S. Laurent, S. Katsahian, C. Fassot, A. I. Tropeano, I. Gautier et al., Aortic Stiffness Is an Independent Predictor of Fatal Stroke in Essential Hypertension, Stroke, vol.34, issue.5, pp.1203-1206, 2003.
DOI : 10.1161/01.STR.0000065428.03209.64

T. J. Pedley, The fluid mechanics of large blood vessels, 1980.
DOI : 10.1017/CBO9780511896996

N. P. Smith, A. J. Pullan, and P. J. Hunter, An Anatomically Based Model of Transient Coronary Blood Flow in the Heart, SIAM Journal on Applied Mathematics, vol.62, issue.3, pp.990-1018, 2002.
DOI : 10.1137/S0036139999355199

S. J. Sherwin, L. Formaggia, and J. Peiró, 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.6-7, 2003.
DOI : 10.1002/fld.543

S. J. Sherwin, O. Shah, D. J. Doorly, Y. Papaharilaou, N. Watkins et al., The inuence of out of plane geometry on the flow within a distal end to side anastomosis, ASME Journal of Biomechanics, vol.122, pp.1-10, 2000.

M. Anliker, R. L. Rockwell, and E. Ogden, Nonlinear analysis of flow pulses and shock waves in arteries, Zeitschrift für angewandte Mathematik und Physik ZAMP, pp.217-246, 1971.

A. C. Barnard, W. A. Hunt, and W. P. , A Theory of Fluid Flow in Compliant Tubes, Biophysical Journal, vol.6, issue.6, pp.717-724, 1966.
DOI : 10.1016/S0006-3495(66)86690-0

J. K. Raines, M. Y. Jaffrin, and A. H. Shapiro, A computer simulation of arterial dynamics in the human leg, Journal of Biomechanics, vol.7, issue.1, pp.77-91, 1974.
DOI : 10.1016/0021-9290(74)90072-4

N. Stergiopulos, D. F. Young, and T. R. Rogge, Computer simulation of arterial flow with applications to arterial and aortic stenoses, Journal of Biomechanics, vol.25, issue.12, pp.1477-1488, 1992.
DOI : 10.1016/0021-9290(92)90060-E

A. Quarteroni, Modelling the cardiovascular system : a mathematical challenge, Mathematics Unlimited?2001 and Beyond, pp.961-972, 2001.

L. Formaggia, F. Nobile, A. Quarteroni, and A. Veneziani, Multiscale modelling of the circulatory system : a preliminary analysis Computing and visualization in science, pp.2-3, 1999.

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.217-250, 2003.
DOI : 10.1023/B:ENGI.0000007979.32871.e2

M. Collette, Cours en ligne, Cours sur la rigidité artérielle, blog : Lemonde

D. J. Kortweg, Uber die fortpflanzungesgechwindigkeit des schalles in elastischen rohern, Ann. Phys. Chem.(NS), vol.5, pp.525-527, 1878.

B. Riemann, Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass, p.1860
DOI : 10.1007/978-3-663-10149-9_1

G. Raugel and R. G. Sell, Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions, Journal of the American Mathematical Society, vol.6, issue.3, pp.503-568, 1993.
DOI : 10.2307/2152776

J. C. Stettler, P. Niederer, and M. Anliker, Theoretical analysis of arterial hemodynamics including the influence of bifurcations, Annals of Biomedical Engineering, vol.102, issue.2, pp.165-175, 1981.
DOI : 10.1007/BF02363534

L. Formaggia, J. F. Gerbeau, F. Nobile, and A. Quarteroni, On the coupling of 3D and 1D Navier???Stokes equations for flow problems in compliant vessels, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.6-7, pp.561-582, 2001.
DOI : 10.1016/S0045-7825(01)00302-4

URL : https://hal.archives-ouvertes.fr/hal-00691928

W. W. Nichols and M. F. O-'rourke, McDonald's blood flow in arteries : theoretical, experimental and clinical principles, 1998.

B. Cockburn and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework, Mathematics of Computation, vol.52, issue.186, pp.411-435, 1989.

