J. R. Anderson, O. Diaz, R. Klucznik, Y. J. Zhang, G. W. Britz et al., Validation of computational fluid dynamics methods with anatomically exact, 3D printed MRI phantoms and 4D pcMRI, 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp.6699-6701, 2014.

J. M. Bland and D. Altman, Statistical methods for assessing agreement between two methods of clinical measurement, The lancet, vol.327, issue.8476, pp.307-310, 1986.

A. Caiazzo and M. Junk, Boundary forces in lattice Boltzmann: Analysis of momentum exchange algorithm, Computers & Mathematics with Applications, vol.55, issue.7, pp.1415-1423, 2008.

P. Chai and R. Mohiaddin, Slice location dependence of aortic regurgitation measurements with MR phase velocity mapping, J Cardiovasc Magn Reson, vol.7, issue.4, pp.705-716, 2005.

D. Chapelle, M. Fragu, V. Mallet, and P. Moireau, Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart, Medical & biological engineering & computing, vol.51, issue.11, pp.1221-1233, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00760887

A. Chaturvedi, C. Hamilton-craig, P. J. Cawley, L. M. Mitsumori, C. M. Otto et al., Quantitating aortic regurgitation by cardiovascular magnetic resonance: significant variations due to slice location and breath holding, Eur Radiol, vol.26, issue.9, pp.3180-3189, 2016.

G. P. Chatzimavroudis, P. G. Walker, J. N. Oshinski, R. H. Franch, R. I. Pettigrew et al., Slice location dependence of aortic regurgitation measurements with MR phase velocity mapping, Magn Reson Med, vol.37, issue.4, pp.545-551, 1997.

S. Chikatamarla, S. Ansumali, and I. V. Karlin, Entropic lattice Boltzmann models for hydrodynamics in three dimensions, Physical review letters, vol.97, issue.1, p.10201, 2006.

, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, vol.360, pp.437-451, 1792.

F. Donati, S. Myerson, M. M. Bissell, N. P. Smith, S. Neubauer et al., Beyond Bernoulli: Improving the Accuracy and Precision of Noninvasive Estimation of Peak Pressure Drops, Circ Cardiovasc Imaging, vol.10, issue.1, p.5207, 2017.

P. Dyverfeldt, M. Bissell, A. J. Barker, A. F. Bolger, C. J. Carlhäll et al., 4D flow cardiovascular magnetic resonance consensus statement, J Cardiovasc Magn Reson, vol.17, issue.1, p.72, 2015.

B. Eckhardt, , 2008.

R. J. Everett, M. A. Clavel, P. Pibarot, and M. R. Dweck, Timing of intervention in aortic stenosis: a review of current and future strategies, Heart, vol.104, issue.24, pp.2067-2076, 2018.

R. Fu?ík, P. Eichler, R. Straka, P. Pau?, J. Klinkovský et al., On optimal node spacing for immersed boundary-lattice Boltzmann method in 2D and 3D, Computers & Mathematics with Applications, vol.77, issue.4, pp.1144-1162, 2019.

M. Gehrke, A. Banari, and T. Rung, Performance of under-resolved, model-free LBM simulations in turbulent shear flows, Progress in Hybrid RANS-LES Modelling, pp.3-18, 2020.

M. Geier, A. Greiner, and J. G. Korvink, Cascaded digital lattice Boltzmann automata for high Reynolds number flow, Physical Review E, vol.73, issue.6, p.66705, 2006.

M. Geier, M. Schönherr, A. Pasquali, and M. Krafczyk, The cumulant lattice Boltzmann equation in three dimensions: Theory and validation, Computers & Mathematics with Applications, vol.70, issue.4, pp.507-547, 2015.

M. Geier, A. Pasquali, and M. Schönherr, Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part I: Derivation and validation, Journal of Computational Physics, vol.348, pp.862-888, 2017.

M. Geier, A. Pasquali, and M. Schönherr, Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion Part II: Application to flow around a sphere at drag crisis, Journal of Computational Physics, vol.348, pp.889-898, 2017.

L. Goubergrits, E. Riesenkampff, P. Yevtushenko, J. Schaller, U. Kertzscher et al., Is MRI-Based CFD Able to Improve Clinical Treatment of Coarctations of Aorta?, Ann Biomed Eng, vol.43, issue.1, pp.168-176, 2015.

Z. Guo and C. Shu, Lattice Boltzmann method and its applications in engineering, vol.3, 2013.

H. Ha, J. Lantz, M. Ziegler, B. Casas, M. Karlsson et al., Evaluation of aortic regurgitation with cardiac magnetic resonance imaging: a systematic review, Sci Rep, vol.7, p.46618, 2017.

Y. Iwamoto, A. Inage, G. Tomlinson, K. J. Lee, L. Grosse-wortmann et al., Direct measurement of aortic regurgitation with phasecontrast magnetic resonance is inaccurate: proposal of an alternative method of quantification, Pediatr Radiol, vol.44, issue.11, pp.1358-1369, 2014.

