Weighted Mean Frequencies: a handcraft Fourier feature for 4D Flow MRI segmentation

In recent decades, the use of 4D Flow MRI images has enabled the quantification of velocity fields within a volume of interest and along the cardiac cycle. However, the lack of resolution and the presence of noise in these biomarkers are significant issues. As indicated by recent studies, it appears that biomarkers such as wall shear stress are particularly impacted by the poor resolution of vessel segmentation. The Phase Contrast Magnetic Resonance Angiography (PC-MRA) is the state-of-the-art method to facilitate segmentation. The objective of this work is to introduce a new handcraft feature that provides a novel visualisation of 4D Flow MRI images, which is useful in the segmentation task. This feature, termed Weighted Mean Frequencies (WMF), is capable of revealing the region in three dimensions where a voxel has been passed by pulsatile flow. Indeed, this feature is representative of the hull of all pulsatile velocity voxels. The value of the feature under discussion is illustrated by two experiments. The experiments involved segmenting 4D Flow MRI images using optimal thresholding and deep learning methods. The results obtained demonstrate a substantial enhancement in terms of IoU and Dice, with a respective increase of 0.12 and 0.13 in comparison with the PC-MRA feature, as evidenced by the deep learning task. This feature has the potential to yield valuable insights that could inform future segmentation processes in other vascular regions, such as the heart or the brain.