TLDR: This research introduces Diff-MSM, a Differentiable MusculoSkeletal Model that uses automatic differentiation to simultaneously and accurately identify human muscle and bone parameters. Unlike previous methods, it doesn’t require direct measurement of internal joint torques, significantly outperforming state-of-the-art baselines in estimating muscle parameters. This breakthrough has potential applications in personalized human-robot interaction, muscle health monitoring, rehabilitation, and sports science.
Personalized human musculoskeletal models are becoming increasingly vital for accurately simulating how humans interact with robots, especially in critical applications like co-transportation or rehabilitation with robotic exoskeletons. These simulations are crucial for verifying safety before real-world deployment. A key challenge in creating these personalized models is accurately identifying subject-specific parameters for both muscles (using Hill-type models) and bones. This is difficult because internal biomechanical variables, such as joint torques, are hard to measure directly in living subjects.
A new approach, called Differentiable MusculoSkeletal Model (Diff-MSM), has been proposed to overcome these challenges. Diff-MSM allows for the simultaneous identification of both muscle and bone parameters using an end-to-end automatic differentiation technique. This innovative method differentiates from measurable muscle activation, through joint torque, to the observable motion, eliminating the need to directly measure internal joint torques. This is a significant advancement as previous methods often struggled with the inaccuracy of estimated bone parameters affecting muscle parameter accuracy, or required separate, multi-stage estimation processes.
How Diff-MSM Works
The Diff-MSM is built upon a human arm musculoskeletal model, MyoArm, which uses the Mujoco physics engine. This model focuses on the arm, including eight muscles (like parts of the Deltoid, Biceps, Triceps, Brachialis, and Brachioradialis) and three movable bones (humerus, ulna, and radius). The model incorporates Hill-type muscle dynamics to calculate muscle forces and joint torques from muscle activation signals. It also uses the Articulated Body Algorithm (ABA) for the forward dynamics of the rigid skeletal body, calculating joint accelerations from joint positions, velocities, and torques.
The core of the parameter identification is formulated as an optimization problem. The system minimizes a loss function, which is the normalized mean squared error between the joint accelerations calculated by a ground truth model and those predicted by the learnable Diff-MSM, given the same muscle activation signals. The entire musculoskeletal dynamics equation is implemented as a differentiable computation graph using PyTorch, allowing for automatic differentiation to calculate gradients and optimize the 54 parameters (24 muscle parameters and 30 bone parameters) simultaneously.
To ensure the physical consistency of the optimized parameters (e.g., positive mass, positive definite inertia matrices), the researchers employed implicit constraint methods. For instance, bone mass is represented in a way that always ensures it’s positive, and the inertia matrix is constructed to always be positive definite. This converts a complex constrained optimization problem into a more manageable unconstrained one. Additionally, a scalar multiplier strategy is used for each parameter to improve the sensitivity of the loss function to parameter changes, ensuring that the learnable parameters operate within a defined range.
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Performance and Implications
Extensive comparative simulations were conducted to evaluate Diff-MSM against state-of-the-art methods. Five different methods were tested, including simulated annealing (a global optimization method) and automatic differentiation with the Adam optimizer, both for optimizing muscle parameters alone and for simultaneously optimizing muscle and bone parameters. The results clearly showed that automatic differentiation-based methods, particularly the proposed Diff-MSM (M4), significantly outperformed simulated annealing methods in minimizing loss and reducing the distance error from ground truth parameters. Notably, simultaneous optimization of muscle and bone parameters with automatic differentiation yielded better results than optimizing muscle parameters alone, a benefit not observed with simulated annealing.
Further simulations, including all inertia tensor parameters, demonstrated that muscle parameters were estimated with exceptional accuracy, converging steadily to their ground truth values. While some bone parameters showed redundancy, their corresponding dynamic coefficients (a minimum set that determines bone dynamic behavior) converged well. The identified parameters also showed excellent generalization ability to new datasets, indicating the robustness of the method.
The accurate estimation of muscle parameters, such as optimal muscle fiber length, maximum isometric force, and maximum contraction velocity, has significant implications. These parameters are crucial indicators of muscle strength and power, which are vital for assessing an individual’s muscle health. Unlike current methods that often measure muscle strength for groups of muscles, this technique could enable monitoring and fine management of individual muscle health, opening new avenues in rehabilitation, sports science, and medical diagnostics. The ability to accurately estimate joint torques from precise muscle parameters could also improve future bone dynamic parameter estimation using advanced robotics techniques.
This pilot study demonstrates the effectiveness of a differentiable human musculoskeletal arm model for simultaneously identifying muscle and bone parameters. The proposed method, detailed in the research paper available at arXiv:2508.13303, represents a substantial step forward in creating high-fidelity personalized musculoskeletal models, with broad potential applications in human-robot interaction, health monitoring, and biomechanics.
