Annals of Biomedical Engineering

, Volume 40, Issue 3, pp 729–741 | Cite as

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

  • D. Gallo
  • G. De Santis
  • F. Negri
  • D. Tresoldi
  • R. Ponzini
  • D. Massai
  • M. A. Deriu
  • P. Segers
  • B. Verhegghe
  • G. Rizzo
  • U. Morbiducci
Article

Abstract

The purpose of this study is to investigate how the imposition of personalized, non-invasively measured blood flow rates as boundary conditions (BCs) influences image-based computational hemodynamic studies in the human aorta. We extracted from 4D phase-contrast MRI acquisitions of a healthy human (1) the geometry of the thoracic aorta with supra-aortic arteries and (2) flow rate waveforms at all boundaries. Flow simulations were carried out, and the implications that the imposition of different BC schemes based on the measured flow rates have on wall shear stress (WSS)-based indicators of abnormal flow were analyzed. Our results show that both the flow rate repartition among the multiple outlets of the aorta and the distribution and magnitude of the WSS-based indicators are strongly influenced by the adopted BC strategy. Keeping as reference hemodynamic model the one where the applied BC scheme allowed to obtain a satisfactory agreement between the computed and the measured flow rate waveforms, differences in WSS-based indicators up to 49% were observed when the other BC strategies were applied. In conclusion, we demonstrate that in subject-specific computational hemodynamics models of the human aorta the imposition of BC settings based on non-invasively measured flow rate waveforms influences indicators of abnormal flow to a large extent. Hence, a BCs set-up assuring realistic, subject-specific instantaneous flow rate distribution must be applied when BCs such as flow rates are prescribed.

Keywords

Aortic arch Magnetic resonance imaging Patient specific Computational fluid dynamics Wall shear stress Outflow boundary conditions 

Abbreviations

AAo

Ascending aorta

BC

Boundary condition

BCA

Brachiocephalic artery

CFD

Computational fluid dynamics

LCCA

Left common carotid artery

LSA

Left subclavian artery

OSI

Oscillatory shear index

PC-MRI

Phase-contrast magnetic resonance imaging

RRT

Relative residence time

TAWSS

Time-averaged wall shear stress

WSS

Wall shear stress

Supplementary material

10439_2011_431_MOESM1_ESM.pdf (106 kb)
Supplementary material 1 (PDF 105 kb)