I. Lomtev, C. B. Quillen, and G. E. Karniadakis, Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes, Journal of Computational Physics, vol.144, issue.2, pp.325-357, 1998.
DOI : 10.1006/jcph.1997.5831

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. C. Simon, M. E. Safar, J. A. Levenson, G. M. London, B. I. Levy et al., An evaluation of large arteries compliance in man, American Journal of Physiology-Heart and Circulatory Physiology, vol.237, issue.5, pp.550-554, 1979.

J. Alastruey, S. M. Moore, K. H. Parker, and T. David, 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.1061-1067, 2008.
DOI : 10.1002/fld.1606

G. Pontrelli and E. Rossoni, Numerical modelling of the pressure wave propagation in the arterial flow. International journal for numerical methods in fluids, pp.6-7, 2003.

G. Pontrelli, A multiscale approach for modelling wave propagation in an arterial segment Computer methods in biomechanics and biomedical engineering, pp.79-89, 2004.

M. Willemet, V. Lacroix, and E. Marchandise, Inlet boundary conditions for blood flow simulations in truncated arterial networks, Journal of Biomechanics, vol.44, issue.5, pp.897-903, 2011.
DOI : 10.1016/j.jbiomech.2010.11.036

P. Segers, F. Dubois, D. De-wachter, and P. Verdonck, Role and relevancy of a cardiovascular simulator, Cardiovascular Engineering, vol.3, pp.48-56, 1998.

W. Miladi, Contributions à l'intéraction fluide-structure dans le système cardio-vasculaire. Modélisations et simulations numériques, UFR des sciences et techniques de l'université de Franche Comete, 2010.

J. Alastruey, Numerical Modelling of Pulse Wave Propagation in the Cardiovascular System : Development , Validation and Clinical Applications, 2006.

A. P. Avolio, Multi-branched model of the human arterial system, Medical & Biological Engineering & Computing, vol.36, issue.6, pp.709-718, 1980.
DOI : 10.1007/BF02441895

P. Segers and P. Verdonck, Role of tapering in aortic wave reflection: hydraulic and mathematical model study, Journal of Biomechanics, vol.33, issue.3, pp.299-306, 2000.
DOI : 10.1016/S0021-9290(99)00180-3

N. Westerhof, F. Bosman, C. J. De-vries, and A. Noordergraaf, Analog studies of the human systemic arterial tree, Journal of Biomechanics, vol.2, issue.2, pp.121-143, 1969.
DOI : 10.1016/0021-9290(69)90024-4

M. Safar, Paroi arterielle et vieillissement vasculaire, Editions scientifques et medicales Elsevier SAS, 2002.

D. Angouras, D. P. Sokolis, T. Dosios, N. Kostomitsopoulos, H. Boudoulas et al., Effect of impaired vasa vasorum flow on the structure and mechanics of the thoracic aorta: implications for the pathogenesis of aortic dissection, European Journal of Cardio-Thoracic Surgery, vol.17, issue.4, pp.468-473, 2000.
DOI : 10.1016/S1010-7940(00)00382-1

E. G. Lakatta, Arterial and Cardiac Aging: Major Shareholders in Cardiovascular Disease Enterprises: Part III: Cellular and Molecular Clues to Heart and Arterial Aging, Circulation, vol.107, issue.3, pp.490-497, 2003.
DOI : 10.1161/01.CIR.0000048894.99865.02

M. Faber and G. Moller-hou, THE HUMAN AORTA, Acta Pathologica Microbiologica Scandinavica, vol.48, issue.suppl. 66, pp.377-382, 1952.
DOI : 10.1111/j.1699-0463.1952.tb00205.x

A. C. Pearson, R. Guo, D. A. Orsinelli, P. F. Binkley, and T. J. Pasierski, Transesophageal echocardiographic assessment of the effects of age, gender, and hypertension on thoracic aortic wall size, thickness, and stiffness, American Heart Journal, vol.128, issue.2, pp.344-351, 1994.
DOI : 10.1016/0002-8703(94)90488-X

A. Redheuil, W. C. Yu, C. O. Wu, E. Mousseaux, A. De-cesare et al., Reduced Ascending Aortic Strain and Distensibility: Earliest Manifestations of Vascular Aging in Humans, Hypertension, vol.55, issue.2, pp.319-326, 2010.
DOI : 10.1161/HYPERTENSIONAHA.109.141275

S. E. Greenwald, Ageing of the conduit arteries, The Journal of Pathology, vol.21, issue.2, pp.157-172, 2007.
DOI : 10.1002/path.2101

M. F. O-'rourke and J. Hashimoto, Mechanical factors in arterial aging : a clinical perspective, Journal of the American College of Cardiology, vol.50, issue.1, pp.1-13, 2007.

