A Physics-Informed Deep Learning Framework for Estimating Muscle Activation Patterns Following Achilles Tendon Repair

Accurate soleus (SOL) activation assessment is essential for Achilles tendon rupture (ATR) recovery, yet direct measurement remains a clinical challenge. This study proposes a physics-informed Transformer Neuromusculoskeletal Model (NMM) to estimate muscle activations during various locomotor tasks. We evaluated the framework using data from 40 participants, including 20 healthy controls and 20 postoperative ATR patients. By integrating forward dynamic constraints, the NMM estimates SOL activation using joint kinematics and a minimal subset of superficial electromyography (tibialis anterior, gastrocnemius medialis, and gastrocnemius lateralis). Performance was validated against conventional benchmarks, including static optimization (SO) and synergistic extrapolation (SYNX), and subsequently applied to evaluate muscle co-activation patterns in ATR patients. Results indicated that NMM preserved superior spectral integrity and yielded more plausible signal energy than SO and SYNX ( p < 0.05). In ATR patients, the model identified a phase-dependent shift in SOL recruitment: reduced activation during early-to-mid stance and compensatory elevation during terminal stance (87.50–100%, p < 0.01). Co-activation analysis corroborated this, showing reduced early-stance but heightened late-stance levels ( p < 0.05). Furthermore, the correlation between the co-activation index and peak torque revealed a transition from efficiency-driven to stability-prioritizing strategies in ATR patients. We conclude that the NMM framework effectively characterizes specific muscle co-activation patterns during ATR recovery. By significantly reducing sensor requirements while maintaining diagnostic depth for deep muscle recruitment, it provides a practical and streamlined tool for routine clinical gait monitoring.