Wall Shear Stress Estimation for 4D Flow MRI Using Navier–Stokes Equation Correction

Jiacheng Zhang, Sean M. Rothenberger, Melissa C. Brindise, Michael Markl, Vitaliy L. Rayz, Pavlos P. Vlachos*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This study introduces a novel wall shear stress (WSS) estimation method for 4D flow MRI. The method improves the WSS accuracy by using the reconstructed pressure gradient and the flow-physics constraints to correct velocity gradient estimation. The method was tested on synthetic 4D flow data of analytical Womersley flow and flow in cerebral aneurysms and applied to in vivo 4D flow data acquired in cerebral aneurysms and aortas. The proposed method’s performance was compared to the state-of-the-art method based on smooth-spline fitting of velocity profile and the WSS calculated from uncorrected velocity gradient. The proposed method improved the WSS accuracy by as much as 100% for the Womersley flow and reduced the underestimation of mean WSS by 39 to 50% for the synthetic aneurysmal flow. The predicted mean WSS from the in vivo aneurysmal data using the proposed method was 31 to 50% higher than the other methods. The predicted aortic WSS using the proposed method was 3 to 6 times higher than the other methods and was consistent with previous CFD studies and the results from recently developed methods that take into account the limited spatial resolution of 4D flow MRI. The proposed method improves the accuracy of WSS estimation from 4D flow MRI, which can help predict blood vessel remodeling and progression of cardiovascular diseases.

Original languageEnglish (US)
JournalAnnals of Biomedical Engineering
StateAccepted/In press - 2022


  • Cerebral aneurysm
  • Fluid dynamics
  • Phase-contrast MRI
  • Pressure field reconstruction
  • Thoracic aorta
  • Wall shear stress

ASJC Scopus subject areas

  • Biomedical Engineering


Dive into the research topics of 'Wall Shear Stress Estimation for 4D Flow MRI Using Navier–Stokes Equation Correction'. Together they form a unique fingerprint.

Cite this