Skip to main content
SpringerLink
Log in

Quantitative Analysis of Bulk Flow in Image-Based Hemodynamic Models of the Carotid Bifurcation: The Influence of Outflow Conditions as Test Case

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

Abstract

Although flow-driven mechanisms associated with vascular physiopathology also deal with four-dimensional phenomena such as species transport, the majority of the research on the subject focuses primarily on wall shear stress as indicator of disturbed flow. Indeed, the role that bulk flow plays in vascular physiopathology has not been thoroughly investigated, partly because of a lack of descriptors that would be able to reduce the intricacy of arterial hemodynamics. Here, an approach is proposed to investigate, in silico, the bulk flow within the carotid bifurcation. For this purpose, we coupled a three-dimensional model of carotid bifurcation with a lumped model of the downstream vasculature. For the sake of comparison, we also imposed three different fixed flow rate repartitions between the internal and external carotid arteries on the three-dimensional model. The bulk flow was characterized by applying a descriptor of helical motion, the helical flow index (HFI) to the model; the HFI has recently been shown to provide an accurate representation of complex flows. Moreover, a new metric is presented to investigate the vorticity dynamics within the bifurcation. Our results highlight the effectiveness of these metrics in the following contexts: (i) identifying and ranking emerging hemodynamic features and (ii) quantifying the influence of the outflow boundary conditions on the composition of the translational and rotational components of the fluid motion. The metrics applied herein allow for a more comprehensive analysis, which may lead to the development of an instrument to relate the bulk flow to vascular pathophysiological events that involve not only fluid-related forces, but also transport phenomena within blood.

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
FIGURE 7
FIGURE 8
FIGURE 9
FIGURE 10

Similar content being viewed by others

References

  1. Araim, O., A. Chen, and B. Sumpio. Hemodynamic forces: effects on atherosclerosis. New Surg. 1:92–100, 2001.

    Google Scholar 

  2. Augst, A. D., B. Ariff, S. A. M. Thom, X. Y. Xu, and A. D. Hughes. Analysis of complex flow and the relationship between blood pressure, wall shear stress, and intima-media thickness in the human carotid artery. Am. J. Physiol. Heart Circ. Physiol. 293:H1031–H1037, 2007.

    Article  CAS  PubMed  Google Scholar 

  3. Antiga, L., M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman. An image-based modelling framework for patient-specific computational hemodynamics. Med. Biol. Eng. Comput. 46(11):1097–1112, 2008.

    Article  PubMed  Google Scholar 

  4. Blanco, P. J., M. R. Pivello, S. A. Urquiza, and R. A. Feijoo. On the potentialities of 3D–1D models in hemodynamics simulations. J. Biomech. 42(7):919–930, 2009.

    Article  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. R. Soc. Lond. A 452:185–197, 1996.

    Article  Google Scholar 

  6. Caro, C. G., C. L. Dumoulin, J. M. Graham, K. H. Parker, and S. P. Souza. Secondary flow in the human common carotid artery imaged by MR angiography. J. Biomech. Eng. 114(1):147–149, 1992.

    Article  CAS  PubMed  Google Scholar 

  7. Caro, C. G., G. J. Fitz, and R. C. Schroter. Arterial wall shear and distribution of early atheroma in man. Nature 223:1159–1160, 1969.

    Article  CAS  PubMed  Google Scholar 

  8. Caro, C. G., G. J. Fitz, and R. C. Schroter. Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc. R. Soc. Lond. B Biol. Sci. 177:109–159, 1971.

    Article  CAS  PubMed  Google Scholar 

  9. Chen, Z. S., Y. B. Fan, X. Y. Deng, and Z. Xu. Swirling flow can suppress flow disturbances in endovascular stents: a numerical study. ASAIO J. 55(6):543–549, 2009.

    Article  PubMed  Google Scholar 

  10. Chien, S. Effects of disturbed flow on endothelial cells. Ann. Biomed. Eng. 36(4):554–562, 2008.

    Article  PubMed  Google Scholar 

  11. Davies, P. F., D. C. Polacek, C. Shi, and B. P. Helmke. The convergence of haemodynamics, genomics, and endothelial structure in studies of the focal origin of atherosclerosis. Biorheology 39:299–306, 2002.

