Determination of subject-specific muscle fatigue rates under static fatiguing operations (1402.1713v1)

Abstract: Cumulative local muscle fatigue may lead to potential musculoskeletal disorder (MSD) risks {\color{red}, and subject-specific muscle fatigability needs to be considered to reduce potential MSD risks.} This study was conducted to determine local muscle fatigue rate at shoulder joint level based on an exponential function derived from a muscle fatigue model. Forty male subjects participated in a fatiguing operation under a static posture with a range of relative force levels (14% - 33%). Remaining maximum muscle strengths were measured after different fatiguing sessions. The time course of strength decline was fitted to the exponential function. Subject-specific fatigue rates of shoulder joint moment strength were determined. Good correspondence ($R^2>0.8$) was found in the regression of the majority (35 out of 40 subjects). Substantial inter-individual variability in fatigue rate was found and discussed.

• The paper demonstrates that an exponential decay model reliably quantifies subject-specific shoulder fatigue rates, with 35 of 40 subjects showing an R² > 0.8.
• It finds that individuals with greater initial strength exhibit faster fatigue rates (mean k = 1.02 min⁻¹, SD = 0.49), suggesting a link to muscle fiber composition.
• The study’s methodology supports personalized risk assessments and ergonomic task design to reduce work-related musculoskeletal disorders.

This paper presents an experimental paper aimed at determining subject-specific muscle fatigue rates for the shoulder joint during static, fatiguing operations, relevant to industrial tasks like overhead drilling (1402.1713). The core idea is to quantify how quickly an individual's muscle strength declines under a sustained load, recognizing that this rate varies significantly between people and impacts their risk of musculoskeletal disorders (MSDs).

The paper builds upon a previously proposed muscle fatigue model by Ma et al. (2008), which describes the rate of decrease in maximum remaining strength ($F_{rem}$) over time ($t$) using a differential equation:

$$\frac{dF_{rem}(t)}{dt} = -k \frac{F_{rem}(t)}{MVC}F_{load}(t)$$

Here, $MVC$ is the initial maximum voluntary contraction strength, $F_{load}(t)$ is the external load, and $k$ is the subject-specific fatigue rate (in min⁻¹), representing the intrinsic fatigability of the muscle group. For static tasks where $F_{load}$ is constant, this model simplifies to an exponential decay function relating the ratio of remaining strength to initial strength over time:

$\frac{F_{rem}(t)}{F_{max}} = e^{-k\,f_{MVC}\,t}$

where $F_{max}$ is equivalent to $MVC$, and $f_{MVC} = F_{load}/MVC$ is the relative load level. The paper aimed to verify if this exponential function accurately models individual strength decline during a static task and if the derived parameter $k$ effectively captures subject-specific fatigue attributes.

Methodology

• Participants: 40 right-handed male industrial workers participated.
• Task: A simulated static overhead drilling task was performed while seated. Subjects held a 2.5 kg mock tool and exerted a constant 25 N force against a suspended beam, mimicking drilling pressure. The posture constrained the right arm's movement primarily to the sagittal plane. This task setup resulted in shoulder joint moment loads ranging from 14% to 33% of the subjects' individual maximum capabilities.
• Measurements:
  • Initial Maximum Voluntary Contraction (MVC) force in the drilling direction was measured.
  • Remaining maximum force ($F_{t_i}$) was measured after holding the static load for nine different durations ($t_i$ = 15, 30, 45, 60, 75, 90, 120, 150, 180 seconds). Sessions were randomized, with sufficient rest and recovery checks between them.
  • Upper limb posture (shoulder, elbow, wrist coordinates) was tracked using a magnetic motion capture system (FASTRAK).
  • Drilling force was measured using a dynamometer.
• Data Analysis:
  • Shoulder joint moments ($\Gamma_{load}$, $\Gamma_{max}$, $\Gamma_{rem}(t_i)$) were calculated using the force measurements and posture data.
  • The exponential fatigue model (adapted for moments) was linearized: $$\frac{\ln\left(\frac{\Gamma_{t_{i}}}{\Gamma_{max}}\right)}{f_{MVC}} = -k\;t_i$$, where $f_{MVC} = \Gamma_{load}/\Gamma_{max}$.
  • Linear regression without an intercept was performed for each subject's data points ($\ln(\Gamma_{t_i}/\Gamma_{max})/f_{MVC}$ vs. $t_i$) to determine their specific fatigue rate $k$ and the goodness of fit ($R^2$).
  • Correlations between $k$ and subject characteristics (joint strength, age, BMI) were analyzed.

Key Findings

• Model Fit: The exponential fatigue model provided a good fit for the majority of subjects (35 out of 40 had $R^2 > 0.8$), indicating its suitability for describing individual shoulder joint fatigue progression under these static conditions. The mean $R^2$ was 0.87.
• Subject-Specific Fatigue Rates: Significant inter-individual variation was observed in the fatigue rate $k$ (Mean = 1.02 min⁻¹, SD = 0.49, Range = 0.37 to 2.29 min⁻¹). This confirms that individuals fatigue at substantially different rates even under the same relative workload.
• Fatigue Rate and Strength: A statistically significant positive correlation was found between the fatigue rate $k$ and the initial maximum shoulder joint moment strength ($r = 0.616, p < 0.05$). Subjects with higher initial strength tended to exhibit faster fatigue rates (higher $k$). This might be linked to differences in muscle fiber type composition (stronger individuals potentially having a higher proportion of less fatigue-resistant Type II fibers).
• Other Factors: No significant correlations were found between fatigue rate $k$ and age or BMI within this participant group.
• Posture Changes: Subjects tended to change their posture slightly as fatigue increased, generally moving the arm closer to the trunk, likely to reduce the moment arm and load on the shoulder. While acknowledged as a potential confounder, the estimated impact on relative load was considered acceptable (<4%).

Conclusions and Implications

The paper successfully demonstrated an experimental method to determine subject-specific fatigue rates ($k$) for the shoulder joint during static tasks using an exponential model. The good fit of the model and the significant variability found in $k$ suggest it is a useful parameter for characterizing individual differences in fatigability.

The practical implications lie in ergonomics and occupational health:

• Personalized Risk Assessment: Knowing individual $k$ values can help tailor MSD risk assessments.
• Work Design: This information can inform physical task assignments (matching less fatigable workers to more demanding tasks), optimize work/rest schedules based on individual fatigue profiles, and guide worker training and selection processes.

Limitations noted include the focus on a simplified static task (neglecting dynamic aspects, vibration, recovery), the specific load range (14-33% MVC), the restriction to male participants, and potential influences from motivation and minor posture adjustments. Further research is suggested to explore gender/age differences, dynamic tasks, and varying load levels.