Content area
The objective of this study was to establish a predictive equation that expresses the daily work exposure as a function of variables that define complex work tasks. The equation was verified with data reported in reviewed publications. The ScienceDirect, PubMed, and ProQuest databases were searched using keywords related to variables that characterize intermittent tasks and those that describe muscle fatigue resulting from these tasks. Inclusion and exclusion criteria were established to focus on task characteristics and study participants. The primary criterion for accepting studies was a quantitative definition of the tasks performed, specifically concerning the level of force exerted over a specified period. Only studies involving healthy individuals aged 18–70 years that reported voluntary muscle contractions were deemed eligible. The adjustment of the prediction equation was based on the assumptions that for the same values of variables that characterize work, the exposure calculated by the equation is equivalent to musculoskeletal load, and that the level of musculoskeletal load at a given time determines the experimentally measured decrease in force capabilities. Thirty-seven datasets of independent variables (those that define work tasks) and dependent variable relevant to the decrease in force capabilities were accepted to establish the equation. Based on the comparison of dependent data from experimental studies with data obtained from calculations using independent variables, the equation that provided the best fit was identified. The correlation between the calculations and experimental results was found to be 0.72. The equation distinguishes work tasks by considering variables such as relative force, time of task, mean exposure, and the similarity of tasks performed throughout the daily work. It provides a tool for determining the work exposure associated with a specific set of tasks, which may cover the entire work shift or only parts of it.
Introduction
Physical work is common in everyday life and at industrial sites. Workers perform tasks ranging from simple grasps to complex dexterous activities daily. Some of them are physically demanding with overuse affecting performance efficiency [1]. Overly strenuous activities impact on musculoskeletal load and may cause cumulative trauma in the structure of the body. Overload of the musculoskeletal system is considered a risk factor for injury and, to the extent, of the development of musculoskeletal disorders [2,3]. In this context, exposure associated with work plays an important role [4].
It is well acknowledged that exposure is related to the tasks performed at work and is determined by body posture, exerted force and work pace [5,6,7]. Muscle load, associated with exposure of work, plays an important role in development of work-related localised muscle fatigue [8]. The load on the musculoskeletal system that the employee experiences as a result of exposure also depends on his strength and performance capabilities [9].
Local muscle fatigue is underpinned by multiple complex mechanisms [10] and it is a known precursor to a number of negative short- and long- term implications. In the short-term perspective, fatigue is associated with decrease in strength capabilities [11]. Loss of strength depends on both the exposure associated with the task performed and with its duration, and can be described as a time-dependent reduction in the force capacity of a muscle or muscle group [12]. As a long-term outcome, localised fatigue has been linked to the development of musculoskeletal disorders [13,14]. Examples of work-related musculoskeletal disorders may include carpal tunnel syndrome [5], epicondylitis [15], rotator cuff disorders [16] and low back pain [17].
Muscle load and fatigue can be assessed through the application of experimental methods that detect the physiological response to exposure [18,19]. Local muscle fatigue can be evaluated by tracking changes in the parameters characterizing a muscle group’s electromyographic signals across time while work-related effort is performed [20]. Another technique to gauge muscular fatigue is to measure the amount of force that has been lost from the muscles group while doing specific tasks [12] or the endurance time, which represents the maximum time during which a particular effort can be maintained [21]. Assessments through the application of experimental methods are linked to particular workplace, which means that there is not one generic assessment that can be applied.
Modelling fatigue or exposure as dependent on variables that characterize work in respect to working postures, exerted forces and repetitions seems more efficient and may have more general and broader application. Therefore, research is looking for a relationship between exposure variables and fatigue. The most common and frequently cited model is that related to maximum endurance time as a measure of fatigue.
Prolonged exertions at the same force level have been studied for the development of fatigue. The study of the duration a subject could maintain a given force level [22] demonstrated the relationship between the percentage of maximum voluntary contraction (MVC) and time. Following those studies, others have determined endurance time as a function of the levels of MVC for different muscle groups [23,24]. As a consequence the relationship between the endurance time and isometric level of muscle effort is quite well established, mostly as an exponential function of the voluntary maximum contraction or the relative force required by the task [25]. There are significant differences among the models expressing the maximum endurance time for isometric exertions developed by different researchers as result of experimental studies. A detailed review of those models was performed by El ahrache et al. [26]. Differences between those models may primarily be attributed to the experimental conditions (methods used, inclusion of endurance limit, individual differences in study participants) and to the way the model is constructed [25,26]. It should be noted, however, that, long-term static loading occurs relatively rarely in real work situations, which limits the applicability of models expressing endurance time as a function of long-term isometric strength level [27].
