Biomechanics-Embedded Deep Learning for Joint Moment Estimation in Clinical Gait Analysis for Cerebral Palsy: A Learnable Hill-Type Pathway.

Accurate lower-limb joint moment estimation is essential for clinical gait analysis in children with cerebral palsy (CP), yet conventional methods require force plates for ground reaction force (GRF) measurement, limiting assessment to specialized laboratories. Although data-driven methods can bypass force plates, learning from limited, heterogeneous CP data is challenging because spasticity and impaired selective motor control alter neuromuscular coordination. We developed a biomechanics-embedded framework to estimate sagittal-plane hip, knee, and ankle moments from three joint angles and four surface electromyography (sEMG) channels. Joint-angle sequences are encoded by a Transformer and sEMG signals by a graph encoder. The fused representation is decoded by a learnable Hill-type pathway and a data-driven residual head. Under 23-fold leave-one-subject-out cross-validation, the final model achieved an overall Pearson correlation coefficient (PCC) of 0.826 and root mean square error (RMSE) of 0.156 N $\cdot $ m/kg. Before self-distillation, the model achieved a PCC of 0.824, compared with 0.771 for the best of 12 capacity-matched baselines. Adding the Hill-type pathway to the data-driven backbone increased PCC from 0.773 to 0.824. Two data-side strategies were examined under limited CP data, namely same-domain self-distillation and healthy-to-CP transfer. Self-distillation yielded a small PCC increase, whereas both healthy-to-CP transfer protocols reduced PCC relative to direct CP training. These findings support further evaluation of biomechanics-embedded models for GRF-free joint moment estimation in CP.