Divergence-free reconstruction for accelerated 3D phase-contrast flow measurements
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KeywordsCompress Sensing Assess Blood Flow Cardiac Coil Array Flow Field Reconstruction Aortic Flow Measurement
In this work an approach is described to efficiently reduce inaccuracies of flow data acquired with reduced data acquisition methods based on the physical prior knowledge of zero divergence in 3D velocity vector fields. The divergence-free condition is implemented using a synergistic combination of normalized convolution and divergence-free radial basis functions. The efficacy of the method is demonstrated for aortic flow measurements obtained from undersampled data.
Cine 3D phase-contrast magnetic resonance imaging (PC-MRI) has emerged as a valuable tool for assessing blood flow patterns [Markl, JCMR’11]. The relatively long acquisition times, however, limit its application in a clinical setting. Over the last years several undersampling techniques such as TSENSE, GRAPPA, PEAK-GRAPPA, k-t SENSE, k-t PCA and Compressed Sensing have been introduced which allow for up to 6-fold acceleration in typical applications [Kozerke, JCMR’08]. Reduced data acquisition schemes may, however, induce additional artifacts, correlated noise and temporal smoothing and hence may compromise overall confidence in the flow data [Blaimer, MRM’11]. It is the objective of the present work to correct for parts of the error by taking into account the physical prior of zero divergence into flow field reconstruction.
Normalized convolution [Knutsson, CVPR’93] describes a local expansion of image data into basis functions by convolution. Divergence-free basis functions [Lowitzsch, Texas’02] were used in combination with normalized convolution in order to incorporate prior knowledge of blood incompressibility into MR image reconstruction of fully sampled as well as undersampled phase contrast images.
In-vivo cine 3D PC-MRI data of the aorta was acquired in 5 healthy volunteers using a 6-element cardiac coil array on a 3T Philips Achieva systems (Philips Healthcare, Best, The Netherlands). 24 heart phases and 26-34 slices were recorded at a spatial resolution of 1.43mm x 1.43mm x 1.75mm. 2x, 4x and 8x undersampling with 75% partial Fourier sampling was simulated. Images were reconstructed with TSENSE (2x,4x) and with k-t PCA (2x,8x). For k-t PCA reconstruction 55 training profiles were used.
It has been shown that image quality of 3D flow measurements reconstructed from undersampled PC-MRI data can be greatly improved by the use of divergence-free basis functions. Hence, this approach shows considerable potential to compensate for increased noise and local data inconsistencies associated with undersampling strategies employed for reducing the long scan times associated with cine 3D PC-MRI.
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