I. V. Karlin, F. Bösch, and S. Chikatamarla, Gibbs' principle for the lattice-kinetic theory of fluid dynamics, Physical Review E, vol.90, issue.3, p.31302, 2014.

J. Kweon, D. H. Yang, G. B. Kim, N. Kim, M. Paek et al., Fourdimensional flow MRI for evaluation of poststenotic turbulent flow in a phantom: comparison with flowmeter and computational fluid dynamics, Eur Radiol, vol.26, issue.10, pp.3588-3597, 2016.

J. C. Lee, K. R. Branch, C. Hamilton-craig, and E. V. Krieger, Evaluation of aortic regurgitation with cardiac magnetic resonance imaging: a systematic review, Heart, vol.104, issue.2, pp.103-110, 2018.

S. Miyazaki, K. Itatani, T. Furusawa, T. Nishino, M. Sugiyama et al., Validation of numerical simulation methods in aortic arch using 4D Flow MRI, Heart Vessels, vol.32, issue.8, pp.1032-1044, 2017.

P. D. Morris, A. Narracott, H. Von-tengg-kobligk, D. Soto, S. Hsiao et al., Computational fluid dynamics modelling in cardiovascular medicine, Heart, vol.102, issue.1, pp.18-28, 2016.

K. S. Nayak, J. F. Nielsen, M. A. Bernstein, M. Markl, P. D. Gatehouse et al., Cardiovascular magnetic resonance phase contrast imaging, J Cardiovasc Magn Reson, vol.17, issue.1, p.71, 2015.

K. R. O'brien, B. R. Cowan, M. Jain, R. A. Stewart, A. J. Kerr et al., MRI Phase Contrast Velocity and Flow Errors in Turbulent Stenotic Jets, J Magn Reson Imaging, vol.28, issue.1, pp.210-218, 2008.

B. Ruijsink, E. Puyol-antón, M. Usman, J. Van-amerom, P. Duong et al., Semi-automatic cardiac and respiratory gated MRI for cardiac assessment during exercise, Molecular Imaging, Reconstruction and Analysis of Moving Body Organs, and Stroke Imaging and Treatment, pp.86-95, 2017.

B. Ruijsink, K. Zugaj, K. Pushparajah, and R. Chabiniok, Model-based indices of early-stage cardiovascular failure and its therapeutic management in Fontan patients, Functional Imaging and Modeling of the Heart, pp.379-387, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02186819

H. Schlichting and K. Gersten, Boundary-layer theory, 2016.

K. V. Sharma, R. Straka, and F. W. Tavares, New Cascaded Thermal Lattice Boltzmann Method for simulations of advection-diffusion and convective heat transfer, International Journal of Thermal Sciences, vol.118, pp.259-277, 2017.

K. V. Sharma, R. Straka, and F. W. Tavares, Lattice Boltzmann Methods for Industrial Applications. Industrial & Engineering Chemistry Research, vol.58, issue.36, pp.16205-16234, 2019.

X. Shen, S. Schnell, A. J. Barker, K. Suwa, L. Tashakkor et al., Voxel-by-voxel 4D flow MRI-based assessment of regional reverse flow in the aorta, J Magn Reson Imaging, vol.47, issue.5, pp.1276-1286, 2018.

J. Sotelo, L. Dux-santoy, A. Guala, J. Rodríguez-palomares, A. Evangelista et al., 3D axial and circumferential wall shear stress from 4D flow MRI data using a finite element method and a laplacian approach, Magn Reson Med, vol.79, issue.5, pp.2816-2823, 2018.

M. B. Srichai, R. P. Lim, S. Wong, and V. S. Lee, Cardiovascular applications of phase-contrast MRI, Am J Roentgenol, vol.192, issue.3, pp.662-675, 2009.

H. ?vihlová, J. Hron, J. Málek, K. Rajagopal, and K. Rajagopal, Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations, Int J of Eng Sci, vol.105, pp.108-127, 2016.

H. ?vihlová, J. Hron, J. Málek, K. Rajagopal, and K. Rajagopal, Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: A study of aortic valve stenosis, Int J of Eng Sci, vol.114, pp.1-15, 2017.

D. C. Wendell, M. M. Samyn, J. R. Cava, M. M. Krolikowski, and J. F. Ladisa, The Impact of Cardiac Motion on Aortic Valve Flow Used in Computational Simulations of the Thoracic Aorta, J Biomech Eng, vol.138, issue.9, p.91001, 2016.

, ) flow profiles for all three valves (mildly, moderately, and severely stenosed, i.e. Mild-, Mod-, Sev-VS, respectively) and all four flow rates that compare the experimental (1.5T and 3T) and LBM-simulated data