# Optimal estimation of forearm muscle activations evoked by implanted electrical stimulation in complete quadriplegia

Valentin Maggioni, Pierre Schegg, Thomas Guiho, Christine Azevedo-Coste, François Bailly

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Valentin Maggioni, Pierre Schegg, Thomas Guiho, Christine Azevedo-Coste, François Bailly. Optimal estimation of forearm muscle activations evoked by implanted electrical stimulation in complete quadriplegia. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16235 . hal-05191790v2

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# Optimal estimation of forearm muscle activations evoked by implanted electrical stimulation in complete quadriplegia

Valentin Maggioni*, Pierre Schegg, Thomas Guiho, Christine Azevedo-Coste, François Bailly

Inria, Université de Montpellier, Montpellier, France

* Corresponding author: valentin.maggioni@inria.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** musculoskeletal model, optimal control, hand and fingers, functional electrical stimulation, quadriplegia, neuroprosthesis

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Muscle activity assessment is crucial to understand both natural and evoked human movements. The most common method to measure it is through surface electromyography (EMG). However, this method presents significant caveats, such as cross-talk from adjacent muscles, or its inability to detect deep-muscles' contractions. A possible solution to address these limitations is multimodal estimation, through the use of a musculoskeletal (MSK) model leveraging kinematic and EMG data. In particular, it is possible to formulate an optimal estimation problem to blend these quantities and estimate the activation of the model's muscles (Bailly et al. 2021). In the present study, we apply this approach to a hand model developed in the context of functional electrical stimulation (FES) of arms' nerves to restore hand movements in individuals with complete quadriplegia via implanted epineural electrodes (Azevedo Coste et al. 2022). Within this framework, this study's main objective is to accurately estimate muscle activations of FES-induced hands movements by fusing kinematics and EMG data.

## 2. Methods

### 2.1 Participant and data acquisition

The kinematic and EMG data used to drive the optimal estimation problem were obtained from a previous clinical trial (NCT05555914) involving an individual with quadriplegia (included 36 months after injury,

injury level C6 AIS B) implanted with two epineural multicontact electrodes wrapped around the median and radial nerves respectively. The participant received proper information (nature of the study, potential risks, expected outcomes, etc.) before giving informed consent. We selected a trial in which a gradual increase of current amplitude was applied to the radial nerve and focused on one movement evoked by the highest stimulus. The induced movement was a five-fingers extension. Hand kinematics was captured with four webcams through markerless motion capture (Maggioni et al. 2025). The recruitment curves were computed from surface recordings of evoked-EMGs from which muscle activations were derived.

### 2.2 Forearm musculoskeletal model

Our musculoskeletal model is based on the one developed and validated in Mc Farland et al. 2023 on OpenSim. The model was adapted to be compatible with Bioptim, a trajectory optimization software (Michaud et al. 2023). We then performed a kinematic validation of the translated model. To that end, the differences between the marker trajectories of the two models were compared over the course of a grasping task. Finally, as the specific measurement selected for this study only involved finger kinematics evoked by radial nerve stimulation, we simplified the model by only keeping the muscle it innervates, leading to a smaller model with 15 joints and 9 muscles.
## 2.3 Optimal control problem

The estimation problem was formulated as a trajectory optimization problem that aims to find the model states (joint positions and velocities), and controls (muscle activations) trajectories that minimize an objective function made of several terms:

* To track the measured hand kinematics.

* To track the muscle activations derived from the recorded EMG data (for 5 recorded muscles).

* To minimize the computed muscle activation (for the remaining 4 muscles).

The optimal solution provides an estimation of all individual muscles' activations, even those for which direct EMG measurements could not be recorded.

## 3. Results and discussion

The measured extension from the clinical trial presented a mean range of motion for each finger joint of 0.23±0.37rad, with muscle activations of 0.092 for the Extensor Digitorum Communis (EDC) and of 0.249 for the Extensor Pollicis Longus (EPL).

For the kinematic validation of the MSK model, the root mean square error (RMSE) between markers trajectories was less than 0.01mm.

The mean RMSE between the kinematics resulting from the optimization and the measured joint movement is 0.06±0.04rad, showing a good kinematics match of the model, with slightly higher errors for the thumb.

