1716, 1994.

    Article  PubMed  CAS  Google Scholar 

  75. Zhao, H., and E. S. G. Shaqfeh. Shear-induced platelet margination in a microchannel. Phys. Rev. E 83:061924, 2011.

    Article  Google Scholar 

  76. Zhuo, R., C. A. Siedlecki, and E. A. Vogler. Competitive-protein adsorption in contact activation of blood Factor XII. Biomaterials 28:4355–4369, 2007.

    Article  PubMed  CAS  Google Scholar 

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  1. Department of Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, 1024 Vagelos Research Laboratory, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Mathew H. Flamm & S. L. Diamond

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Associate Editor Michael R. King oversaw the review of this article.

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Flamm, M.H., Diamond, S.L. Multiscale Systems Biology and Physics of Thrombosis Under Flow. Ann Biomed Eng 40, 2355–2364 (2012). https://doi.org/10.1007/s10439-012-0557-9

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