Physics and Morphology Constrained Quantitative Susceptibility Based Segmentation of Cerebral Veins

Abstract

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 U-Net. In addition to supervised Dice and cross-entropy losses, the network incorporated two self-supervised 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.