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All issues Volume 57 / No 3 (May-June 2023) ESAIM: M2AN, 57 3 (2023) 1839-1861 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
Page(s) 1839 - 1861
DOI https://doi.org/10.1051/m2an/2023021
Published online 14 June 2023
  1. M. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M.E. Rognes and G.N. Wells, The FEniCS project version 1.5. Arch. Numer. Software 3 (2015). [Google Scholar]
  2. H. Baumgartner, P. Bonhoeffer, N. De Groot, F. de Haan, J. Deanfield, N. Galie, M. Gatzoulis, C. Gohlke-Baerwolf and The Task Force on the Management of Grown-up Congenital Heart Disease of the European Society of Cardiology (ESC), ESC Guidelines for the management of grown-up congenital heart disease (new version 2010). Eur. Heart J. 31 (2010) 2915–2957. [CrossRef] [PubMed] [Google Scholar]
  3. C. Bertoglio, R. Núñez, F. Galarce, D. Nordsletten and A. Osses, Relative pressure estimation from velocity measurements in blood flows: state-of-art and new approaches. Int. J. Numer. Methods Biomed. Eng. 34 (2017) e2925. [Google Scholar]
  4. S. Brenner and L.R. Scott, The Mathematical Theory of Finite Elements. Springer, New York (2008). [CrossRef] [Google Scholar]
  5. J. Brüning, F. Hellmeier, P. Yevtushenko, T. Kühne and L. Goubergrits, Uncertainty quantification for non-invasive assessment of pressure drop across a coarctation of the aorta using CFD. Cardiovasc. Eng. Technol. 9 (2018) 582–596. [Google Scholar]
  6. A. de Vecchi, R.E. Clough, N.R. Gaddum, M. Rutten, P. Lamata, T. Schaeffter, D. Nordsletten and N. Smith, Catheter-induced errors in pressure measurements in vessels: an in-vitro and numerical study. IEEE Trans. Biomed. Eng. 61 (2014) 1844–1850. [CrossRef] [PubMed] [Google Scholar]
  7. D. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. Springer-Verlag, Berlin, Heidelberg (2012). [CrossRef] [Google Scholar]
  8. T. Ebbers, L. Wigström, A. Bolger, J. Engvall and M. Karlsson, Estimation of relative cardiovascular pressure using time-resolved three-dimensional phase contrast MRI. Magn. Reson. Med 45 (2001) 872–879. [CrossRef] [Google Scholar]
  9. A. Ern and J.L. Guermond, Theory and Practice of Finite Elements. Springer, New York (2004). [CrossRef] [Google Scholar]
  10. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations: theory and algorithms, in Springer Series in Computational Mathematics, Vol. 5, Springer-Verlag (1986). [CrossRef] [Google Scholar]
  11. J.L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 6011–6045. [Google Scholar]
  12. T. Hughes, L. Franca and M. Balestra, A new finite element formulation for computational fluis dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods. Appl. Mech. Eng. 59 (1986) 85–99. [CrossRef] [Google Scholar]
  13. S.B. Krittian, P. Lamata, C. Michler, D.A. Nordsletten, J. Bock, C.P. Bradley, A. Pitcher, P.J. Kilner, M. Markl and N.P. Smith, A finite-element approach to the direct computation of relative cardiovascular pressure from time-resolved MR velocity data. Med. Image Anal. 16 (2012) 1029–1037. [CrossRef] [Google Scholar]
  14. M. Markl, A. Frydrychowicz, S. Kozerke, M. Hope and O. Wieben, 4D flow MRI. J. Magn. Reson. Imaging 36 (2012) 1015–1036. [CrossRef] [Google Scholar]
  15. C. Montalba, J. Urbina, J. Sotelo, M.E. Andia, C. Tejos, P. Irarrazaval, D.E. Hurtado, I. Valverde and S. Uribe, Variability of 4D flow parameters when subjected to changes in MRI acquisition parameters using a realistic thoracic aortic phantom. Magn. Reson. Med. 79 (2018) 1882–1892. [CrossRef] [PubMed] [Google Scholar]
  16. D. Nolte, J. Urbina, J. Sotelo, L. Sok, C. Montalba, I. Valverde, A. Osses, S. Uribe and C. Bertoglio, Validation of 4D flow based relative pressure maps in aortic flows. Med. Image Anal. 74 (2021) 102195. [CrossRef] [Google Scholar]
  17. H. Omran, H. Schmidt, M. Hackenbroch, S. Illien, P. Bernhardt, G. von der Recke, R. Fimmers, S. Flacke, G. Layer and C. Pohl, Silent and apparent cerebral embolism after retrograde catheterisation of the aortic valve in valvular stenosis: a prospective, randomised study. Lancet 361 (2003) 1241–1246. [CrossRef] [PubMed] [Google Scholar]
  18. D. Pacheco and O. Steinbach, A continuous finite element framework for the pressure poisson equation allowing non-Newtonian and compressible flow behavior. Int. J. Numer. Methods Fluids (2020) 1–11. [Google Scholar]
  19. S. Rhebergen and G.N. Wells, A hybridizable discontinuous galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field. J. Sci. Comput. 76 (2018) 1484–1501. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Soulat, P. McCarthy and M. Markl, 4D flow with MRI, Annu. Rev. Biomed. Eng. 22 (2020). [Google Scholar]
  21. O. Steinbach, Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements, Springer, New York (2008). [CrossRef] [Google Scholar]
  22. J. Urbina, J.A. Sotelo, D. Springmüller, C. Montalba, K. Letelier, C. Tejos, P. Irarrázaval, M.E. Andia, R. Razavi, I. Valverde and S.A. Uribe, Realistic aortic phantom to study hemodynamics using MRI and cardiac catheterization in normal and aortic coarctation conditions. J. Magn. Reson. Imag. 44 (2016) 683–697. [CrossRef] [Google Scholar]
  23. H. Švihlová, J. Hron, J. Málek, K.R. Rajagopoal and K. Rajagopoal, Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations. Int. J. Eng. Sci. 105 (2016) 108–127. [CrossRef] [Google Scholar]
  24. A. Vahanian et al., Guidelines on the management of valvular heart disease (version 2012). Eur. Heart J. 19 (2012) 2451–2496. [Google Scholar]
  25. R. Vitiello, B.W. McCrindle, D. Nykanen, R. Freedom and L. Benson, Complications associated with pediatric cardiac catheterization. J. Am. Coll. Cardiol. 32 (1998) 1433–1440. [CrossRef] [Google Scholar]
  26. T. Warburton and J.S. Hesthaven, On the constants in hp-finite element trace inverse inequalities. Comput. Methods Appl. Mech. Eng. 192 (2003) 2765–2773. [Google Scholar]
  27. R. Michael Wyman, R.D. Safian, V. Portway, J.J. Skillman, R.G. McKay and D.S. Baim, Current complications of diagnostic and therapeutic cardiac catheterization. J. Am. Coll. Cardiol. 12 (1988) 1400–1406. [CrossRef] [Google Scholar]

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