A Physics-Informed Loss Function for Boundary-Consistent and Robust Artery Segmentation in DSA Sequences

Abstract: Accurate extraction and segmentation of the cerebral arteries from digital subtraction angiography (DSA) sequences is essential for developing reliable clinical management models of complex cerebrovascular diseases. Conventional loss functions often rely solely on pixel-wise overlap, overlooking the geometric and physical consistency of vascular boundaries, which can lead to fragmented or unstable vessel predictions. To overcome this limitation, we propose a novel \textit{Physics-Informed Loss} (PIL) that models the interaction between the predicted and ground-truth boundaries as an elastic process inspired by dislocation theory in materials physics. This formulation introduces a physics-based regularization term that enforces smooth contour evolution and structural consistency, allowing the network to better capture fine vascular geometry. The proposed loss is integrated into several segmentation architectures, including U-Net, U-Net++, SegFormer, and MedFormer, and evaluated on two public benchmarks: DIAS and DSCA. Experimental results demonstrate that PIL consistently outperforms conventional loss functions such as Cross-Entropy, Dice, Active Contour, and Surface losses, achieving superior sensitivity, F1 score, and boundary coherence. These findings confirm that the incorporation of physics-based boundary interactions into deep neural networks improves both the precision and robustness of vascular segmentation in dynamic angiographic imaging. The implementation of the proposed method is publicly available at https://github.com/irfantahir301/Physicsis_loss.