References

  1. 1.
    Antiga, L., M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman. An image-based modelling framework for patient-specific computational haemodynamics. Med. Biol. Eng. Comput. 46(11):1097–1112, 2008.PubMedCrossRefGoogle Scholar
  2. 2.
    Augst, A. D., D. C. Barratt, A. D. Hughes, S. A. Thom, and X. Y. Xu. Various issues relating to computational fluid dynamics simulations of carotid bifurcation flow based on models reconstructed from three-dimensional ultrasound images. Proc. Inst. Mech. Eng. H 217(5):393–403, 2003.PubMedGoogle Scholar
  3. 3.
    Barakat, A. I., T. Karino, and C. K. Colton. Microcinematographic studies of flow patterns in the excised rabbit aorta and its major branches. Biorheology 34(3):195–221, 1997.PubMedCrossRefGoogle Scholar
  4. 4.
    Boussel, L., V. Rayz, G. Acevedo-Bolton, M. T. Lawton, R. Higashida, W. S. Smith, W. L. Young, and D. Saloner. Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics. Magn. Reson. Med. 61(2):409–417, 2009.Google Scholar
  5. 5.
    Cebral, J. R., M. A. Castro, S. Appanaboyina, C. M. Putman, D. Millan, and A. F. Frangi. Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity. IEEE Trans. Med. Imaging 24(4):457–467, 2004.CrossRefGoogle Scholar
  6. 6.
    De Santis, G., M. De Beule, P. Segers, P. Verdonck, and B. Verhegghe. Patient-specific computational haemodynamics: generation of structured and conformal hexahedral meshes from triangulated surfaces of vascular bifurcations. Comput. Methods Biomech. Biomed. Eng. doi: 10.1080/10255842.2010.495066, 2011.
  7. 7.
    De Santis, G., P. Mortier, M. De Beule, P. Segers, P. Verdonck, and B. Verhegghe. Patient-specific computational fluid dynamics: structured mesh generation from coronary angiography. Med. Biol. Eng. Comput. 48(4):371–380, 2010.PubMedCrossRefGoogle Scholar
  8. 8.
    Del Gaudio, C., U. Morbiducci, and M. Grigioni. Time dependent non-newtonian numerical study of the flow field in a realistic model of the aortic arch. Int. J. Artif. Organs. 29(7):709–718, 2006.PubMedGoogle Scholar
  9. 9.
    Formaggia, L., J. F. Gerbeau, F. Nobile, and A. Quarteroni. On the coupling of 3D and 1D navier-stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191(6-7):561–582, 2001.CrossRefGoogle Scholar
  10. 10.
    Formaggia, L., J. F. Gerbeau, F. Nobile, and A. Quarteroni. Numerical treatment of defective boundary conditions for the Navier–Stokes equation. SIAM J. Numer. Anal. 40:376–401, 2002.CrossRefGoogle Scholar
  11. 11.
    Formaggia, L., A. Veneziani, and C. Vergara. A new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics. SIAM J. Numer. Anal. 46(6):2769–2794, 2008.CrossRefGoogle Scholar
  12. 12.
    Grinberg, L., and G. E. M. Karniadakis. Outflow boundary conditions for arterial networks with multiple outlets. Ann. Biomed. Eng. 36(9):1496–1514, 2008.PubMedCrossRefGoogle Scholar
  13. 13.
    Groen, H. C., L. Simons, Q. J. van den Bouwhuijsen, E. M. Bosboom, F. J. Gijsen, A. G. van der Giessen, F. N. van de Fosse, A. Hofman, A. F. van der Steen, J. C. Witteman, A. van der Lugt, and J. J. Wentzel. MRI-based quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries. J. Biomech. 43(12):2332–2338, 2010.PubMedCrossRefGoogle Scholar
  14. 14.
    He, X., and D. N. Ku. Pulsatile flow in the human left coronary artery bifurcation: average conditions. ASME J. Biomech. Eng. 118(1):74–82, 1996.CrossRefGoogle Scholar
  15. 15.
    Heywood, J., R. Rannacher, and S. Turek. Artificial boundary and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22:325–352, 1996.CrossRefGoogle Scholar
  16. 16.
    Himburg, H. A., D. M. Grzybowski, A. Hazel, J. A. LaMack, X. M. Li, and M. H. Friedman. Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability. Am. J. Physiol. Heart Circ. Physiol. 286(5):H1916–H1922, 2004.PubMedCrossRefGoogle Scholar
  17. 17.
    Kim, H. J., C. A. Figueroa, T. J. R. Hughes, K. E. Jansen, and C. A. Taylor. Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow. Comput. Methods Appl. Mech. Eng. 198:3551–3556, 2009.CrossRefGoogle Scholar
  18. 18.
    Ku, D. N., D. P. Giddens, C. K. Zarins, and S. Glagov. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low and oscillating shear stress. Arteriosclerosis 5(3):293–302, 1985.PubMedCrossRefGoogle Scholar
  19. 19.
    Lee, S. W., L. Antiga, J. D. Spence, and D. A. Steinman. Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39(8):2341–2347, 2008.PubMedCrossRefGoogle Scholar
  20. 20.
    Lee, S. W., L. Antiga, and D. A. Steinman. Correlations among indicators of disturbed flow at the normal carotid bifurcation. ASME J. Biomech. Eng. 131(6):061013, 7 pp, 2009.Google Scholar
  21. 21.
    Liu, X., Y. Fan, and X. Deng. Effect of spiral flow on the transport of oxygen in the aorta: a numerical study. Ann. Biomed. Eng. 38(3):917–926, 2009.PubMedCrossRefGoogle Scholar
  22. 22.
    Liu, X., Y. Fan, X. Deng, and F. Zhan. Effect of non-newtonian and pulsatile blood flow on mass transport in the human aorta. J. Biomech. 44(6):1123–1131, 2011.PubMedCrossRefGoogle Scholar
  23. 23.
    Liu, X., F. Pu, Y. Fan, X. Deng, D. Li, and S. Li. A numerical study on the flow of blood and the transport of LDL in the human aorta: the physiological significance of the helical flow in the aortic arch. Am. J. Physiol. Heart Circ. Physiol. 297:H163–H170, 2009.PubMedCrossRefGoogle Scholar
