title: Errors in the estimation of wall shear stress by maximum Doppler velocity.
abstract: OBJECTIVE
  Wall shear stress (WSS) is an important parameter with links to vascular (dys)function. Difficult to measure directly, WSS is often inferred from maximum spectral Doppler velocity (Vmax) by assuming fully-developed flow, which is valid only if the vessel is long and straight. Motivated by evidence that even slight/local curvatures in the nominally straight common carotid artery (CCA) prevent flow from fully developing, we investigated the effects of velocity profile skewing on Vmax-derived WSS.
  
  
  METHODS
  Velocity profiles, representing different degrees of skewing, were extracted from the CCA of image-based computational fluid dynamics (CFD) simulations carried out as part of the VALIDATE study. Maximum velocities were calculated from idealised sample volumes and used to estimate WSS via fully-developed (Poiseuille or Womersley) velocity profiles, for comparison with the actual (i.e. CFD-derived) WSS.
  
  
  RESULTS
  For cycle-averaged WSS, mild velocity profile skewing caused ±25% errors by assuming Poiseuille or Womersley profiles, while severe skewing caused a median error of 30% (maximum 55%). Peak systolic WSS was underestimated by ~50% irrespective of skewing with Poiseuille; using a Womersley profile removed this bias, but ±30% errors remained. Errors were greatest in late systole, when skewing was most pronounced. Skewing also introduced large circumferential WSS variations: ±60%, and up to ±100%, of the circumferentially averaged value.
  
  
  CONCLUSIONS
  Vmax-derived WSS may be prone to substantial variable errors related to velocity profile skewing, and cannot detect possibly large circumferential WSS variations. Caution should be exercised when making assumptions about velocity profile shape to calculate WSS, even in vessels usually considered long and straight.
authors: Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd, Toronto, Ontario M5S 3G8, Canada. jmynard@mie.utoronto.ca
authors: Jonathan P
authors: JP
authors: Mynard
authors: Bruce A
authors: BA
authors: Wasserman
authors: David A
authors: DA
authors: Steinman
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000792:Angiography / Q000379:methods; D050197:Atherosclerosis / Q000473:pathology*; D001783:Blood Flow Velocity; D001916:Brachial Artery / Q000473:pathology; D017536:Carotid Artery, Common / Q000473:pathology*; D003198:Computer Simulation; D005263:Femoral Artery / Q000473:pathology; D006801:Humans; D057446:Hydrodynamics; D008279:Magnetic Resonance Imaging; D008875:Middle Aged; D008955:Models, Cardiovascular; D015203:Reproducibility of Results; D013314:Stress, Mechanical; D018608:Ultrasonography, Doppler / Q000379:methods*
references: Ultrasound Med Biol. 2008 May;34(5):760-74
references: 18295392
references: Circulation. 1996 Dec 15;94(12):3257-62
references: 8989138
references: J Appl Physiol (1985). 2003 Feb;94(2):485-9
references: 12391066
references: Atherosclerosis. 2006 Mar;185(1):108-13
references: 16005010
references: J Magn Reson Imaging. 2006 Dec;24(6):1386-92
references: 17083089
references: Stroke. 1997 May;28(5):993-8
references: 9158640
references: Ultrasound Med Biol. 2006 Nov;32(11):1661-70
references: 17112953
references: J Magn Reson Imaging. 2012 Jul;36(1):128-38
references: 22336966
references: Ultrasound Med Biol. 2005 May;31(5):663-71
references: 15866416
references: J Biomech Eng. 2010 Dec;132(12):121008
references: 21142322
references: J Am Coll Cardiol. 1998 Jul;32(1):128-34
references: 9669260
references: Am J Physiol Heart Circ Physiol. 2006 Dec;291(6):H3043-9
references: 16861699
references: Cardiovasc Res. 1990 Feb;24(2):129-36
references: 2328518
references: Ultrasound Med Biol. 2013 May;39(5):870-81
references: 23453373
references: Acta Radiol. 2008 May;49(4):442-9
references: 18415789
references: Physiol Meas. 2008 May;29(5):585-94
references: 18460763
references: Am J Physiol Heart Circ Physiol. 2005 Feb;288(2):H822-8
references: 15345491
references: Ultrasound Med Biol. 1995;21(2):171-85
references: 7571127
references: J Biomech Eng. 2006 Jun;128(3):371-9
references: 16706586
references: Physiol Meas. 2008 Nov;29(11):1335-49
references: 18854602
references: J Biomech. 2009 Aug 7;42(11):1664-72
references: 19481210
references: Arterioscler Thromb Vasc Biol. 1998 Dec;18(12):1877-84
references: 9848879
references: Atherosclerosis. 2001 May;156(1):171-6
references: 11369011
references: Am J Hypertens. 2000 Aug;13(8):892-8
references: 10950397
references: Med Biol Eng Comput. 2009 Jun;47(6):641-8
references: 19308476
references: Stroke. 2004 Feb;35(2):464-8
references: 14726547
references: Magn Reson Med. 2010 Jun;63(6):1537-47
references: 20512857
references: J Appl Physiol (1985). 2006 Nov;101(5):1412-8
references: 16825527
references: Atherosclerosis. 2007 Apr;191(2):276-80
references: 16828101
references: Am J Physiol Heart Circ Physiol. 2007 Aug;293(2):H1031-7
references: 17449549
references: JAMA. 1999 Dec 1;282(21):2035-42
references: 10591386
references: Vasc Med. 2012 Aug;17(4):231-4
references: 22848085
references: J Gerontol A Biol Sci Med Sci. 2008 Dec;63(12):1416-9
references: 19126858
references: Prog Cardiovasc Dis. 2007 Mar-Apr;49(5):307-29
references: 17329179
references: Physiol Meas. 2011 Dec;32(12):1885-97
references: 22031538