Bäbler, M. U., M. Morbidelli. Analysis of the aggregation-fragmentation population balance equation with application to coagulation. J. Colloid Interface Sci. 316(2):428–441, 2007. doi:10.1016/j.jcis.2007.08.029.

Article  PubMed  Google Scholar 

Barthelmes, G., S. Pratsinis, H. Buggisch. Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation. Chem. Eng. Sci. 58(13): 2893–2902, 2003. doi:10.1016/S0009-2509(03)00133-7.

Article  CAS  Google Scholar 

Bell, D. N., S. Spain, H. L. Goldsmith. Adenosine diphosphate-induced aggregation of human platelets in flow through tubes. II. Effect of shear rate, donor sex, and ADP concentration. Biophys. J. 56(5):829–843, 1989. Doi:10.1016/S0006-3495(89)82729-8.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Blatz, P. J., A. V. Tobolsky. Note on the kinetics of systems manifesting simultaneous polymerization-depolymerization phenomena. J. Phys. Chem. 49(2):77–80, 1945. doi:10.1021/j150440a004.

Article  CAS  Google Scholar 

Born, G. V. R., M. Hume. Effects of the numbers and sizes of platelet aggregates on the optical density of plasma. Nature 215(5105):1027–1029, 1967. doi:10.1038/2151027a0.

Article  CAS  PubMed  Google Scholar 

Chang, H. N., C. R. Robertson. Platelet aggregation by laminar shear and Brownian motion. Ann. Biomed. Eng. 4(2):151–183, 1976. doi:10.1007/BF02363645

Article  CAS  PubMed  Google Scholar 

David, P., A. C. Nair, V. Menon, D. Tripathi. Laser light scattering studies from blood platelets and their aggregates. Colloids Surf. B 6(2):101–114, 1996. doi:10.1016/0927-7765(95)01236-2.

Article  CAS  Google Scholar 

Diamond, S. L. Systems biology of coagulation. J. Thromb. Haemostasis 11(Suppl.1):224–232, 2013. doi:10.1111/jth.12220

Frojmovic, M. M., J. G. Milton. Human platelet size, shape, and related functions in health and disease. Physiol. Rev. 62(1):185–261, 1982.

CAS  PubMed  Google Scholar 

Goldsmith, H. L., D. N. Bell, S. Braovac, A. Steinberg, F. McIntosh. Physical and chemical effects of red cells in the shear-induced aggregation of human platelets. Biophys. J. 69(4):1584–95, 1995. Doi:10.1016/S0006-3495(95)80031-7.

Goldsmith, H. L., D. N. Bell, S. Spain, F. A. McIntosh. Effect of red blood cells and their aggregates on platelets and white cells in flowing blood. Biorheology 36(5–6):461–468, 1999.

CAS  PubMed  Google Scholar 

Goldsmith, H. L., S. Spain. Margination of leukocytes in blood flow through small tubes. Microvasc. Res. 27(2):204–222, 1984. doi:10.1016/0026-2862(84)90054-2.

Article  CAS  PubMed  Google Scholar 

Huang, P. Y., J. D. Hellums. Aggregation and disaggregation kinetics of human blood platelets: Part III. The disaggregation under shear stress of platelet aggregates. Biophys. J. 65(1):354–361 (1993a). doi:10.1016/S0006-3495(93)81080-4.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Huang, P. Y., J. D. Hellums. Aggregation and disaggregation kinetics of human blood platelets: Part I. Development and validation of a population balance method. Biophys. J. 65(1):334–43, 1993c. doi:10.1016/S0006-3495(93)81078-6.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Huang, P. Y., J. D. Hellums. Aggregation and disaggregation kinetics of human blood platelets: Part II. Shear-induced platelet aggregation. Biophys. J. 65(1):344–53, 1993b. doi:10.1016/S0006-3495(93)81079-8.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Hund, S. J., J. F. Antaki, An extended convection diffusion model for red blood cell-enhanced transport of thrombocytes and leukocytes. Phys. Med. Biol. 54(20):6415–6435, 2009. doi:10.1088/0031-9155/54/20/024.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Kao, S. V., S. G. Mason. Dispersion of particles by shear. Nature 253(5493):619–621, 1975. doi:10.1038/253619a0.