Much less is known about how intermittent effort at submaximal levels influences the development of muscle fatigue. Intermittent strength efforts are considered to be less fatiguing compared to sustained efforts at the same level [28,29]. However, there might be some doubts if lower fatigue is a consequence of intermittent character of load or muscle fatigue development is affected by the overall effort and not the intermittent characteristics [30,31]. One may assume that if different muscle exertions have the same overall workload, the development of muscle fatigue should be the same. However, Seghers and Spaepen [32] stated that it was unclear what effect different loading patterns with the same overall mean load would have. To maintain the same mean muscle load across conditions would require manipulating variables that describe performed tasks in a systematic manner and for that purpose solid models are required. It leads to the conclusion that model which would determine exposure as a function of variables characterising complex work is needed [33,34]. Establishing such a relationship would allow for the optimization of work related load and fatigue through the optimization of exposure.
Models of relationship between the endurance time and constant load on a determined level or even intermittent load at two or three levels provide important data. However, those models are hardly applicable for assessment of work related exposure in real work places, especially when job rotation becomes one of the main protective measures against the development of musculoskeletal disorders [35]. In complex production systems, manual operations still dominate, hence work tasks are affected by high variability determined by various levels of force and various postures. As such, reliable models of exposure are dependent on the specific characteristics of any workplace, and are dearly needed. Roman-Liu [36] proposed an equation that calculates exposure related to the performance of a repetitive task using the upper limbs, which is defined by cycle duration, mean load and the number of cycle phases. Taking into account that the equation only refers to repetitive efforts and does not consider exposure of daily work or include the duration of breaks, it would be necessary to modify the equation in such a way that it becomes applicable to general working conditions. In this context, the aim of this study was to enlarge the concept proposed by Roman-Liu [36] by presenting a model for daily work exposure. Hence, a predictive equation was proposed and verified that expresses an exposure index associated with daily work as a function of variables that characterize each task performed as part of a job.
The paper’s content can be separated into a theoretical and an experimental sections. The theoretical section outlines the concept of work tasks, the variables that define work tasks and an equation that calculates the exposure index as a function of these variables. The experimental section presents the findings of a comparative analysis between model calculations and already published experimental data. Additionally included is an analysis of the variations in the exposure depending on how tasks are structured throughout the working day.
Methods
Exposure variables
Exposure was proven to stem mostly from physical factors, namely posture and force applied during any physical activity at a given point in time. Changes in the variables of either of these two factors also change the magnitude of exposure. Typically, posture is determined by the angles at the joints, and exerted force is determined by its type and absolute value. The force can also be expressed as a relative value, calculated as the ratio of the absolute exerted force to the MVC for the same type of force and body posture. Thus, the variables that determine posture, the amount and the type of force exerted, are expressed by one variable: relative force. Commonly, however, a daily work consists of numerous changes in body posture and/or exerted force. This implies changes in muscles load, and can be described as a continuous function of time or as a quasi-static function. In the latter case, a continuous function is sampled and the duration and corresponding value of the load are assigned to individual samples, namely tasks (Fig 1).
[Figure omitted. See PDF.]
Daily work consists of main operations (Mo) that include basic operations (Bo) and each basic operation consists of a sequence of tasks. A daily work may consist of only one basic operation repeated over work shift. In this case, the Mo is the same as the Bo ones. Most often, however, a daily work consists of many Bo. Some of the Bo may be repeated when they occur one after another or they may occur many times in different sequences. Similarly, Mo which make up daily work may be repeated. It may also be the case that daily work consists only of one operation, which is a unique sequence of tasks that cover the entire work shift. Tasks, Bo and Mo are described by several variables.
Each task is assigned the level of relative force of the task (RF) and a duration of this task. These two variables are treated as primary exposure variables and are consistent with those presented for repeated efforts in the study by Roman-Liu [36] and earlier studies by Mathiassen and Winkel [37]. On the basis of those two primary variables it is possible to calculate a few more (secondary variables), including cumulative time of work duration, which is equivalent to the total work time and is calculated as the sum of the task duration. Work duration corresponds to the cycle time outlined in the aforementioned studies [36,37]. The cyclic work discussed in the research by Mathiassen and Winkel [36] was built on a cycle made up of two tasks. The study by Roman-Liu [36] describes a model as being defined by the quantity of tasks in a single cycle. In presented hear model work is characterized by the total number of tasks thought the working time that is under analysis. Mean exposure (ME) is calculated as the sum of task RF multiplied by its duration, and then divided by the sum of tasks duration (Eq 1). The variable ME is equivalent to the average load [37] or integrated cycle load [36]. Variables in addition to those discussed previously in the aforementioned studies are relative time (RT) and task similarity (SP). RT illustrates the mean duration of one task and is calculated with Eq 2. For assessment of exposure, it is also important to note how similar or different are the successive tasks in terms of RF. The SP calculations are based on the sum of two numbers related to the number of tasks with the same RF (Eq 3). The first number expresses the number of times that the most frequent task occurs. The latter number expresses the second most common number of the same tasks. Table 1 presents summary of the exposure variables and the relationships between them.
