Biomechanics and Modeling in Mechanobiology

, Volume 10, Issue 3, pp 339–355 | Cite as

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

  • Umberto Morbiducci
  • Raffaele Ponzini
  • Giovanna Rizzo
  • Marcello Cadioli
  • Antonio Esposito
  • Franco Maria Montevecchi
  • Alberto Redaelli
Original Paper


The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.


4D phase-contrast MRI Perfusion Spiral flow Fluid mechanics Aortic arch Hemodynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

10237_2010_238_MOESM1_ESM.mpeg (532 kb)
ESM 1 (MPEG 532 kb)


  1. Amirbekian S, Long RC, Consolini MA, Suo J, Willett NJ, Fielden SW, Giddens DP, Taylor WR, Oshinski JN (2009) In vivo assessment of blood flow patterns in abdominal aorta of mice with MRI: implications for AAA localization. Am J Physiol Heart Circ Physiol 297: H1290–H1295CrossRefGoogle Scholar
  2. Baciewicz FA, Penney DG, Marinelli WA, Marinelli R (1991) Torsional ventricular motion and rotary blood flow. What is the clinical significance. Card Chron 5: 1–8Google Scholar
  3. Bellhouse BJ, Talbot L (1969) The fluid mechanics of the aortic valve. J Fluid Mech 35: 721–736CrossRefGoogle Scholar
  4. Bera AK, Jarque CM (1981) Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence. Econ Lett 7(4): 313–318CrossRefGoogle Scholar
  5. Bogren HG, Buonocore MH (1999) 4D magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects. J Magn Reson Imaging 10: 861–869CrossRefGoogle Scholar
  6. Buonocore MH, Bogren HG (1999) Analysis of flow patterns using MRI. Int J Card Imaging 15: 99–103CrossRefGoogle Scholar
  7. Caro CG, Doorly DJ, Tarnawski M, Scott KT, Long Q, Dumoulin CL (1996) Non-planar curvature and branching of arteries and non-planar-type flow. Proc R Soc Lond A 452: 185–197MathSciNetMATHCrossRefGoogle Scholar
  8. Chandran KB (1993) Flow dynamics in the human aorta. J Biomech Eng 115: 611–616CrossRefGoogle Scholar
  9. Chen Q, Chen S, Eyink GL (2003) The joint cascade of energy and helicity in three-dimensional turbulence. Phys Fluids 15: 361–374MathSciNetCrossRefGoogle Scholar
  10. Chen ZS, Fan YB, Deng XY, Xu Z (2009) Swirling flow can suppress flow disturbances in endovascular stents: a numerical study. ASAIO J 55(6): 543–549CrossRefGoogle Scholar
  11. Darmofal DL, Haimes R (1996) An analysis of 3D particle path integration algorithms. J Comput Phys 123: 182–195MATHCrossRefGoogle Scholar
  12. David L, Esnault A, Calluaud D (2002) Comparison of techniques of interpolation for 2D and 3D velocimetry. In: Proceedings of the eleventh international symposium on applications of laser techniques to fluid mechanics, LisbonGoogle Scholar
  13. Fan Y, Xu Z, Jiang W, Deng X, Wang K, Sun A (2008) An S-type bypass can improve the hemodynamics in the bypassed arteries and suppress intimal hyperplasia along the host artery floor. J Biomech 41: 2498–2505CrossRefGoogle Scholar
  14. Firmin D, Keegan J (2001) Navigator echoes in cardiac magnetic resonance. J Cardiovasc Magn Reson 3: 183–193CrossRefGoogle Scholar
  15. Frazin LJ, Lanza G, Vonesh M, Khasho F, Spitzzeri C, McGee S, Mehlman D, Chandran KB, Talano J, McPherson D (1990) Functional chiral asymmetry in descending thoracic aorta. Circulation 82: 1985–1994Google Scholar
  16. Frydrychowicz A, Harloff A, Jung B, Zaitsev M, Weigang E, Bley TA, Langer M, Hennig J, Markl M (2007) Time-resolved, 3-dimensional magnetic resonance flow analysis at 3 T: visualization of normal and pathological aortic vascular haemodynamics. J Comput Assist Tomogr 31: 9–15CrossRefGoogle Scholar
  17. Frydrychowicz A, Arnold R, Hirtler D, Schlensak C, Stalder AF, Hennig J, Langer M, Markl M (2008a) Multidirectional flow analysis by cardiovascular magnetic resonance in aneurysm development following repair of aortic coarctation. J Cardiovasc Magn Reson 10(1): 30CrossRefGoogle Scholar
  18. Frydrychowicz A, Arnold R, Harloff A, Schlensak C, Hennig J, Langer M, Markl M (2008b) Images in cardiovascular medicine. In vivo dimensional flow connectivity mapping after extracardiac total cavopulmonary connection. Circulation 118: e16–e17CrossRefGoogle Scholar
  19. Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO (2006) Optimal vortex formation as an index of cardiac health. Proc Natl Acad Sci USA 103: 6305–6308CrossRefGoogle Scholar
