M. V. Abakumov, I. V. Ashmetkov, N. B. Esikova, V. B. Koshelev, S. I. Mukhin et al., Strategy of mathematical cardiovascular system modeling, Matematicheskoe Modelirovanie, issue.2, pp.12-106, 2000.

J. Alastruey, A. W. Khir, K. S. Matthys, P. Segers, S. J. Sherwin et al., Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements, Journal of Biomechanics, vol.44, issue.12, pp.44-2250, 2011.
DOI : 10.1016/j.jbiomech.2011.05.041

N. Bessonov, A. Sequeira, S. Simakov, Y. Vassilevski, and V. , Volpert Methods of blood flow modelling

J. Alastruey, S. M. Moore, K. H. Parker, T. David, J. Peiró et al., 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, vol.125, issue.8, pp.56-1061, 2008.
DOI : 10.1002/fld.1606

J. Alastruey, K. H. Parker, J. Peiró, and S. J. Sherwin, Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation, Communications in Computational Physics, vol.4, issue.2, pp.317-336, 2008.

A. G. Alenitsyn, A. S. Kondratyev, I. Mikhailova, and I. Siddique, Mathematical modeling of thrombus growth in microvessels, Journal of Prime Research in Mathematics, vol.4, pp.195-205, 2008.

D. Alizadehrad, Y. Imai, K. Nakaaki, T. Ishikawa, and T. Yamaguchi, Parallel Simulation of Cellular Flow in Microvessels Using a Particle Method, Journal of Biomechanical Science and Engineering, vol.7, issue.1, pp.57-71, 2012.
DOI : 10.1299/jbse.7.57

T. Almomani, H. S. Udaykumar, J. S. Marshall, and K. B. Chandran, Micro-scale Dynamic Simulation of Erythrocyte???Platelet Interaction in Blood Flow, Annals of Biomedical Engineering, vol.114, issue.5, pp.905-920, 2008.
DOI : 10.1007/s10439-008-9478-z

M. Anand and K. R. , A shear-thinning viscoelastic fluid model for describing the flow of blood, Int. J. of Cardiovascular Medicine and Science, vol.4, issue.2, pp.59-68, 2004.

M. Anand, K. Rajagopal, and K. R. , 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, Journal of Theoretical Biology, vol.253, issue.4, pp.725-738, 2008.
DOI : 10.1016/j.jtbi.2008.04.015

G. Astarita and G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, Journal of Applied Mechanics, vol.42, issue.3, 1974.
DOI : 10.1115/1.3423693

P. Bagchi, Mesoscale Simulation of Blood Flow in Small Vessels, Biophysical Journal, vol.92, issue.6, pp.1858-1877, 2007.
DOI : 10.1529/biophysj.106.095042

H. A. Barnes, Thixotropy???a review, Journal of Non-Newtonian Fluid Mechanics, vol.70, issue.1-2, pp.1-33, 1997.
DOI : 10.1016/S0377-0257(97)00004-9

N. M. Bessonov, S. F. Golovashchenko, and V. Volpert, Numerical Modelling of Contact Elastic-Plastic Flows, Mathematical Modelling of Natural Phenomena, vol.4, issue.1, pp.44-87, 2008.
DOI : 10.1051/mmnp/20094103

N. Bessonov, E. Babushkina, S. F. Golovashchenko, A. Tosenberger, F. Ataullakhanov et al., Numerical Modelling of Cell Distribution in Blood Flow, Mathematical Modelling of Natural Phenomena, vol.9, issue.6, pp.69-84, 2014.
DOI : 10.1051/mmnp/20149606

P. J. Blanco and R. A. Feijóo, A 3D-1D-0D Computational model for the entire cardiovascular system, Computational Mechanics, pp.5887-5911, 2010.

