Divergence-free constrained phase unwrapping and denoising for 4D flow MRI
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Divergence-free constrained phase unwrapping and denoising for 4D flow MRI

4D flow magnetic resonance imaging (MRI) allows for in vivo acquisition of time-resolved three-dimensional (3D) blood flow, thus enabling quantitative analysis of volumetric, time-varying hemodynamic quantities such as flow rates, wall shear stress (WSS), pressure difference, etc. 4D flow MRI is based on the phase contrast technique which encodes the blood velocity into the MRI signal phase data based on a predefined velocity encoding sensitivity parameter (venc). The acquired phase for the velocity outside the range of (-venc, venc) is wrapped and leads to erroneous velocity measurement (velocity aliasing), therefore promoting the use of high venc in clinical applications to avoid aliasing. However, using a high venc leads to a high noise level since the velocity-to-noise ratio is inversely proportional to venc. One strategy to capture the wide dynamic range while maintaining the low noise level is to algorithmically unwrap the wrapped phase data acquired using low venc.

In the present study, a novel phase unwrapping method was proposed and evaluated for 4D flow MRI. The unwrapped phase field was obtained by integrating the phase variations (the spatial and temporal changes of the phase data) estimated from the wrapped phase data using weighted least-squares. The divergence-free constraint derived from the conservation of mass for incompressible blood flow was incorporated to regulate and denoise the resulting phase field. The proposed method was tested on synthetic phase data of left ventricular flow and in vitro 4D flow measurement of Poiseuille flow. The method was additionally applied to in vivo 4D flow measurements in the thoracic aorta from 30 human subjects. The performance of the proposed method was compared to the state-of-the-art 4D single-step Laplacian algorithm. The synthetic phase data were completely unwrapped by the proposed method for all the cases with velocity encoding (venc) as low as 20% of the maximum velocity and signal-to-noise ratio as low as 5. The in vitro Poiseuille flow data was completely unwrapped with a 60% increase in the velocity-to-noise ratio. For the in vivo aortic datasets with a venc ratio less than 0.4, the proposed method significantly improved the success rate by as much as 40% and reduced the velocity error levels by a factor of 10 compared to the state-of-the-art method. The divergence-free constrained method exhibits reliability and robustness on phase unwrapping and shows improved accuracy of velocity and hemodynamic quantities by unwrapping the low-venc 4D flow MRI data.




The proposed constrained weighted least-squares unwrapping (CWLS) employs the divergence-free constraint for blood flow and the measurement uncertainty to enhance the unwrapping for 4D flow MRI. The method was evaluated using synthetic data (a), validated with in vitro data (b), and applied to in vivo data.




(a) Statistical distributions of unwrapping success rate for the artificially wrapped datasets. (b) The u phase fields an artificially wrapped BAV dataset. (c-d) With real-aliasing, the u phase fields at peak systole on the center x-y plane at peak systole for one BAV dataset (c) and one TAV-AA dataset (d)

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