Endothelial shear stress estimation in the human carotid artery based on Womersley versus Poiseuille flow

  • Janina C. V. Schwarz
  • Raphaël Duivenvoorden
  • Aart J. Nederveen
  • Erik S. G. Stroes
  • Ed VanBavel
Original Paper


Endothelial shear stress (ESS) dynamics are a major determinant of atherosclerosis development. The frequently used Poiseuille method to estimate ESS dynamics has important limitations. Therefore, we investigated whether Womersley flow may provide a better alternative for estimation of ESS while requiring equally simple hemodynamic parameters. Common carotid blood flow, centerline velocity, lumen diameter and mean wall thickness (MWT) were measured with 3T-MRI in 45 subjects at three different occasions. Mean ESS and two measures of pulsatility [shear pulsatility index (SPI) and oscillatory shear index (OSI)] were estimated based on Poiseuille and Womersley flow and compared to the more complex velocity gradient modelling method. The association between ESS and MWT was tested with multiple linear regression analysis; interscan reproducibility was assessed using intraclass correlation coefficients (ICC). Mean ESS and pulsatility indices based on Womersley flow (ESSwq β = −0.18, P = 0.04; SPIwq β = 0.24, P = 0.02; OSIwq β = 0.18, P = 0.045), showed equally good correlations with carotid MWT as the velocity gradient method (ESSvg β = −0.23, P = 0.01; SPIvg β = 0.21, P = 0.02; OSIvg β = 0.07, P = 0.47). This in contrast to the Poiseuille flow method that only showed a good correlation for mean ESS (ESSpq β = −0.18, P = 0.04; SPIpq β = 0.14, P = 0.14; OSIpq β = 0.04, P = 0.69). Womersley and Poiseuille methods had high intraclass correlation coefficients indicating good interscan reproducibility (both ICC = 0.84, 95 % confidence interval 0.75–0.90). Estimation of ESS dynamics based on Womersley flow modelling is superior to Poiseuille flow modelling and has good interscan reproducibility.


Endothelial shear stress Cardiovascular magnetic resonance Common carotid artery Intima media thickness 



3.0 Tesla magnetic resonance imaging


Endothelial shear rate


Endothelial shear stress


Intraclass correlation coefficient


Lumen area


Mean wall thickness


Oscillatory shear index


Blood flow rate


Shear pulsatility index


Centerline velocity



We would like to thank A.M. van den Berg for assisting in the data acquisition. JCVS was supported by Grant 01C-204 (EMINENCE project) from the Center for Translational Molecular Medicine.

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10554_2014_571_MOESM1_ESM.pdf (397 kb)
Supplementary material 1 (PDF 397 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Janina C. V. Schwarz
    • 1
  • Raphaël Duivenvoorden
    • 2
  • Aart J. Nederveen
    • 3
  • Erik S. G. Stroes
    • 2
  • Ed VanBavel
    • 1
  1. 1.Department of Biomedical Engineering and Physics, Academic Medical CenterUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Vascular Medicine, Academic Medical CenterUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Department of Radiology, Academic Medical CenterUniversity of AmsterdamAmsterdamThe Netherlands

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