Magnetic resonance angiography (MRA) is an imaging modality for visualising blood vessels. It is useful for several diagnostic applications and for assessing the risk of adverse events such as haemorrhagic stroke (resulting from the rupture of aneurysms in blood vessels). However, MRAs are not acquired routinely, hence, an approach to synthesise blood vessel segmentations from more routinely acquired MR contrasts such as T1 and T2, would be useful. We present an encoder-decoder model for synthesising segmentations of the main cerebral arteries in the circle of Willis (CoW) from only T2 MRI. We propose a two-phase multi-objective learning approach, which captures both global and local features. It uses learned local attention maps generated by dilating the segmentation labels, which forces the network to only extract information from the T2 MRI relevant to synthesising the CoW. Our synthetic vessel segmentations generated from only T2 MRI achieved a mean Dice score of $0.79 \pm 0.03$ in testing, compared to state-of-the-art segmentation networks such as transformer U-Net ($0.71 \pm 0.04$) and nnU-net($0.68 \pm 0.05$), while using only a fraction of the parameters. The main qualitative difference between our synthetic vessel segmentations and the comparative models was in the sharper resolution of the CoW vessel segments, especially in the posterior circulation.
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