Errors in the estimation of wall shear stress by maximum Doppler velocity

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 (V_max) 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 V_max-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. Conclusion: V_max-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.