Functional muscle group- and sex-specific parameters for a three-compartment controller muscle fatigue model applied to isometric contractions
Introduction
Muscle fatigue is an inevitable but reversible byproduct of physical exertion which manifests in a temporarily reduced force capacity for the muscles involved in the activity (Bigland-Ritchie et al., 1995). It is a complex biochemical process (Vøllestad, 1997) that affects all skeletal muscle for all activity types regardless of duration, but the extent to which each muscle is affected can depend on a multitude of physiological, task, and external factors (Chaffin, 1973). Since it is eminently desirable that tasks never demand more of the worker than their physical limits to prevent the incidence of injuries, it is immensely helpful to predict how a certain task affects muscle strength over time. Measuring strength declines over the course of a real-world task can be tedious, time-consuming, and invasive, and the results will likely be inapplicable to another person or situation. Mathematical models of fatigue overcome these difficulties with their predictive abilities. While each model may be suitable for a certain subset of tasks and may specify its own limitations, in general it can reasonably predict the course of strength decline for a particular joint in the human body (Rashedi and Nussbaum, 2015).
The three-compartment controller (3CC) family of models (Frey-Law et al., 2012, Looft et al., 2018, Xia and Frey Law, 2008) divide the constituent motor units (MU) of a muscle into three states or compartments—resting, active, and fatigued—and calculate the relative size of each to estimate the extent of fatigue. They specify rules (Eqs. (1), (2), (3), (4), (5), (6)) for determining the rate at which MUs transition from one state into another.
Here, , , and are the fraction of motor units in the muscle that are currently resting, active, and fatigued, respectively. is a bidirectional activation-deactivation drive. F and R are the fatigue and recovery rate constants, respectively, and is a recovery multiplier that is a discontinuous function of target load (TL) and a unitless optimization parameter k. r is defined by Eq. (7). The model is relatively insensitive to the muscle force development () and relaxation () factors (Xia and Frey-Law, 2008), so a constant value of 10 is chosen for both.
The 3CC model, in its present form, was developed by first determining the values of F and R by running a 2-parameter sweep against sustained isometric contraction (SIC) data. Endurance time (ET) was chosen as the output variable for differing input task intensities (Frey-Law et al., 2012). This approach ensured the best possible F and R values for predicting ET for a given sustained task intensity, but not necessarily for predicting the precise course of fatigue during that period. k was then determined by running a 1-parameter sensitivity analysis using the predetermined F and R values against intermittent isometric contraction (IIC) data, but at this stage the input and output variables were reversed—torque declines were estimated for given input times (Looft et al., 2018). k—subsequently calculated—produced the best fit to IIC data for the given F and R values. Ideally, all three parameters would have been chosen independently for IIC data, but it is likely that the F and R values obtained thereby would have conflicted with those obtained from the SIC data since the two optimization steps had different variables as their objective functions. It is therefore of interest to analyze the performance of the model when SIC data is held to the same standard as IIC data, and to obtain parameter sets that represent all isometric tasks equally well.
Additionally, most real-world tasks asymmetrically and alternately load agonistic and antagonistic muscle groups around the active joints. Furthermore, since synergists assist the agonistic muscles, it is desirable to obtain parameters that represent both agonists and synergists together—hereon referred to as functional muscle groups (FMG)—for a given directional contraction. Also of interest are the differences in fatigability between men and women, which, if present, will manifest in different model parameters for the sexes and reduced prediction errors. In this study, we analyze the effects of segregating a large isometric contraction (IC) database variously on the basis of sex and FMG to refine the applicability of the 3CC-r model to specific individuals and situations. We treat both SIC and IIC data as belonging to a continuum of isometric contraction (IC) data bearing three common attributes—TL, duty cycle (DC) and cycle time (CT). The distinction between SICs and IICs are made by assigning DC = 100% for SICs while IICs inherently have DC < 100%. We segregate the data by active joint, by FMG, and then by both FMG and sex and run this data through the model to estimate the parameters that best represent each segregated dataset.
Section snippets
Data aggregation and extraction
The data drawn on here has previously been used to derive, in parts, the F and R parameters for the original 3CC model, and the enhanced recovery parameter (r) for modified 3CC-r model. The publications considered for inclusion in the dataset were those cited in the prior exhaustive meta-analyses of SICs (Frey-Law and Avin, 2010) and of IICs (Looft et al., 2018), but with additional exclusion criteria. As with the original meta-analyses, data from adults 18–55 years of age with no
Results
While quantifying the effects of segregating joint level data by FMG, averages are calculated only for the ankle, elbow, and hand/grip joints and their respective constituent muscle groups. The knee joint is excluded from these analyses since data was only available for knee extensors, so no further division of data on the basis of FMG was possible for that joint. The simplest error calculation method, with no distinction being made regarding sex (S) or FMG but with separate model parameters
Discussion
It is generally accepted that agonistic and antagonistic muscle groups around a joint have different force production capabilities, but less attention has been paid to any potential difference in their fatiguabilities. Markedly different fatigue rates have been observed in a handful of experimental studies involving the hip and the knee (Brasileiro et al., 2018, Kawabata et al., 2000, Krantz et al., 2020), but it remains to be seen whether this result holds true for joints in the upper body.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is supported in part by the National Science Foundation (Award CBET # 1703093 and 1849279; 2014278 and 2014281). The authors also wish to thank Alexandra Elbakyan for her invaluable assistance in data aggregation.
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2024, Human Movement ScienceSensitivity analysis of sex- and functional muscle group-specific parameters for a three-compartment-controller model of muscle fatigue
2022, Journal of BiomechanicsCitation Excerpt :The three-compartment-controller with enhanced recovery (3CC-r) model (Looft et al., 2018) can predict strength decline during both SICs and IICs, and it has previously been indicated that it could be employed for dynamic contractions as well (Xia and Frey-Law, 2008). Moreover, its model parameters have been calculated at the functional muscle group level for both sexes separately for isometric contractions (Rakshit et al., 2021), but the robustness of the model parameters was not examined. Rashedi and Nussbaum (2015) conducted a sensitivity analysis of the 3CC-r model which, at the time, did not include an augmented rest recovery parameter.