4D flow MRI velocity uncertainty quantification

Purpose: An automatic method is presented for estimating 4D flow MRI velocity measurement uncertainty in each voxel. The velocity distance (VD) metric, a statistical distance between the measured velocity and local error distribution, is introduced as a novel measure of 4D flow MRI velocity measurement quality. Methods: The method uses mass conservation to assess the local velocity error variance and the standardized difference of means (SDM) velocity to estimate the velocity error correlations. VD is evaluated as the Mahalanobis distance between the local velocity measurement and the local error distribution. The uncertainty model is validated synthetically and tested in vitro under different flow resolutions and noise levels. The VD's application is demonstrated on two in vivo thoracic vasculature 4D flow datasets. Results: Synthetic results show the proposed uncertainty quantification method is sensitive to aliased regions across various velocity-to-noise ratios and assesses velocity error correlations in four- and six-point acquisitions with correlation errors at or under 3.2%. In vitro results demonstrate the method's sensitivity to spatial resolution, venc settings, partial volume effects, and phase wrapping error sources. Applying VD to assess in vivo 4D flow MRI in the aorta demonstrates the expected increase in measured velocity quality with contrast administration and systolic flow. Conclusion: The proposed 4D flow MRI uncertainty quantification method assesses velocity measurement error owing to sources including noise, intravoxel phase dispersion, and velocity aliasing. This method enables rigorous comparison of 4D flow MRI datasets obtained in longitudinal studies, across patient populations, and with different MRI systems.