Validation of Numerical Simulations of Thoracic Aorta Hemodynamics: Comparison with In Vivo Measurements and Stochastic Sensitivity Analysis



Computational fluid dynamics (CFD) and 4D-flow magnetic resonance imaging (MRI) are synergically used for the simulation and the analysis of the flow in a patient-specific geometry of a healthy thoracic aorta.


CFD simulations are carried out through the open-source code SimVascular. The MRI data are used, first, to provide patient-specific boundary conditions. In particular, the experimentally acquired flow rate waveform is imposed at the inlet, while at the outlets the RCR parameters of the Windkessel model are tuned in order to match the experimentally measured fractions of flow rate exiting each domain outlet during an entire cardiac cycle. Then, the MRI data are used to validate the results of the hemodynamic simulations. As expected, with a rigid-wall model the computed flow rate waveforms at the outlets do not show the time lag respect to the inlet waveform conversely found in MRI data. We therefore evaluate the effect of wall compliance by using a linear elastic model with homogeneous and isotropic properties and changing the value of the Young’s modulus. A stochastic analysis based on the polynomial chaos approach is adopted, which allows continuous response surfaces to be obtained in the parameter space starting from a few deterministic simulations.


The flow rate waveform can be accurately reproduced by the compliant simulations in the ascending aorta; on the other hand, in the aortic arch and in the descending aorta, the experimental time delay can be matched with low values of the Young’s modulus, close to the average value estimated from experiments. However, by decreasing the Young’s modulus the underestimation of the peak flow rate becomes more significant. As for the velocity maps, we found a generally good qualitative agreement of simulations with MRI data. The main difference is that the simulations overestimate the extent of reverse flow regions or predict reverse flow when it is absent in the experimental data. Finally, a significant sensitivity to wall compliance of instantaneous shear stresses during large part of the cardiac cycle period is observed; the variability of the time-averaged wall shear stresses remains however very low.


In summary, a successful integration of hemodynamic simulations and of MRI data for a patient-specific simulation has been shown. The wall compliance seems to have a significant impact on the numerical predictions; a larger wall elasticity generally improves the agreement with experimental data.

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  1. 1.

    Anderson, A. E., B. J. Ellis, and J. A. Weiss. Verification, validation and sensitivity studies in computational biomechanics. Comput. Methods Biomech. Biomed. Eng. 10(3):171, 2007.

    Article  Google Scholar 

  2. 2.

    Arbia, G., I. E. Vignon-Clementel, T. Y. Hsia, and J. F. Gerbeau. Modified Navier–Stokes equations for the outflow boundary conditions in hemodynamics. Eur. J. Mech. B 60:175, 2016.

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Boccadifuoco, A., A. Mariotti, S. Celi, N. Martini, and M. V. Salvetti. Uncertainty quantification in numerical simulations of the flow in thoracic aortic aneurysms. ECCOMAS Congr. 2016 Proc. 7th Eur. Congr. Comput. Methods Appl. Sci. Eng. 3:6226, 2016.

    Google Scholar 

  4. 4.

    Boccadifuoco, A., A. Mariotti, S. Celi, N. Martini, and M. V. Salvetti. Effects of inlet conditions in the simulation of hemodynamics in a thoracic aortic aneurysm. AIMETA 2017 Proc. 23rd Conf. Ital. Assoc. Theor. Appl. Mech. 2:1706, 2017.

    Google Scholar 

  5. 5.

    Boccadifuoco, A., A. Mariotti, S. Celi, N. Martini, and M. V. Salvetti. Impact of uncertainties in outflow boundary conditions on the predictions of hemodynamic simulations of ascending thoracic aortic aneurysms. Comput. Fluids 165: 96, 2018.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Bozzi, S., U. Morbiducci, D. Gallo, R. Ponzini, G. Rizzo, C. Bignardi, and G. Passoni. Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta. Comput. Methods Biomech. Biomed. Eng. 20(10):1104, 2017.

    Article  Google Scholar 

  7. 7.

    Caballero, A. D., and S. Laín. A review on computational fluid dynamics modelling in human thoracic aorta. Cardiovasc. Eng. Technol. 4(2):103, 2013.

    Article  Google Scholar 

  8. 8.

    Campo-Deano, L., M. S. N. Oliveira, and F. T. Pinho. A review of computational hemodynamics in middle cerebral aneurysms and rheological models for blood flow. Appl. Mech. Rev. 67(3):030801, 2015.

    Article  Google Scholar 

  9. 9.

    Capellini, K., E. Vignali, E. Costa, E. Gasparotti, M. E. Biancolini, L. Landini, V. Positano, and S. Celi. Computational fluid dynamic study for aTAA hemodynamics: an integrated image-based and radial basis functions mesh morphing approach. J. Biomech. Eng. 140(11):111007, 2018.

    Article  Google Scholar 

  10. 10.

    Celi, S., and S. Berti. Chap. 1. In: Aneurysm. Rijeka: InTech, 2012, p. 326.

  11. 11.

    Celi, S., and S. Berti. Three-dimensional sensitivity assessment of thoracic aortic aneurysm wall stress: a probabilistic finite-element study. Eur. J. Cardiothorac. Surg. 45(3):467, 2014.

