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 patients with ATR. 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 coactivation patterns in patients with ATR. Results indicated that NMM preserved superior spectral integrity and yielded more plausible signal energy than SO and SYNX (P < 0.05). In patients with ATR, the model identified a phase-dependent shift in SOL recruitment: reduced activation during early-to-midstance and compensatory elevation during terminal stance (87.50%-100%, P < 0.01). Coactivation analysis corroborated this, showing reduced early stance but heightened late-stance levels (P < 0.05). Furthermore, the correlation between the coactivation index and peak torque revealed a transition from efficiency-driven to stability-prioritizing strategies in patients with ATR. We conclude that the NMM framework effectively characterizes specific muscle coactivation 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.NEW & NOTEWORTHY This study presents a physics-informed deep learning framework for reconstructing soleus activation after Achilles tendon repair from clinically accessible kinematics and limited EMG. The model outperformed conventional approaches in physiological fidelity and identified delayed, terminal-stance-dominant soleus recruitment with altered coactivation, offering a scalable and noninvasive approach for monitoring postoperative neuromuscular recovery.