Changes in flow and wall stresses through arterial constrictions offset from the centre of the vessel

Abstract

Blood flow through small, obstructed vessels is studied by computing flows in tubes featuring three dimensional sinusoidal constrictions. A high order spectral element algorithm determines the extent of physiological flow characteristics such as recirculation zones and wall shear stress (WSS). Comparisons find that an increase in constriction eccentricity gives rise to more intense WSS. Moreover, these irregular flow conditions persist further downstream. Consistently, shear rate increases with Reynolds number and constriction eccentricity. Vorticity perpendicular to the constriction geometry and shear rate both increase with blockage ratio. In axisymmetric geometries, dissipation of the shear layers associated with downstream recirculation occurs more quickly. With larger constriction eccentricities, zones of high WSS are found on the far wall downstream of the constriction. This could lead to degradation of the wall tissue. References Blackburn, H. M. and Sherwin, S. J., Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows, J. Fluid Mech., 533, 2005, 297--327. doi:10.1017/S0022112005004271 Blackburn, H. M and Sherwin, S. J., Instability modes and transition of pulsatile stenotic flow: pulse-period dependence, J. Fluid Mech., 573, 2007, 57--88. doi:10.1017/S0022112006003740 Chytilova, E., Malik, J., Kasalova, Z., Dolezalova, R., Stulc, T., and Ceska, R., Lower wall shear rate of the common carotid artery in treated type 2 diabetes mellitus with metabolic syndrome, Accepted for publication in Physiological Research, 2008. http://www.biomed.cas.cz/physiolres/pdf/prepress/1445.pdf Dodds, S. R, The Haemodynamics of Asymmetric Stenoses, Eur. J. Vasc. Endovasc. Surg., 24, 2002, 332--337. doi:10.1053/ejvs.2002.1729 Griffith, M. D., Hourigan, K. and Thompson, M. C., Numerically Modelling Blockage Effects on the Flow between Flat Plates, 15th Australasian Fluid Mechanics Conference, 2004, The University of Sydney, Sydney, Australia. http://www.aeromech.usyd.edu.au/15afmc/proceedings/papers/AFMC00103.pdf Jung, H., Choi, J. W., and Park, C. G., Asymmetric Flows of non-Newtonian Fluids in Symmetric Stenosed Artery, Korea-Australia Rheology J., 16, 2004, 101--108. http://www.rheology.or.kr/down/16-2(6).pdf Karniadakis, G. E., Orszag, S. A. and Israeli, M., High-order splitting methods for the incompressible Navier--Stokes equations, J. Comput. Phys., 97, 1991, 414--443. doi:10.1016/0021-9991(91)90007-8 Karniadakis, G. E. and Sherwin, S. J., 2005, Spectral/hp Element Methods for CFD, 2nd ed., Oxford University Press, Oxford. Li, M. X., Beech-Brandt, J. J., John, L. R., Hopkins, P. R., and Easson, W. J., Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses, Journal of Biomechanics, 40, 2007, 3715--3724. doi:10.1016/j.jbiomech.2007.06.023 Liu, G. T., Wang, X. J., Ai, B. Q. and Liu, L. G., Numerical study of pulsating flow through a tapered artery with stenosis, Chinese Journal of Physics, 42, 2004, 401--409. http://psroc.phys.ntu.edu.tw/cjp/v42/401.pdf NHS Direct, 2006, Coronary Angioplasty, BMJ Publishing Group Ltd, England and Wales, National Health Service clinical evidence for patients. http://besttreatments.bmj.com/btuk/pdf/18627.pdf Ridker, P. M., On evolutionary biology, inflammation, infection, and the causes of atherosclerosis, Circulation, 105, 2002, 2--4. http://circ.ahajournals.org/cgi/reprint/105/1/2 Ross, R., Cell Biology of Atherosclerosis, Annu. Rev. Physiol., 57, 1995, 791--804. doi:10.1146/annurev.ph.57.030195.004043 Sheard, G. J. and Ryan, K., Pressure-driven flow past spheres moving in a circular tube, J. Fluid Mech., 592, 2007, 233--262. doi:10.1017/S0022112007008543 Thomas, S. M., The current role of catheter angiography, Imaging, 13, 2001, 366--375. http://imaging.birjournals.org/cgi/content/full/13/5/366