Skip to main content
SpringerLink
Log in

Effect of Spiral Flow on the Transport of Oxygen in the Aorta: A Numerical Study

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

To test the hypothesis that the spiral flow pattern in the human aorta may play a beneficial role in the transport of oxygen, hence sparing the ascending aorta from atherosclerosis, a comparative study on the distribution of oxygen flux to the arterial wall was carried out numerically for three aorta models. The first one (Model 1) was constructed based on MRI images of a human aorta acquired in vivo. The second (Model 2) was made the same as Model 1 but without the three branches. The third (Model 3) was similar to Model 2 only with the aortic torsion removed. The results showed that without the torsion, the flow fashion in Model 3 was very different from the swirling flows in Models 1 and 2 and exhibited the typical characteristics of Dean flow with two symmetrical helical structures. In Models 1 and 2, the average Sherwood number (Sh) in the ascending aorta with the presence of a strong spiral flow was not only higher than that in the inner wall of the descending aorta where the spiral flow faded out, but also generally higher than that in Model 3. The comparison between Models 2 and 3 demonstrated that the averaged Sh from ascending aorta to aortic arch was relatively higher for Model 2. In conclusion, the spiral or swirling flow may have certain physiological significance in the aorta and play a positive role in the transport of oxygen by enhancing oxygen flux to the arterial wall.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  1. Back, L. H., J. R. Radbill, and D. W. Crawford. Analysis of oxygen transport from pulsatile viscous blood flow to diseased coronary arteries of man. J. Biomech. 10:763–774, 1977.

    Article  CAS  PubMed  Google Scholar 

  2. Berceli, S. A., V. S. Warty, R. A. Sheppeck, W. A. Mandarino, S. K. Tanksale, and H. S. Borovetz. Hemodynamics and low density lipoprotein metabolism. Rates of low density lipoprotein incorporation and degradation along medial and lateral walls of the rabbit aorto-iliac bifurcation. Arteriosclerosis 10:686–694, 1990.

    CAS  PubMed  Google Scholar 

  3. Bogren, H. G., and M. H. Buonocore. 4D magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects. J. Magn. Reson. Imaging 10:861–869, 1999.

    Article  CAS  PubMed  Google Scholar 

  4. Buerk, D. G., and T. K. Goldstick. Arterial wall oxygen consumption rate varies spatially. Am. J. Physiol. 243:H948–H959, 1982.

    CAS  PubMed  Google Scholar 

  5. Caro, C. G., D. J. Doorly, M. Tarnawski, K. T. Scott, Q. Long, and C. L. Dumoulin. Non-planar curvature and branching of arteries and non-planar-type flow. Proc. Roy. Soc. Lond. A 452:185–197, 1996.

    Article  Google Scholar 

  6. Caro, C. G., T. J. Pedley, R. C. Schroter, and W. A. Seed. The Mechanics of the Circulation. Oxford: Oxford University Press, 1978.

    Google Scholar 

  7. Coppola, G., and C. Caro. Oxygen mass transfer in a model three-dimensional artery. J. R. Soc. Interface 5:1067–1075, 2008.

    Article  CAS  PubMed  Google Scholar 

  8. Deng, X. Y., Y. Marois, T. How, Y. Merhi, M. King, R. Guidoin, and T. Karino. Luminal surface concentration of lipoprotein (LDL) and its effect on the wall uptake of cholesterol by canine carotid arteries. J. Vasc. Surg. 21:135–145, 1995.

    Article  CAS  PubMed  Google Scholar 

  9. Friedman, M. H. Geometric risk factors for arteriosclerosis. Johns Hopkins APL Technical Digest (Appl. Phys. Lab.) 4:85–95, 1983.

    Google Scholar 

  10. Friedman, M. H., C. B. Bargeron, D. D. Duncan, G. M. Hutchins, and F. F. Mark. Effects of arterial compliance and non-Newtonian rheology on correlations between intimal thickness and wall shear. J. Biomech. Eng. 114:317–320, 1992.

    Article  CAS  PubMed  Google Scholar 

  11. Fung, Y. C. Biomechanics: Circulation (2nd ed.). New York: Springer, p. 108, 1997.

    Google Scholar 

  12. Gould, S. E. Pathology of the Heart and Blood Vessels. Illinois: Charles & Thomas, pp. 953–960, 1968.

    Google Scholar 

  13. Hope, T. A., M. Markl, L. Wigström, M. T. Alley, D. C. Miller, and R. J. Herfkens. Comparison of flow patterns in ascending aortic aneurysms and volunteers using four-dimensional magnetic resonance velocity mapping. J. Magn. Reson. Imaging 26:1471–1479, 2007.

    Article  PubMed  Google Scholar 

  14. Houston, J. G., S. J. Gandy, D. G. Sheppard, J. B. Dick, J. J. Belch, and P. A. Stonebridge. 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 18:169–174, 2003.