C. Vlachopoulos, K. Aznaouridis, and C. Stefanadis, Prediction of Cardiovascular Events and All-Cause Mortality With Arterial Stiffness, Journal of the American College of Cardiology, vol.55, issue.13, pp.1318-1327, 2010.
DOI : 10.1016/j.jacc.2009.10.061

W. W. Nichols, M. F. O-'rourke, and C. Vlachopoulos, McDonald's blood flow in arteries, Theoretical, experimental and clinical Principles, 2011.

H. Sesso, M. Stampfer, B. Rosner, C. Hennekens, J. Gaziano et al., Systolic and Diastolic Blood Pressure, Pulse Pressure, and Mean Arterial Pressure as Predictors of Cardiovascular Disease Risk in Men, Hypertension, vol.36, issue.5, pp.801-807, 2000.
DOI : 10.1161/01.HYP.36.5.801

B. Lamia, J. Teboul, X. Monnet, C. Richard, and D. Chemla, Hemodynamic correlates of radial pulse pressure in ICU patients : an arterial tonometric study, 18th Annual Congress of the European Society of Intensive Care Medicine, pp.152-580, 2005.

J. Levick, An introduction to cardiovascular physiology, 2003.

R. Burattini and S. Natalucci, Complex and frequency-dependent compliance of viscoelastic windkessel resolves contradictions in elastic windkessels, Medical Engineering & Physics, vol.20, issue.7, pp.502-514, 1998.
DOI : 10.1016/S1350-4533(98)00055-1

C. M. Quick, D. S. Berger, and A. Noordergraaf, Apparent arterial compliance, American Journal of Physiology-Heart and Circulatory Physiology, vol.274, issue.4, pp.1393-1403, 1998.

R. Burattini and K. B. Campbell, Physiological Relevance of Uniform Elastic Tube-Models to Infer Descending Aortic Wave Reflection: A Problem of Identifiability, Annals of Biomedical Engineering, vol.28, issue.5, pp.512-523, 2000.
DOI : 10.1114/1.291

L. R. John, Forward electrical transmission line model of the human arterial system, Medical & Biological Engineering & Computing, vol.41, issue.3, pp.312-321, 2004.
DOI : 10.1007/BF02344705

C. M. Quick, D. S. Berger, R. H. Stewart, G. A. Laine, C. J. Hartley et al., Resolving the Hemodynamic Inverse Problem, IEEE Transactions on Biomedical Engineering, vol.53, issue.3, pp.361-368, 2006.
DOI : 10.1109/TBME.2005.869664

D. A. Steinman, Image-Based Computational Fluid Dynamics Modeling in Realistic Arterial Geometries, Annals of Biomedical Engineering, vol.30, issue.4, pp.483-497, 2002.
DOI : 10.1114/1.1467679

D. A. Steinman and C. A. Taylor, Flow Imaging and Computing: Large Artery Hemodynamics, Annals of Biomedical Engineering, vol.35, issue.12, pp.1704-1709, 2005.
DOI : 10.1007/s10439-005-8772-2

S. Julius, A. Amery, L. S. Whitlock, and J. Conway, Influence of Age on the Hemodynamic Response to Exercise, Circulation, vol.36, issue.2, pp.222-252, 1967.
DOI : 10.1161/01.CIR.36.2.222

J. W. Remington, C. R. Noback, W. F. Hamilton, and J. J. Gold, Volume elasticity characteristics of the human aorta and prediction of the stroke volume from the pressure pulse, American Journal of Physiology, vol.153, issue.2, pp.298-308, 1948.