[Figure omitted. See PDF.]
(1)
where:
ME – mean exposure
RFi – relative force of an i-th task
TTi – duration of an i-th task
(2)
where:
RT – relative time
TTi – duration of an i-th task
k – number of tasks
(3)
where:
SP – task similarity
s1 – the first largest number of the same task
s2 – the second largest number of the same task
k – number of tasks
In summary, the presented model expands on the task variables of the previous model dedicated to repetitive tasks of upper limbs [36] by adding the concepts of: relative time of task, task similarity and operation. Exposure can be calculated in relation to one operation, a set of operations or daily work. The modified equation was verified by results from experimental studies that present force capability decrease as a reaction to exposure.
Search strategy of relevant publications for equation modification
The search was performed in selected electronic databases, namely: ScienceDirect, PubMed and ProQuest. Keywords, abstracts and titles were scanned for the following, individually and in combinations: resumption time, endurance time, work-rest cycle, load, force, strength, torque, intermittent, fatigue, voluntary, activation, contraction, decline, decrease, drop, exhaustion, sustain. Additionally, reference lists of analysed papers, including review ones, were scanned to identify non-indexed papers that might meet the eligibility criteria.
Relevant studies were identified, synthesized and analysed culminating in a comprehensive description of changes in exerted force with time, which was defined as local fatigue associated with performed tasks. The predictive equation being the aim of analysis, done on the reviewed studies, is dedicated to the assessment of exposure that is related to the performance of work of specific characteristics. Therefore, inclusion and exclusion criteria were set to focus on task characteristics and working-age of study participants. Thus, the main criterion for accepting studies was a quantitative definition of the task performed in terms of the level of force exerted over a given period of time. Only studies that reported voluntary muscle contractions and were carried out on individuals without impairments that could affect the performance were included. This implies that the eligible studies showed variations in force capabilities over time during task execution, along with a clear description of the tasks in terms of their RF levels and corresponding durations. Only studies involving healthy individuals aged 18–70 years were considered eligible. If different variants were presented in a paper and at least one of the variants was eligible, the study was qualified for analysis. Excluded were studies that comprised any type of electrical muscle stimulation introduced during performance or were done on patients with neurodegenerative illnesses. An important criterion for excluding a paper from the analysis was the exertion of dynamic force.
Data analysis verifying the modified equation
The main aim behind the analysis of experimental data was to determine the mathematical equation of exposure, expressed quantitatively by the Work Exposure Index (WEI), as a function of exposure variables. In order to achieve this goal, an equation developed in earlier studies [36] was modified, interrogating the best fit between the WEI equation and experimental data. Data from the literature had to be combined in order to verify the equation. Analysis was based on the assumption that exposure related to a performed task calculated by WEI, as a function of exposure variables, is equivalent to the load on the musculoskeletal system of the experimental participants. The level of musculoskeletal load (ML) at a given time determines the decrease in force capabilities measured experimentally. Therefore, ML was treated as a dependent variable derived from empirical studies.
The nature of the published data used for the equation verification precludes the standard way of combining means and standard deviations from different studies. Usually, the consolidation of data deals with a situation where pooled variables are of the same type (e.g., endurance time). In cases where a value of a variable changes over time, there are pooled those values that were recorded at the same moment in time. In analysis presented in this paper the reviewed studies differ not only in populations and test methods, but also in the duration of the experiment and time span of force measurements differed among studies. There were experiments with a given effort completion time and tests with endurance time. Both endurance time and effort completion time have been defined differently in different studies. Common among studies was that they reported set of values of force assigned to time over different time schedules. That allowed for approximation of changes in force capabilities over time via a logarithmic function. This function is specific for each case reported in each study and after normalization allows the comparison of data.
The first step in the analysis was to determine, for each study case, the regression logarithmic function expressing decrease in force capacity (FC) during the exposure (the performance of tasks) as a function of time (Eq 4).