  20. Grigioni M, Daniele C, Morbiducci U, Del Gaudio C, D’Avenio G, Balducci A, Barbaro V (2005) A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending. J Biomech 38: 1375–1386CrossRefGoogle Scholar
  21. Hope TA, Markl M, Wigström L, Alley MT, Miller DC, Herfkens RJ (2007) Comparison of flow patterns in ascending aortic aneurysms and volunteers using four-dimensional magnetic resonance velocity mapping. J Magn Reson Imaging 26: 1471–1479CrossRefGoogle Scholar
  22. Houston JG, Gandy SJ, Sheppard DG, Dick JB, Belch JJ, Stonebridge PA (2003) Two-dimensional flow quantitative MRI of aortic arch blood flow patterns: Effect of age, sex, and presence of carotid atheromatous disease on prevalence of spiral blood flow. J Magn Reson Imaging 18: 169–174CrossRefGoogle Scholar
  23. Kilner PJ, Yang GZ, Mohiaddin RH, Firmin DN, Longmore DB (1993) Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation 88: 2235–2247Google Scholar
  24. Kilner PJ, Yang GZ, Wilkes AJ, Mohiaddin RH, Firmin DN, Yacoub MH (2000) Asymmetric redirection of flow through the heart. Nature 404: 759–761CrossRefGoogle Scholar
  25. Kolmogorov AN (1956) Foundations of the theory of probability, 2nd English edn. Chelsea Publishing Company, New York (translation edited by Nathan Morrison)Google Scholar
  26. Ku DN, Giddens DP (1983) Pulsatile flow in a model carotid bifurcation. Arteriosclerosis 3: 31–39Google Scholar
  27. Liu X, Pu F, Fan Y, Deng X, Li D, Li S (2009) 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–H170CrossRefGoogle Scholar
  28. Malek AM, Alper SL, Izumo S (1999) Hemodynamic shear stress and its role in atherosclerosis. JAMA 282: 2035–2042CrossRefGoogle Scholar
  29. Markl M, Draney MT, Hope MD, Levin JM, Chan FP, Alley MT, Pelc NJ, Herfkens RJ (2004) Time-resolved 3-dimensional velocity mapping in the thoracic aorta: visualization of 3-directional blood flow patterns in healthy volunteers and patients. J Comput Assist Tomogr 28: 459–468CrossRefGoogle Scholar
  30. Markl M, Harloff A, Föll D, Langer M, Hennig J, Frydrychowicz A (2007) Sclerotic aortic valve: flow-sensitive 4-dimensional magnetic resonance imaging reveals 3 distinct flow-pattern changes. Circulation 116: e336–e337CrossRefGoogle Scholar
  31. Marsden AL, Feinstein JA, Taylor CA (2008) A computational framework for derivative-free optimization of cardiovascular geometries. Comput Methods Appl Mech Eng 197: 1890–1905MathSciNetMATHCrossRefGoogle Scholar
  32. Mininni PD, Alexakis A, Pouquet A (2006) Large scale flow effects, energy transfer, and self-similarity on turbulence. Phys Rev E 74: 016303CrossRefGoogle Scholar
  33. Moffatt HK (1969) The degree of knottedness of tangled vortex lines. J Fluid Mech 36: 17–29CrossRefGoogle Scholar
  34. Moffatt HK (1990) The energy spectrum of knots and links. Nature 347: 367–369CrossRefGoogle Scholar
  35. Moffatt HK, Tsinober A (1992) Helicity in laminar and turbulent flow. Ann Rev Fluid Mech 24: 281–312MathSciNetCrossRefGoogle Scholar
  36. Morbiducci U, Ponzini R, Grigioni M, Redaelli A (2007a) Helical flow as fluid dynamic signature for atherogenesis in aortocoronary bypass. A numeric study. J Biomech 40: 519–534CrossRefGoogle Scholar
  37. Morbiducci U, Lemma M, Ponzini R, Boi A, Bondavalli L, Antona C, Montevecchi FM, Redaelli A (2007b) Does flow dynamics of the magnetic vascular coupling for distal anastomosis in coronary artery bypass grafting contribute to the risk of graft failure. Int J Artif Organs 30: 628–639Google Scholar
  38. Morbiducci U, Ponzini R, Rizzo G, Cadioli M, Esposito A, De Cobelli F, Del Maschio A, Montevecchi FM, Redaelli A (2009a) In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast MRI. Ann Biomed Eng 37: 516–531CrossRefGoogle Scholar
  39. Morbiducci U, Ponzini R, Nobili M, Massai D, Montevecchi FM, Bluestein D, Redaelli A (2009b) Blood damage safety of prosthetic heart valves. Shear induced platelet activation and local flow dynamics: a fluid-structure interaction approach. J Biomech 42(12): 1952–1960CrossRefGoogle Scholar
  40. Morbiducci U, Gallo D, Ponzini R, Massai D, Antiga L, Redaelli A, Montevecchi FM (2010) 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. doi:10.1007/s10439-010-0099-y
