C. Taylor and C. Figueroa, Patient-Specific Modeling of Cardiovascular Mechanics, Annual Review of Biomedical Engineering, vol.11, issue.1, pp.109-134, 2009.
DOI : 10.1146/annurev.bioeng.10.061807.160521

K. Takizawa, Y. Bazilevs, and T. Tezduyar, Space???Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid???Structure Interaction Modeling, Archives of Computational Methods in Engineering, vol.31, issue.2, pp.171-225, 2012.
DOI : 10.1007/s11831-012-9071-3

A. Figueroa, S. Baek, C. Taylor, and J. Humphrey, A computational framework for fluid???solid-growth modeling in cardiovascular simulations, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.45-46, pp.3583-3602, 2009.
DOI : 10.1016/j.cma.2008.09.013

E. Moghadam, M. Vignon-clementel, I. Figliola, R. Marsden, and A. , A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations, Journal of Computational Physics, vol.244, pp.63-79, 2013.
DOI : 10.1016/j.jcp.2012.07.035

URL : https://hal.archives-ouvertes.fr/hal-00765816

A. Marsden, Optimization in Cardiovascular Modeling, Annual Review of Fluid Mechanics, vol.46, issue.1, pp.519-546, 2014.
DOI : 10.1146/annurev-fluid-010313-141341

J. Humphrey, Vascular Adaptation and Mechanical Homeostasis at Tissue, Cellular, and Sub-cellular Levels, Cell Biochemistry and Biophysics, vol.121, issue.3, pp.53-78, 2008.
DOI : 10.1007/s12013-007-9002-3

A. Valentin and J. Humphrey, Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.287, issue.3, pp.3585-3606, 1902.
DOI : 10.1152/ajpheart.00094.2004

G. Troianowski, C. Taylor, and J. Feinstein, Vignon-Clementel I. Three-dimensional simulations in Glenn patients: clinically based boundary conditions, hemodynamic results and sensitivity to input data, Journal of Biomechanical Engineering, vol.133, issue.11, pp.111-117, 2011.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1699114

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Pattern Analysis and Machine Intelligence, IEEE Transactions on, issue.6, pp.721-741, 1984.

R. Neal, Slice sampling, The Annals of Statistics, vol.31, issue.3, pp.705-741, 2003.
DOI : 10.1214/aos/1056562461

A. Gelfand and A. Smith, Sampling-Based Approaches to Calculating Marginal Densities, Journal of the American Statistical Association, vol.4, issue.410, pp.398-409, 1990.
DOI : 10.1080/01621459.1986.10478240

L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, vol.22, issue.4, pp.1701-1728, 1994.
DOI : 10.1214/aos/1176325750

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949.
DOI : 10.1080/01621459.1949.10483310

D. Lucor, C. Su, and G. Karniadakis, Generalized polynomial chaos and random oscillators, International Journal for Numerical Methods in Engineering, vol.60, issue.3, pp.571-596, 2004.
DOI : 10.1002/nme.976

R. Ghanem, P. D. Spanos, . Schiavazzi-et-al, and . Doi, Stochastic finite elements: a spectral approach, pp.10-1002, 2003.
DOI : 10.1007/978-1-4612-3094-6

F. Nobile, R. Tempone, and C. Webster, A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.46, issue.5, pp.2309-2345, 2008.
DOI : 10.1137/060663660

I. Babu?ka, F. Nobile, and R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Review, vol.52, issue.2, pp.317-355, 2010.
DOI : 10.1137/100786356

X. Ma and N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, Journal of Computational Physics, vol.228, issue.8, pp.3084-3113, 2009.
DOI : 10.1016/j.jcp.2009.01.006

F. Nobile, R. Tempone, and C. Webster, An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.46, issue.5, pp.2411-2442, 2008.
DOI : 10.1137/070680540

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

O. Ernst, A. Mugler, H. Starkloff, and E. Ullmann, On the convergence of generalized polynomial chaos expansions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.2, pp.317-339, 2012.
DOI : 10.1051/m2an/2011045

X. Wan and G. Karniadakis, Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures, SIAM Journal on Scientific Computing, vol.28, issue.3, pp.901-928, 2006.
DOI : 10.1137/050627630

J. Witteveen and G. Iaccarino, Simplex Stochastic Collocation with Random Sampling and Extrapolation for Nonhypercube Probability Spaces, SIAM Journal on Scientific Computing, vol.34, issue.2, p.814, 2012.
DOI : 10.1137/100817504

T. Chantrasmi, A. Doostan, and G. Iaccarino, Pad?????Legendre approximants for uncertainty analysis with discontinuous response surfaces, Journal of Computational Physics, vol.228, issue.19, pp.7159-7180, 2009.
DOI : 10.1016/j.jcp.2009.06.024

A. Doostan and H. Owhadi, A non-adapted sparse approximation of PDEs with stochastic inputs, Journal of Computational Physics, vol.230, issue.8, pp.3015-3034, 2011.
DOI : 10.1016/j.jcp.2011.01.002