J. C. Bramwell and A. V. Hill, The Velocity of the Pulse Wave in Man, Proceedings of the Royal Society of London. Series B, Containing Papers of a Biological Character, pp.298-306, 1922.
DOI : 10.1098/rspb.1922.0022

N. H. Hwang, V. T. Turitto, and M. R. Yen, Advances in cardiovascular engineering, 2013.
DOI : 10.1007/978-1-4757-4421-7

P. A. Doriot, P. A. Dorsaz, and L. D. Benedetti, In-vivo measurements of wall shear stress in human coronary arteries. Coronary artery disease, pp.495-502, 2000.

N. Westerhof, N. Stergiopulos, and M. I. Noble, Snapshots of hemodynamics : an aid for clinical research and graduate education, 2010.
DOI : 10.1007/978-1-4419-6363-5

J. T. Ottesen, M. S. Olufsen, and J. K. Larsen, Applied mathematical models in human physiology, 2004.
DOI : 10.1137/1.9780898718287

P. G. Ciarlet, Introduction to linear shell theory. Gauthiers-Villars, 1998.

A. C. Barnard, W. A. Hunt, and W. P. , A Theory of Fluid Flow in Compliant Tubes, Biophysical Journal, vol.6, issue.6, pp.717-724, 1966.
DOI : 10.1016/S0006-3495(66)86690-0

T. J. Hughes, A study of the one-dimensional theory of arterial pulse propagation, 1974.

T. J. Hughes and J. Lubliner, On the one-dimensional theory of blood flow in the larger vessels, Mathematical Biosciences, vol.18, issue.1-2, pp.161-170, 1973.
DOI : 10.1016/0025-5564(73)90027-8

D. L. Schultz, D. S. Tunstall-pedoe, G. De, J. Lee, A. J. Gunning et al., Velocity Distribution and Transition in the Arterial System, pp.172-202, 1969.
DOI : 10.1002/9780470719671.ch11

T. J. Pedley, R. C. Schroter, and W. A. , Seed and al. The mechanics of the circulation, 1978.

G. J. Langewouters, K. H. Wesseling, and W. J. Goedhard, The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model, Journal of Biomechanics, vol.17, issue.6, pp.425-435, 1984.
DOI : 10.1016/0021-9290(84)90034-4

L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations, p.191, 1993.
DOI : 10.1007/978-3-0348-8579-9

J. Donea, S. Giuliani, H. Laval, and L. Quartapelle, Time-accurate solution of advection-diffusion problems by finite elements, Computer Methods in Applied Mechanics and Engineering, vol.45, issue.1-3, pp.123-145, 1984.
DOI : 10.1016/0045-7825(84)90153-1

K. W. Thompson, Time dependent boundary conditions for hyperbolic systems, Journal of Computational Physics, vol.68, issue.1, pp.1-24, 1987.
DOI : 10.1016/0021-9991(87)90041-6

A. Quarteroni and L. Formaggia, Mathematical Modelling and Numerical Simulation of the Cardiovascular System. Modelling of Living Systems, Handbook of Numerical Analysis Series, 2003.

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.3-4, 2003.
DOI : 10.1023/B:ENGI.0000007980.01347.29

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 and the physical science of solids, vol.61, pp.1-48, 2000.
DOI : 10.1007/0-306-48389-0_1

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

J. Stettler, P. Niederer, and M. Anliker, Nonlinear mathematical models of the arterial system Handbook of Bioengineering, 1987.

M. Olufsen and J. Ottesen, A fluid dynamical model of the aorta with bifurcations. Tekst 297, 1995.

M. A. Fernández, V. Milisic, and A. Quarteroni, Analysis of a Geometrical Multiscale Blood Flow Model Based on the Coupling of ODEs and Hyperbolic PDEs, Multiscale Modeling & Simulation, vol.4, issue.1, pp.215-236, 2005.
DOI : 10.1137/030602010

R. Botnar, G. Rappitsch, and M. B. Scheidegger, Hemodynamics in the carotid artery bifurcation:, Journal of Biomechanics, vol.33, issue.2, pp.137-144, 2000.
DOI : 10.1016/S0021-9290(99)00164-5

Y. C. Fung, Mechanical properties of living tissues, Biomechanics, 1993.

K. H. Parker and C. J. Jones, Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics, Journal of Biomechanical Engineering, vol.112, issue.3, pp.322-326, 1990.
DOI : 10.1115/1.2891191

E. Bollache, Caractérisation hémodynamique de l'aorte thoracique par IRM, tonométrie d'applanation et simulations numériques, Thèse de doctorat, 2014.

