Multi-scale Gaussian product-of-experts for missing sequence multiple sclerosis lesion segmentation.

Objective: To develop and evaluate a unified framework for multiple sclerosis (MS) white matter lesion segmentation that operates robustly under clinically prevalent missing sequence magnetic resonance imaging conditions. Methods: We propose a multi-scale Gaussian product-of-experts framework (MG-PoE) integrated into nnU-Net, where sequence-specific inputs are independently processed through a shared encoder and parameterized as Gaussian experts before combination through precision-weighted product-of-experts (PoE) fusion at each encoder scale. The unified fusion rule handles different sequence configurations without requiring subset-specific architectures. The framework was systematically evaluated under different sequence configurations on diverse datasets (MSSEG2016, MS3SEG, and MSLesSeg24). Results: On the five-sequence MSSEG2016, the proposed framework achieved the best overall performance compared to benchmark methods across all full-sequence and partially observed multisequence settings, with a mean Dice Similarity Coefficient (DSC) of 0.7029, a mean 95th percentile Hausdorff distance (HD95) of 22.4030, and a mean Composite Score (CS) of 0.7235 across the 26 sequence configurations. On MS3SEG, MG-PoE achieved the highest mean DSC and CS across the full sequence and missing-sequence settings, with significant improvements over competing methods, while HD95 performance was generally comparable. In zero-shot evaluation on MSLesSeg24, the method achieved the best overall DSC and HD95 in the full sequence setting (DSC, 0.5566; HD95, 27.3729) and the best mean DSC, HD95 and CS across the missing-sequence settings (DSC, 0.5096; HD95, 30.5054; CS, 0.5811). Conclusion: The MG-PoE framework provides a unified approach to missing-sequence MS lesion segmentation, achieving favorable performance on independent datasets and providing initial evidence of cross-dataset robustness.