P. J. Blanco, S. M. Watanabe, M. A. Passos, P. A. Lemos, and R. A. Feijóo, An Anatomically Detailed Arterial Network Model for One-Dimensional Computational Hemodynamics, IEEE Transactions on Biomedical Engineering, vol.62, issue.2, pp.62-736, 2015.
DOI : 10.1109/TBME.2014.2364522

T. Bodnar, K. Rajagopal, and A. Sequeira, Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model, Mathematical Modelling of Natural Phenomena, vol.6, issue.5, pp.1-24, 2011.
DOI : 10.1051/mmnp/20116501

T. Bodnar and A. Sequeria, Numerical Simulation of the Coagulation Dynamics of Blood, Computational and Mathematical Methods in Medicine, vol.9, issue.2, pp.83-104, 2008.
DOI : 10.1080/17486700701852784

C. Bui, V. Lleras, and O. Pantz, Dynamics of red blood cells in 2d, ESAIM: Proceedings, vol.28, pp.182-194, 2009.
DOI : 10.1051/proc/2009046

URL : https://hal.archives-ouvertes.fr/hal-00784177

A. Ya, M. A. Bunicheva, S. I. Menyailova, N. V. Mukhin, A. P. Sosnin et al., Studying the influence of gravitational overloads on the parameters of blood flow in vessels of greater circulation, Mathematical Models and Computer Simulations, vol.5, issue.1, pp.81-91, 2013.

A. Ya, S. I. Bunicheva, N. V. Mukhin, A. P. Sosnin, and . Favorskii, Numerical experiment in hemodynamics, Differential Equations, vol.40, issue.7, pp.984-999, 2004.

G. A. Buxton and N. Clarke, Computational Phlebology: The Simulation of a Vein Valve, Journal of Biological Physics, vol.37, issue.6, pp.507-521, 2006.
DOI : 10.1007/s10867-007-9033-4

S. Cani´ccani´c and 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, pp.26-1161, 2003.

S. Cani´ccani´c, J. Tamba?-ca, G. Guidoboni, A. Mikeli´cmikeli´c, C. J. Hartley et al., Modeling Viscoelastic Behavior of Arterial Walls and Their Interaction with Pulsatile Blood Flow, SIAM Journal on Applied Mathematics, vol.67, issue.1, pp.164-193, 2006.
DOI : 10.1137/060651562

C. G. Caro, T. J. Pedley, R. C. Schroter, and W. , A. Seed. The Mechanics of the Circulation, 1978.
URL : https://hal.archives-ouvertes.fr/hal-00144820

C. G. Caro, T. J. Pedley, R. C. Schroter, and W. A. , Seed. The Mechanics of the Circulation, 2012.

S. E. Charm and G. S. Kurland, Blood Flow and Microcirculation, 1974.

I. L. Chernyavsky and N. A. Kudryashov, A Mathematical Model for Autoregulation of the Arterial Lumen by Endothelium-Derived Relaxing Factor, Advanced Science Letters, vol.1, issue.2, pp.226-230, 2008.
DOI : 10.1166/asl.2008.024

S. Chien, S. Usami, R. J. Dellenback, and M. I. Gregersen, Shear Dependence of Effective Cell Volume as a Determinant of Blood Viscosity, Science, vol.168, issue.3934, pp.168-977, 1970.
DOI : 10.1126/science.168.3934.977

S. Chien, R. G. King, R. Skalak, S. Usami, and A. L. Copley, Viscoelastic properties of human blood and red cell suspensions, Biorheology, pp.12-341, 1975.

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, pp.28-241, 1991.

E. Crepeau and M. Sorine, A reduced model of pulsatile flow in an arterial compartment, Chaos, Solitons & Fractals, vol.34, issue.2, pp.594-605, 2007.
DOI : 10.1016/j.chaos.2006.03.096

L. M. Crowl and A. L. Fogelson, Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells, International Journal for Numerical Methods in Biomedical Engineering, vol.36, issue.5, pp.3-4, 2010.
DOI : 10.1002/cnm.1274

T. David, S. Alzaidi, and H. Farr, Coupled autoregulation models in the cerebro-vasculature, Journal of Engineering Mathematics, vol.92, issue.5, pp.403-415, 2009.
DOI : 10.1007/s10665-009-9274-2

A. Dicarlo, P. Nardinocchi, G. Pontrelli, and L. Teresi, A heterogeneous approach for modelling blood flow in an arterial segment, Simulations in Biomedicine V, pp.69-78, 2003.

