Physics and Morphology Constrained Quantitative Susceptibility Based Segmentation of Cerebral Veins

Purpose: Quantitative susceptibility mapping (QSM) provides venous contrast through the paramagnetic susceptibility of deoxyhemoglobin and can be used to estimate oxygen extraction fraction (OEF), a marker of cerebral metabolism. However, cerebral vein segmentation remains challenging due to artifacts, variability across QSM reconstruction methods, and limited sensitivity of conventional vessel-filtering approaches to small cortical veins. This study proposes a physics- and morphology-constrained deep learning framework for cerebral vein segmentation on QSM. Methods: Thirty subjects were manually segmented and used to train an attention-gated UNet. In addition to supervised Dice and cross-entropy losses, the network incorporated two selfsupervised constraints. A physics-informed loss enforced consistency between the measured local field and a field simulated from predicted veins using dipole convolution. A Frangi vesselness loss encouraged anatomically plausible tubular structures. Segmentation performance was evaluated on an independent multi-center cohort and compared with a prior vessel-filtering method and a supervised U-Net baseline. Physiological relevance was assessed by comparing QSM-derived venous OEF with calibrated fMRI-derived OEF. Results: The proposed model achieved superior segmentation performance (centreline Dice = 0.70 {+/-} 0.08) compared with MSVF (0.44 {+/-} 0.09) and the U-Net baseline (0.57 {+/-} 0.14). Improvements were most pronounced in smaller veins, resulting in greater vessel continuity. Venous OEF derived from the proposed framework demonstrated stronger agreement with calibrated fMRI-derived OEF than the previous approach. Conclusion: Combining supervised learning with physics- and morphology-based constraints improves vein segmentation and enhances the sensitivity of QSM-derived OEF measurements. Code and model weights are publicly available at https://github.com/QuantitativePhysiologyImagingLab/VeinSeg