    Article  Google Scholar 

  12. 12.

    Celi, S., F. Di Puccio, and P. Forte. Advances in finite element simulations of elastosonography for breast lesion detection. J. Biomech. Eng. 133(8):081006, 2011.

    Article  Google Scholar 

  13. 13.

    Chiastra, C., S. Migliori, F. Burzotta, G. Dubini, and F. Migliavacca. Patient-specific modeling of stented coronary arteries reconstructed from optical coherence tomography: towards a widespread clinical use of fluid dynamics analyses. J. Cardiovasc. Transl. Res. 11:1–17, 2017.

    Google Scholar 

  14. 14.

    Condemi, F., S. Campisi, M. Viallon, T. Troalen, G. Xuexin, A. J. Barker, M. Markl, P. Croisille, O. Trabelsi, C. Cavinato, A. Duprey, and S. Avril. Fluid- and biomechanical analysis of ascending thoracic aorta aneurysm with concomitant aortic insufficiency. Ann. Biomed. Eng. 45(12):2921, 2017.

    Article  Google Scholar 

  15. 15.

    Dumoulin, C. L., S. P. Souza, M. F. Walker, and W. Wagle. Three dimensional phase contrast angiography. Magn. Reson. Med. 9(1):139, 1989.

    Article  Google Scholar 

  16. 16.

    Eck, V. G., W. P. Donders, J. Sturdy, J. Feinberg, T. Delhaas, L. R. Hellevik, and W. Huberts. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int. J. Numer. Methods Biomed. Eng. 32(8):e02755, 2015.

    MathSciNet  Article  Google Scholar 

  17. 17.

    Eck, V. G., J. Sturdy, and L. R. Hellevik. Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions. J. Biomech. 50:188, 2017.

    Article  Google Scholar 

  18. 18.

    Esmaily Moghadam, M., Y. Bazilevs, T. Y. Hsia, I. Vignon-Clementel, and A. Marsden. A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput. Mech. 48(3):277, 2011.

    MathSciNet  Article  MATH  Google Scholar 

  19. 19.

    Figueroa, C. A., I. E. Vignon-Clementel, K. E. Jansen, T. J. R. Hughes, and C. A. Taylor. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Eng. 195(41–43):5685, 2006.

    MathSciNet  Article  MATH  Google Scholar 

  20. 20.

    Gallo, v, G. De Santis, F. Negri, D. Tresoldi, R. Ponzini, D. Massai, M. A. Deriu, P. Segers, B. Verhegghe, G. Rizzo, and U. Morbiducci. 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. Ann. Biomed. Eng. 40(3):729, 2012.

    Article  Google Scholar 

  21. 21.

    Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6):15, 2006.

    Article  Google Scholar 

  22. 22.

    Huberts, W., K. Van Canneyt, P. Segers, J. H. M. Tordoir, P. Verdonck, and E. M. H. Bosboom. Experimental validation of a pulse wave propagation model for predicting hemodynamics after vascular access surgery. J. Biomech. 45(9):1684, 2012.

    Article  Google Scholar 

  23. 23.

    Jansen, K. E., C. H. Whiting, and G. M. Hulbert. A generalized-\(\alpha\) method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput. Methods Appl. Mech. Eng. 190(3–4):305, 2000.

    MathSciNet  Article  MATH  Google Scholar 

  24. 24.

    Korteweg, D. Uber die fortpflanzungsgeschwindigkeit des schalles in elastiischen rohren. Ann. Phys. Chem. 5:52537, 1878.

    Google Scholar 

  25. 25.

    Lantz, J., J. Renner, and M. Karlsson. Wall shear stress in a subject specific human aorta—influence of fluid–structure interaction. Int. J. Appl. Mech. 3(4):759, 2011.

    Article  Google Scholar 

  26. 26.

    Markl, M., A. Frydrychowicz, S. Kozerke, M. Hope, and O. Wieben. 4D flow MRI. J. Magn. Reson. Imaging 36(5): 1015, 2012.

    Article  Google Scholar 

  27. 27.

    Morbiducci, U., D. Gallo, S. Cristofanelli, R. Ponzini, M. A. Deriu, G. Rizzo, and D. A. Steinman. A rational approach to defining principal axes of multidirectional wall shear stress in realistic vascular geometries, with application to the study of the influence of helical flow on wall shear stress directionality in aorta. J. Biomech. 48(6):899, 2015.

    Article  Google Scholar 

  28. 28.

    Morbiducci, U., 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. J. Biomech. 46(1):102, 2013.

    Article  Google Scholar 

  29. 29.

    Pasta, S., A. Rinaudo, A. Luca, M. Pilato, C. Scardulla, T. G. Gleason, and D. A. Vorp. Difference in hemodynamic and wall stress of ascending thoracic aortic aneurysms with bicuspid and tricuspid aortic valve. J. Biomech. 46(10):1729, 2013.

    Article  Google Scholar 

  30. 30.

    Pirola, S., Z. Cheng, O. A. Jarral, D. P. O’Regan, J. R. Pepper, T. Athanasiou, and X. Y. Xu. On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics. J. Biomech. 60:15, 2017.