L. Dintenfass, Blood Microrheology -Viscosity Factors in Blood Flow, Ischaemia and Thrombosis, 1971.

L. Dintenfass, Blood Viscosity, Hyperviscosity and Hyperviscosaemia, 1985.

M. M. Dupin, I. Halliday, C. M. Care, L. Alboul, and L. L. Munn, Modeling the flow of dense suspensions of deformable particles in three dimensions, Physical Review E, vol.75, issue.6, pp.75-066707, 2007.
DOI : 10.1103/PhysRevE.75.066707

W. Dzwinel, K. Boryczko, and D. A. Yuen, Modeling mesoscopic fluids with discrete-particles methods. Algorithms and results Finely Dispersed Particles: Micro-, Nano-, and Atto-Engineering, pp.715-778

A. Elgarayhi, E. K. El-shewy, A. A. Mahmoud, and A. A. Elhakem, Propagation of Nonlinear Pressure Waves in Blood, ISRN Computational Biology, vol.2013, p.436267, 2013.
DOI : 10.1007/BF02459491

E. A. Evans and R. M. Hochmuth, Membrane viscoelasticity, Biophysical Journal, vol.16, issue.1, p.111, 1976.
DOI : 10.1016/S0006-3495(76)85658-5

URL : http://doi.org/10.1016/s0006-3495(76)85658-5

D. Fedosov, B. Caswell, and G. E. Karniadakis, General coarse-grained red blood cell models: I. Mechanics, 2009.

D. Fedosov, B. Caswell, and G. E. Karniadakis, A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics, Biophysical Journal, vol.98, issue.10, pp.98-2215, 2010.
DOI : 10.1016/j.bpj.2010.02.002

D. A. Fedosov, Multiscale Modeling of Blood Flow and Soft Matter, 2010.

D. A. Fedosov, H. Lei, B. Caswell, S. Suresh, and G. E. Karniadakis, Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria, PLoS Computational Biology, vol.11, issue.12, 2011.
DOI : 10.1371/journal.pcbi.1002270.t002

D. A. Fedosov, H. Noguchi, and G. Gompper, Multiscale modeling of blood flow: from single cells to blood rheology, Biomechanics and Modeling in Mechanobiology, vol.83, issue.1, pp.239-258, 2014.
DOI : 10.1007/s10237-013-0497-9

D. A. Fedosov, I. V. Pivkin, and G. E. Karniadakis, Velocity limit in DPD simulations of wall-bounded flows, Journal of Computational Physics, vol.227, issue.4, pp.2540-2559, 2008.
DOI : 10.1016/j.jcp.2007.11.009

N. Filipovic, M. Kojic, and A. Tsuda, Modelling thrombosis using dissipative particle dynamics method, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.115, issue.3, pp.366-3265, 2008.
DOI : 10.1016/j.thromres.2004.08.029

A. L. Fogelson, Cell-based models of blood clotting Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interaction, pp.234-169, 2007.

L. Formaggia, D. Lamponi, M. Tuveri, and A. Veneziani, Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart, Computer Methods in Biomechanics and Biomedical Engineering, vol.35, issue.5, pp.273-288, 2006.
DOI : 10.1016/0021-9290(69)90024-4

L. Formaggia, D. Lamponi, and A. Quarteroni, One-dimensional models for blood flow in arteries, Journal of Engineering Mathematics, vol.47, issue.3/4, pp.47-251, 2003.
DOI : 10.1023/B:ENGI.0000007980.01347.29

T. K. Gaik and H. Demiray, Forced Korteweg-de Vries???Burgers equation in an elastic tube filled with a variable viscosity fluid, Chaos, Solitons & Fractals, vol.38, issue.4, pp.1134-1145, 2008.
DOI : 10.1016/j.chaos.2007.02.005

T. Gamilov, Y. Ivanov, P. Kopylov, S. Simakov, and Y. Vassilevski, Patient Specific Haemodynamic Modeling after Occlusion Treatment in Leg, Mathematical Modelling of Natural Phenomena, vol.9, issue.6, pp.85-97, 2014.
DOI : 10.1051/mmnp/20149607

H. L. Goldsmith and V. T. Turitto, Rheological aspects of thrombosis and haemostasis: basic principles and applications, Thrombosis and Haemostasis, vol.55, issue.3, pp.415-435, 1986.

S. S. Grigorjan, Y. Z. Saakjan, and A. K. Tsaturjan, On the mechanisms of generation of Korotkoff sounds. Doklady of Academy of Science of the SSSR, pp.570-574, 1980.

