Journal of The Royal Society Interface
Restricted accessResearch articles

Effect of reverse flow on the pattern of wall shear stress near arterial branches

    Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier–Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

    References

    • 1
      Caro C. G., Fitz-Gerald J. M.& Schroter R.. 1971Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc. R. Soc. Lond. B 177, 109–159.doi:10.1098/rspb.1971.0019 (doi:10.1098/rspb.1971.0019). Link, ISIGoogle Scholar
    • 2
      Ku D. N., Giddens D. P., Zarins C. K.& Glagov S.. 1985Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 5, 293–302. Crossref, PubMedGoogle Scholar
    • 3
      Weinberg P. D.. 2002Disease patterns at arterial branches and their relation to flow. Biorheology 39, 533–537. PubMed, ISIGoogle Scholar
    • 4
      Kazakidi A., Sherwin S. J.& Weinberg P. D.. 2009Effect of Reynolds number and flow division on patterns of haemodynamic wall shear stress near branch points in the descending thoracic aorta. J. R. Soc. Interface 6, 539–548.doi:10.1098/rsif.2008.0323 (doi:10.1098/rsif.2008.0323). Link, ISIGoogle Scholar
    • 5
      Sherwin S. J.& Karniadakis G. E.. 1996Tetrahedral hp finite elements: algorithms and flow simulations. J. Comput. Phys. 124, 14–45.doi:10.1006/jcph.1996.0042 (doi:10.1006/jcph.1996.0042). Crossref, ISIGoogle Scholar
    • 6
      Khan S.& Haust M. D.. 1979Variations in the aortic origin of intercostal arteries in man. Anat. Rec. 195, 545–551.doi:10.1002/ar.1091950313 (doi:10.1002/ar.1091950313). Crossref, PubMedGoogle Scholar
    • 7
      Caro C. G., Pedley T. J., Schroter R. C.& Seed W. A.. 1978The mechanics of the circulation. Oxford, UK: Oxford University Press. Google Scholar
    • 8
      Cornhill J. F.& Roach M. R.. 1976A quantitative study of the localization of atherosclerotic lesions in the rabbit aorta. Atherosclerosis 23, 489–501.doi:10.1016/0021-9150(76)90009-5 (doi:10.1016/0021-9150(76)90009-5). Crossref, PubMed, ISIGoogle Scholar
    • 9
      Nichols W. W.& O'Rourke M. F.. 1998McDonald's blood flow in arteries: theoretical, experimental and clinical principles, 4th edn.London, UK: Arnold. Google Scholar
    • 10
      Pedley T. J.. 1980The fluid mechanics of large blood vessels. Cambridge, UK: Cambridge University Press. CrossrefGoogle Scholar
    • 11
      Sobey I. J.. 1977Laminar boundary-layer flow past a two-dimensional slot. J. Fluid Mech. 83, 33–47.doi:10.1017/S0022112077001025 (doi:10.1017/S0022112077001025). Crossref, ISIGoogle Scholar
    • 12
      Tutty O. R.. 1988Flow in a tube with a small side branch. J. Fluid Mech. 191, 79–109.doi:10.1017/S0022112088001521 (doi:10.1017/S0022112088001521). Crossref, ISIGoogle Scholar
    • 13
      Sherwin S. J.& Blackburn H. M.. 2005Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows. J. Fluid Mech. 533, 297–327.doi:10.1017/S0022112005004271 (doi:10.1017/S0022112005004271). Crossref, ISIGoogle Scholar
    • 14
      Landau L. D.& Lifshitz E. M.. 1959Fluid mechanics. Oxford, UK: Pergamon Press. Google Scholar
    • 15
      Loudon C.& Tordesillas A.. 1998The use of the dimensionless Womersley number to characterize the unsteady nature of internal flow. J. Theor. Biol. 191, 63–78.doi:10.1006/jtbi.1997.0564 (doi:10.1006/jtbi.1997.0564). Crossref, PubMed, ISIGoogle Scholar
    • 16
      Womersley J. R.. 1955Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563. Crossref, PubMed, ISIGoogle Scholar
    • 17