Article  CAS  Google Scholar 

Kostoglou, M., A. J. Karabelas. On the self-similarity of the aggregationGçôfragmentation equilibrium particle size distribution. J. Aerosol Sci. 30(2):157–162, 1999. doi:10.1016/S0021-8502(98)00045-7.

Kramer, T., Clark, M. Incorporation of aggregate breakup in the simulation of orthokinetic coagulation. J. Colloid Interface Sci. 216(1):116–126 (1999). doi:10.1006/jcis.1999.6305.

Article  CAS  PubMed  Google Scholar 

Kroll, M. H., J. D. Hellums, L. V. McIntire, A. I. Schafer, J. L. Moake. Platelets and shear stress. Blood 88(5):1525–1541, 1996.

CAS  PubMed  Google Scholar 

Kuharsky, A. L., A. L. Fogelson. Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J. 80(3):1050–1074, 2001. doi:10.1016/S0006-3495(01)76085-7.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Kumar, S., Ramkrishna, D. On the solution of population balance equations by discretizationGçöI. A fixed pivot technique. Chem. Eng. Sci. 51(8):1311–1332, 1996. doi:10.1016/0009-2509(96)88489-2.

Landolfi, R., R. De Cristofaro, E. De Candia, B. Rocca, B. Bizzi. Effect of fibrinogen concentration on the velocity of platelet aggregation. Blood 78(2):377–381, 1991. doi:10.1016/0049-3848(91)90490-N.

CAS  PubMed  Google Scholar 

Lattuada, M., P. Sandkühler, H. Wu, J. Sefcik, M. Morbidelli. Aggregation kinetics of polymer colloids in reaction limited regime: experiments and simulations. Adv. Colloid Interface Sci. 103(1):33–56, 2003. doi:10.1016/S0001-8686(02)00082-9.

Article  CAS  PubMed  Google Scholar 

Leiderman, K., A. L. Fogelson. Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Math. Med. Biol. 28(1):47–84, 2011. doi:10.1093/imammb/dqq005.

Article  PubMed  PubMed Central  Google Scholar 

Lin, M. Y., H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin. Universality in colloid aggregation. Nature 339(6223):360–362, 1989. doi:10.1038/339360a0.

Article  CAS  Google Scholar 

Moiseyev, G., P. Z. Bar-Yoseph. Computational modeling of thrombosis as a tool in the design and optimization of vascular implants. J. Biomech. 46(2):248–252 (2013). doi:10.1016/j.jbiomech.2012.11.002.

Article  PubMed  Google Scholar 

Nesbitt, W. S., E. Westein, F. J. Tovar-Lopez, E. Tolouei, A. Mitchell, J. Fu, J. Carberry, A. Fouras, S. P. Jackson. A shear gradient-dependent platelet aggregation mechanism drives thrombus formation. Nat. Med. 15(6):665–673, 2009. doi:10.1038/nm.1955.

Article  CAS  PubMed  Google Scholar 

Oliphant, T. E. Python for scientific computing. Comput. Sci. Eng. 9(3):10–20, 2007. doi:10.1109/MCSE.2007.58.

Article  CAS  Google Scholar 

Pandya, J., L. Spielman. Floc breakage in agitated suspensions: theory and data processing strategy. J. Colloid Interface Sci. 90(2):517–531, 1982. doi:10.1016/0021-9797(82)90317-4.

Article  CAS  Google Scholar 

Pandya, J., L. Spielman. Floc breakage in agitated suspensions: effect of agitation rate. Chem. Eng. Sci. 38(12):1983–1992, 1983. doi:10.1016/0009-2509(83)80102-X.

Article  CAS  Google Scholar 

Paulus, J. M. Platelet size in man. Blood 46(3):321–36, 1975.

CAS  PubMed  Google Scholar 

Pedocchi, F., I. Piedra-Cueva. Camp and SteinGçös velocity gradient formalization. J. Environ. Eng. 131(10):1369–1376, 2005. doi:10.1061/(ASCE)0733-9372(2005)131:10(1369).

Article  CAS  Google Scholar 

Reif, F. Statistical Physics 398 (McGraw-Hill, New York, 1967).

