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Math. Model. Nat. Phenom.
Volume 11, Number 1, 2016
Reviews in mathematical modelling
Page(s) 1 - 25
Published online 03 December 2015
  1. M.V. Abakumov, I.V. Ashmetkov, N.B. Esikova, V.B. Koshelev, S.I. Mukhin, N.V. Sosnin, V.F. Tishkin, A.P. Favorskij, A.B. Khrulenko. Strategy of mathematical cardiovascular system modeling. Matematicheskoe Modelirovanie, 12 (2000), no. 2, 106-117.
  2. J. Alastruey, A.W. Khir, K.S. Matthys, P. Segers, S.J. Sherwin, P.R. Verdonck, Kim H. Parker, J. Peiró. Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements. Journal of Biomechanics, 44 (2011), 2250-2258. [CrossRef] [PubMed]
  3. J. Alastruey, S.M. Moore, K.H. Parker, T. David, J. Peiró, S.J. Sherwin. Reduced modelling of blood flow in the cerebral circulation: Coupling 1-D, 0-D and cerebral auto-regulation models. International journal for numerical methods in fluids, 56 (2008), no. 8, 1061-1067. [CrossRef]
  4. J. Alastruey, K.H. Parker, J. Peiró, S.J. Sherwin. Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Communications in Computational Physics, 4 (2008), no. 2, 317-336.
  5. A.G. Alenitsyn, A.S. Kondratyev, I. Mikhailova, I. Siddique. Mathematical modeling of thrombus growth in microvessels. Journal of Prime Research in Mathematics, 4 (2008), 195-205.
  6. D. Alizadehrad, Y. Imai, K. Nakaaki, T. Ishikawa, T. Yamaguchi. Parallel simulation of cellular flow in microvessels using a particle method. Journal of Biomechanical Science and Engineering, 7 (2012), no. 1, 57-71. [CrossRef]
  7. M.P. Allen, D.J. Tidesley. Computer Simulation of Liquids. Clarendon, Oxford, 1987.
  8. T. AlMomani, H.S. Udaykumar, J.S. Marshall, K.B. Chandran. Micro-scale dynamic simulation of erythrocyte-platelet interaction in blood flow. Annals of Biomedical Engineering, 36 (2008), no. 6, 905-920. [CrossRef] [PubMed]
  9. M. Anand and K.R. Rajagopal. A shear-thinning viscoelastic fluid model for describing the flow of blood. Int. J. of Cardiovascular Medicine and Science, 4 (2004), no. 2, 59–68.
  10. M. Anand, K. Rajagopal, K.R. Rajagopal. A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J. Theor. Biol., 253 (2008), no. 4, 725–738. [CrossRef] [PubMed]
  11. G. Astarita, G. Marrucci. Principles of Non-Newtonian Fluid Mechanics. McGraw Hill, 1974.
  12. P. Bagchi. Mesoscale simulation of blood flow in small vessels. Biophysical Journal, 92 (2007), no. 6, 1858-1877.[PubMed: 17208982]. [CrossRef] [PubMed]
  13. H. A. Barnes. Thixotropy - a review. J. Non-Newtonian Fluid Mech., 70 (1997), 1–33. [CrossRef]
  14. N. M. Bessonov, S.F. Golovashchenko, V. Volpert. Numerical modelling of contact elastic-plastic flows. Math. Model. Nat. Phenom., 4 (2008), no. 1, 44-87. [CrossRef] [EDP Sciences]
  15. N. Bessonov, E. Babushkina, S.F. Golovashchenko, A. Tosenberger, F. Ataullakhanov, M. Panteleev, A. Tokarev, V. Volpert. Numerical modelling of cell distribution in blood flow. Math. Model. Nat. Phenom., 9 (2014), no. 6, 69-84. [CrossRef] [EDP Sciences] [MathSciNet]
  16. P.J. Blanco, R.A. Feijóo. A 3D-1D-0D Computational model for the entire cardiovascular system. Computational Mechanics, eds. E.Dvorking, M. Goldschmit, M. Storti, XXIX (2010), 5887-5911.