    CAS  PubMed  Google Scholar 

  12. Doorly, D. J., S. J. Sherwin, P. T. Franke, and J. Peiró. Vortical flow structure identification and flow transport in arteries. Comput. Methods Biomech. Biomed. Eng. 5(3):261–273, 2002.

    Article  CAS  Google Scholar 

  13. Fan, Y., Z. Xu, W. Jiang, X. Deng, K. Wang, and A. Sun. An S-type bypass can improve the hemodynamics in the bypassed arteries and suppress intimal hyperplasia along the host artery floor. J. Biomech. 41:2498–2505, 2008.

    Article  PubMed  Google Scholar 

  14. Ford, M. D., N. Alperin, S. H. Lee, D. W. Holdsworth, and D. A. Steinman. Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries. Physiol. Meas. 26(4):447–488, 2005.

    Article  Google Scholar 

  15. 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.

    Article  Google Scholar 

  16. Formaggia, L., J. F. Gerbeau, F. Nobile, and A. Quarteroni. Numerical treatment of defective boundary conditions for the Navier–Stokes equations. SIAM J. Numer. Anal. 40(1):376–401, 2002.

    Article  Google Scholar 

  17. Friedman, M. H., C. B. Bargeron, O. J. Deters, G. M. Hutchins, and F. F. Mark. Correlation between wall shear and intimal thickness at a coronary artery branch. Atherosclerosis 68:27–33, 1987.

    Article  CAS  PubMed  Google Scholar 

  18. Giddens, D. P., C. K. Zarins, and S. Glagov. The role of fluid mechanics in the localization and detection of atherosclerosis. J. Biomech. Eng. 115(4B):588–595, 1993.

    Article  CAS  PubMed  Google Scholar 

  19. Grigioni, M., C. Daniele, U. Morbiducci, C. Del Gaudio, G. D’Avenio, A. Balducci, and V. Barbaro. A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending. J. Biomech. 38:1375–1386, 2005.

    Article  PubMed  Google Scholar 

  20. Grigioni, M., U. Morbiducci, G. D’Avenio, G. Di Benedetto, and C. Del Gaudio. Proposal for a new formulation of the power law mathematical model for blood trauma prediction. Biomech. Model. Mechanobiol. 4(4):249–260, 2005.

    Article  PubMed  Google Scholar 

  21. Himburg, H. A., and M. H. Friedman. Correspondence of low mean shear and high armonic content in the porcine iliac arteries. J. Biomech. Eng. 128(6):852–856, 2006.

    Article  PubMed  Google Scholar 

  22. 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.

    Article  CAS  PubMed  Google Scholar 

  23. Hsiai, T. K., S. K. Cho, P. K. Wong, M. Ing, A. Salazar, A. Sevanian, M. Navab, L. L. Demer, and C. M. Ho. Monocyte recruitment to endothelial cells in response to oscillatory shear stress. FASEB J. 17(12):1648–1657, 2003.

    Article  CAS  PubMed  Google Scholar 

  24. Hyun, S., C. Kleinstreuer, P. W. Longest, and C. Chen. Particle-hemodynamics simulations and design options for surgical reconstruction of diseased carotid artery bifurcations. J. Biomech. Eng. 126(4):118–195, 2004.

    Google Scholar 

  25. Karino, T. Microscopic structure of disturbed flows in the arterial and venous system, and its implication in the localization of vascular disease. Int. Angiol. 5(4):297–313, 1986.

    CAS  PubMed  Google Scholar 

  26. Kroll, M. H., J. D. Hellums, L. V. McIntire, A. L. Schafer, and J. L. Moake. Platelets and shear stress. Blood 88(5):1525–1541, 1996.

    CAS  PubMed  Google Scholar 

  27. Ku, D. N., and D. P. Giddens. Pulsatile flow in a model carotid bifurcation. Arteriosclerosis 3:31–39, 1983.

    CAS  PubMed  Google Scholar 

  28. 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.