Google Scholar 

Saffman, P. G., J. S. Turner. On the collision of drops in turbulent clouds. J. Fluid Mech. 1(01):16–30, 1956. doi:10.1017/S0022112056000020.

Article  Google Scholar 

Schneider, S. W., S. Nuschele, A. Wixforth, C. Gorzelanny, A. Alexander-Katz, R.R. Netz, M.F. Schneider. Shear-induced unfolding triggers adhesion of von Willebrand factor fibers. Proc. Natl. Acad. Sci. USA. 104(19):7899–903,2007. doi:10.1073/pnas.0608422104.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Singh, I., E. Themistou, L. Porcar, S. Neelamegham. Fluid shear induces conformation change in human blood protein von Willebrand factor in solution. Biophys. J. 96(6):2313–2320, 2009. doi:10.1016/j.bpj.2008.12.3900.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Slomkowski, S, J. V. Alemán, R. G. Gilbert, M. Hess, K. Horie, R. G. Jones, P. Kubisa, I. Meisel, W. Mormann, S. Penczek, R. F. T. Stepto. Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011). Pure Appl. Chem. 83(12):2229–2259, 2011. doi:.10.1351/PAC-REC-10-06-03

Article  CAS  Google Scholar 

Soos, M, J. Sefcik, M. Morbidelli. Investigation of aggregation, breakage and restructuring kinetics of colloidal dispersions in turbulent flows by population balance modeling and static light scattering. Chem. Eng. Sci. 61(8):2349–2363, 2006. doi:10.1016/j.ces.2005.11.001.

Article  CAS  Google Scholar 

Sorensen, C. M. The mobility of fractal aggregates: a review. Aerosol Sci. Technol. 45(7):765–779, 2011. doi:10.1080/02786826.2011.560909.

Article  CAS  Google Scholar 

Sorensen, E. N., G. W. Burgreen, W. R. Wagner, J. F. Antaki, Computational simulation of platelet deposition and activation: II. Results for Poiseuille flow over collagen. Ann. Biomed. Eng. 27(4):449–458, 1999.

Article  CAS  PubMed  Google Scholar 

Sorensen, E. N., G. W. Burgreen, W. R. Wagner, J. F. Antaki. Computational simulation of platelet deposition and activation: I. Model development and properties. Ann. Biomed. Eng. 27(4):436–48, 1999.

Article  CAS  PubMed  Google Scholar 

Spicer, P. T., S. E. Pratsinis. Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 42(6):1612–1620, 1996. doi:10.1002/aic.690420612.

Article  CAS  Google Scholar 

Spicer, P. T., S. E. Pratsinis, J. Raper, R. Amal, G. Bushell, G. Meesters. Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol. 97(1):26–34, 1998. doi:10.1016/S0032-5910(97)03389-5.

Article  CAS  Google Scholar 

Spicer, P. T., S. E. Pratsinis, M. D. Trennepohl, G. H. M. Meesters. Coagulation and fragmentation: the variation of shear rate and the time lag for attainment of steady state. Ind. Eng. Chem. Res. 35(9):3074–3080, 1996. doi:10.1021/ie950786n.

Article  CAS  Google Scholar 

von Smoluchowski, M. R. Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Physikalische Zeitschrift 17:585–599, 1916.

Google Scholar 

von Smoluchowski, M. R., Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Zeitschrift fuer physikalische Chemie 92(1912):129–168, 1917.

Google Scholar 

Westein, E., A. D. van der Meer, M. J. E. Kuijpers, J. P. Frimat, A. van den Berg, J. W. M. Heemskerk. Atherosclerotic geometries exacerbate pathological thrombus formation poststenosis in a von Willebrand factor-dependent manner. Proc. Natl. Acad. Sci. USA 110(4):1357–1362, 2013. doi:10.1073/pnas.1209905110.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Xia, Z., M. M. Frojmovic. Aggregation efficiency of activated normal or fixed platelets in a simple shear field: effect of shear and fibrinogen occupancy. Biophys. J. 66(6):2190–201, 1994. doi:10.1016/S0006-3495(94)81015-X.

Article  CAS  PubMed  PubMed Central  Google Scholar