  24. 24.
    Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamic shear stress and its role in atherosclerosis. JAMA 282:2035–2042, 1999.PubMedCrossRefGoogle Scholar
  25. 25.
    Moore, J. E., C. Xu, S. Glagov, C. K. Zarins, and D. N. Ku. Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 110(2):225–240, 1994.PubMedCrossRefGoogle Scholar
  26. 26.
    Morbiducci, U., D. Gallo, D. Massai, R. Ponzini, M. A. Deriu, L. Antiga, A. Redaelli, and F. M. Montevecchi. On the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation. J. Biomech. 44:2427–2438, 2011.PubMedCrossRefGoogle Scholar
  27. 27.
    Morbiducci, U., D. Gallo, R. Ponzini, D. Massai, L. Antiga, A. Redaelli, and F. M. Montevecchi. Quantitative analysis of bulk flow in image-based haemodynamic models of the carotid bifurcation: the influence of outflow conditions as test case. Ann. Biomed. Eng. 38(12):3688–3705, 2010.PubMedCrossRefGoogle Scholar
  28. 28.
    Morbiducci, U., R. Ponzini, G. Rizzo, M. Cadioli, A. Esposito, F. M. Montevecchi, and A. Redaelli. Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study. Biomech. Model. Mechanobiol. 10:339–355, 2011.PubMedCrossRefGoogle Scholar
  29. 29.
    Morbiducci, U., D. Gallo, D. Massai, F. Consolo, R. Ponzini, L. Antiga, C. Bignardi, M. A. Deriu, and A. Redaelli. Outflow conditions for image-based haemodynamic models of the carotid bifurcation. Implications for indicators of abnormal flow. J. Biomech. Eng. 132:091005, 11 pp, 2010.Google Scholar
  30. 30.
    Morbiducci, U., R. Ponzini, G. Rizzo, M. Cadioli, A. Esposito, F. De Cobelli, A. Del Maschio, F. M. Montevecchi, and A. Redaelli. In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast MRI. Ann. Biomed. Eng. 37:516–531, 2009.Google Scholar
  31. 31.
    Olufsen, M. S. Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. 276:H257–H268, 1999.PubMedGoogle Scholar
  32. 32.
    Ponzini, R., M. Lemma, U. Morbiducci, F. M. Montevecchi, and A. Redaelli. Doppler derived quantitative flow estimate in coronary artery bypass graft: a computational multi-scale model for the evaluation of the current theory. Med. Eng. Phys. 30(7):809–816, 2008.PubMedCrossRefGoogle Scholar
  33. 33.
    Quarteroni, A., S. Ragni, and A. Veneziani. Coupling between lumped and distributed models for blood flow problems. Comput. Visual. Sci. 4:111–124, 2001.CrossRefGoogle Scholar
  34. 34.
    Shahcheraghi, N., H. A. Dwyer, A. Y. Cheer, A. I. Barakat, and T. Rutaganira. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J. Biomech. Eng. 124:378–388, 2002.PubMedCrossRefGoogle Scholar
  35. 35.
    Spilker, R. L., and C. A. Taylor. Tuning multidomain hemodynamic simulations to match physiological measurements. Ann. Biomed. Eng. 38(8):2635–2648, 2010.PubMedCrossRefGoogle Scholar
  36. 36.
    Tan, F. P. P., A. Borghi, R. H. Mohiaddin, N. B. Wood, S. Thom, and X. Y. Xu. Analysis of flow patterns in a patient-specific thoracic aneurysm model. Comput. Struct. 87:680–690, 2009.CrossRefGoogle Scholar
  37. 37.
    Taylor, C. A., C. P. Cheng, L. A. Espinosa, B. T. Tang, D. Parker, and R. J. Herfkens. In vivo quantification of blood flow and wall shear stress in the human abdominal aorta during lower limb exercise. Ann. Biomed. Eng. 30:402–408, 2002.Google Scholar
  38. 38.
    Trachet, B., M. Renard, G. De Santis, S. Staelens, J. De Backer, L. Antiga, B. Loeys, and P. Segers. An integrated framework to quantitatively link mouse-specific hemodynamics to aneurysm formation in angiotensin II—infused ApoE−/− mice. Ann. Biomed. Eng. doi: 10.1007/s10439-011-0330-5, 2011.
  39. 39.
    Van der Giessen, A. G., H. C. Groen, P. A. Doriot, P. J. de Feyter, A. F. van der Steen, F. N. van de Fosse, J. J. Wentzel, and F. J. Gijsen. The influence of boundary conditions on wall shear stress distribution in patient specific coronary trees. J. Biomech. 44(6):1089–1095, 2011.PubMedCrossRefGoogle Scholar
  40. 40.
    Veneziani, A., and C. Vergara. Flow rate defective boundary conditions in haemodynamics simulations. Int. J. Numer. Methods Fluids 47(8–9):803–816, 2005.CrossRefGoogle Scholar
  41. 41.
    Vignon-Clementel, I. E., C. A. Figueroa, K. E. Jansenc, and C. A. Taylor. Outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 195:3776–3796, 2006.CrossRefGoogle Scholar
  42. 42.
    Wen, C., A. Yang, L. Tseng, and J. Chai. Investigation of pulsatile flowfield in healthy thoracic aorta models. Ann. Biomed. Eng. 38(2):391–402, 2010.PubMedCrossRefGoogle Scholar
  43. 43.
    Westerhof, N., J. W. Lankhaar, and B. E. Westerhof. The arterial windkessel. Med. Biol. Eng. Comput. 47(2):131–141, 2009.PubMedCrossRefGoogle Scholar
  44. 44.
    White, F. M. Viscous Fluid Flow. New York: McGraw-Hill, 1979.Google Scholar

Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  • D. Gallo
    • 1
  • G. De Santis
    • 2
  • F. Negri
    • 1
  • D. Tresoldi
    • 3
  • R. Ponzini
    • 4
  • D. Massai
    • 1
  • M. A. Deriu
    • 1
  • P. Segers
    • 2
  • B. Verhegghe
    • 2
  • G. Rizzo
    • 3
  • U. Morbiducci
    • 1
  1. 1.Department of MechanicsPolitecnico di TorinoTurinItaly
  2. 2.IBiTech-bioMMedaGhent UniversityGhentBelgium
  3. 3.IBFM, Research National CouncilMilanItaly
  4. 4.CILEA, Consorzio Interuniversitario per l’Elaborazione e l’AutomazioneMilanItaly

Personalised recommendations