    Article  PubMed  Google Scholar 

  15. Hueper, W. C. Arteriosclerosis. Arch. Path. 39:162–182, 1945.

    Google Scholar 

  16. Hultén, L. M., and M. Levin. The role of hypoxia in atherosclerosis. Curr. Opin. Lipidol. 20:409–414, 2009.

    Article  PubMed  Google Scholar 

  17. Jin, S., J. Oshinski, and D. P. Giddens. Effects of wall motion and compliance on flow patterns in the ascending aorta. J. Biomech. Eng. 125:347–354, 2003.

    Article  PubMed  Google Scholar 

  18. Karino, T., T. Asakura, and S. Mabuchi. Role of hemodynamic factors in atherogenesis. Adv. Exp. Med. Biol. 242:51–57, 1988.

    CAS  PubMed  Google Scholar 

  19. Kilner, P. J., G. Z. Yang, R. H. Mohiaddin, D. N. Firmin, and D. B. Longmore. Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation 88:2235–2247, 1993.

    CAS  PubMed  Google Scholar 

  20. Kjeldsen, K., P. Astrup, and J. Wanstrup. Reversal of rabbit atheromatosis by hyperoxia. J. Atheroscler. Res. 10:173–178, 1969.

    Article  CAS  PubMed  Google Scholar 

  21. Kjeldsen, K., J. Wanstrup, and P. Astrup. Enhancing influence of arterial hypoxia on the development of atheromatosis in cholesterol-fed rabbits. J. Atheroscler. Res. 8:835–845, 1968.

    Article  CAS  PubMed  Google Scholar 

  22. Kolandavel, M. K., E. T. Fruend, S. Ringgaard, and P. G. Walker. The effects of time varying curvature on species transport in coronary arteries. Ann. Biomed. Eng. 34:1820–1832, 2006.

    Article  PubMed  Google Scholar 

  23. Ku, D. N. Blood flow in arteries. Annu. Rev. Fluid Mech. 29:399–434, 1997.

    Article  Google Scholar 

  24. Lattimore, J. D., I. Wilcox, S. Nakhla, M. Langenfeld, W. Jessup, and D. S. Celermajer. Repetitive hypoxia increases lipid loading in human macrophages—a potentially atherogenic effect. Atherosclerosis 179:255–259, 2005.

    Article  CAS  PubMed  Google Scholar 

  25. Levy, Y., D. Degani, and A. Seginer. Graphical visualization of vortical flows by means of helicity. AIAA J. 28:1347–1352, 1990.

    Article  Google Scholar 

  26. Liu, X., F. Pu, Y. B. Fan, X. Y. Deng, D. Y. Li, and S. Y. 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.

    Article  CAS  PubMed  Google Scholar 

  27. Ma, P., X. Li, and D. N. Ku. Heat and mass transfer in a separated flow region for high Prandtl and Schmidt numbers under pulsatile flow conditions. Int. J. Heat Mass Transfer 37:2723–2736, 1994.

    Article  CAS  Google Scholar 

  28. Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamic shear stress and its role in atherosclerosis. JAMA 282:2035–2042, 1999.

    Article  CAS  PubMed  Google Scholar 

  29. Matsushita, H., R. Morishita, T. Nata, M. Aoki, H. Nakagami, Y. Taniyama, K. Yamamoto, J. Higaki, K. Yasufumi, and T. Ogihara. Hypoxia-induced endothelial apoptosis through nuclear factor-kappaB (NF-kappaB)-mediated bcl-2 suppression: in vivo evidence of the importance of NF-kappaB in endothelial cell regulation. Circ. Res. 12:974–981, 2000.

    Google Scholar 

  30. Moffatt, H. K. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 36:17–29, 1969.

    Article  Google Scholar 

  31. Moore, J. A., and C. R. Ethier. Oxygen mass transfer calculations in large arteries. J. Biomech. Eng. 119:469–475, 1997.

    Article  CAS  PubMed  Google Scholar 

  32. Moore, J. E., S. E. Maiser, Jr., D. N. Ku, and P. Boesiger. Hemodynamics in the abdominal aorta: a comparison of in vitro and in vivo measurements. J. Appl. Physiol. 76:1520–1527, 1994.

    PubMed  Google Scholar 

  33. Morbiducci, U., R. Ponzini, M. Grigioni, and A. Redaelli. Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study. J. Biomech. 40:519–534, 2007.

    Article  PubMed  Google Scholar 

  34. Nerem, R. M. Vascular fluid mechanics, the arterial wall, and atherosclerosis. J. Biomech. Eng. 114:274–282, 1992.

    Article  CAS  PubMed  Google Scholar 

  35. O’Callaghan, S., M. Walsh, and T. McGloughlin. Numerical modelling of Newtonian and non-Newtonian representation of blood in a distal end-to-side vascular bypass graft anastomosis. Med. Eng. Phys. 28:70–74, 2006.

    Article  PubMed  Google Scholar 

  36. Ogawa, S., H. Gerlach, C. Esposito, A. Pasagian-Macaulay, J. Brett, and D. Stern. Hypoxia modulates the barrier and coagulant function of cultured bovine endothelium. Increased monolayer permeability and induction of procoagulant properties. J. Clin. Invest. 85:1090–1098, 1990.