      He X.& Ku D.. 1996Pulsatile flow in the human left coronary artery bifurcation: average conditions. J. Biomech. Eng. 118, 74–82.doi:10.1115/1.2795948 (doi:10.1115/1.2795948). Crossref, PubMed, ISIGoogle Scholar
    • 18
      Peiró J., Giordana S., Griffith C.& Sherwin S. J.. 2002High-order algorithms for vascular flow modelling. Int. J. Numer. Methods Fluids 40, 137–151.doi:10.1002/fld.270 (doi:10.1002/fld.270). Crossref, ISIGoogle Scholar
    • 19
      Sherwin S. J.& Peiró J.. 2002Mesh generation in curvilinear domains using high-order elements. Int. J. Numer. Methods Eng. 53, 207–223.doi:10.1002/nme.397 (doi:10.1002/nme.397). Crossref, ISIGoogle Scholar
    • 20
      Giordana S., Sherwin S. J., Peiró J., Doorly D. J., Crane J. S., Lee K. E., Cheshire N. J.& Caro C. G.. 2005Local and global geometric influence on steady flow in distal anastomoses of peripheral by-pass grafts. J. Biomech. Eng. 127, 1087–1098.doi:10.1115/1.2073507 (doi:10.1115/1.2073507). Crossref, PubMed, ISIGoogle Scholar
    • 21
      Karniadakis G.& Sherwin S. J.. 2005Spectral/hp element methods for computational fluid dynamics, 2nd edn.Oxford, UK: Oxford Science Publications. CrossrefGoogle Scholar
    • 22
      Sherwin S. J., Shah O., Doorly D. J., Peiró J., Papaharilaou Y., Watkins N., Caro C. G.& Dumoulin C. L.. 2000The influence of out-of-plane geometry on the flow within a distal end-to-side anastomosis. J. Biomech. Eng. 122, 86–95.doi:10.1115/1.429630 (doi:10.1115/1.429630). Crossref, PubMed, ISIGoogle Scholar
    • 23
      Sloop G., Perret R., Brahney J.& Oalmann M.. 1998A description of two morphologic patterns of aortic fatty streaks, and a hypothesis of their pathogenesis. Atherosclerosis 141, 153–160.doi:10.1016/S0021-9150(98)00167-1 (doi:10.1016/S0021-9150(98)00167-1). Crossref, PubMed, ISIGoogle Scholar
    • 24
      Kazakidi A.. 2008Computational studies of blood flow at arterial branches in relation to the localisation of atherosclerosis. PhD thesis,Imperial College London, London, UK. Google Scholar
    • 25
      Tuck E. O.. 1970Unsteady flow of a viscous fluid from a source in a wall. J. Fluid Mech. 41, 641–652.doi:10.1017/S0022112070000800 (doi:10.1017/S0022112070000800). Crossref, ISIGoogle Scholar
    • 26
      DeMestre N. J.& Guiney D. C.. 1971Low Reynolds number oscillatory flow through a hole in a wall. J. Fluid Mech. 47, 657–666.doi:10.1017/S0022112071001307 (doi:10.1017/S0022112071001307). Crossref, ISIGoogle Scholar
    • 27
      Buchanan J. R., Kleinstreuer C., Truskey G. A.& Lei M.. 1999Relation between non-uniform hemodynamics and sites of altered permeability and lesion growth at the rabbit aorto-coeliac junction. Atherosclerosis 143, 27–40.doi:10.1016/S0021-9150(98)00264-0 (doi:10.1016/S0021-9150(98)00264-0). Crossref, PubMed, ISIGoogle Scholar
    • 28
      Liepsch D. W.. 1990Effect of blood flow parameters on flow patterns at arterial bifurcations—studies in models. Blood flow in large arteries: applications to atherogenesis and clinical medicine (ed. & Liepsch D. W.), pp. 63–76. Basel, Switzerland: Karger. Google Scholar
    • 29
      Secomb T. W.. 1978Flow in a channel with pulsating walls. J. Fluid Mech. 88, 273–288.doi:10.1017/S0022112078002104 (doi:10.1017/S0022112078002104). Crossref, ISIGoogle Scholar
    • 30
      O'Dea R. D.& Waters S. L.. 2006Flow and solute uptake in a twisting tube. J. Fluid Mech. 562, 173–182.doi:10.1017/S0022112006001194 (doi:10.1017/S0022112006001194). Crossref, ISIGoogle Scholar