The mean RMSE between the 5 measured muscle activation and their mean counterparts resulting from the optimization is 0.01±0.01, which is negligible compared to the measured activations. The detailed muscle activations for other muscles of the model are shown in Fig. 1.

The optimization problem estimated activations values for some of the deep muscles of the arm that could not be measured through surface EMG. The studied movement consisted in an evoked fingers extension induced by electric stimulation of the radial nerve and the model was simplified accordingly. Our future work will focus on diversifying the studied movements with a more complete forearm model.

## 4. Conclusions

In this study, forearm muscles activations were successfully estimated (including deep muscles' ones) during finger movements elicited by FES on a person with quadriplegia. The proposed method fuses kinematics

<figure><img src="image_3.png" /></figure>

*Muscles for which no surface EMG data was measurable

**Figure 1.** Bar graph of the mean forearm muscle activation obtained with the optimal control problem solution (in purple) and the measured values (in green). The represented muscles are: Extensor Indicis Proprius (EIC), Extensor Digitorum Communis (EDCL, EDCR, EDCM, EDCI), Extensor Digiti Minimi (EDM), Extensor Pollicis Longus (EPL), Extensor Pollicis Brevis (EPB), and Abductor Pollicis Longus (APL).

and EMG measurement using a MSK model and a trajectory optimization framework. Future work will focus on a wider range of movements, including the wrist and a more complete model.

## Conflict of Interest Statement

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

## Contributor Roles

V.M: Data curation, Investigation, Methodology, Software, Validation, Visualization, Writing-original draft, Writing-review & editing. P.S: Methodology, Software, Resources, Validation, Writing-review & editing. T.G: Software, Resources, Writing-review & editing. C.A-C: Conceptualization, Data
curation, Formal analysis, Funding acquisition, Project administration, Resources, Supervision, Writing-review & editing. F.B: Conceptualization, Data curation, Formal analysis, Funding acquisition, Project administration, Software, Resources, Supervision, Writing-review & editing.

## Funding

This research was funded by the European Union's Horizon Europe research and innovation program under the EIC Pathfinder project AI-HAND (grant agreement No. 101099916), and the ANR program (Grant no: ANR-23-CE19-0005). As well as I-SITE MUSE, Université de Montpellier.

## Data, software, code availability

The Bioptim software suite used for solving the optimal control problem is fully open-source and available at: https://github.com/pyomeca/bioptim

## References

Bailly, F., Ceglia, A., Michaud, B., Rouleau, D. M., & Begon, M. (2021). Real-time and dynamically consistent estimation of muscle forces using a moving horizon emg-marker tracking algorithm—application to upper limb biomechanics. *Frontiers in bioengineering and biotechnology*, 9, 642742. https://doi.org/10.3389/fbioe.2021.642742

Azevedo Coste, C., William, L., Fonseca, L., Hiairrassary, A., Andreu, D., Geffrier, A., ... & Guiraud, D. (2022). Activating effective functional hand movements in individuals with complete tetraplegia through neural stimulation. *Scientific Reports*, 12(1), 16189. https://doi.org/10.1038/s41598-022-19906-x

Maggioni, V., Azevedo-Coste, C., Durand, S., & Bailly, F. (2025). Optimisation and comparison of markerless and marker-based motion capture methods for hand and finger movement analysis. *Sensors*, 25(4), 1079. https://doi.org/10.3390/s25041079

McFarland, D. C., Binder-Markey, B. I., Nichols, J. A., Wohlman, S. J., De Bruin, M., & Murray, W. M. (2022). A musculoskeletal model of the hand and wrist capable of simulating functional tasks. *IEEE transactions on biomedical engineering*, 70(5), 1424–1435. https://doi.org/10.1109/TBME.2022.3217722

Michaud, B., Bailly, F., Charbonneau, E., Ceglia, A., Sanchez, L., & Begon, M. (2022). Bioptim, a python

framework for musculoskeletal optimal control in biomechanics. *IEEE Transactions on Systems, Man, and Cybernetics: Systems*, 53(1), 321–332. https://doi.org/10.1109/TSMC.2022.3183831