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# Data efficient muscle parameter estimation: Application to the Human Upper Limb

Pierre Schegg, François Bailly

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Pierre Schegg, François Bailly. Data efficient muscle parameter estimation: Application to the Human Upper Limb. 20th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, Sep 2025, Barcelona, Spain. hal-05360427

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https://hal.science/hal-05360427v1

Submitted on 12 Nov 2025

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# DATA-EFFICIENT MUSCLE PARAMETER ESTIMATION:
APPLICATION TO THE HUMAN UPPER LIMB

Pierre Schegg (1), François Bailly (1)

1. CAMIN, Inria, Univ Montpellier, Montpellier, France

## 1. Introduction

Numerical simulations of musculoskeletal models are widely used to study and predict human movement. To be viable, these models need to be personalized to each subject. A key challenge lies in understanding how specific movements influence the observability of muscle parameters to optimize model calibration experimental protocols by providing trajectories which excite these parameters, reducing experiment duration and complexity. In this article we use an open source motion dataset of the upper limb to explore data-efficient muscle parameter estimation of the upper limb.

## 2. Materials and Methods

We use an open-source dataset[1] featuring 17 healthy subjects performing arm movements in the sagittal plane with two scenarios: single-joint (elbow) movements and multi-joint (shoulder and elbow) movements. We convert the calibrated model for each participant to the bioptim[2] format using the `osim_to_biomod`<fnref n="1" /> software. The resulting model has 3 rigid bodies and 2 degrees of freedom actuated by 12 muscles. A generic forward simulation is set up in bioptim to compute the joint torque produced by the muscles as a function of the model, the experimental muscle activation, the angle and angular velocity of the joint and the muscle parameters. Optimal length and maximum isometric force are then optimized for each muscle using the optuna[3] library.

## 3. Results

Fig. 1 illustrates how computation time and joint torque Normalized Root Mean Squared Error (NRMSE) vary with the number of calibration samples. Reducing samples by a factor of 10 decreases computation time by 2.75

times and raises the mean NRMSE by 8.7%. A threefold reduction halves computation time while increasing mean NRMSE by 1.4%

<figure><img src="image_4.png" /><figcaption>Fig1: Comparison of optimization time and joint torque NRMSE depending on the number of calibration samples used.</figcaption></figure>

## 4. Discussion and Conclusions

This study demonstrates that a small amount of high-quality data allows to calibrate a model as effectively as larger datasets, enabling shorter experiments and faster computation. Future work will focus on selecting data sequences which optimize parameter observability. Additionally, the motions in this study are 2-dimensional. This affects the observability of parameters for muscles which are not strongly implicated in these degrees of freedom. Future work will extend this method to 3-dimensional motions which leverage more muscles.

## 5. References

1. Quesada, L., et al. (2024). EMG-to-torque models for exoskeleton assistance: a framework for the evaluation of in situ calibration. *Biorxiv*, 2024-01.

2. Michaud, B., et al. (2022). Bioptim, a python framework for musculoskeletal optimal control in biomechanics. *IEEE Transactions on Systems, Man, and Cybernetics: Systems*, 53(1), 321-332.

3. Takuya Akiba, et al. 2019. Optuna: A Next-generation Hyperparameter Optimization Framework. *In KDD*.

**Acknowledgements:**

This work was funded by ANR (Grant no: ANR-23-CE19-0005).

<footnote n="1">¹ https://github.com/pyomeca/osim_to_biomod</footnote>