G. W. Hedstrom, Nonreflecting boundary conditions for nonlinear hyperbolic systems, Journal of Computational Physics, vol.30, issue.2, pp.222-237, 1979.
DOI : 10.1016/0021-9991(79)90100-1

L. Sherwin, J. Formaggia, and . Peiró, Computational modelling of 1d blood flow with variable mechanical properties, Proceedings of ECCOMAS CFD 2001, 2001.

S. Laurent, J. Cockcroft, L. Van-bortel, P. Boutouyrie, C. Giannattasio et al., Expert consensus document on arterial stiffness: methodological issues and clinical applications, European Heart Journal, vol.27, issue.21, pp.2588-605, 2006.
DOI : 10.1093/eurheartj/ehl254

S. S. Hickson, M. Butlin, M. Graves, V. Taviani, A. P. Avolio et al., The Relationship of Age With Regional Aortic Stiffness and Diameter, JACC: Cardiovascular Imaging, vol.3, issue.12, pp.1247-1255, 2010.
DOI : 10.1016/j.jcmg.2010.09.016

K. S. Matthys, J. Alastruey, J. Peiró, A. W. Khir, P. Segers et al., Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements, Journal of Biomechanics, vol.40, issue.15, pp.3476-86, 2007.
DOI : 10.1016/j.jbiomech.2007.05.027

P. Segers, F. Dubois, D. De-wachter, and P. Verdonck, Role and relevancy of a cardiovascular simulator, Cardiovascular Engineering, vol.3, pp.48-56, 1998.

L. Dumas, Inverse problems for blood flow simulation, International Conference on Engineering Optimization, 2008.

]. L. Dumas, P. Boutouyrie, and E. Bozec, An optimal reconstruction of the human arterial tree from doppler echotracking measurements, Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference companion, GECCO Companion '12, pp.517-522, 2012.
DOI : 10.1145/2330784.2330866

J. C. Stettler, P. Niederer, and M. Anliker, Theoretical analysis of arterial hemodynamics including the influence of bifurcations, Annals of Biomedical Engineering, vol.90, issue.No. 1, pp.145-164, 1981.
DOI : 10.1007/BF02363533

A. Quarteroni, M. Tuveri, and A. Veneziani, Computational vascular fluid dynamics: problems, models and methods, Computing and Visualization in Science, vol.2, issue.4, pp.163-197, 2000.
DOI : 10.1007/s007910050039

L. Formaggia, F. Nobile, and A. Quarteroni, A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis, Lecture Notes in Computational Science and Engineering, vol.19, pp.137-153, 2002.
DOI : 10.1007/978-3-642-56288-4_10

D. Xiu and G. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

H. Ogura, Orthogonal functionals of the Poisson process Information Theory, IEEE Transactions on, vol.18, issue.4, pp.473-481, 1972.

W. Schoutens, Stochastic processes in the Askey scheme, 1999.

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

R. Cameron and W. Martin, The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, The Annals of Mathematics, vol.48, issue.2, pp.385-392, 1947.
DOI : 10.2307/1969178

I. M. Sobol, Sensitivity estimates for nonlinear mathematical models, Mathematical Modeling and Computational Experiment, vol.1, pp.407-414, 1993.

G. Iaccarino, Quantification of uncertainty in flow simulations using probabilistic methods. Nato research and technology organization Neuilly, 2009.

Z. Sandor and P. Andras, Alternative sampling methods for estimating multivariate normal probabilities, Journal of Econometrics, vol.120, issue.2, pp.207-234, 2004.
DOI : 10.1016/S0304-4076(03)00212-4

H. G. Beyer and H. P. Schwefel, Evolution strategies?A comprehensive introduction, Natural Computing, vol.1, issue.1, pp.3-52, 2002.
DOI : 10.1023/A:1015059928466

N. Hansen, N. , and A. Ostermeier, Completely Derandomized Self-Adaptation in Evolution Strategies, Evolutionary Computation, vol.9, issue.2, pp.159-195, 2001.
DOI : 10.1016/0004-3702(95)00124-7

S. Rogers, J. M. Massaro, Q. A. Truong, A. A. Mahabadi, M. F. Kriegel et al., Distribution, determinants, and normal reference values of thoracic and abdominal aortic diameters by Computed Tomography (from the Framingham Heart Study). The American journal of cardiology, pp.1510-1516, 2013.