S. S. Grigorjan, Y. Z. Saakjan, and A. K. Tsatutjan, To the theory of Korotkoff method, Biomechanics, pp.15-16, 1984.

R. D. Groot and P. B. Warren, Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, The Journal of Chemical Physics, vol.107, issue.11, pp.4423-4435, 1997.
DOI : 10.1063/1.474784

R. D. Guy, A. L. Fogelson, and J. P. Keener, Fibrin gel formation in a shear flow, Mathematical Medicine and Biology, vol.24, issue.1, pp.111-130, 2007.
DOI : 10.1093/imammb/dql022

G. A. Holzapfel, T. C. Gasser, and R. W. Ogden, A new Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models, Journal of Elasticity, pp.61-62, 2000.
DOI : 10.1007/0-306-48389-0_1

URL : https://hal.archives-ouvertes.fr/hal-01297725

S. M. Hosseini and J. J. Feng, A particle-based model for the transport of erythrocytes in capillaries, Chemical Engineering Science, vol.64, issue.22, pp.4488-4497, 2009.
DOI : 10.1016/j.ces.2008.11.028

Y. Imai, H. Kondo, T. Ishikawa, C. T. Lim, and T. Yamaguchi, Modeling of hemodynamics arising from malaria infection, Journal of Biomechanics, vol.43, issue.7, pp.1386-1393, 2010.
DOI : 10.1016/j.jbiomech.2010.01.011

Y. Imai, K. Nakaaki, H. Kondo, T. Ishikawa, C. T. Lim et al., Margination of red blood cells infected by Plasmodium falciparum in a microvessel, Journal of Biomechanics, vol.44, issue.8, pp.44-1553, 2011.
DOI : 10.1016/j.jbiomech.2011.02.084

M. Karttunen, I. Vattulainen, and A. Lukkarinen, A Novel Methods in Soft Matter Simulations, 2004.
DOI : 10.1007/b95265

J. Keener and J. Sneyd, Mathematical Physiology. II: Systems Physiology, 2008.

A. S. Kholodov, Some dynamical models of external breathing and haemodynamics accounting for their coupling and substance transport, Computer Models and Medicine Progress, pp.127-163, 2001.

A. S. Kholodov, A. V. Evdokimov, and S. S. Simakov, Numerical simulation of peripheral circulation and substance transfer with 2D models Mathematical biology: recent trends, pp.22-29, 2006.

S. Kim, Y. I. Cho, A. H. Jeon, B. Hogenauer, and K. R. Kensey, A new method for blood viscosity measurement, Journal of Non-Newtonian Fluid Mechanics, vol.94, issue.1, pp.94-141, 2000.
DOI : 10.1016/S0377-0257(00)00127-0

C. S. Kim, C. Kris, and D. Kwak, Numerical Models of Human Circulatory System under Altered Gravity: Brain Circulation, 42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004.
DOI : 10.2514/6.2004-1092

J. F. Koleski and 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, pp.37-46, 1991.

V. Koshelev, S. Mukhin, T. Sokolova, N. Sosnin, and A. Favorski, Mathematical modelling of cardio-vascular hemodynamics with account of neuroregulation, Matematicheskoe Modelirovanie, vol.19, issue.3, pp.15-28, 2007.

W. Kroon, W. Huberts, M. Bosboom, and 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, vol.261, issue.4, 2012.
DOI : 10.1007/s11517-009-0449-9

P. W. Kuchel and E. D. , Parametric-Equation Representation of Biconcave Erythrocytes, Bulletin of Mathematical Biology, vol.61, issue.2, pp.61-209, 1999.
DOI : 10.1006/bulm.1998.0064

I. Larrabidea, P. J. Blanco, S. A. Urquiza, E. A. Dari, M. J. Véneref et al., HeMoLab ??? Hemodynamics Modelling Laboratory: An application for modelling the human cardiovascular system, Computers in Biology and Medicine, vol.42, issue.10, pp.42-993, 2012.
DOI : 10.1016/j.compbiomed.2012.07.011

M. B. Lawrence and T. A. Springer, Leukocytes roll on a selectin at physiological flow rates: distinction from and prerequisite for adhesion through integrins, Cell, pp.65-859, 1991.

