Mathematical Models of Localized Muscle Fatigue: Sensitivity Analysis and Assessment of Two Occupationally-Relevant Models

Assessment of muscle fatigability using isometric repetitive handgrip strength in frail older adults. A cross-sectional study

BACKGROUND

Fatigue has a significant impact on physical performance and quality of life in older adults, but is subjectively assessed in the Fried phenotype, so early deterioration may be overlooked. This study explores whether repetitive handgrip strength (HGS) provides an objective method of differentiating levels of frailty by comparing fatigue and recovery ratios with subjective measures and their correlations with frailty indicators.

METHODS

Participants (n = 217) were included based on mobility and cognitive function (MMSE > 17), with exclusions for neuromuscular disease or hand injury. The protocol consisted of two 10-maximal grip assessments one hour apart, calculating fatigue ratios 1 and 2 (maximum/mean force) at each session and recovery ratios between sessions. Logistic regression analysed associations between Fried's criteria components (Unintentional Weight Loss, Exhaustion Single Question, Multidimensional Fatigue Inventory (MFI), Short Physical Performance Battery (SPPB), Physical Activity Scale for the Elderly (PASE), standard Maximum HGS, Fatigue Ratio, and Recovery Ratio).

RESULTS

Among the participants (58 non-frail, 68 pre-frail, 91 frail; ages 74.7, 79.4, 83.8 years), significant differences were found for Fatigue Ratio 1 of 1.12 (non-frail), 1.23 (pre-frail), 1.40 (frail), Fatigue Ratio 2 of 1.12, 1.21, 1.45, and Recovery Ratio of 1.03, 1.01, 0.90, respectively. Fatigue Ratios 1, 2 and Recovery correlated more strongly with frailty status (r = 0.67, 0.69, -0.68) than MFI (r = 0.50), standard maximum HGS (r = -0.51) or a single fatigue question (r = 0.21). In logistic regression for predicting fatigue (MFI), Fatigue Ratio (OR = 1.51, p < 0.001) and Recovery Ratio (OR = 0.83, p = 0.022) were stronger predictors than single-question fatigue (OR = 1.15, p = 0.047) and maximum HGS. For predicting frailty, physical performance (SPPB) was the strongest predictor (OR = 0.72, p < 0.001), followed by Fatigue Ratio 1 (OR = 1.28, p < 0.001), with a higher Recovery Ratio reducing frailty risk (OR = 0.86, p = 0.050).

CONCLUSION

The repetitive HGS protocol is equivalent to the SPPB in assessing frailty and outperforms standard HGS and subjective fatigue measures. This objective method supports the identification of frailty by measuring strength, fatigue resistance and recovery capacity.

Enhancing Biophysical Muscle Fatigue Model in the Dynamic Context of Soccer

In the field of muscle fatigue models (MFMs), the prior research has demonstrated success in fitting data in specific contexts, but it falls short in addressing the diverse efforts and rapid changes in exertion typical of soccer matches. This study builds upon the existing model, aiming to enhance its applicability and robustness to dynamic demand shifts. The objective is to encapsulate the complexities of soccer dynamics with a streamlined set of parameters. Our refined model achieved a slight improvement in the R2 score in the maximum hand-grip test, increasing from 0.87 to 0.89 compared to the existing model. It also demonstrated dynamic change robustness in a soccer-specific 1 min drill and 15 min treadmill protocol extracted from the literature. Through individualized fitting on a 10-repetition 80 m sprint test for a soccer player, the model exhibited R2 scores between 0.62 and 0.80. Furthermore, when tested with actual soccer match data, it maintained a robust performance, with the average R2 scores ranging from 0.70 to 0.72. The proposed approach holds the potential to advance the understanding of tactical decisions by correlating them with real-time physical performance, offering opportunities for more informed strategies and ultimately enhancing team performance.

Slouched and erect sitting postures affect upper limb maximum voluntary force levels and fatiguability: a randomized experimental study

Occupational ApplicationsModifying the spinal curvature is an empirical approach to treating upper limb musculoskeletal disorders, often attributed to the balance between physical stress and individual functional capacities. We completed an experimental biomechanical study to quantify the effect of seated spinal posture on upper limb functional capacities. Isometric maximum muscle voluntary forces (MVFs) were measured at participants' shoulder, elbow, and wrist. Fatiguability was also assessed during a repetitive painting task. Participants were asked to assume both slouched and erect spinal postures, in a random order. In the erect posture, participants achieved higher shoulder and elbow isometric MVF levels and took longer to reach a fatigue threshold. Thus, spinal posture tends to remotely influence upper limb functional capacities, especially at the shoulder and elbow. Ergonomists should consider spinal posture even when focusing on musculoskeletal disorders of the upper limb.Technical AbstractBackground: Musculoskeletal disorders are a major public health issue, and current treatments often remain unsatisfactory. Treatments based on spinal curvature modifications are empirically used for upper limb musculoskeletal disorders.

PURPOSE

To determine whether a slouched or erect sitting posture has an effect on upper limb functional capacities, with tests and outcomes focused on the risk of upper limb musculoskeletal disorders.