G. F. Mitchell, J. C. Tardif, J. M. Arnold, G. Marchiori, T. X. O-'brien et al., Pulsatile Hemodynamics in Congestive Heart Failure, Hypertension, vol.38, issue.6, pp.1433-1442, 2001.
DOI : 10.1161/hy1201.098298

M. E. Safar and G. M. London, The arterial system in human hypertension, Textbook of hypertension. Londres : Blackwell Scientific, pp.85-102, 1994.

A. G. Brown, Y. B. Shi, A. Marzo, C. Staicu, I. Valverde et al., Accuracy vs. computational time: Translating aortic simulations to the clinic, Journal of Biomechanics, vol.45, issue.3, pp.516-523, 2012.
DOI : 10.1016/j.jbiomech.2011.11.041

D. Gallo, G. De-santis, F. Negri, D. Tresoldi, R. Ponzini et al., On the Use of In Vivo Measured Flow Rates as Boundary Conditions for Image-Based Hemodynamic Models of the Human Aorta: Implications for Indicators of Abnormal Flow, Annals of Biomedical Engineering, vol.47, issue.2, pp.729-741, 2012.
DOI : 10.1007/s10439-011-0431-1

A. Kyriakou, E. Neufeld, D. Szczerba, W. Kainz, R. Luechinger et al., Patient-specific simulations and measurements of the magneto-hemodynamic effect in human primary vessels, Physiological Measurement, vol.33, issue.2, p.117, 2012.
DOI : 10.1088/0967-3334/33/2/117

J. Lantz and M. Karlsson, Large eddy simulation of LDL surface concentration in a subject specific human aorta, Journal of Biomechanics, vol.45, issue.3, pp.537-542, 2012.
DOI : 10.1016/j.jbiomech.2011.11.039

M. Midulla, R. Moreno, A. Baali, M. Chau, A. Negre-salvayre et al., Haemodynamic imaging of thoracic stent-grafts by computational fluid dynamics (CFD): presentation of a patient-specific method combining magnetic resonance imaging and numerical simulations, European Radiology, vol.45, issue.10, pp.2094-2102, 2012.
DOI : 10.1007/s00330-012-2465-7

URL : https://hal.archives-ouvertes.fr/inserm-00726879

P. Reymond, F. Perren, F. Lazeyras, and N. Stergiopulos, Patient-specific mean pressure drop in the systemic arterial tree, a comparison between 1-D and 3-D models, Journal of Biomechanics, vol.45, issue.15, pp.2499-2505, 2012.
DOI : 10.1016/j.jbiomech.2012.07.020

K. M. Tse, R. Chang, H. P. Lee, S. P. Lim, S. K. Venkatesh et al., A computational fluid dynamics study on geometrical influence of the aorta on haemodynamics, European Journal of Cardio-Thoracic Surgery, vol.43, issue.4, p.388, 2012.
DOI : 10.1093/ejcts/ezs388

U. Morbiducci, R. Ponzini, D. Gallo, C. Bignardi, and G. Rizzo, Inflow boundary conditions for image-based computational hemodynamics: Impact of idealized versus measured velocity profiles in the human aorta, Journal of Biomechanics, vol.46, issue.1, pp.102-109, 2013.
DOI : 10.1016/j.jbiomech.2012.10.012

K. H. Parker and C. J. Jones, Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics, Journal of Biomechanical Engineering, vol.112, issue.3, pp.322-326, 1990.
DOI : 10.1115/1.2891191

E. Rooz, D. F. Young, and T. R. Rogge, A Finite-Element Simulation of Pulsatile Flow in Flexible Obstructed Tubes, Journal of Biomechanical Engineering, vol.104, issue.2, pp.119-124, 1982.
DOI : 10.1115/1.3138324