R. C. Leif and J. Vinograd, THE DISTRIBUTION OF BUOYANT DENSITY OF HUMAN ERYTHROCYTES IN BOVINE ALBUMIN SOLUTIONS, Proc. Natl. Acad. Sci. USA, pp.520-528, 1964.
DOI : 10.1073/pnas.51.3.520

S. Leibler and A. C. Maggs, Simulation of shape changes and adhesion phenomena in an elastic model of erythrocytes., Proc. Natl. Acad. Sci. USA, pp.6433-6435, 1990.
DOI : 10.1073/pnas.87.16.6433

D. Liepsch, . St, and . Moravec, Pulsatile flow of non-Newtonian fluid in distensible models of human arteries, Biorheology, vol.21, pp.571-586, 1984.

K. Logana, R. Balossino, F. Migliavacca, G. Pennati, E. L. Bove et al., Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation, Journal of Biomechanics, vol.38, issue.5, pp.1129-1141, 2005.
DOI : 10.1016/j.jbiomech.2004.05.027

L. Lopez, I. M. Duck, and W. A. Hunt, On the Shape of the Erythrocyte, Biophysical Journal, vol.8, issue.11, pp.1228-1235, 1968.
DOI : 10.1016/S0006-3495(68)86552-X

K. Low, R. Van-loon, I. Sazonov, R. L. Bevan, and P. Nithiarasu, An improved baseline model for a human arterial network to study the impact of aneurysms on pressure-flow waveforms, International Journal for Numerical Methods in Biomedical Engineering, vol.41, issue.5, pp.28-1224, 2012.
DOI : 10.1002/cnm.2533

G. D. Lowe and E. , I and II, Clinical Blood Rheology, 1998.

J. L. Mcwhirter, H. Noguchi, and G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, Proceedings of the National Academy of Sciences, vol.106, issue.15, pp.6039-6043, 2009.
DOI : 10.1073/pnas.0811484106

E. W. Merrill, E. R. Gilliland, G. Cokelet, H. Shin, A. Britten et al., Rheology of Human Blood, near and at Zero Flow, Biophysical Journal, vol.3, issue.3, pp.199-213, 1963.
DOI : 10.1016/S0006-3495(63)86816-2

E. W. Merrill, G. C. Cokelet, A. Britten, and R. E. Wells, Non-Newtonian Rheology of Human Blood - Effect of Fibrinogen Deduced by "Subtraction", Circulation Research, vol.13, issue.1, pp.48-55, 1963.
DOI : 10.1161/01.RES.13.1.48

V. Milisi´cmilisi´c and A. Quarteroni, Analysis of lumped parameter models for blood flow simulations and their relation with 1D models, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.4, pp.613-632, 2004.
DOI : 10.1051/m2an:2004036

N. Mohandas and P. G. Gallagher, Red cell membrane: past, present, and future, Blood, vol.112, issue.10, pp.3939-3948, 2008.
DOI : 10.1182/blood-2008-07-161166

P. C. Moller, J. Mewis, and D. Bonn, Yield stress and thixotropy: on the difficulty of measuring yield stresses in practice, Soft Matter, vol.50, issue.4, pp.274-288, 2006.
DOI : 10.1039/b517840a

Y. Mori and 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, vol.43, issue.1, pp.75-100, 2009.
DOI : 10.1016/j.aam.2009.01.004

L. O. Müller, C. Parés, and E. Toro, Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties, Journal of Computational Physics, vol.242, pp.242-53, 2013.
DOI : 10.1016/j.jcp.2013.01.050

L. O. Müller and 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, vol.59, issue.4, pp.681-725, 2014.
DOI : 10.1002/cnm.2622

L. L. Munn and M. M. Dupin, Blood Cell Interactions and Segregation in Flow, Annals of Biomedical Engineering, vol.80, issue.4, pp.534-544, 2008.
DOI : 10.1007/s10439-007-9429-0

S. Muñoz-san-martín, J. L. Sebastián, M. Sancho1, and G. Alvarez, Modeling human erythrocyte shape and size abnormalities . arXiv:q-bio, p.14, 2005.