  17. P.J. Blanco, S.M. Watanabe, M.A.R.F. Passos, P.A. Lemos, R.A. Feijóo. An anatomically detailed arterial network model for one-dimensional computational hemodynamics. IEEE Transaction on Biomedical Engineering, 62 (2015), no. 2, 736-753. [CrossRef]
  18. T. Bodnar, K. Rajagopal, A. Sequeira. Simulation of the three-dimensional flow of blood using a shear-thinning viscoelastic fluid model. Math. Model. Nat. Phenom., 6 (2011), no. 5, 1-24. [CrossRef] [EDP Sciences]
  19. T. Bodnar, A. Sequeria. Numerical simulation of the coagulation dynamics of blood. Computational and Mathematical Methods in Medicine, 9 (2008), no. 2, 83–104. [CrossRef] [MathSciNet]
  20. C. Bui, V. Lleras, O. Pantz. Dynamics of red blood cells in 2d. ESAIM: Proc., 28 (2009), 182-194. [CrossRef] [EDP Sciences]
  21. A. Ya. Bunicheva, M. A. Menyailova, S. I. Mukhin, N. V. Sosnin, A. P. Favorskii. Studying the influence of gravitational overloads on the parameters of blood flow in vessels of greater circulation. Mathematical Models and Computer Simulations, 5 (2013), no. 1, 81-91. [CrossRef] [MathSciNet]
  22. A.Ya. Bunicheva, S.I. Mukhin, N.V. Sosnin, A.P. Favorskii. Numerical experiment in hemodynamics. Differential Equations, 40 (2004), no. 7, 984-999. [CrossRef] [MathSciNet]
  23. G.A. Buxton, N. Clarke. Computational phlebology: the simulation of a vein valve. Journal of Biological Physics, 32 (2006), no. 6, 507-521. [CrossRef] [PubMed]
  24. S. Čanić, E.H. Kim. Mathematical analysis of the quasilinear eects in a hyperbolic model blood ow through compliant axi-symmetric vessels. Mathematical Methods in the Applied Sciences, 26 (2003), 1161-1186. [CrossRef]
  25. S. Čanić, J. Tambača, G. Guidoboni, A. Mikelić, C.J. Hartley, A. Rosenstrauch. Modeling viscoelastic behaviour of arterial walls and their interaction with pulsatile blood flow. SIAM Journal of Applied Mathematics, 67 (2006), no. 1, 164-193. [CrossRef]
  26. C. G. Caro, T. J. Pedley, R. C. Schroter, W. A. Seed. The Mechanics of the Circulation. Oxford University Press, 1978.
  27. C.G. Caro, T.J. Pedley, R.C. Schroter, W.A. Seed. The Mechanics of the Circulation. 2nd Edition, Cambridge University Press, 2012.
  28. S. E. Charm, G. S. Kurland. Blood Flow and Microcirculation. John Wiley & Sons, 1974.
  29. I.L. Chernyavsky, N.A. Kudryashov. A Mathematical model for autoregulation of the arterial lumen by endothelium-derived relaxing factor. Advanced Science Letters, 1 (2008), no. 2, 226-230. [CrossRef]
  30. S. Chien, S. Usami, R.J. Dellenback, M.I. Gregersen. Shear dependence of effective cell volume as a determinant of blood viscosity. Science, 168 (1970), 977–979. [CrossRef] [PubMed]
  31. S. Chien, R. G. King, R. Skalak, S. Usami, and A. L. Copley. Viscoelastic properties of human blood and red cell suspensions. Biorheology, 12 (1975), 341–346. [PubMed]
  32. Y. I. Cho and K. R. Kensey. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part I: Steady flows. Biorheology, 28 (1991), 241–262. [PubMed]
  33. E. Crepeau, M. Sorine. A reduced model of pulsatile flow in an arterial compartment. Chaos Solitons & Fractals, 34 (2007), no. 2, 594-605. [CrossRef] [MathSciNet]
  34. L.M. Crowl, A.L. Fogelson. Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Int. J. Numer. Method Biomed. Eng., 26 (2010), no. 3-4, 471-487. [CrossRef] [PubMed]
  35. T. David, S. Alzaidi, H. Farr. Coupled autoregulation models in the cerebro-vasculature. Journal of Engineering Mathematics, 64 (2009), 403-415. [CrossRef]
  36. A. DiCarlo, P. Nardinocchi, G. Pontrelli, L. Teresi. A heterogeneous approach for modelling blood flow in an arterial segment. Simulations in Biomedicine V, WIT Press, 69-78, 2003.