D. Schiavazzi, A. Doostan, and G. Iaccarino, SPARSE MULTIRESOLUTION REGRESSION FOR UNCERTAINTY PROPAGATION, International Journal for Uncertainty Quantification, vol.4, issue.4, pp.303-331, 2014.
DOI : 10.1615/Int.J.UncertaintyQuantification.2014010147

D. Xiu and S. 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

A. Marsden, J. Feinstein, and C. Taylor, A computational framework for derivative-free optimization of cardiovascular geometries, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.21-24, pp.1890-1905, 2008.
DOI : 10.1016/j.cma.2007.12.009

S. Sankaran and A. Marsden, The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow, Physics of Fluids, vol.22, issue.12, pp.121-902, 2010.
DOI : 10.1063/1.3529444

S. Sankaran and A. Marsden, A Stochastic Collocation Method for Uncertainty Quantification and Propagation in Cardiovascular Simulations, Journal of Biomechanical Engineering, vol.133, issue.3, pp.31-32, 2011.
DOI : 10.1115/1.4003259

S. Sankaran, J. Humphrey, and A. Marsden, An efficient framework for optimization and parameter sensitivity analysis in arterial growth and remodeling computations, Computer Methods in Applied Mechanics and Engineering, vol.256, pp.200-210, 2013.
DOI : 10.1016/j.cma.2012.12.013

P. Chen, A. Quarteroni, and G. Rozza, Simulation-based uncertainty quantification of human arterial network hemodynamics, International Journal for Numerical Methods in Biomedical Engineering, vol.358, issue.9289, pp.698-721, 2013.
DOI : 10.1002/cnm.2554

D. Elia, M. Perego, M. Veneziani, and A. , A variational data assimilation procedure for the incompressible navier-stokes equations in hemodynamics, Journal of Scientific Computing, vol.52, issue.2, pp.340-359, 2012.

P. Moireau, C. Bertoglio, N. Xiao, C. Figueroa, C. Taylor et al., Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data, Biomechanics and Modeling in Mechanobiology, vol.27, issue.7, pp.475-496, 2013.
DOI : 10.1007/s10237-012-0418-3

URL : https://hal.archives-ouvertes.fr/hal-00760703

C. Corsini, C. Baker, E. Kung, S. Schievano, G. Arbia et al., An integrated approach to patient-specific predictive modeling for single ventricle heart palliation, Computer Methods in Biomechanics and Biomedical Engineering, vol.84, issue.1, pp.1-18, 2013.
DOI : 10.1080/10255840903413565

URL : https://hal.archives-ouvertes.fr/hal-00918643

E. Kung, A. Baretta, C. Baker, G. Arbia, G. Biglino et al., Predictive modeling of the virtual Hemi-Fontan operation for second stage single ventricle palliation: Two patient-specific cases, Journal of Biomechanics, vol.46, issue.2, pp.423-429, 2013.
DOI : 10.1016/j.jbiomech.2012.10.023

URL : https://hal.archives-ouvertes.fr/hal-00765797

F. Fontan and E. Baudet, Surgical repair of tricuspid atresia, Thorax, vol.26, issue.3, pp.240-248, 1971.
DOI : 10.1136/thx.26.3.240

D. Schiavazzi, E. Kung, A. Marsden, C. Baker, G. Pennati et al., Hemodynamic effects of left pulmonary artery stenosis following superior cavopulmonary connection: a patient-specic multiscale modeling study 2014

F. Migliavacca, G. Pennati, G. Dubini, R. Fumero, R. Pietrabissa et al., Modeling of the norwood circulation: effects of shunt size, vascular resistances, and heart rate, American Journal of Physiology- Heart and Circulatory Physiology, vol.280, issue.5, pp.2076-2086, 2001.

R. Spilker, J. Feinstein, D. Parker, V. Reddy, and C. Taylor, Morphometry-Based Impedance Boundary Conditions for Patient-Specific Modeling of Blood Flow in Pulmonary Arteries, Annals of Biomedical Engineering, vol.55, issue.4, pp.546-559, 2007.
DOI : 10.1007/s10439-006-9240-3

C. Taylor, T. Hughes, and C. Zarins, Finite element modeling of blood flow in arteries, Computer Methods in Applied Mechanics and Engineering, vol.158, issue.1-2, pp.155-196, 1998.
DOI : 10.1016/S0045-7825(98)80008-X

I. Vignon-clementel, C. Figueroa, K. Jansen, and C. Taylor, Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.29-32, pp.3776-3796, 2006.
DOI : 10.1016/j.cma.2005.04.014

M. Moghadam, Y. Bazilevs, T. Hsia, I. Vignon-clementel, and A. Marsden, A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations, Computational Mechanics, vol.65, issue.41???43, pp.277-291, 2011.
DOI : 10.1007/s00466-011-0599-0

