Wall Shear Stress Estimation for 4D Flow MRI using Navier-Stokes Equation Correction
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Wall Shear Stress Estimation for 4D Flow MRI using Navier-Stokes Equation Correction

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.

(a) The flow chart of the WSS estimation procedure with PG-VGC method. (b) The schematic demonstrates that the flow data in the whole region of interest (ROI) is used for enhancing the WSS estimation. The ROI consists of the voxels within the lumen and the partial volume voxels whose centers locate inside the surfaces representing the vessel wall. The green box and red box indicate the data in the core-flow and near-wall regions, respectively.
(a) The statistical distributions and mean values of the TAWSS estimated from in vivo 4D flow data of the BT aneurysm and the ICA aneurysm. (b) The time-dependent median and IQR of the WSS estimated from the in vivo 4D flow data in a cardiac cycle. (c) The spatial distributions of the TAWSS estimated from the in vivo 4D flow data.

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