Wall shear stress and flow stability in a model fusiform aneurysm

Gregory John Sheard, Kris Ryan

Abstract


Levels of wall shear stress in arterial blood flow are known to contribute to the integrity of wall tissue, and are believed to have a bearing on the pathogenesis of aneurysm disease. The flow of fluid through a model aneurysm was computed using a spectral element algorithm to study the distribution of wall shear stress and the stability of the flow to non-axisymmetric perturbations. Substantially higher mean and fluctuating wall shear stress components were found in the distal (downstream) region of the aneurysm bulge when compared to recent experimental measurements. A global stability analysis demonstrates that flow conditions consistent with a human aorta will produce non-axisymmetric flow in an aneurysm consistent with that modeled here. These results demonstrate the necessity for detailed numerical modeling of these flows to accurately resolve the near wall fluid stresses.

References
  • D. L. Fry. Acute vascular endothelial changes associated with increased blood velocity gradients. Circ. Res., 22:165--197, 1968.
  • G. E. Karniadakis, M. Israeli, and S. A. Orszag. High-order splitting methods for the incompressible Navier--Stokes equations. J. Comp. Phys., 97:414--443, 1991.
  • S. Kondo, N. Hashimoto, H. Kikuchi, F. Hazama, I. Nagata, and H. Kataoka. Cerebral aneurysms arising at nonbranching sites. an experimental study. Stroke, 28(2):398--403, 1997.
  • D. N. Ku, 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 oscillating shear stress. Arterioscler. Thromb. Vasc. Biol., 5:293--302, 1985.
  • J. C. Lasheras. The biomechanics of arterial aneurysms. Ann. Rev. Fluid Mech., 39:293--319, 2007. doi:10.1146/annurev.fluid.39.050905.110128.
  • R. B. Lehoucq, D. C. Sorenson, and C. Yang. ARPACK Users' Guide. SIAM: Philadelphia, PA, 1998. http://www.caam.rice.edu/software/ARPACK/UG/ug.html.
  • S. Oyre, E. M. Pedersen, S. Ringgaard, P. Boesiger, and W. P. Paaske. In vivo wall shear stress measured by magnetic resonance velocity mapping in the normal human abdominal aorta. Eur. J. Vasc. Endovasc. Surg., 13(3):263--271, 1997.
  • R. B. Rutherford. Randomized EVAR trials and advent of level I evidence: A paradigm shift in management of large abdominal aortic aneurysms? Semin. Vasc. Surg., 19(2):69--74, 2006. doi:10.1053/j.semvascsurg.2006.03.001.
  • A.-V. Salsac, S. R. Sparks, J.-M. Chomaz, and J. C. Lasheras. Evolution of the wall shear stresses during the progressive enlargement of symmetric abdominal aortic aneurysm. J. Fluid Mech., 560:19--51, 2006. doi:10.1017/S00221120060036X.
  • G. J. Sheard and K. Ryan. Pressure-driven flow past spheres moving in a circular tube. J. Fluid Mech., 592:233--262, 2007. doi:10.1017/S0022112007008543.
  • A. Astradsson and J. Astrup. An intracranial aneurysm in one identical twin, but no anerusym in the other. Br. J. Neurosurg., 15(2):168--171, 2001.
  • T. B. M. Wilmink, C. R. G. Quick, and N. E. Day. The association between cigarette smoking and abdominal aortic aneurysms. J. Vasc. Surg., 30:1099--1105, 1999.
  • J. R. Womersley. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol., 127:553--563, 1955.
  • D. Barkley and R. D. Henderson. Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech., 322:215--241, 1996.
  • H. M. Blackburn and J. M. Lopez. On three-dimensional quasi-periodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids, 15(8):L57--L60, 2003. doi:10.1063/1.1591771.
  • H. M. Blackburn and S. J. Sherwin. Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flow in cylindrical geometries. J. Comput. Phys., 197:759--778, 2004. doi:10.1016/j.jcp.2004.02.013.

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1420



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.