  37. L. Dintenfass. Blood Microrheology -Viscosity Factors in Blood Flow, Ischaemia and Thrombosis. Butterworth, 1971.
  38. L. Dintenfass. Blood Viscosity, Hyperviscosity and Hyperviscosaemia. MTP Press Limited, 1985.
  39. M.M. Dupin, I. Halliday, C.M. Care, L. Alboul, L.L. Munn, Modeling the flow of dense suspensions of deformable particles in three dimensions, Physical Review E, 75 (2007), 066707. [CrossRef]
  40. W. Dzwinel, K. Boryczko, D.A. Yuen. Modeling mesoscopic fluids with discrete-particles methods. Algorithms and results. In: Spasic AM, Hsu JP (eds) Finely Dispersed Particles: Micro-, Nano-, and Atto-Engineering. Taylor & Francis, CRC Press, 715-778.
  41. A. Elgarayhi, E.K. El-Shewy, A.A. Mahmoud, A.A. Elhakem. Propagation of nonlinear pressure waves in blood. ISRN Computational Biology, 2013, Article ID 436267.
  42. E. A. Evans, R. M. Hochmuth. Membrane viscoelasticity. Biophys. J., 16 (1976), no. 1, 111.
  43. D. Fedosov, B. Caswell, G.E. Karniadakis, General coarse-grained red blood cell models: I. Mechanics, 2009, arXiv:0905.0042 [q-bio.CB].
  44. D. Fedosov, B. Caswell, G.E. Karniadakis, A multiscale red blood cell model with accurate mechanics, rheology, and dynamics, Biophysical Journal, 98 (2010), 2215-2225. [CrossRef] [PubMed]
  45. D.A. Fedosov, Multiscale Modeling of Blood Flow and Soft Matter, PhD dissertation at Brown University, (2010).
  46. D.A. Fedosov, H. Lei, B. Caswell, S. Suresh, G.E. Karniadakis, Multiscale modeling of red blood cell mechanics and blood flow in malaria. PLoS Computational Biology, 7 (2011), 12, [CrossRef] [PubMed]
  47. D.A. Fedosov, H. Noguchi, G. Gompper. Multiscale modeling of blood flow: from single cells to blood rheology. Biomech. Model. Mechanobiol., 13 (2014), 239-258. [CrossRef] [PubMed]
  48. D.A. Fedosov, I.V. Pivkin, G.E. Karniadakis, Velocity limit in DPD simulations of wall-bounded flows. J. Comp. Phys., 227 (2008) 2540-2559. [CrossRef] [MathSciNet]
  49. N. Filipovic, M. Kojic, A. Tsuda. Modelling thrombosis using dissipative particle dynamics method. Phil. Trans. R. Soc. A, 366 (2008), 3265–3279. [CrossRef]
  50. A.L. Fogelson. Cell-based models of blood clotting. Single-Cell-Based Models in Biology and Medicine (ed. by A.R.A. Anderson, M.A.J. Chaplain, K.A. Rejniak), Mathematics and Biosciences in Interaction, p. 234-169, Birkhäuser Verlag Basel, 2007.
  51. L. Formaggia, D. Lamponi, M. Tuveri, A. Veneziani. Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Computer Methods in Biomechanics and Biomedical Engineering, 9 (2006), no. 5, 273-288. [CrossRef] [PubMed]
  52. L. Formaggia, D. Lamponi, A. Quarteroni. One-dimensional models for blood flow in arteries. Journal of Engineering Mathematics, 47 (2003), 251-276. [CrossRef] [MathSciNet]
