# 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, IFESS 2025: International Functional Electrical Stimulation Society 2025 (part of RehabWeek 2025), May 2025, Chicago, United States. [hal-05119463](https://HAL Id: hal-05119463)

Submitted on 18 Jun 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Optimized Stimulation Patterns for FES-stimulated Cycling Using an Experimentally Identified Physiological Muscle Model

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

¹INRIA, University of Montpellier, France
francois.bailly@inria.fr

**Introduction:** Functional Electrical Stimulation (FES) assisted cycling has demonstrated to be efficient in preventing physical function decline while increasing musculoskeletal health [1]. The stimulation parameters are frequently defined in a time-consuming procedure and experimentally tuned due to subject-specific biomechanical and electrophysiological characteristics. Numerical simulation can be used to explore stimulation patterns or advanced control strategies that generate optimized muscle forces and joint kinematics. In particular, trajectory optimization is an efficient method to explore novel control strategies, guided by the system's dynamics and task-related constraints. In this paper, a physiological FES-stimulated muscle model [2, 3], accounting for the calcium-troponin complex dynamics, is calibrated using experimental torque data from one participant with paraplegia. The personalized model is then used in a musculoskeletal pedaling simulation in which stimulation pulse durations are optimized using numerical optimal control.

**Methods:** One male participant with spinal cord injury (T6; AIS A) participated in the study. A commercially available recumbent tadpole trike (ICE Adventure, ICE, Falmouth, Cornwall, UK) was fixed on an instrumented cycling stationary trainer (KICKR Smart Trainer, Wahoo, Atlanta, Georgia, US) with the original crankset being replaced by a power-meter crank (2INPOWER, Rotor Bike Components, Madrid, Spain) to measure torque and pedaling power. Calf supports (HASE® Bikes, Waltrop, Germany) 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).

<figure><img src="image_2.png" /><figcaption>Figure 1: a: Lower limb musculoskeletal model with FES-stimulated muscles; b: optimized stimulation pattern; c: resulting pedaling cadence; d: resulting pedaling power.</figcaption></figure>

**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.

**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.

## References

[1] van der Scheer, J. W., Goosey-Tolfrey, V. L., Valentino, S. E., Davis, G. M., & Ho, C. H. (2021). Functional electrical stimulation cycling exercise after spinal cord injury: a systematic review of health and fitness-related outcomes. *Journal of NeuroEngineering and Rehabilitation, 18*(1), 99.

[2] Coelho-Magalhães, T., Coste, C. A., & Bailly, F. (2024). FES-induced musculoskeletal trajectory optimization with an adapted muscle model. In *FESS Conference 2024 in Bath, United Kingdom*.

[3] 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)*.

[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.