    CAS  PubMed  Google Scholar 

  29. Laganà, K., G. Dubini, F. Migliavacca, R. Pietrabissa, G. Pennati, A. Veneziani, and A. Quarteroni. Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures. Biorheology 39(3–4):359–364, 2002.

    PubMed  Google Scholar 

  30. Lee, S. W., L. Antiga, and D. A. Steinman. Correlations among indicators of disturbed flow at the normal carotid bifurcation. J. Biomech. Eng. 131(6):061013, 2009.

    Article  PubMed  Google Scholar 

  31. Lee, S. W., and D. A. Steinman. On the relative importance of rheology for image-based CFD models of the carotid bifurcation. J. Biomech. Eng. 129(2):273–278, 2007.

    Article  PubMed  Google Scholar 

  32. 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.

    Article  CAS  PubMed  Google Scholar 

  33. Ma, P., X. Li, and D. N. Ku. Convective mass transfer at the carotid bifurcation. J. Biomech. 30:565–571, 1997.

    Article  CAS  PubMed  Google Scholar 

  34. 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 

  35. Marshall, I., P. Papathanasopoulou, and W. Wartolowska. Carotid flow rates and flow division at the bifurcation in healthy volunteers. Physiol. Meas. 25(3):691–697, 2004.

    Article  PubMed  Google Scholar 

  36. Migliavacca, F., R. Balossino, G. Pennati, G. Dubini, T. Y. Hsia, M. R. de Leval, and E. L. Bove. Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. J. Biomech. 39(6):1010–1020, 2006.

    Article  PubMed  Google Scholar 

  37. Milner, J. S., J. A. Moore, B. K. Rutt, and D. A. Steinman. Hemodynamics of human carotid artery bifurcations: computational studies with models reconstructed from magnetic resonance imaging of normal subjects. J. Vasc. Surg. 28:143–156, 1998.

    Article  CAS  PubMed  Google Scholar 

  38. Moffatt, H. K. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35(1):17–29, 1969.

    Article  Google Scholar 

  39. Moffatt, H. K., and A. Tsinober. Helicity in laminar and turbulent flow. Annu. Rev. Fluid Mech. 24:281–312, 1992.

    Article  Google Scholar 

  40. Moore, J. E., Jr., 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 behaviour and relationship to atherosclerosis. Atherosclerosis 110(2):225–240, 1994.

    Article  CAS  PubMed  Google Scholar 

  41. 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. 2010. doi:10.1115/1.4001886.

  42. Morbiducci, U., M. Lemma, R. Ponzini, A. Boi, L. Bondavalli, C. Antona, F. M. Montevecchi, and A. Redaelli. 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 30:628–639, 2007.

    CAS  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  44. Morbiducci, U., R. Ponzini, M. Nobili, D. Massai, F. M. Montevecchi, D. Bluestein, and A. Redaelli. Blood damage safety of prosthetic heart valves. Shear-induced platelet activation and local flow dynamics: a fluid-structure interaction approach. J. Biomech. 42(12):1952–1960, 2009.

    Article  PubMed  Google Scholar 

  45. 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.

    Article  PubMed  Google Scholar 

  46. Moyle, K. R., L. Antiga, and D. A. Steinman. Inlet conditions for image-based CFD models of the carotid bifurcation: is it reasonable to assume fully developed flow? J. Biomech. Eng. 128(3):371–379, 2006.

    Article  PubMed  Google Scholar 

  47. Perktold, K., and G. Rappitsch. Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech. 28(7):845–856, 1995.

    Article  CAS  PubMed  Google Scholar 

  48. 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.

    Article  PubMed  Google Scholar 

  49. Pritchard, W. F., P. F. Davies, Z. Derafshi, D. C. Polacek, R. Tsao, R. O. Dull, S. A. Jones, and D. P. Giddens. Effects of wall shear stress and fluid recirculation on the localization of circulating monocytes in a three-dimensional flow model. J. Biomech. 28(12):1459–1469, 1995.

    Article  CAS  PubMed  Google Scholar 

  50. Quarteroni, A., S. Ragni, and A. Veneziani. Coupling between lumped and distributed models for blood flow problems. Comput. Visual. Sci. 4:111–124, 2001.

