Physics-Informed Deep Learning for Musculoskeletal Modeling

Computational musculoskeletal (MSK) analysis plays a pivotal role in understanding human movement, enabling applications ranging from clinical rehabilitation assessment and injury prevention to assistive device control and sports performance optimization. Accurate estimation of muscle activation and force is essential for these applications, yet remains technically challenging as these variables are difficult to measure directly in vivo. Two dominant paradigms have emerged: physics-based methods and data-driven methods. While physics-based methods offer biomechanically consistent estimates, they face critical implementation challenges. Forward dynamics approaches map neural commands (typically derived from surface electromyography, sEMG) to kinematics, but are often hindered by measurement constraints (e.g., the inaccessibility of deep muscles) and extensive calibration requirements. Conversely, inverse dynamics approaches must resolve the MSK redundancy problem via optimization, resulting in high computational latency that precludes real-time applications. Data-driven methods offer automatic feature discovery and computational efficiency, but they introduce a dependency on physics-based labels for training and lack biomechanical constraints, which can enable physiologically implausible predictions.

This thesis addresses these complementary limitations by developing physics-informed deep learning frameworks that embed MSK dynamics. By integrating muscle activation dynamics, Hill-type muscle-tendon mechanics, and the equation of motion within loss functions, the frameworks achieve physically consistent predictions with millisecond-level end-to-end inference. This methodology enables label-free training and is systematically applied to resolve problems in both forward and inverse dynamics, ranging from single-joint to multi-joint systems. To accomplish this objective, the following efforts were undertaken: 1) A physics-informed deep learning framework was developed for muscle force prediction from unlabeled sEMG signals. By embedding MSK dynamics into the loss function, this approach achieves comparable performance to supervised baselines while eliminating labeled data requirements. Subject-specific muscle-tendon parameters are jointly optimized as learnable variables during training. 2) A knowledge-based deep learning framework was proposed for time-efficient inverse dynamics in single-joint systems. By integrating MSK model dynamics, performance criteria from traditional optimization, and physiological boundary conditions into the loss function, this method directly estimates muscle activations and forces from joint kinematics without any label information. 3) To extend the framework to multi-joint systems, a Multi-Joint Cross-Attention BiGRU (MJCA-BiGRU) architecture was developed, coupled with integration of comprehensive multi-joint dynamics into physics-informed training. The MJCA module captures inter-joint coordination through attention mechanisms. Complete multi-joint MSK dynamics (mass matrices, Coriolis forces) and external forces are embedded into loss functions, enabling label-free training while ensuring biomechanical consistency across coordinated systems.

Across the three studies, a consistent set of findings emerges. First, embedding MSK dynamics into the training loss is sufficient to produce physiologically plausible muscle activations and forces without labeled supervision, in both forward (sEMG to force and motion) and inverse (kinematics to muscle states) dynamics. Second, the proposed frameworks achieve accuracy comparable to supervised baselines in both cases, where the supervision is derived from an optimized forward MSK model (forward case) and from static optimization (inverse case), while reducing inference time to the millisecond range. Third, all three frameworks exhibit a reasonable degree of robustness and cross-subject and cross-condition generalization, suggesting that embedded physics helps the networks learn transferable biomechanical relationships rather than dataset-specific patterns. The principal conclusion is that physics-informed deep learning offers a unified paradigm for MSK modeling, in which forward and inverse dynamics share the same core principle of using embedded physics as a substitute for labeled data, achieving label efficiency and real-time inference while conferring a degree of biomechanical interpretability on the learned model. Future work will extend the frameworks to 3D multi-DOF and pathological movements, replace manual loss-weight tuning with automated balancing, and incorporate multi-modal sensing and online adaptation. More broadly, by loosening the dependence on labeled data and laboratory instrumentation, the proposed frameworks point toward MSK analysis tools usable beyond the biomechanics laboratory, in routine clinical assessment, home-based rehabilitation, and closed-loop control of assistive devices.