METHODS

Randomized experimental study, crossover design. Twenty-two right-handed healthy participants from the local area were assessed in a research laboratory. Participants' spinal curvatures were increased or decreased, through verbal instructions and light touch, to place them in a slouched or an erect posture that was stable and easily maintained, in a random order. Isometric maximum muscle voluntary forces (MVFs) were measured. Participants also performed a repetitive task that simulated painting, with fatigue level assessed using the CR10 Borg scale. Upper limb positioning, task setting, and instructions to participants were standardized., and the investigator was blind to the results of MVF measurements. The main outcomes were normalized differences in MVF values and time-to-reach "7" on the CR10 scale.

RESULTS

There were significantly higher MVF values in the erect posture for the shoulder and elbow, with respective mean (SD) normalized differences of 11.4 (18.2) and 11.8 (19.2)%; differences approached significance at the wrist [7.7 (18.5)%]. The normalized difference in time-to-reach "7" on the CR10 scale was significantly higher in the erect posture (by 11.4%).

CONCLUSIONS

Spinal posture modified individual upper limb functional capacities and could thus influence the risk of upper limb musculoskeletal disorders.

Evidence of movement variability patterns during a repetitive pointing task until exhaustion

Human movement is characterized by its variability: the same task is never performed twice in exactly the same way. This variability is believed to play a functional role in movement performance and adaptability, as well as in preventing musculoskeletal damage. This article focuses on the time-evolution of movement variability throughout a repetitive pointing task until exhaustion. The kinematics of 13 subjects performing the pointing task is analyzed. Principal Component Analysis of joint angles identifies joint coordinations for each pointing cycle, and cycle-by-cycle comparison highlights movement variability. Non-supervised clustering reveals that subjects adopt successive coordination patterns at an intra-individual level. Inter-individual variability is characterized by the number and type of such patterns: from 3 to 5 patterns, mobilizing the trunk, the shoulder and the upper limbs differently. Movement variability exists even in a seemingly basic and constrained task. It appears in the very early stages of fatigue onset, and may correspond to adaptative coordination responses throughout task performance. This observation should encourage workstation designers to better account for movement variability in order to preserve operators' health and safety.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Modelling muscle recovery from a fatigued state in isometric contractions for the ankle joint

Current models of localized muscular fatigue are capable of predicting performance in isometric tasks with reasonable accuracy. However, they do not account for the effect of continuously-varying task intensities on muscular recovery from a fatigued state. In this work, we propose and evaluate three continuous functions for modelling recovery to replace a dichotomous step-function in the three-compartment controller (3CC-r) model of muscle fatigue (Looft et al., 2018) and validate their predictions with previously collected data in the literature for intermittent and sustained isometric tasks of the ankle joint performed at different intensities. When compared to experimental data the accuracy of one of the three proposed models of recovery is found to be nearly the same as that yielded by the original step-function, but this seemingly-identical accuracy may be a limitation of the dataset used. A superelliptical curve relating recovery factor to task intensity is proposed to be the closest replacement for the step function as it depicts both the elevated value of recovery factor for near-rest activities as well as a nearly-constant value for low-to-high-intensity tasks.

Modification of a three-compartment muscle fatigue model to predict peak torque decline during intermittent tasks

This study aimed to test whether adding a rest recovery parameter, r, to the analytical three-compartment controller (3CC) fatigue model (Xia and Frey Law, 2008) will improve fatigue estimates during intermittent contractions. The 3CC muscle fatigue model uses differential equations to predict the flow of muscle between three muscle states: Resting (MR), Active (MA), and Fatigued (MF). This model uses a feedback controller to match the active state to target loads and two joint-specific parameters: F, fatigue rate controlling flow from active to fatigued compartments) and R, the recovery rate controlling flow from the fatigued to the resting compartments. This model does well to predict intensity-endurance time curves for sustained isometric tasks. However, previous studies find when rest intervals are present that the model over predicts fatigue. Intermittent rest periods would allow for the occurrence of subsequent reactive vasodilation and post-contraction hyperemia. We hypothesize a modified 3CC-r fatigue model will improve predictions of force decay during intermittent contractions with the addition of a rest recovery parameter, r, to augment recovery during rest intervals, representing muscle re-perfusion. A meta-analysis compiling intermittent fatigue data from 63 publications reporting decline in peak torque (% torque decline) were used for comparison. The original model over-predicted fatigue development from 19 to 29% torque decline; the addition of a rest multiplier significantly improved fatigue estimates to 6-10% torque decline. We conclude the addition of a rest multiplier to the three-compartment controller fatigue model provides a physiologically consistent modification for tasks involving rest intervals, resulting in improved estimates of muscle fatigue.

Modelling endurance and resumption times for repetitive one-hand pushing

This study's objective was to develop models of endurance time (ET), as a function of load level (LL), and of resumption time (RT) after loading as a function of both LL and loading time (LT) for repeated loadings. Ten male participants with experience in construction work each performed 15 different one-handed repetaed pushing tasks at shoulder height with varied exerted force and duration. These data were used to create regression models predicting ET and RT. It is concluded that power law relationships are most appropriate to use when modelling ET and RT. While the data the equations are based on are limited regarding number of participants, gender, postures, magnitude and type of exerted force, the paper suggests how this kind of modelling can be used in job design and in further research. Practitioner Summary: Adequate muscular recovery during work-shifts is important to create sustainable jobs. This paper describes mathematical modelling and presents models for endurance times and resumption times (an aspect of recovery need), based on data from an empirical study. The models can be used to help manage fatigue levels in job design.