# Optimized Stimulation Patterns for FES-stimulated Cycling Using an Experimentally Identified Physiological Muscle Model

Tiago Coelho-Magalhães, Christine Azevedo-Coste, François Bailly

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Tiago Coelho-Magalhães, Christine Azevedo-Coste, François Bailly. Optimized Stimulation Patterns for FES-stimulated Cycling Using an Experimentally Identified Physiological Muscle Model. 28th Annual Conference of the International Functional Electrical Stimulation Society - Rehabweek 2025, May 2025, Chicago, United States. hal-05119468

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Submitted on 18 Jun 2025

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# OPTIMIZED STIMULATION PATTERNS FOR FES-STIMULATED CYCLING USING AN EXPERIMENTALLY IDENTIFIED PHYSIOLOGICAL MUSCLE MODEL

Tiago Coelho-Magalhães¹, Christine Azevedo-Coste¹, François Bailly¹

¹CAMIN, INRIA, University of Montpellier, Montpellier, France

tiago.coelho-magalhaes@inria.fr

## INTRODUCTION

Numerical simulation can be used to explore Functional Electrical Stimulation (FES) patterns and advanced control strategies for generating optimized muscle forces and joint kinematics. In particular, trajectory optimization is an efficient method to discover novel control strategies, guided by the system's dynamics and task-related constraints [1, 2].

In this work, a physiological FES-stimulated muscle model [3], accounting for the calcium-troponin complex dynamics, is first calibrated using experimental torque data from one participant with paraplegia. The personalized model is then used in a musculoskeletal pedaling simulation in which the instantaneous pulse duration of the stimulation is optimized using numerical optimal control.

## METHODS

One male participant with spinal cord injury (T6; AIS A) participated in the study. A tadpole trike was fixed on a stationary cycling trainer with the original crankset being replaced by a power-meter crank to measure torque and pedaling power. Calf supports were fixed to the pedals to keep the ankle joint at 90° and restrict the leg movement to the sagittal plane. Isometric crank torques were recorded along the pedaling cycle at several knee angles (from 70° to 120° in 10° steps) first stimulating the rectus femoris and vastus lateralis muscles and then the hamstrings. The data obtained was used to solve a global trajectory optimization problem to identify the muscle parameters, using the Bioptim software [4]. Then, the identified model was used in predictive simulation in which the stimulation pulse duration was optimized to produce a 15-Watt pedaling motion at 4.4 rad.s⁻¹ (42 rpm).

## RESULTS

Figure 1.a shows the lower limb musculoskeletal model used in the FES-assisted cycling simulations. Figure 1.b presents the stimulation pattern, highlighting the specific phases of the pedaling cycle during which each muscle is activated, over a 3-second simulation featuring coordinated agonist and antagonist activation. The resulting pedaling cadence was 4.5 ± 0.8 rad.s⁻¹ (Fig. 1.c), and the corresponding power output was 10.2 ± 6.0 W (Fig. 1.d). Power output increased progressively over time, approaching a mean pedaling power closer to the target towards the end of the simulation.

<figure><img src="image_2.png" /><figcaption>Figure 1: a) Lower limb musculoskeletal model adapted for FES-assisted cycling simulations; b) Stimulation pattern corresponding to a 15-W target pedaling power output; c) resulting pedaling cadence; d) output power measured at the crank axis.</figcaption></figure>

## DISCUSSION AND CONCLUSION

This study presents a first step towards improving the realism of FES-driven simulations and showcases the possibility of using physiological model-based control of FES-assisted cycling, with possible application in various other FES-assisted tasks

<footnote>[1] Coelho-Magalhães, T., Azevedo-Coste, C., & Bailly, F. (2024). FES-induced musculoskeletal trajectory optimization with an adapted muscle model. In FESS Conference 2024 in Bath, UK.</footnote>

<footnote>[2] Coelho-Magalhães, T.; Azevedo-Coste, C.; Bailly, F. (2025) Numerical-Optimal-Control-Compliant Physiology-Based Muscle Model for Electrically Stimulated Induced Contractions. Under review in IEEE Transactions on Medical Robotics and Bionics (T-MRB).</footnote>

<footnote>[3] Ding, J., Wexler, A. S., & Binder-Macleod, S. A. (2002). A mathematical model that predicts the force-frequency relationship of human skeletal muscle. Muscle & Nerve: Official Journal of the American Association of Electrodiagnostic Medicine, 26(4), 477-485.</footnote>

<footnote>[4] 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.</footnote>