A three-dimensional model of primary thrombus formation based on fluid dynamics and level sets

References

• C. Batty and R. Bridson, Accurate viscous free surfaces for buckling, coiling, and rotating liquids, Eurographics/ACM SIGGRAPH symposium on computer animation, Dublin, Ireland, 2008.
   Google Scholar
• C. Batty and R. Bridson, An implementation of the variational viscosity method from the SCA paper: Accurate viscous free surfaces for buckling, coiling, and rotating liquids, 2008. Available at https://github.com/christopherbatty/VariationalViscosity3D.
   Google Scholar
• N. Begent and G.V.R. Born, Growth rate in vivo of platelet thrombi, produced by iontophoresis of ADP, as a function of mean blood flow velocity, Nature 227 (1970), pp. 926–930. doi: 10.1038/227926a0
   PubMed Web of Science ®Google Scholar
• R. Bridson, Fluid Simulation for Computer Graphics, A K Peters, Ltd., Wellesley, MA, 2008.
   Google Scholar
• S. Cito, M.D. Mazzeo, and L. Badimon, A review of macroscopic thrombus modeling methods, Thromb. Res. 131 (2013), pp. 116–124. doi: 10.1016/j.thromres.2012.11.020
   PubMed Web of Science ®Google Scholar
• N. Filipovic, M. Kojic, and A. Tsuda, Modelling thrombosis using dissipative particle dynamics method, Philos. Trans. A. Math. Phys. Eng. Sci. 336 (2008), pp. 99–106.
   Google Scholar
• B. Furie and B.C. Furie, Mechanisms of thrombus formation, N. Engl. J. Med.359 (2008), pp. 938–949. doi: 10.1056/NEJMra0801082
   PubMed Web of Science ®Google Scholar
• P.G. Giarlet, A Iserles, R.V. Kohn, and M.H. Wright, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, New York, 1999.
   Google Scholar
• K. Jurk and B.E. Kehrel, Platelets: Physiology and biochemistry, Semin. Thromb. Hemost. 31 (2005), pp. 381–392. doi: 10.1055/s-2005-916671
   PubMed Web of Science ®Google Scholar
• H. Kamada, Ki. Tsubota, M. Nakamura, S. Wada, T. Ishikawa, and T. Yamaguchi, A three-dimensional particle simulation of the formation and collapse of a primary thrombus, Internat. J. Numer. Methods Biomed. Engrg.26 (2010), pp. 488–500. doi: 10.1002/cnm.1367
   Web of Science ®Google Scholar
• H. Kamada, K. Tsubota, M. Nakamura, S. Wada, T. Ishikawa, and T. Yamaguchi, Computational study on effect of stenosis on primary thrombus formation, Biorheology 48 (2011), pp. 99–114.
   PubMed Web of Science ®Google Scholar
• H. Kamada, Y. Imai, M. Nakamura, T. Ishikawa, and T. Yamaguchi, Computational study on thrombus formation regulated by platelet glycoprotein and blood flow shear, Microvasc. Res. 89 (2013), pp. 95–106. doi: 10.1016/j.mvr.2013.05.006
   PubMed Web of Science ®Google Scholar
• H. Miyazaki and T. Yamaguchi, Formation and destruction of primary thrombi under the influence of blood flow and von Willebrand factor analyzed by a discrete element method, Biorheology 40 (2003), pp. 265–572.
   PubMed Web of Science ®Google Scholar
• D. Mori, K. Yano, K. Tsubota, T. Ishikawa, S. Wada, and T. Yamaguchi, Computational study on effect of red blood cells on primary thrombus formation, Thromb. Res. 123 (2008), pp. 114–121. doi: 10.1016/j.thromres.2008.03.006
   PubMed Web of Science ®Google Scholar
• S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, Vol. 153, Springer-Verlag, New York, 2003.
   Google Scholar
• D. Penney, Module 6, Hemodynamics, 2002. Available at http://www.coheadquarters.com/PennLibr/MyPhysiology/lect5/table5.01.htm.
   Google Scholar
• A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, and V. Volpert, Modelling of thrombus growth and growth stop in flow by the method of dissipative particle dynamics, Russian J. Numer. Anal. Math. Modelling 27 (2012), pp. 1–16. doi: 10.1515/rnam-2012-0029
   Web of Science ®Google Scholar
• Z. Xu, M. Alber, N. Chen, M.M. Kamocka, and E.D. Rosen, A multiscale model of thrombus development, J. R. Soc. Interface 5 (2008), pp. 705–722. doi: 10.1098/rsif.2007.1202
   PubMed Web of Science ®Google Scholar
• Z. Xu, M. Alber, 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 (2009), pp. 769–779. doi: 10.1039/B812429A
   Web of Science ®Google Scholar
• Z. Xu, 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 (2010), pp. 1723–1732. doi: 10.1016/j.bpj.2009.12.4331
   PubMed Web of Science ®Google Scholar