  53. L. Formaggia, A. Quarteroni, A. Veneziani. Cardiovascular mathematics. Vol. 1. Springer, Heidelberg, 2009.
  54. T.K. Gaik, H. Demiray. Forced Korteweg-de Vries-Burgers equation in an elastic tube filled with a variable viscosity fluid. Chaos Solitons & Fractals, 38 (2008), 1134-1145. [CrossRef] [MathSciNet]
  55. T. Gamilov, Y. Ivanov, P. Kopylov, S. Simakov, Y. Vassilevski. Patient specific haemodynamic modeling after occlusion treatment in leg. Math. Model. Nat. Phenom., 9 (2014), no. 6, 85-97. [CrossRef] [EDP Sciences] [MathSciNet]
  56. H.L. Goldsmith, V.T. Turitto. Rheological aspects of thrombosis and haemostasis: basic principles and applications. Thrombosis and Haemostasis, 55 (1986), no. 3, 415-435. [PubMed]
  57. S. S. Grigorjan, Y.Z. Saakjan, A. K. Tsaturjan. On the mechanisms of generation of Korotkoff sounds. Doklady of Academy of Science of the SSSR, 251 (1980), 570-574 (in Russian).
  58. S.S. Grigorjan, Y.Z. Saakjan, A.K. Tsatutjan. To the theory of Korotkoff method. Biomechanics, (1984), 15-16,
  59. R.D. Groot, P.B. Warren, Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys., 107 (1997), no. 11, 4423–4435. [CrossRef]
  60. R.D. Guy, A.L. Fogelson, J.P. Keener. Fibrin gel formation in a shear flow. Math. Med. Biol. 24 (2007), no. 1, 111–130. [CrossRef] [PubMed]
  61. G.A. Holzapfel, T.C. Gasser, R.W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity, 61 (2000), 1-48. [CrossRef] [MathSciNet]
  62. S.M. Hosseini, J.J. Feng. A particle-based model for the transport of erythrocytes in capillaries. Chem. Eng. Sci., 64 (2009), 4488-4497. [CrossRef]
  63. Y. Imai, H. Kondo, T. Ishikawa, C.T. Lim, T. Yamaguchi. Modeling of hemodynamics arising from malaria infection. Journal of Biomechanics, 43 (2010), 1386-1393. [CrossRef] [PubMed]
  64. Y. Imai, K. Nakaaki, H. Kondo, T. Ishikawa, C.T. Lim, T. Yamaguchi. Margination of red blood cells infected by Plasmodium falciparum in a microvessel. Journal of Biomechanics, 44 (2011), 1553-1558. [CrossRef] [PubMed]
  65. M. Karttunen, I. Vattulainen, A. Lukkarinen. A Novel Methods in Soft Matter Simulations. Springer, Berlin, 2004.
  66. J.Keener, J.Sneyd. Mathematical Physiology. II: Systems Physiology. Springer, 2nd edition, 2008.
  67. A.S. Kholodov. Some dynamical models of external breathing and haemodynamics accounting for their coupling and substance transport. Computer Models and Medicine Progress, Nauka, Moscow, 127-163, 2001 (in Russian).
  68. A.S. Kholodov, A.V. Evdokimov, S.S. Simakov. Numerical simulation of peripheral circulation and substance transfer with 2D models. Mathematical biology: recent trends, eds. P. Chandra, R. Kumar, 22-29, 2006.
  69. S. Kim, Y.I. Cho, A. H. Jeon, B. Hogenauer, K.R. Kensey. A new method for blood viscosity measurement. J. Non-Newtonian Fluid Mech., 94 (2000), 47-56. [CrossRef]
  70. C.S. Kim, C. Kris, D. Kwak. Numerical models of human circulatory system under altered gravity: brain circulation. AIAA Paper No. 2004-1092, AIAA 42nd Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2004.
  71. J.F. Koleski, E.C. Eckstein. Near wall concentration profiles of 1.0 and 2.5 μm beads during flow of blood suspensions, Trans. Ann. Soc. Intern. Organs, 37 (1991), 9-12. [CrossRef]
  72. V. Koshelev, S. Mukhin, T. Sokolova, N. Sosnin, A. Favorski. Mathematical modelling of cardio-vascular hemodynamics with account of neuroregulation. Matematicheskoe Modelirovanie, 19 (2007), no. 3, 15-28 (in Russian).
  73. W. Kroon, W. Huberts, M. Bosboom, F. van de Vosse. A numerical method of reduced complexity for simulating vascular hemodynamics using coupled 0D lumped and 1D wave propagation models. Computational and Mathematical Methods in Medicine, (2012), Article ID 156094.
