3D Segmentation of Pathological Muscle with a Physics-Informed Latent-Regularized U-Net

Objective: We developed a data-efficient deep learning framework for three-dimensional segmentation of pathological musculoskeletal anatomy from magnetic resonance imaging (MRI) when only limited manual annotations are available. Methods: We developed a Physics-Informed Latent-Regularized U-Net (PILR-U-Net) that combines transfer learning from healthy MRI, latent-space anatomical regularization, and elasticity-based physics-informed constraints. The physics-informed loss enforces mechanical equilibrium, near-incompressibility, and spatial smoothness of predicted deformation fields. The framework was evaluated on MRI datasets from 50 participants with cerebral palsy across 15 lower-limb musculoskeletal structures using sparse manual annotations. Performance was assessed using volumetric overlap, boundary accuracy, volume error, sensitivity, and precision. Ablation experiments evaluated the individual contributions of latent-space and physics-informed regularization. Results: Our experimental results show accurate segmentations with three-dimensional Dice coefficients ranging from 0.750 to 0.943 across evaluated structures, while most structures exhibited low surface-distance errors. Predicted deformation fields maintained positive Jacobian determinants near unity and smooth strain-energy distributions. Ablation analysis showed that both regularization components improved performance, with removal of physics-informed regularization producing the largest reductions in Dice accuracy and increases in boundary error. Conclusion: PILR-U-Net enables accurate and anatomically plausible segmentation of pathological musculoskeletal MRI under sparse supervision. Significance: Incorporating anatomical priors and biomechanical constraints into deep segmentation networks may reduce dependence on extensive pathological annotations and support patient-specific musculoskeletal modeling and clinical analysis.