Physiologically Constrained Musculoskeletal Neural Network for Multi-DoF Joint Kinematics Estimation from Partially Observed sEMG

The quest to decode human movement from muscle signals has evolved over decades, driven by advances in biomechanics, signal processing, and machine learning. Early biomechanical models like OpenSim provided detailed simulations of muscle-tendon dynamics but faced limitations in real-time application due to reliance on extensive measurements and computational complexity. Data-driven approaches, including CNNs, LSTMs, and Transformers, have demonstrated impressive accuracy in static or controlled scenarios but often lack physiological interpretability and struggle with unmeasured muscles. Recent hybrid methods like PINNs and PENNs attempted to incorporate physical laws into neural networks, yet they still depend on costly labels such as muscle forces or joint torques. The challenge remains: how to accurately estimate multi-DoF joint kinematics from limited sEMG signals while inferring unmeasured muscle activity, ensuring physiological plausibility and robustness across diverse movements. Addressing this gap is crucial for advancing clinical diagnostics, prosthetic control, and human-robot interaction, where comprehensive muscle information is often unavailable or impractical to measure.

The core problem tackled in this research is the partial observability of muscle activity via sEMG, which limits the direct measurement of all task-relevant muscles, especially deep or small muscles. Existing models often assume a one-to-one correspondence between sEMG channels and muscles, neglecting unmeasured muscles' contributions, leading to physiologically implausible force sharing and inaccurate kinematic predictions. Moreover, models trained solely on structured movements fail to generalize to unstructured or rapid motions. The challenge is to develop a model that can accurately estimate multi-DoF joint angles from limited measurements, infer the activation of unmeasured muscles, and maintain physiological consistency without relying on expensive biomechanical labels or overly simplified assumptions.

This study introduces several key innovations:

1) Embedding Hill muscle-tendon dynamics directly into a neural network architecture, enabling the model to learn muscle force generation end-to-end.

2) Designing a composite loss function that combines joint kinematic errors, muscle synergy regularization via fixed W matrices from NMF, and anatomy-guided activation trend regularization, which constrains the underdetermined muscle activation inference.

3) Removing the assumption of a strict one-to-one mapping between sEMG channels and muscles, allowing the model to estimate activations for both measured and unmeasured muscles simultaneously.

4) Achieving physiologically plausible parameter estimates that stay within known biological ranges, validated through ablation studies.

These innovations collectively enable the model to perform accurate, interpretable, and generalizable multi-DoF motion estimation under partial observation conditions.

• �� Data preprocessing: Raw sEMG signals are band-pass filtered (20-450Hz), rectified, and low-pass filtered at 4Hz to extract envelopes. These are normalized by MVC and segmented into overlapping windows (length 32, stride 1).
• �� Muscle activation estimation: A lightweight CNN encoder with convolutional layers (32 and 64 filters, kernel size 5), followed by global average pooling and residual fully connected layers, outputs activation probabilities for all muscles (measured and unmeasured).
• �� Embedded Hill muscle-tendon model: For each muscle, compute active and passive forces based on parameters like maximum isometric force, fiber length, pennation angle, and tendon length. These forces generate muscle torques via moment arms.
• �� Joint dynamics: Use a personalized dynamic model (mass matrix, Coriolis, gravity) to relate muscle forces to joint angles, velocities, and accelerations, integrating forces over time.
• �� Loss function: Combines three components—(1) joint kinematic loss (angle and velocity errors), (2) muscle synergy regularization (via fixed W matrices from NMF), and (3) anatomy-guided activation trend regularization (correlation of activation changes between related muscles).
• �� Training: End-to-end optimization using AdamW, batch size 64, early stopping, regularization with dropout.
• �� Evaluation: Performance assessed via NRMSE, R2, CC, and SC across multiple motion types, with baseline comparisons to CNN, Bi-LSTM, CNN-LSTM, and Transformer models.

• �� Dataset: Six healthy subjects performed wrist movements (CW, CCW, ∞, RND), with kinematic data captured by Vicon at 250Hz and sEMG signals from five muscles at 2000Hz.
• �� Data processing: Band-pass filtering, envelope extraction, normalization, and segmentation.
• �� Model training: Data split into training, validation, and test sets; hyperparameters tuned (learning rate 1e-4, regularization coefficients); training with early stopping.
• �� Evaluation metrics: NRMSE and R2 for kinematic accuracy; CC and SC for muscle activation plausibility.
• �� Baseline models: CNN, Bi-LSTM, CNN-LSTM, and PET, trained under identical conditions for fair comparison.
• �� Ablation studies: Removing unmeasured muscles or regularization components to assess their impact on performance.

• �� MSK-NN consistently outperforms baselines with an average NRMSE reduction of XX% and R2 increase of XX%, especially under unstructured random motions where it maintains R2 > 0.80.
• �� The inferred activations for unmeasured muscles like ECRB show high correlation (CC > 0.67) with recorded sEMG signals, confirming physiological plausibility.
• �� Parameter estimates stay within known physiological ranges, and ablation experiments demonstrate that unmeasured muscles significantly contribute to accurate kinematic predictions, validating the model’s physiological grounding.

• �� Clinical rehabilitation: Precise joint kinematics estimation from limited EMG signals can enhance personalized therapy.
• �� Prosthetic control: Inferring unmeasured muscle activity improves natural movement decoding in prosthetic devices.
• �� Human-robot interaction: Reliable motion prediction from partial signals enables more intuitive robotic assistance.
• �� Sports science: Monitoring muscle coordination and joint dynamics during complex movements for performance optimization.

• �� Performance drops in highly dynamic or rapid movements, due to limited training data diversity and static muscle parameters.
• �� Does not explicitly model fatigue, soft tissue nonlinearities, or joint soft tissues, which are relevant in real-world scenarios.
• �� Computational complexity limits real-time deployment; model simplification and hardware acceleration are needed for practical use.