J. P. Mynard and 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, vol.53, issue.5, pp.367-417, 2008.
DOI : 10.1002/cnm.1117

Q. D. Nguyen and D. V. Boger, Measuring the Flow Properties of Yield Stress Fluids, Annual Review of Fluid Mechanics, vol.24, issue.1, pp.47-88, 1992.
DOI : 10.1146/annurev.fl.24.010192.000403

H. Noguchi and G. Gompper, Shape transitions of fluid vesicles and red blood cells in capillary flows, Proceedings of the National Academy of Sciences, vol.102, issue.40, pp.14159-14164, 2005.
DOI : 10.1073/pnas.0504243102

D. Obrist, B. Weber, A. Buck, and P. Jenny, Red blood cell distribution in simplified capillary networks, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.15, issue.9, 2010.
DOI : 10.1038/nm.2022

T. Ohashi, H. Liu, and T. Yamaguchi, Computational Fluid Dynamic Simulation of the Flow through Venous Valve, Clinical Application of Computational Mechanics to the Cardiovascular System, pp.186-189, 2000.
DOI : 10.1007/978-4-431-67921-9_18

M. S. Olufsen, C. S. Peskin, W. Y. Kim, E. M. Pedersen, A. Nadim et al., Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions, Annals of Biomedical Engineering, vol.28, issue.11, pp.28-1281, 2000.
DOI : 10.1114/1.1326031

R. G. Owens, A new microstructure-based constitutive model for human blood, Journal of Non-Newtonian Fluid Mechanics, vol.140, issue.1-3, pp.57-70, 2006.
DOI : 10.1016/j.jnnfm.2006.01.015

E. Ozawa, K. Bottom, X. Xiao, and R. D. Kamm, Numerical Simulation of Enhanced External Counterpulsation, Annals of Biomedical Engineering, vol.29, issue.4, pp.29-284, 2001.
DOI : 10.1114/1.1359448

Q. Pan, R. Wang, B. Reglin, G. Cai, J. Yan et al., A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks, Journal of Biomedical Engineering, issue.1, p.136, 2014.

T. J. Pedley and X. Y. Luo, Modelling flow and oscillations in collapsible tubes. Theoretical and Computational Fluid Dynamics, pp.277-294, 1998.

D. Pinho, A. Pereira, R. Lima, T. Ishikawa, Y. Imai et al., Red blood cell dispersion in 100 µm glass capillaries: the temperature effect, WCB 2010, pp.31-1067, 2010.

E. Pinto, B. Taboada, R. Rodrigues, V. Faustino, A. Pereira et al., Cell-free layer (CFL) analysis in a polydimethysiloxane (PDMS) microchannel: a global approach, WebmedCentral Biomedical Engineering, vol.4, issue.8, p.4374, 2013.

I. V. Pivkin and G. E. Karniadakis, Accurate Coarse-Grained Modeling of Red Blood Cells, Physical Review Letters, vol.101, issue.11, p.118105, 2008.
DOI : 10.1103/PhysRevLett.101.118105

I. V. Pivkin and G. E. Karniadakis, A new method to impose no-slip boundary conditions in dissipative particle dynamics, Journal of Computational Physics, vol.207, issue.1, pp.114-128, 2005.
DOI : 10.1016/j.jcp.2005.01.006

I. V. Pivkin, P. D. Richardson, and G. Karniadakis, Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi, Proceedings of the National Academy of Sciences, vol.103, issue.46, pp.17164-17169, 2006.
DOI : 10.1073/pnas.0608546103

A. S. Popel and P. C. Johnson, MICROCIRCULATION AND HEMORHEOLOGY, Annual Review of Fluid Mechanics, vol.37, issue.1, pp.43-69, 2005.
DOI : 10.1146/annurev.fluid.37.042604.133933

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3000688

C. Pozrikidis, Modeling and Simulation of Capsules and Biological Cells, 2003.
DOI : 10.1201/9780203503959

D. Quemada, Rheology of concentrated disperse systems III. General features of the proposed non-newtonian model. Comparison with experimental data, Rheologica Acta, vol.16, issue.6, pp.643-653, 1978.
DOI : 10.1007/BF01522037

K. R. Rajagopal and A. R. Srinivasa, A thermodynamic frame work for rate type fluid models, Journal of Non-Newtonian Fluid Mechanics, vol.88, issue.3, pp.207-227, 2000.
DOI : 10.1016/S0377-0257(99)00023-3

A. M. Robertson, A. Sequeira, M. V. Kameneva, and . Hemorheology, Hemodynamical Flows: Modeling, Analysis and Simulation, Oberwolfach Seminars), pp.63-120, 2008.

