4D flow MRI Velocity Gradient Correction Using Bias Error Estimates*

4D flow MRI provides time-resolved, 3-directional measurements of cardiovascular flow. Limited spatial resolution and partial volume (PV) effects introduce bias error in MRI-measured velocity fields, in turn, reducing the accuracy of velocity gradients derived from 4D flow data. We developed a model to estimate the instantaneous bias error distribution due to insufficient spatial resolution and PV effects, which was validated with synthetic, in vitro, and in vivo 4D flow MRI measurements. Herein, we investigated the improvement in the accuracy of near-wall velocity gradients derived from 4D flow data corrected for bias error. Synthetic 4D flow datasets were generated for Womersley flow in a 1 cm vessel with varying Womersley number, voxel size, and saturation ratio. Velocity gradients at the wall calculated from the 4D flow data with and without the bias error correction were compared to those from the analytical Womersley solution. Across all cases, removing the velocity bias error reduced the error of the near-wall velocity gradients, with the RMS gradient errors being 20.0% and 7.6% for the uncorrected and corrected 4D flow data, respectively, relative to the true gradient at the wall. Efforts are ongoing to apply the bias error correction to in vitro and in vivo 4D flow data.