(4)
where:
FC – force capacity during the performance of tasks
A and B – coefficients of logarithmic function specific for each variant of study
time – duration of performance of task on load B
The A and B coefficients differed between study cases. In order to normalize, the logarithmic function was transformed in such a way so that the constant value of the function, expressing the first measurement (coefficient A), equals to 100 and the B coefficient expressing decrease in force capabilities that equals to ML. Studies presented variables that characterized performed task in a way that allowed for its description in terms of the exposure variables (Table 1). Based on set of those two variables (primary exposure variables), for each study case secondary exposure variables (ME, RT and SP) were calculated with equations from 1 to 3. As a result was obtained sets of values of coefficients standing in front of the logarithm (ML) assigned to a set of ME, RT and SP values. Calculations of WEI, that was compared to ML, were performed as a function of variables ME, RT, SP specified for each case identified from experimental studies (Fig 2).
[Figure omitted. See PDF.]
Statistical analysis was performed with the package Statistica 10. The analytical regression analysis focused on finding the best fit between ML and WEI with ME, RT, SP datasets. The Spearman correlation coefficients were calculated for comparison in order to test the relationship between the calculations performed with the model and experimental data (namely WEI and ML). The best fit determined using the linear regression function and Spearman’s R yielded the WEI equation.
Results
Characteristics of the studies and data extraction
The systematic search identified 2,390 potentially eligible studies (Fig 3). Of these, 728 were obtained from PubMed, 755 from ScienceDirect, and 907 from ProQuest. After excluding 802 duplicate papers, 1,588 papers were screened for eligibility based on their titles and abstracts according to the specified criteria. Studies were excluded from further analysis if they involved non-human subjects (n = 70), participants under 18 years of age, or individuals with diseases, impairments, or disabilities (n = 738). Research that focused on non-isometric strength efforts, such as training or exercise (n = 619), as well as studies where strength was derived from muscle stimulation (n = 70), were also excluded. Following a full-text review, 65 additional studies were excluded due to insufficient data (n = 13), the use of only one level of continuous force (n = 42), results previously reported in other publications (n = 3), or force values derived from muscle stimulation (n = 7). Two studies were included from the reference lists of the reviewed papers. Ultimately, a total of 22 studies were included for data extraction. Based on the information selected for analysis and the aim of this review, the number of study participants and primary exposure variables were extracted from each retrieved paper.
[Figure omitted. See PDF.]
Table 2 presents the characteristics of the study qualified for further analysis grouped according to values of variables that characterize the performed task. Data presented in the published studies included here, namely force measured in time, were organized descriptively in tables or figures. In each case, force was exerted in a given pattern for a given time with a given rest time. An in-depth detailed analysis of the research methods outlined in each of the reviewed paper formed the foundation for the work design created from tasks. The extracted data were assigned to the primary exposure variables. The work design with values assigned to the primary variables formed foundations for calculating the secondary exposure variables. The tasks were integrated in operations according to study description. Description also detailed the number of repetitions for each operation. The work design presented in Table 2 is in form of an equation, with each Bo depicted as the sum of the tasks, while the Mo is expressed as the sum of the Bo multiplied by the number of their repetitions, and optionally with additional tasks. This indicates that, for example, the equation Mo01 = 11*Bo + t3 + t2 should be interpreted as the Mo labelled as 01 made up of Bo (consisting of t1 and t2) repeated eleven times, with the extra tasks t3 and t2 also factored into this Mo.
[Figure omitted. See PDF.]
Studies varied due to the type of force. The largest number of studies examine knee extension [39,40,43,44,49,51,53,55,58]. The following is handgrip which is mentioned in six publications [12,41,48,54,57,58]. Three studies [38,52,53] report elbow flexion, while elbow extension is noted in one study [56]. Four studies [42,45,46,50] focused on foot flexion (both plantar and dorsi). The force of the thumb appears once [47].
All results from the selected publications were summarized for a group of 367 people. The majority of studies were carried out on people aged between 21 and 36 years. Only two studies focused on the older age group around 70 years (28 people in total).
Exposure as a function of task variables
Twenty-three papers provided 37 sets of data (study cases). Linking cases with the same value of ME, RT and SP across all studies resulted in 31 sets associated with the ML coefficient, which were then used for regression analysis. This analysis provided the modified equation of exposure related to task performance (Eq 5).