    Article  Google Scholar 

  31. 31.

    Quicken, S., W. P. Donders, E. M. J. van Disseldorp, K. Gashi, B. M. E. Mees, F. N. van de Vosse, R. G. P. Lopata, T. Delhaas, and W. Huberts. Application of an adaptive polynomial chaos expansion on computationally expensive three-dimensional cardiovascular models for uncertainty quantification and sensitivity analysis. J. Biomech. Eng. 138(12):121010, 2016.

    Article  Google Scholar 

  32. 32.

    Sankaran, S., H. J. Kim, G. Choi, and C. A. Taylor. Uncertainty quantification in coronary blood flow simulations: impact of geometry, boundary conditions and blood viscosity. J. Biomech. 49:2540, 2016.

    Article  Google Scholar 

  33. 33.

    Sankaran, S., and A. L. Marsden. A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations. J. Biomech. Eng. 133(3):031001, 2011.

    Article  Google Scholar 

  34. 34.

    Sarrami-Foroushani, A., M. N. Esfahany, A. Nasiraei Moghaddam, H. Saligheh Rad, K. Firouznia, M. Shakiba, H. Ghanaati, I. D. Wilkinson, and A. F. Frangi. Velocity measurement in carotid artery: quantitative comparison of time-resolved 3D phase-contrast MRI and image-based computational fluid dynamics. Iran. J. Radiol. 12(4):e18286, 2015.

    Article  Google Scholar 

  35. 35.

    Schiavazzi, D. E., G. Arbia, C. Baker, A. M. Hlavacek, T. Y. Hsia, A. L. Marsden, and I. E. Vignon-Clementel. Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation. Int. J. Numer. Methods Biomed. Eng. 32(3):1, 2016.

    Article  Google Scholar 

  36. 36.

    Szajer, J., and K. Ho-Shon. A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations—a review. Magn. Reson. Imaging 48:62, 2018.

    Article  Google Scholar 

  37. 37.

    Taddei, F., S. Martelli, B. Reggiani, L. Cristofolini, and M. Viceconti. Finite-element modeling of bones from CT data: sensitivity to geometry and material uncertainties. IEEE Trans. Biomed. Eng. 53(11):2194, 2006.

    Article  Google Scholar 

  38. 38.

    Tran, J. S., D. E. Schiavazzi, A. B. Ramachandra, A. M. Kahn, and A. L. Marsden. Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations. Comput. Fluids 142:128, 2017.

    MathSciNet  Article  MATH  Google Scholar 

  39. 39.

    Updegrove, A., N. M. Wilson, J. Merkow, H. Lan, A. L. Marsden, and S. C. Shadden. SimVascular: an open source pipeline for cardiovascular simulation. Ann. Biomed. Eng. 45:1–17, 2016.

    Google Scholar 

  40. 40.

    Vignon-Clementel, I. E., C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput. Methods Biomech. Biomed. Eng. 13(5):625, 2010.

    Article  Google Scholar 

  41. 41.

    Wang, Y., D. Joannic, P. Juillion, A. Monnet, P. Delassus, A. Lalande, and J. F. Fontaine. Validation of the strain assessment of a phantom of abdominal aortic aneurysm: comparison of results obtained from magnetic resonance imaging and stereovision measurements. J. Biomech. Eng. (2018).

  42. 42.

    Westerhof, N., J. W. Lankhaar, and B. E. Westerhof. The arterial Windkessel. Med. Biol. Eng. Comput. 47(2):131, 2009.

    Article  Google Scholar 

  43. 43.

    Whiting, C. H., and K. E. Jansen. A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int. J. Numer. Methods Fluids 35(1):93, 2001.

    Article  MATH  Google Scholar 

  44. 44.

    Wuyts, F. L., V. J. Vanhuyse, G. J. Langewouters, W. F. Decraemer, E. R. Raman, and S. Buyle. Elastic properties of human aortas in relation to age and atherosclerosis: a structural model. Phys. Med. Biol. 40(10):1577, 1995.

    Article  Google Scholar 

  45. 45.

    Xiu, D., and G. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2):619, 2003.

    MathSciNet  Article  MATH  Google Scholar 

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The authors are grateful to Pau Simarro for his precious contribution in carrying out the numerical simulations.


No funding was received.

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Correspondence to Alessandro Mariotti.

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All procedures performed in studies involving human participants were in accordance with the ethical standards of the Institutional and/or National Research Committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. No animal studies were carried out for this study.

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Associate Editors Dr. David A. Steinman, Dr. Francesco Migliavacca, and Dr. Ajit P. Yoganathan oversaw the review of this article.

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Boccadifuoco, A., Mariotti, A., Capellini, K. et al. Validation of Numerical Simulations of Thoracic Aorta Hemodynamics: Comparison with In Vivo Measurements and Stochastic Sensitivity Analysis. Cardiovasc Eng Tech 9, 688–706 (2018).

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  • Aorta
  • Computational fluid dynamics
  • Magnetic resonance imaging
  • Validation
  • Polynomial chaos expansion