  74. P.W. Kuchel, E.D. Fackerell. Parametric-equation representation of biconcave erythrocytes. Bulletin of Mathematical Biology, 61 (1999), 209-220. [CrossRef] [PubMed]
  75. I. Larrabidea, P.J. Blanco, S.A. Urquiza, E.A. Dari, M.J. Véneref, N.A. de Souza e Silvac, R.A. Feijóo. HeMoLab - hemodynamics modelling laboratory: an application for modelling the human cardiovascular system. Computers in Biology and Medicine, 42 (2012), 993-1004. [CrossRef] [PubMed]
  76. M. B. Lawrence, T. A. Springer. Leukocytes roll on a selectin at physiological flow rates: distinction from and prerequisite for adhesion through integrins. Cell, 65 (1991), 859-873. [CrossRef] [PubMed]
  77. R.C. Leif, J. Vinograd, The Distribution of Buoyant Density of Human Erythrocytes in Bovine Albumin Solutions, Proc. Natl. Acad. Sci. USA, 51 (1964), 3, [CrossRef]
  78. S. Leibler, A.C. Maggs, Simulation of shape changes and adhesion phenomena in an elastic model of erythrocytes. Proc. Natl. Acad. Sci. USA, 87 (1990), 6433-6435. [CrossRef]
  79. D. Liepsch, St. Moravec. Pulsatile flow of non-Newtonian fluid in distensible models of human arteries. Biorheology, 21 (1984), 571-586. [PubMed]
  80. K. Logana, R. Balossino, F. Migliavacca, G. Pennati, E.L. Bove, M.R. Leval, G. Dubini, Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusion in the univentricular circulation. Journal of Biomechanics, 38 (2005), no. 5, 1129-1141. [CrossRef] [PubMed]
  81. L. Lopez, I.M. Duck, W.A. Hunt. On the shape of the erythrocyte. Biophys. J., 8 (1968), no. 11, 1228-1235. [CrossRef] [PubMed]
  82. K. Low, R. van Loon, I. Sazonov, R.L.T. Bevan, P. Nithiarasu. An improved baseline model for a human arterial network to study the impact of aneurysms on pressure-flow waveforms. International Journal of Numerical Methods in Biomedical Engineering, 28 (2012), 1224-1246. [CrossRef]
  83. G. D. O. Lowe, Ed. Clinical Blood Rheology, Vol. I and II. CRC Press, Boca Raton, Florida, 1998.
  84. J.L. McWhirter, H. Noguchi, G. Gompper. Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. PNAS, 106 (2009), no. 15, 6039-6043. [CrossRef]
  85. E. W. Merrill, E. R. Gilliland, G. Cokelet, H. Shin, A. Britten, R. E. Wells, Jr.. Rheology of human blood, near and at zero flow. Effects of temperature and hematocrit level. Biophys. J., 3 (1963), 199–213. [CrossRef] [PubMed]
  86. E. W. Merrill, G. C. Cokelet, A. Britten, R. E. Wells. Non-Newtonian rheology of human blood. Effect of fibrinogen deduced by subtraction. Circulat. Res., 13 (1963), 48–55. [CrossRef]
  87. V. Milisić, A. Quarteroni. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM: Mathematical Modelling and Numerical Analysis, 38 (2004), no. 4, 613-632. [CrossRef] [EDP Sciences]
  88. N. Mohandas, P.G. Gallagher, Red cell membrane: past, present, and future. Blood, 112 (2008)m 3939-3948. [CrossRef] [PubMed]
  89. P.C. F. Moller, J. Mewis, D. Bonn. Yield stress and thixotropy: on the difficulty of measuring yield stress in practice. Soft Matter, 2 (2006), 274–288. [CrossRef]
  90. Y. Mori, C. Peskin. A universal programmable fiber architecture for the representation of a general incompressible linearly elastic material as a fiber-reinforced fluid. Advances in Applied Mathematics, 43 (2009), no. 1, 75-100. [CrossRef]
  91. L.O. Müller, C. Parés, E. Toro. Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. Journal of Computational Physics, 242 (2013), 53-85. [CrossRef]
  92. L.O. Müller, E. Toro. A global multiscale mathematical model for the human circulation with emphasis on the venous system. International Journal for Numerical Methods in Biomedical Engineering, 30 (2014), no. 7, 681-725. [CrossRef] [MathSciNet] [PubMed]
  93. L.L. Munn, M.M. Dupin, Blood Cell Interactions and Segregation in Flow. Annals of Biomedical Engineering, 36 (2008), no. 4, 534-544. [CrossRef] [PubMed]
  94. S. Muñoz San Martín, J.L. Sebastián, M. Sancho1, G. Álvarez. Modeling human erythrocyte shape and size abnormalities. arXiv:q-bio/0507024 [q-bio.QM], 14 Jul 2005.
