Maximizing Task Endurance through Muscle Fatigue Minimization with Consideration of Muscle Fatigability and Task Contribution: an in-Silico FES Study of Handcycling

Technical Summary: Maximizing Task Endurance through Muscle Fatigue Minimization in FES-Driven Handcycling

Problem Statement
Functional Electrical Stimulation (FES) is a rehabilitation technique used to restore motor function following neuromusculoskeletal disorders. However, its clinical utility is significantly hindered by the premature onset of peripheral muscle fatigue. Unlike natural recruitment, which preferentially activates slow-twitch fibers during endurance tasks, FES synchronously activates motor units under electrodes with limited fiber-type selectivity, leading to rapid fatigue. While various strategies exist to mitigate fatigue at the muscle level (e.g., modulating frequency or pulse width), they often fail to account for the mechanical redundancy of the musculoskeletal system. Current optimal control methods for FES frequently treat fatigue as a disturbance rather than a state to be minimized, and existing cost functions (typically minimizing electrical charge or pulse width) have not been rigorously compared for their ability to prolong task duration. This study addresses the gap in identifying cost functions and weighting strategies that maximize task endurance in a redundant upper-limb system.

Methodology
The study employed an in-silico approach using a 2-degree-of-freedom, 4-muscle musculoskeletal model of the right upper limb (anterior/posterior deltoids, biceps, triceps) adapted for a hand-cycling task at 60 RPM. The system dynamics combined a musculoskeletal model with the Ding et al. (2003, 2007) phenomenological FES pulse width and fatigue models.

The core of the methodology involved a Receding Horizon Optimal Control (RHOC) scheme. Due to the computational intractability of solving a single 20-minute optimization, the problem was broken into windows of 2 to 5 crank cycles. The study proceeded in three distinct phases:

1. Cost Function Comparison: Seventeen cost functions were evaluated, combining four normed archetypes (average, quadratic, cubic, infinity) with five physiological/stimulation variables (pulse width, muscle force, stress, power, and fatigue state $a'$). These were compared against a standard clinical-like stimulation pattern.
2. Bayesian Optimization: A Bayesian optimization approach was used as an outer-loop black-box method to tune muscle-specific weights within a quadratic fatigue cost function. This aimed to maximize the number of completed cycles before task failure, exploring a search space of weights for the four muscles.
3. Physiological Weight Derivation: To address the high computational cost of Bayesian optimization (135 hours), an original, interpretable method was proposed. This method calculated muscle weights based on two metrics: muscle fatigability (rate of force decline under high demand) and mechanical criticality (unique torque contribution and support before negative torque zones).

Key Contributions

• Systematic Comparison of Cost Functions: The study provides a comprehensive evaluation of 17 cost function variations, demonstrating that the choice of the targeted variable has a significantly larger impact on endurance than the mathematical norm archetype.
• Weighted Optimization Strategy: It introduces a framework for incorporating muscle-specific weights into FES optimal control, moving beyond uniform cost functions to account for physiological differences (fatigability) and mechanical roles.
• Interpretable Weighting Heuristic: The paper proposes a rapid (<1 second) calculation method for muscle weights based on fatigability and mechanical criticality, offering a practical alternative to computationally expensive Bayesian optimization while achieving comparable performance.
• Identification of Failure Mechanisms: The study identifies that task failure in handcycling is not solely due to global fatigue but is driven by specific muscles (notably the anterior deltoid and biceps) reaching saturation, highlighting the need for adaptive redistribution of effort.

Results

• Cost Function Performance: The fatigue-minimization cost function ($\phi_{a'}^2$) yielded the best endurance outcome, achieving 74.7% more cycles than the standard pulse width minimization ($\phi_{pw}^1$) and 42.9% more than muscle stress minimization. The optimized variable (fatigue) accounted for 49.8% of the variance in endurance, while the norm archetype accounted for 20.4%.
• Bayesian Optimization: Optimizing muscle-specific weights via Bayesian methods increased endurance by an additional 40.6% (reaching 1,729 cycles) compared to the unweighted fatigue minimization. This strategy successfully redistributed effort toward the more fatigue-resistant triceps and away from the rapidly fatiguing anterior deltoid. However, this approach required 135 hours of computation, limiting immediate clinical applicability.
• Physiological Weighting: The proposed heuristic method, which incorporated muscle fatigability and mechanical criticality, achieved a 37.6% increase in endurance (1,692 cycles) compared to the unweighted baseline. This result was nearly identical to the Bayesian-optimized result but was computed in less than one second.
• Stimulation Patterns: Optimized strategies shifted from uniform distribution to adaptive patterns. For instance, fatigue minimization promoted brief stimulation bursts with longer pulse widths, whereas pulse width minimization favored low, distributed control. The weighted strategies balanced fatigue progression, delaying the point at which critical muscles (anterior deltoid, biceps) reached 50% force capacity.

Significance
The paper argues that maximizing task endurance in FES rehabilitation requires moving beyond simple charge minimization. The primary significance lies in demonstrating that accounting for the multifactorial nature of endurance—specifically the interplay between muscle-specific fatigability and mechanical criticality—is essential for prolonging FES-driven activity.

The study concludes that while minimizing the fatigue state variable is the most effective cost function archetype, its performance is heavily dependent on how the controller distributes effort among redundant muscles. The proposed weighting method offers a practical, interpretable, and computationally efficient solution to personalize stimulation strategies without the prohibitive cost of iterative optimization. By preventing the premature exhaustion of mechanically critical or highly fatigable muscles, these strategies support the potential for longer, more effective rehabilitation sessions, addressing a key barrier to the clinical adoption of FES.