    Article  CAS  PubMed  Google Scholar 

  37. Okamoto, R., M. Hatani, M. Tsukitani, A. Suehiro, M. Fujino, N. Imai, S. Takano, Y. Watanabe, and H. Fukuzaki. The effect of oxygen on the development of atherosclerosis in WHHL rabbits. Atherosclerosis 47:47–53, 1983.

    Article  CAS  PubMed  Google Scholar 

  38. Qiu, Y., and J. M. Tarbell. Numerical simulation of oxygen mass transfer in a compliant curved tube model of a coronary artery. Ann. Biomed. Eng. 28:26–38, 2000.

    Article  CAS  PubMed  Google Scholar 

  39. Rodkiewicz, C. M. Localization of early atherosclerotic lesions in the aortic arch in the light of fluid flow. J. Biomech. 8:149–156, 1975.

    Article  CAS  PubMed  Google Scholar 

  40. Rydberg, E. K., A. Krettek, C. Ullström, K. Ekström, P. A. Svensson, L. M. Carlsson, A. C. Jönsson-Rylander, G. I. Hansson, W. McPheat, O. Wiklund, B. G. Ohlsson, and L. M. Hultén. Hypoxia increases LDL oxidation and expression of 15-lipoxygenase-2 in human macrophages. Arterioscler. Thromb. Vasc. Biol. 24:2040–2045, 2004.

    Article  CAS  PubMed  Google Scholar 

  41. Sabbah, H. N., F. Khaja, J. F. Brymer, E. T. Hawkins, and P. D. Stein. Blood velocity in the right coronary: relation to the distribution of atherosclerotic lesions. Am. J. Cardiol. 53:1008–1012, 1984.

    Article  CAS  PubMed  Google Scholar 

  42. Santilli, S. M., R. B. Stevens, J. G. Anderson, W. D. Payne, and M. D. Caldwell. Transarterial wall oxygen gradients at the dog carotid bifurcation. Am. J. Physiol. 268:H155–H161, 1995.

    CAS  PubMed  Google Scholar 

  43. Schneiderman, G., and T. K. Goldstick. Significance of luminal plasma layer resistance in arterial wall oxygen supply. Atherosclerosis 31:11–20, 1978.

    Article  CAS  PubMed  Google Scholar 

  44. Schneiderman, G., L. F. Mockros, and T. K. Goldstick. Effect of pulsatility on oxygen transport to the human arterial wall. J. Biomech. 15:849–858, 1982.

    Article  CAS  PubMed  Google Scholar 

  45. Seed, W. A., and N. B. Wood. Velocity patterns in the aorta. Cardiovasc. Res. 5:319–330, 1971.

    Article  CAS  PubMed  Google Scholar 

  46. Segadal, L., and K. Matre. Blood velocity distribution in the human ascending aorta. Circulation 76:90–100, 1987.

    CAS  PubMed  Google Scholar 

  47. 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. 124:378–387, 2002.

    Article  CAS  PubMed  Google Scholar 

  48. Sluimer, J. C., J. M. Gasc, J. L. van Wanroij, N. Kisters, M. Groeneweg, M. D. Sollewijn Gelpke, J. P. Cleutjens, L. H. van den Akker, P. Corvol, B. G. Wouters, M. J. Daemen, and A. P. Bijnens. Hypoxia, hypoxia-inducible transcription factor, and macrophages in human atherosclerotic plaques are correlated with intraplaque angiogenesis. J. Am. Coll. Cardiol. 51:1258–1265, 2008.

    Article  CAS  PubMed  Google Scholar 

  49. Stein, T. R., J. C. Martin, and K. H. Keller. Steady-state oxygen transport through red blood cell suspensions. J. Appl. Physiol. 31:397–402, 1971.

    CAS  PubMed  Google Scholar 

  50. Tada, S., and J. M. Tarbell. Oxygen mass transport in a compliant carotid bifurcation model. Ann. Biomed. Eng. 34:1389–1399, 2006.

    Article  PubMed  Google Scholar 

  51. Tarbell, J. M. Mass transport in arteries and the localization of atherosclerosis. Annu. Rev. Biomed. Eng. 5:79–118, 2003.

    Article  CAS  PubMed  Google Scholar 

  52. Yashiro, K., H. Shiratori, and H. Hamada. Haemodynamics determined by a genetic programme govern asymmetric development of the aortic arch. Nature 450:285–288, 2007.

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This work was supported by Grants-in-Aid from the National Natural Science Foundation of China (No. 10632010, 30670517).

Author information

Authors and Affiliations

  1. School of Biological Science & Medical Engineering, Beihang University, Beijing, 100191, China

    Xiao Liu, Yubo Fan & Xiaoyan Deng

Authors
  1. Xiao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yubo Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoyan Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyan Deng.

Additional information

Associate Editor Gerald Saidel oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, X., Fan, Y. & Deng, X. Effect of Spiral Flow on the Transport of Oxygen in the Aorta: A Numerical Study. Ann Biomed Eng 38, 917–926 (2010). https://doi.org/10.1007/s10439-009-9878-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-009-9878-8

Keywords

Search

Navigation