  95. J.P. Mynard, P. Nithiarasu. A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Communications in Numerical Methods in Engineering, 24 (2008), no. 5, 367-417. [CrossRef]
  96. Q. D. Nguyen, D. V. Boger. Measuring the flow properties of yield stress fluids. Annual Reviews, 24 (1992), 47–88.
  97. H. Noguchi, G. Gompper. Shape transitions of fluid vesicles and red blood cells in capillary flows. PNAS, 102 (2005), no. 40, 14159-14164. [CrossRef]
  98. D. Obrist, B. Weber, A. Buck, P. Jenny. Red blood cell distribution in simplified capillary networks, Phil. Trans. R. Soc. A, 368 (2010), doi: 10.1098/rsta.2010.0045.
  99. T. Ohashi, H. Liu, T. Yamaguchi. Computational fluid dynamic simulation of the flow through venous valve. In: Clinical Application of Computational Mechanics to the Cardiovascular System, 186–189, Springer, 2000.
  100. M.S. Olufsen, C.S. Peskin, W.Y. Kim, E.M. Pedersen, A. Nadim, J. Larsen. Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Annals of Biomedical Engineering, 28 (2000), 1281-1299. [CrossRef] [PubMed]
  101. R. G. Owens. A new microstructure-based constitutive model for human blood, J. Non -Newtonian Fluid Mech., 14 (2006), 57-70. [CrossRef]
  102. E. Ozawa, K. Bottom, X. Xiao R.D. Kamm. Numerical simulation of enhanced external counterpulsation. Annals of Biomedical Engineering, 29 (2001), 284-297. [CrossRef] [PubMed]
  103. Q. Pan, R. Wang, B. Reglin, G. Cai, J. Yan, A.R. Pries, G. Ning. A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks. Journal of Biomedical Engineering, 136 (2014), no. 1, 011009.
  104. T.J. Pedley, X.Y. Luo. Modelling flow and oscillations in collapsible tubes. Theoretical and Computational Fluid Dynamics, 10 (1998), 277-294. [CrossRef]
  105. D. Pinho, A. Pereira, R. Lima, T. Ishikawa, Y. Imai, T. Yamaguchi. Red blood cell dispersion in 100 μm glass capillaries: the temperature effect. C.T. Lim and J.C.H. Goh (Eds.), WCB 2010, IFMBE Proceedings, 31 (2010), 1067–1070.
  106. E. Pinto, B. Taboada, R. Rodrigues, V. Faustino, A. Pereira, R. Lima. Cell-free layer (CFL) analysis in a polydimethysiloxane (PDMS) microchannel: a global approach. WebmedCentral Biomedical Engineering, 4 (2013), 8, WMC004374.
  107. I.V. Pivkin, G.E. Karniadakis, Accurate coarse-grained modeling of red blood cells. Physical Review letters, 101 (2008), 118105. [CrossRef] [PubMed]
  108. I.V. Pivkin, G.E. Karniadakis. A new method to impose no-slip boundary conditions in dissipative particle dynamics. J. Comp. Phys., 207 (2005), 114-128. [CrossRef]
  109. I.V. Pivkin, P.D. Richardson, G. Karniadakis. Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi. PNAS, 103 (2006), 17164–17169. [CrossRef]
  110. A. S. Popel, P. C. Johnson. Microcirculation and hemorheology. Annu. Rev. Fluid Mech., 37 (2005), 43–69. [CrossRef] [PubMed]