M. Rosar and C. Peskin, Fluid flow in collapsible elastic tubes: a three-dimensional numerical model, New York Journal of Mathematics, vol.7, pp.281-302, 2001.

U. D. Schiller, Dissipative Particle Dynamics. A Study of the Methodological Background, 2005.

H. Schmid-schönbein and R. E. Wells, Rheological properties of human erythrocytes and their influence upon the ???Anomalous??? viscosity of blood, Physiology Rev, vol.63, pp.147-219, 1971.
DOI : 10.1007/BFb0047743

G. W. Scott-blair, An Equation for the Flow of Blood, Plasma and Serum through Glass Capillaries, Nature, vol.10, issue.4661, pp.613-614, 1959.
DOI : 10.1038/183613a0

S. Sherwin, V. Franke, J. Peiró, and K. Parker, One-dimensional modelling of a vascular network in space-time variables, Journal of Engineering Mathematics, vol.47, issue.3/4, pp.47-217, 2003.
DOI : 10.1023/B:ENGI.0000007979.32871.e2

S. J. Sherwin, L. Formaggia, J. Peiró, and 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, vol.2, issue.12, pp.43-673, 2003.
DOI : 10.1002/fld.543

Y. Shi, P. Lawford, and R. Hose, Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System, BioMedical Engineering OnLine, vol.10, issue.1, p.33, 2011.
DOI : 10.1111/j.1525-1594.2008.00628.x

S. S. Simakov, T. M. Gamilov, and Y. N. Soe, Computational study of blood flow in lower extremities under intense physical load, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.28, issue.5, pp.485-504, 2013.
DOI : 10.1515/rnam-2013-0027

S. S. Simakov and A. S. Kholodov, Computational study of oxygen concentration in human blood under low frequency disturbances, Mathematical Models and Computer Simulations, vol.1, issue.2, pp.283-295, 2009.
DOI : 10.1134/S2070048209020112

R. Skalak, A. Tozeren, R. Zarda, and S. Chein, Strain Energy Function of Red Blood Cell Membranes, Biophysical Journal, vol.13, issue.3, pp.245-264, 1973.
DOI : 10.1016/S0006-3495(73)85983-1

M. F. Snyder and V. C. Rideout, Computer Simulation Studies of the Venous Circulation, IEEE Transactions on Biomedical Engineering, vol.16, issue.4, pp.16-325, 1969.
DOI : 10.1109/TBME.1969.4502663

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao et al., Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria, Acta Biomaterialia, vol.1, issue.1, pp.15-30, 2005.
DOI : 10.1016/j.actbio.2004.09.001

C. R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E. D. Rosen et al., Modelling platelet-blood flow interaction using the subcellular element Langevin method, Journal of The Royal Society Interface, vol.29, issue.11, pp.1760-1771, 2011.
DOI : 10.1021/la0701475

G. B. Thurston, Viscoelasticity of Human Blood, Biophysical Journal, vol.12, issue.9, pp.1205-1217, 1972.
DOI : 10.1016/S0006-3495(72)86156-3

G. B. Thurston, Non-Newtonian viscosity of human blood: Flow induced changes in microstructure, Biorheology, issue.2, pp.31-179, 1994.

G. B. Thurston, Viscoelastic properties of blood and blood analogs Advances in Hemodynamics and Hemorheology, pp.1-30, 1996.

A. A. Tokarev, A. A. Butylin, and F. I. Ataullakhanov, Platelet Adhesion from Shear Blood Flow Is Controlled by Near-Wall Rebounding Collisions with Erythrocytes, Biophysical Journal, vol.100, issue.4, pp.799-808, 2011.
DOI : 10.1016/j.bpj.2010.12.3740

A. A. Tokarev, A. A. Butylin, and F. I. Ataullakhanov, Platelet transport and adhesion in shear blood flow: the role of erythrocytes, Computer Research and Modeling, vol.4, issue.1, pp.185-200, 2012.