  41. Ponzini R, Morbiducci U, Iannaccone F, Rizzo G, Cadioli M, Vismara R, Redaelli A (2009) Synthetic 4D phase contrast MRI datasets: a CFD-based approach for the validation of advanced fluid-dynamics calculations in vivo. In: Tavares JM, Natal Jorge RM (eds) Proceedings of VIPIMAGE 2009, Second Ecomas Thematic Conference on Computational Vision and Medical Image Processing, Porto. CRC Press, Taylor & Francis Group, pp 195–199Google Scholar
  42. Ricca RL (2009) Structural complexity and dynamical systems. In: Ricca RL (eds) Lectures on topological fluid mechanics. Lecture notes in mathematics. Springer, Berlin, pp 167–186CrossRefGoogle Scholar
  43. Seed WA, Wood NB (1971) Velocity patterns in the aorta. Cardiovasc Res 5: 319–330CrossRefGoogle Scholar
  44. Segadal L, Matre K (1987) Blood velocity distribution in the human ascending aorta. Circulation 76: 90–100Google Scholar
  45. Shadden SC, Taylor CA (2008) Characterization of coherent structures in the cardiovascular system. Ann Biomed Eng 36(7): 1152–1162CrossRefGoogle Scholar
  46. Shadden SC, Astorino A, Gerbeau JF (2010) Computational analysis of an aortic valve jet with Lagrangian coherent structures. Chaos 20: 017512MathSciNetCrossRefGoogle Scholar
  47. Spilt A, Box FM, van Geest RJ, Reiber JH, Kunz P, Kamper AM, Blauw GJ, van Buchem MA (2002) Reproducibility of total cerebral blood flow measurements using phase contrast magnetic resonance imaging. J Magn Reson Imaging 16: 1–5CrossRefGoogle Scholar
  48. Steinman DA (2000) Simulated pathline visualization of computed periodic blood flow patterns. J Biomech 33: 623–628CrossRefGoogle Scholar
  49. Stonebridge PA, Brophy CM (1991) Spiral laminar flow in arteries. Lancet 338: 1360–1361CrossRefGoogle Scholar
  50. Stonebridge PA, Hoskins PR, Allan PL, Belch JF (1996) Spiral laminar flow in vivo. Clin Sci (Lond) 91: 17–21Google Scholar
  51. Sun A, Fan Y, Deng X (2009) Numerical investigation of blood flow in the distal end of an axis-deviated arterial bypass model. Biorheology 46: 83–92Google Scholar
  52. Teitelbaum T, Mininni PD (2009) Effect of helicity and rotation on the free decay of turbulent flows. Phys Rev Lett 103: 014501CrossRefGoogle Scholar
  53. Tsinober A, Levich E (1983) On the helical nature of three dimensional coherent structures in turbulent flows. Phys Lett 99: 321–323CrossRefGoogle Scholar
  54. Weigang E, Kari FA, Beyersdorf F, Luehr M, Etz CD, Frydrychowicz A, Harloff A, Markl M (2008) Flow-sensitive four-dimensional magnetic resonance imaging: flow patterns in ascending aortic aneurysms. Eur J Cardiothorac Surg 34: 11–16CrossRefGoogle Scholar
  55. Wigström L, Ebbers T, Fyrenius A, Karlsson M, Engvall J, Wranne B, Bolger AF (1999) Particle trace visualization of intracardiac flow using time-resolved 3D phase contrast MRI. Magn Reson Med 41: 793–799CrossRefGoogle Scholar
  56. Yashiro K, Shiratori H, Hamada H (2007) Haemodynamics determined by a genetic programme govern asymmetric development of the aortic arch. Nature 450: 285–288CrossRefGoogle Scholar
  57. Yearwood TL, Chandran KB (1982) Physiological pulsatile flow experiments in a model of the human aortic arch. J Biomech 15(9): 683–704CrossRefGoogle Scholar
  58. Zhan F, Fan Y, Deng X (2010) Swirling flow created in a glass tube suppressed platelet adhesion to the surface of the tube: its implication in the design of small-caliber arterial grafts. Thromb Res 125(5): 413–418CrossRefGoogle Scholar
  59. Zheng T, Fan Y, Xiong Y, Jiang W, Deng X (2009) Hemodynamic performance study on small diameter helical grafts. ASAIO J 55: 192–199CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Umberto Morbiducci
    • 1
  • Raffaele Ponzini
    • 2
  • Giovanna Rizzo
    • 3
  • Marcello Cadioli
    • 4
  • Antonio Esposito
    • 5
  • Franco Maria Montevecchi
    • 1
  • Alberto Redaelli
    • 6
  1. 1.Department of MechanicsPolitecnico di TorinoTurinItaly
  2. 2.CILEA, Interuniversity ConsortiumMilanItaly
  3. 3.Istituto di Bioimmagini e Fisiologia MolecolareResearch National CouncilMilanItaly
  4. 4.Philips Medical SystemsMilanItaly
  5. 5.Department of RadiologyScientific Institute H S RaffaeleMilanItaly
  6. 6.Department of BioengineeringPolitecnico di MilanoMilanItaly

Personalised recommendations