  111. C. Pozrikidis. Modeling and Simulation of Capsules and Biological Cells, Chapman & Hall/CRC, 2003.
  112. D. Quemada. Rheology of concentrated disperse systems III. General features of the proposed non-Newtonian model. Comparison with experimental data. Rheological Acta, 17 (1978), 643-653. [CrossRef]
  113. K.R. Rajagopal, A.R. Srinivasa. A thermodynamic frame work for rate type fluid models. Journal of Non-Newtonian Fluid Mechanics, 80 (2000), 207–227. [CrossRef]
  114. A.M.Robertson, A.Sequeira, M.V. Kameneva. Hemorheology. In G.P. Galdi, R. Rannacher, A.M. Robertson, S. Turek (Eds.) Hemodynamical Flows: Modeling, Analysis and Simulation. (Oberwolfach Seminars), Birkhäuser Verlag, 37, 63-120, 2008.
  115. M.C. Roco, editor. Particulate Two-Phase Flow. Series in Chemical Engineering. Butterworth-Heinemann Publ., 1993.
  116. M. Rosar, C. Peskin. Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York Journal of Mathematics, 7 (2001), 281–302. [MathSciNet]
  117. U.D. Schiller. Dissipative Particle Dynamics. A Study of the Methodological Background. Diploma thesis at Faculty of Physics University of Bielefeld, 2005.
  118. H. Schmid-Schönbein, R. E. Wells. Rheological properties of human erythrocytes and their influence upon anomalous viscosity of blood. Physiology Rev., 63 (1971), 147–219.
  119. G. W. Scott-Blair. An equation for the flow of blood, plasma and serum through glass capillaries. Nature, 183 (1959), 613–614. [CrossRef]
  120. S. Sherwin, V. Franke, J. Peiró, K. Parker. One-dimensional modelling of a vascular network in space-time variables. Journal of Engineering Mathematics, 47 (2003), 217-250. [CrossRef]
  121. S.J. Sherwin, L. Formaggia, J. Peiró, V. Franke. Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. International Journal for Numerical Methods in Fluids, 43 (2003), 673-700. [CrossRef]
  122. Y. Shi, P. Lawford, R. Hose. Review of zero-D and 1-D models of blood flow in the cardiovascular system. BioMedical Engineering Online, 10:33 (2011), doi:10.1186/1475-925X-10-33.
  123. S.S. Simakov, T.M. Gamilov, Y.N. Soe. Computational study of blood flow in lower extremities under intense physical load. Russian Journal of Numerical Analysis and Mathematical Modelling, 28 (2013), no. 5, 485-504. [CrossRef] [MathSciNet]
  124. S.S. Simakov, A.S. Kholodov. Computational study of oxygen concentration in human blood under low frequency disturbances. Mathematical Models and Computer Simulations, 1 (2009), 283-295. [CrossRef] [MathSciNet]
  125. R. Skalak, A. Tozeren, R. Zarda, S. Chein. Strain energy function of red blood cell membranes. Biophysical Journal 13 (1973), no. 3, 245-264 [PubMed: 4697236]. [CrossRef] [PubMed]
  126. M.F. Snyder, V.C. Rideout. Computer simulation studies of the venous circulation. IEEE Transactions on Bio-Medical Engineering, BME-16 (1969) no. 4, 325-334.
  127. S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, T. Seufferlein. Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomaterialia, 1 (2005), 15-30. [CrossRef] [PubMed]
  128. C.R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E.D. Rosen, M. Alber. Modelling platelet - blood flow interaction using the subcellular element Langevin method. J. R. Soc. Interface, 8 (2011), 1760-1771. [CrossRef] [PubMed]
  129. G. B. Thurston. Viscoelasticity of human blood. Biophys. J., 12 (1972), 1205–1217. [CrossRef] [PubMed]
  130. G.B. Thurston. Non-Newtonian viscosity of human blood: Flow induced changes in microstructure. Biorheology, 31 (1994), no. 2, 179–192. [PubMed]
  131. G. B. Thurston. Viscoelastic properties of blood and blood analogs. Advances in Hemodynamics and Hemorheology, 1 (1996), 1–30. [CrossRef]
  132. A.A. Tokarev, A.A. Butylin, F.I. Ataullakhanov. Platelet adhesion from shear blood flow is controlled by near-wall rebounding collisions with erythrocytes. Biophys. J., 100 (2011), no. 4, 799-808. [CrossRef] [PubMed]
  133. A.A. Tokarev, A.A. Butylin, F.I. Ataullakhanov. Platelet transport and adhesion in shear blood flow: the role of erythrocytes. Computer Research and Modeling, 4 (2012), no. 1, 185-200 (Russian).