G. Porenta, D. F. Young, and T. R. Rogge, A Finite-Element Model of Blood Flow in Arteries Including Taper, Branches, and Obstructions, Journal of Biomechanical Engineering, vol.108, issue.2, pp.161-167, 1986.
DOI : 10.1115/1.3138596

I. Surovtsova, Effects of compliance mismatch on blood flow in an artery with endovascular prosthesis, Journal of Biomechanics, vol.38, issue.10, pp.2078-2086, 2005.
DOI : 10.1016/j.jbiomech.2004.09.004

D. Elad, D. Katz, E. Kimmel, and S. Einav, Numerical schemes for unsteady fluid flow through collapsible tubes, Journal of Biomedical Engineering, vol.13, issue.1, pp.10-18, 1991.
DOI : 10.1016/0141-5425(91)90038-9

C. W. Li and H. D. Cheng, A nonlinear fluid model for pulmonary blood circulation, Journal of Biomechanics, vol.26, issue.6, pp.653-664, 1993.
DOI : 10.1016/0021-9290(93)90029-E

M. S. Olufsen, Structured tree outflow condition for blood flow in larger systemic arteries American journal of physiology-Heart and circulatory physiology, pp.257-268, 1999.

B. S. Brook, S. A. Falle, and T. J. Pedley, Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state, Journal of Fluid Mechanics, vol.396, pp.223-256, 1999.
DOI : 10.1017/S0022112099006084

V. L. Streeter, W. F. Keitzer, and D. F. Bohr, Pulsatile Pressure and Flow Through Distensible Vessels, Circulation Research, vol.13, issue.1, pp.3-20, 1963.
DOI : 10.1161/01.RES.13.1.3

W. E. Bodley, The non-linearities of arterial blood flow, Physics in Medicine and Biology, vol.16, issue.4, pp.663-672, 1971.
DOI : 10.1088/0031-9155/16/4/010

J. Wan, B. Steele, S. A. Spicer, S. Strohband, G. R. Feijoo et al., A One-dimensional Finite Element Method for Simulation-based Medical Planning for Cardiovascular Disease, Computer Methods in Biomechanics and Biomedical Engineering, vol.276, issue.3, pp.195-206, 2002.
DOI : 10.1016/0141-5425(91)90100-L

B. S. Brook and T. J. , A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties, Journal of Biomechanics, vol.35, issue.1, pp.95-107, 2002.
DOI : 10.1016/S0021-9290(01)00159-2

P. Reymond, F. Merenda, F. Perren, D. Rufenacht, and N. Stergiopulos, Validation of a one-dimensional model of the systemic arterial tree, AJP: Heart and Circulatory Physiology, vol.297, issue.1, pp.208-222, 2009.
DOI : 10.1152/ajpheart.00037.2009

T. H. Hughes, C. Taylor, and C. Zarins, Finite element modeling of blood flow in arteries Computer methods in applied mechanics and engineering, pp.155-196, 1998.

J. J. Wang and K. H. Parker, Wave propagation in a model of the arterial circulation, Journal of Biomechanics, vol.37, issue.4, pp.457-470, 2004.
DOI : 10.1016/j.jbiomech.2003.09.007

J. J. Wang, A. B. O-'brien, N. G. Shrive, K. H. Parker, and J. V. Tyberg, Time-domain representation of ventricular-arterial coupling as a windkessel and wave system, American Journal of Physiology - Heart and Circulatory Physiology, vol.284, issue.4, pp.1358-1368, 2003.
DOI : 10.1152/ajpheart.00175.2002

P. Reymond, Y. Bohraus, F. Perren, F. Lazeyras, and N. Stergiopulos, Validation of a patient-specific one-dimensional model of the systemic arterial tree, AJP: Heart and Circulatory Physiology, vol.301, issue.3, pp.1173-1182, 2011.
DOI : 10.1152/ajpheart.00821.2010

D. H. Bergel, The dynamic elastic properties of the arterial wall, The Journal of Physiology, vol.156, issue.3, pp.458-469, 1961.
DOI : 10.1113/jphysiol.1961.sp006687