A. A. Tokarev, A. A. Butylin, E. A. Ermakova, E. E. Shnol, G. P. Panasenko et al., Finite Platelet Size Could Be Responsible for Platelet Margination Effect, Biophysical Journal, vol.101, issue.8, pp.1835-1843, 2011.
DOI : 10.1016/j.bpj.2011.08.031

URL : https://hal.archives-ouvertes.fr/hal-00869290

A. Tokarev, I. Sirakov, G. Panasenko, V. Volpert, E. Shnol et al., Continuous mathematical model of platelet thrombus formation in blood flow, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.27, issue.2, pp.192-212, 2012.
DOI : 10.1515/rnam-2012-0011

URL : https://hal.archives-ouvertes.fr/hal-00753091

A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, and V. Volpert, Particle Dynamics Methods of Blood Flow Simulations, Mathematical Modelling of Natural Phenomena, vol.6, issue.5, pp.320-332, 2011.
DOI : 10.1051/mmnp/20116512

URL : https://hal.archives-ouvertes.fr/hal-00653688

A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev et al., Modelling of thrombus growth in flow with a DPD-PDE method, Journal of Theoretical Biology, vol.337, pp.337-367, 2013.
DOI : 10.1016/j.jtbi.2013.07.023

K. Tsubota and 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, vol.52, issue.2, pp.52-356, 2010.
DOI : 10.1016/j.ijmecsci.2009.10.007

K. Tsubota, S. Wada, H. Kamada, Y. Kitagawa, R. Lima et al., A particle method for blood flow simulation, application to flowing red blood cells and platelets, Journal of the Earth Simulator, vol.5, pp.2-7, 2006.

F. J. Walburn and D. J. Schneck, A constitutive equation for whole human blood, Biorheology, vol.13, pp.201-210, 1976.

. Yu, S. Vassilevskii, V. Simakov, Y. Salamatova, T. Ivanov et al., Numerical issues of modelling blood flow in networks of vessels with pathologies, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.26, issue.6, pp.605-622, 2011.

Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, and T. Dobroserdova, Blood Flow Simulation in Atherosclerotic Vascular Network Using Fiber-Spring Representation of Diseased Wall, Mathematical Modelling of Natural Phenomena, vol.6, issue.5, pp.333-349, 2011.
DOI : 10.1051/mmnp/20116513

Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, and T. Dobroserdova, Vessel Wall Models for Simulation of Atherosclerotic Vascular Networks, Mathematical Modelling of Natural Phenomena, vol.6, issue.7, pp.82-99, 2011.
DOI : 10.1051/mmnp:20116707

F. N. Van-de-vosse and N. Stergiopulos, Pulse Wave Propagation in the Arterial Tree, Annual Review of Fluid Mechanics, vol.43, issue.1, pp.467-499, 2011.
DOI : 10.1146/annurev-fluid-122109-160730

N. Xiao, J. Alastruey-arimon, and C. A. Figueroa, A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models, International Journal for Numerical Methods in Biomedical Engineering, vol.168, issue.2, pp.204-231, 2014.
DOI : 10.1002/cnm.2598

Z. Xu, N. Chen, M. M. Kamocka, E. D. Rosen, and M. Alber, A multiscale model of thrombus development, Journal of The Royal Society Interface, vol.84, issue.5, pp.5-705, 2008.
DOI : 10.1016/S0049-3848(96)00197-1

C. Yeh, A. C. Calvez, and E. C. Eckstein, An estimated shape function for drift in a platelet-transport model, Biophysical Journal, vol.67, issue.3, pp.1252-1259, 1994.
DOI : 10.1016/S0006-3495(94)80595-8

C. Yeh and E. C. Eckstein, Transient lateral transport of platelet-sized particles in flowing blood suspensions, Biophysical Journal, vol.66, issue.5, pp.1706-1716, 1994.
DOI : 10.1016/S0006-3495(94)80962-2

K. K. Yeleswarapu, M. V. Kameneva, K. R. Rajagopal, and J. F. Antaki, The flow of blood in tubes: theory and experiment, Mechanics Research Communications, vol.25, issue.3, pp.25-257, 1998.
DOI : 10.1016/S0093-6413(98)00036-6

J. Zhang, P. C. Johnson, and A. S. Popel, Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows, Microvascular Research, vol.77, issue.3, pp.77-265, 2009.
DOI : 10.1016/j.mvr.2009.01.010