URL : https://hal.archives-ouvertes.fr/hal-00650986

M. Esmaily-moghadam, Y. Bazilevs, and A. Marsden, A new preconditioning technique for implicitly coupled multidomain simulations with applications to hemodynamics, Computational Mechanics, vol.35, issue.1, pp.1141-1152, 2013.
DOI : 10.1007/s00466-013-0868-1

T. Hsia, S. Khambadkone, A. Redington, F. Migliavacca, J. Deanfield et al., Effects of Respiration and Gravity on Infradiaphragmatic Venous Flow in Normal and Fontan Patients, Circulation, vol.102, issue.Supplement 3, p.148, 2000.
DOI : 10.1161/01.CIR.102.suppl_3.III-148

Y. Mori, T. Nakanishi, T. Ishii, Y. Imai, and M. Nakazawa, Relation of pulmonary venous wedge pressures to pulmonary artery pressures in patients with single ventricle physiology, The American Journal of Cardiology, vol.91, issue.6, pp.772-774, 2003.
DOI : 10.1016/S0002-9149(02)03430-6

J. Thompson, P. Moore, and D. Teitel, Pulmonary venous wedge pressures accurately predict pulmonary arterial pressures in children with single ventricle physiology, Pediatric Cardiology, vol.24, issue.6, pp.531-537, 2003.

K. Hill, D. Janssen, D. Ohmstede, and T. Doyle, Pulmonary venous wedge pressure provides a safe and accurate estimate of pulmonary arterial pressure in children with shunt-dependent pulmonary blood flow, Catheterization and Cardiovascular Interventions, vol.116, issue.12, pp.747-752, 2009.
DOI : 10.1002/ccd.22084

S. Fratz, T. Chung, G. Greil, M. Samyn, A. Taylor et al., Guidelines and protocols for cardiovascular magnetic resonance in children and adults with congenital heart disease: SCMR expert consensus group on congenital heart disease, Journal of Cardiovascular Magnetic Resonance, vol.15, issue.1, pp.1-26, 2013.
DOI : 10.1081/JCMR-120022267

C. Loeber, S. Goldberg, G. Marx, M. Carrier, and R. Emery, How much does aortic and pulmonary artery area vary during the cardiac cycle?, American Heart Journal, vol.113, issue.1, pp.95-100, 1987.
DOI : 10.1016/0002-8703(87)90015-9

A. Azzalini, D. Valle, and A. , The multivariate skew-normal distribution, Biometrika, vol.83, issue.4, pp.715-726, 1996.
DOI : 10.1093/biomet/83.4.715

H. Miao, X. Xia, A. Perelson, and H. Wu, On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics, SIAM Review, vol.53, issue.1, pp.3-39, 2011.
DOI : 10.1137/090757009

B. Seeley and D. Young, Effect of geometry on pressure losses across models of arterial stenoses, Journal of Biomechanics, vol.9, issue.7, pp.439-448, 1976.
DOI : 10.1016/0021-9290(76)90086-5

M. Mckay, R. Beckman, and W. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.21, issue.2, pp.239-245, 1979.

K. Petras, Smolyak cubature of given polynomial degree with few nodes for increasing dimension, Numerische Mathematik, vol.93, issue.4, pp.729-753, 2003.
DOI : 10.1007/s002110200401

A. Genz and B. Keister, Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight, Journal of Computational and Applied Mathematics, vol.71, issue.2, pp.299-309, 1996.
DOI : 10.1016/0377-0427(95)00232-4

W. Gilks, Markov Chain Monte Carlo, 2005.
DOI : 10.1002/0470011815.b2a14021

E. Acar, Effects of the correlation model, the trend model, and the number of training points on the accuracy of Kriging metamodels, Expert Systems, vol.47, issue.5, pp.418-428, 2013.
DOI : 10.1111/j.1468-0394.2012.00646.x

M. Stein, Interpolation of spatial data: some theory for Kriging, 1999.
DOI : 10.1007/978-1-4612-1494-6

W. Yang, J. Feinstein, and A. Marsden, Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.33-36, pp.2135-2149, 2010.
DOI : 10.1016/j.cma.2010.03.012

W. Yang, I. Vignon-clementel, G. Troianowski, V. Reddy, J. Feinstein et al., Hepatic blood flow distribution and performance in conventional and novel Y-graft Fontan geometries: A case series computational fluid dynamics study, The Journal of Thoracic and Cardiovascular Surgery, vol.143, issue.5, pp.1086-1097, 2012.
DOI : 10.1016/j.jtcvs.2011.06.042

URL : https://hal.archives-ouvertes.fr/hal-00649953

W. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Dokl. Akad. Nauk SSSR, vol.4, issue.123, 1963.

G. Arbia, C. Corsini, M. Moghadam, A. Marsden, F. Migliavacca et al., Numerical blood flow simulation in surgical corrections: what do we need for an accurate analysis?, Journal of Surgical Research, vol.186, issue.1, pp.44-55, 2014.
DOI : 10.1016/j.jss.2013.07.037

URL : https://hal.archives-ouvertes.fr/hal-00911298