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This work introduces a 4D-flow magnetic resonance imaging (MRI) pressurereconstruction method which employs weighted least-squares (WLS) for pressureintegration. Pressure gradients are calculated from the velocity fields, andvelocity errors are estimated from the velocity divergence for incompressibleflow. Pressure gradient errors are estimated by propagating the velocity errorsthrough Navier-Stokes momentum equation. A weight matrix is generated based onthe pressure gradient errors, then employed for pressure reconstruction. Thepressure reconstruction method was demonstrated and analyzed using syntheticvelocity fields as well as Poiseuille flow measured using in vitro 4D-flow MRI.Performance of the proposed WLS method was compared to the method of solvingthe pressure Poisson equation which has been the primary method used in theprevious studies. Error analysis indicated that the proposed method is morerobust to velocity measurement errors. Improvement on pressure results wasfound to be more significant for the cases with spatially-varying velocityerror level, with reductions in error ranging from 50% to over 200%. Finally,the method was applied to flow in a patient-specific cerebral aneurysm.Validation was performed with in vitro flow data collected using ParticleTracking Velocimetry (PTV) and Shake the Box (STB) method, and in vivo flowmeasurement obtained using 4D-flow MRI. Pressure calculated by WLS, as opposedto the Poisson equation, was more consistent with the flow structures andshowed better agreement between the in vivo and in vitro data. These resultssuggest the utility of WLS method to obtain reliable pressure field fromclinical flow measurement data.

4D-Flow MRI Pressure Estimation Using Velocity Measurement-Error based Weighted Least-Squares