  134. A.A. Tokarev, A.A. Butylin, E.A. Ermakova, E.E. Shnol, G.P. Panasenko, F.I. Ataullakhanov. Finite platelet size could be responsible for platelet margination effect. Biophysical Journal, 101 (2011), 1835-1843. [CrossRef] [PubMed]
  135. A. Tokarev, I. Sirakov, G. Panasenko, V. Volpert, E. Shnol, A. Butylin, F. Ataullakhanov. Continuous mathematical model of platelet thrombus formation in blood flow. Russian Journal of Numerical Analysis and Mathematical Modelling, 27 (2012), no. 2, 192-212. [CrossRef]
  136. A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, V. Volpert. Particle dynamics methods of blood flow simulations. Math. Model. Nat. Phenom., 6 (2011), no. 5, 320–332. [CrossRef] [EDP Sciences]
  137. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert. Modelling of thrombus growth in flow with a DPD-PDE method. Journal of Theoretical Biology, 337 (2013), 30-41. [CrossRef] [MathSciNet] [PubMed]
  138. K. Tsubota, S. Wada. Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane’s natural state. International Journal of Mechanical Sciences, 52 (2010), 356-364. [CrossRef]
  139. K. Tsubota, S. Wada, H. Kamada, Y. Kitagawa, R. Lima, T. Yamaguchi. A particle method for blood flow simulation, application to flowing red blood cells and platelets. Journal of the Earth Simulator, 5 (2006), 2-7.
  140. F. J. Walburn, D. J. Schneck. A constitutive equation for whole human blood. Biorheology, 13 (1976), 201–210. [PubMed]
  141. Yu. Vassilevskii, S. Simakov, V. Salamatova, Yu. Ivanov, T. Dobroserdova. Numerical issues of modelling blood flow in networks of vessels with pathologies. Russian Journal of Numerical Analysis and Mathematical Modelling, 26 (2011), no. 6, 605-622.
  142. Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, T. Dobroserdova. Blood flow simulation in atherosclerotic vascular network using fiber-spring representation of diseased wall. Math. Model. Nat. Phenom., 6 (2011), no. 5, 333-349. [CrossRef] [EDP Sciences]
  143. Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, T. Dobroserdova. Vessel wall models for simulation of atherosclerotic vascular networks. Math. Model. Nat. Phenom., 6 (2011), no. 7, 82-99. [CrossRef] [EDP Sciences]
  144. F.N. van de Vosse, N. Stergiopulos. Pulse wave propagation in the arterial tree. Annual Review of Fluid Mechanics, 43 (2011), 467-499. [CrossRef]
  145. N. Xiao, J. Alastruey-Arimon, C.A. Figueroa. A systematic comparison between 1D and 3D hemodynamics in compliant arterial models. International Journal for Numerical Methods in Biomedical Engineering. 30 (2014), no. 2, 204-231. [CrossRef] [MathSciNet] [PubMed]
  146. Z. Xu, N. Chen, M.M. Kamocka, E.D. Rosen, M. Alber. A multiscale model of thrombus development. J. R. Soc. Interface, 5 (2008), 705–722. [CrossRef] [PubMed]
  147. C. Yeh, A.C. Calvez, E.c. Eckstein. An estimated shape function for drift in a platelet-transport model. Biophysical Journal, 67 (1994), 1252-1259. [CrossRef] [PubMed]
  148. C. Yeh, E.C. Eckstein. Transient lateral transport of platelet-sized particles in flowing blood suspensions. Biophysical Journal, 66 (1994), 1706-1716. [CrossRef] [PubMed]
  149. K.K. Yeleswarapu, M.V. Kameneva, K. R. Rajagopal, J. F. Antaki. The flow of blood in tubes: Theory and experiment. Mechanics Research Communications, 25 (1998), no. 3, 257–262. [CrossRef]
  150. J. Zhang, P.C. Johnson, A.S. Popel. Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc Res., 77 (2009), 265-272. [CrossRef] [PubMed]

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