    Article  Google Scholar 

  51. Quarteroni, A., and A. Veneziani. Analysis of a geometrical multiscale model based on the coupling of ODE and PDE for blood flow simulations. Multiscale Model. Simul. 1(2):173–195, 2003.

    Article  Google Scholar 

  52. Redaelli, A., and F. M. Montevecchi. Computational evaluation of intraventricular pressure gradients based on a fluid-structure approach. J. Biomech. Eng. 118(4):529–537, 1996.

    Article  CAS  PubMed  Google Scholar 

  53. 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 

  54. 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 

  55. Steinman, D. A. Image-based computational fluid dynamics modelling in realistic arterial geometries. Ann. Biomed. Eng. 124(2):166–175, 2002.

    Google Scholar 

  56. Stonebridge, P. A., P. R. Hoskins, P. L. Allan, and J. F. Belch. Spiral laminar flow in vivo. Clin. Sci. (Lond.) 91:17–21, 1996.

    CAS  Google Scholar 

  57. Sun, A., Y. Fan, and X. Deng. Numerical investigation of blood flow in the distal end of an axis-deviated arterial bypass model. Biorheology 46:83–92, 2009.

    PubMed  Google Scholar 

  58. Sun, N., N. B. Wood, A. D. Hughes, S. A. M. Thom, and X. Y. Xu. Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model. Am. J. Physiol. Heart Circ. Physiol. 292:H3148–H3157, 2007.

    Article  CAS  PubMed  Google Scholar 

  59. Thomas, J. B., J. S. Milner, B. K. Rutt, and D. A. Steinman. Reproducibility of image-based computational fluid dynamics models of the human carotid bifurcation. Ann. Biomed. Eng. 31(2):132–141, 2003.

    Article  PubMed  Google Scholar 

  60. Urquiza, S. A., P. J. Blanco, M. J. Vénere, and R. A. Feijoo. Multidimensional modelling for the carotid artery blood flow. Comput. Methods Appl. Mech. Eng. 195:4002–4017, 2006.

    Article  Google Scholar 

  61. Wake, A. K., J. N. Oshinski, A. R. Tannenbaum, and D. P. Giddens. Choice of in vivo versus idealized velocity boundary conditions influences physiologically relevant flow patterns in a subject-specific simulation of flow in the human carotid bifurcation. J. Biomech. Eng. 131(2):021013, 2009.

    Article  PubMed  Google Scholar 

  62. Westerhof, N., J. W. Lankhaar, and B. E. Westerhof. The arterial Windkessel. Med. Biol. Eng. Comput. 47(2):131–141, 2009.

    Article  PubMed  Google Scholar 

  63. Zhan, F., Y. Fan, and X. Deng. 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):413–418, 2010.

    Article  CAS  PubMed  Google Scholar 

  64. Zheng, T., Y. Fan, Y. Xiong, W. Jiang, and X. Deng. Hemodynamic performance study on small diameter helical grafts. ASAIO J. 55:192–199, 2009.

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Turin, Italy

    Umberto Morbiducci, Diego Gallo, Diana Massai & Franco M. Montevecchi

  2. CILEA, Interuniversity consortium, Milan, Italy

    Raffaele Ponzini

  3. Mario Negri Institute, Bergamo, Italy

    Luca Antiga

  4. Department of Bioengineering, Politecnico di Milano, Milan, Italy

    Alberto Redaelli

Authors
  1. Umberto Morbiducci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diego Gallo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raffaele Ponzini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Diana Massai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luca Antiga
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Franco M. Montevecchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Alberto Redaelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Umberto Morbiducci.

Additional information

Associate Editor Scott L. Diamond oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morbiducci, U., Gallo, D., Ponzini, R. et al. Quantitative Analysis of Bulk Flow in Image-Based Hemodynamic Models of the Carotid Bifurcation: The Influence of Outflow Conditions as Test Case. Ann Biomed Eng 38, 3688–3705 (2010). https://doi.org/10.1007/s10439-010-0102-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-010-0102-7

Keywords

Search

Navigation