V. Martin, F. Clement, A. Decoene, and J. F. Gerbeau, Parameter identification for a one-dimensional blood flow model, ESAIM : Proceedings. EDP Sciences, pp.174-200, 2005.
DOI : 10.1051/proc:2005014

URL : https://hal.archives-ouvertes.fr/hal-00700366

J. Alastruey, Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed, Journal of Biomechanics, vol.44, issue.5, pp.885-891, 2011.
DOI : 10.1016/j.jbiomech.2010.12.002

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.1281-1299, 2000.
DOI : 10.1114/1.1326031

B. N. Steele, J. Wan, J. P. Ku, T. J. Hughes, and C. A. Taylor, In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts, IEEE Transactions on Biomedical Engineering, vol.50, issue.6, pp.649-656, 2003.
DOI : 10.1109/TBME.2003.812201

K. Hayashi, H. Handa, and S. Nagasawa, Stiffness and elastic behavior of human intracranial and extracranial arteries, Journal of Biomechanics, vol.13, issue.2, pp.175-184, 1980.
DOI : 10.1016/0021-9290(80)90191-8

N. P. Smith, A. J. Pullan, and P. J. Hunter, An Anatomically Based Model of Transient Coronary Blood Flow in the Heart, SIAM Journal on Applied Mathematics, vol.62, issue.3, pp.990-1018, 2002.
DOI : 10.1137/S0036139999355199

D. Xiu and S. J. Sherwin, Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network, Journal of Computational Physics, vol.226, issue.2, pp.1385-1407, 2007.
DOI : 10.1016/j.jcp.2007.05.020

S. Hamza, F. Anstett-collin, R. Kiébré, and M. Basset, Analyse de sensibilité basée sur les polynômes du chaos pour des modèles de type boîte noire

P. Chen, A. Quarteroni, and G. Rozza, Simulation-based uncertainty quantification of human arterial network hemodynamics. International journal for numerical methods in biomedical engineering, pp.698-721, 2013.

F. Antonini-canterin, S. Carerj, V. Di, and . Bello, Arterial stiffness and ventricular stiffness: a couple of diseases or a coupling disease? A review from the cardiologist's point of view, European Journal of Echocardiography, vol.10, issue.1, 2008.
DOI : 10.1093/ejechocard/jen236

E. Novak and K. Ritter, Simple cubature formulas with high polynomial exactness. Constructive approximation, pp.499-522, 1999.

E. Novak and K. Ritter, High dimensional integration of smooth functions over cubes, Numerische Mathematik, vol.75, issue.1, pp.79-97, 1996.
DOI : 10.1007/s002110050231

E. Novak and K. Ritter, The Curse of Dimension and a Universal Method For Numerical Integration, Birkhäuser Basel, pp.177-187, 1997.
DOI : 10.1007/978-3-0348-8871-4_15

G. Evans, Practical Numerical Integration, 1993.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1970.

A. Gil, J. Segura, and N. M. Temme, Numerical methods for special functions, 2007.
DOI : 10.1137/1.9780898717822

C. W. Clenshaw and A. R. Curtis, A method for numerical integration on an automatic computer, Numerische Mathematik, vol.9, issue.1, pp.197-205, 1960.
DOI : 10.1007/BF01386223

H. Brass, Bounds for Peano kernels, Numerical Integration IV, pp.39-55, 1993.
DOI : 10.1007/978-3-0348-6338-4_4

S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Mathematics, Doklady, vol.4, pp.240-243, 1963.

T. Gerstner and M. Griebel, Numerical integration using sparse grids. Numerical algorithms, pp.3-4, 1998.

G. W. Wasilkowski and H. Wozniakowski, Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems, Journal of Complexity, vol.11, issue.1, pp.1-56, 1995.
DOI : 10.1006/jcom.1995.1001

«. Deux-États, et (A u r , u u r ) provenant de la discontinuité de deux états de références U l = (A l , u l ) et U r = (A r , u r ), p.32

P. Patient and D. Formulation, les variations temporelles numériques de section et de vitesse comparées aux données cliniques, p.50

P. Patient and T. Formulation, les variations temporelles numériques de section et de vitesse comparées aux données cliniques, p.51