(5)
where:
WEI – Work Exposure Index related to the performance of a given tasks
ME – mean exposure as calculated by Eq 1
RT – relative time as calculated by Eq 2 divided by 1 s
SP – tasks similarity as calculated by Eq 3
All variables are dimensionless. The relationship between ML and WEI, as expressed through a linear regression function, is presented in Fig 4. The figure illustrates the relationship between independent variables from experimental studies (ML) and dependent variables (WEI), which is the result of calculations performed using the developed equation. The musculoskeletal load assessed in the experimental studies, represented by ML, arises from performing tasks defined by set of 37 exposure variables. WEI, in turn, represents the exposure calculated for each of sets of these variables. The regression line has a slope of 0.99, nearly equal to 1, and an intercept of 0.005, which is approximately zero. The Spearman correlation coefficient is 0.72 with p < 0.001. All this confirms the strong correlation between these two sets of 37 data.
[Figure omitted. See PDF.]
WEI – Work Exposure Index calculated with equation, ML– muscle load assessed based on results derived from reviewed studies.
The exposure is a source of fatigue that develops during task performance. Muscle fatigue can be defined as a reduction in the ability to produce force. This means that fatigue can be expressed as a decrease in force capability induced by sustained or repeated muscular contractions [8,12,59]. In this study, the decrease is quantitively expressed by Eq 4, which implies that FC can be the measure of fatigue developing under particular exposure associated with the executed work tasks. WEI assesses the level of this exposure. The analysis presented in this paper (Fig 2) proved strong correlation between ML and WEI (Fig 4). Thus, it can be inferred that WEI can act as a coefficient before the logarithmic function that describes fatigue occurring with the duration of work. This further implies that the coefficient B in Eq 4 can be replaced by WEI, assuming that the coefficient A is normalized.
WEI is calculated based on two secondary exposure variables: RF and ME. To illustrate the impact of these variables on WEI, Fig 5 presents a surface graph depicting WEI as a function of RF and ME, while Fig 6 shows the changes in WEI as a function of RT for seven fixed values of ME. Both figures demonstrate the combined effect of the ME and RT variables on changes in WEI values. The lowest WEI values occur for RT ranging from a few seconds to about 50 seconds, depending on the ME. Additionally, when RF exceeds the minimum value, the increase in exposure is gradual; however, for RT values below the minimum, the increase in WEI becomes steep. This illustrates a greater increase in exposure when tasks are characterized by short durations, with a steeper increase when exertion of higher force is required. However, it is important to note that when relative force is high and task duration increases, the exposure represented by WEI also rises rapidly. An increase in relative force leads to a more pronounced rise in WEI at longer duration of tasks.
[Figure omitted. See PDF.]
WEI – Work Exposure Index, RT – relative time, ME – mean exposure, task similarity (SP) equals 1.5.
[Figure omitted. See PDF.]
WEI – Work Exposure Index, RT – relative time, ME – mean exposure, task similarity (SP) equals 1.5.
Model utilized in real-work – example
Table 2 presents the characteristics of the Mo that were assigned to the cases in the individual studies in laboratory conditions. Many of these operations are simple two-tasks that differ only in the level of force and the duration of the individual tasks. Some of them are more complex, which means that they consist of simple Bo repeated several times and several additional tasks.
One of the main strategies used to reduce employee exposure to excessive workload is job rotation. The established mathematical equation that calculates WEI can be a good tool supporting the process of developing such a job rotation formula that would be optimal from the perspective of musculoskeletal load of all workers involved in work process. Mo characterized in Table 2 can be taken into theoretical consideration of work process optimization. Many possibilities of organizing these operations can be considered. WEI can be compared between the scenario where one employee repeats the entire set of operations, set of few selected ones and the scenario where each employee completes one main operation from Table 2 and repeats it multiple times during the workday.
Fig 7 presents WEI values for two scenarios. In the first scenario, only one main operation, marked in a manner analogous to that in Table 2, is performed throughout the entire working day (solid bars). In the second scenario, all operations are combined into daily work (hatched box). The WEI values for the option where one main operation is repeated throughout the workday differ significantly. The operation marked as Mo26 has the lowest WEI at 0.98, while the operation designated as Mo32 has an exceptionally high exposure of 15.17. The average WEI value for all operations is 4.57. When operations are conducted in a scenario where every worker completes a set of all operations, the WEI is 3.75, which is lower than the average WEI across all operations. In certain instances, the WEI for the combined daily work scenario is higher than that for a single operation performed during the workday. There are twelve cases where a worker would experience higher exposure in this option compared to performing only one operation, and another four cases where the WEI would be at a very similar level. However, eighteen workers would have lower exposures if each worker performs a complete set of operations. In one case (Mo32), the exposure is nearly four times lower, and in two other cases (Mo18 and Mo20), it is nearly three times lower. Additionally, two workers would have exposures that are more than twice as low (Mo06 and Mo16).
[Figure omitted. See PDF.]
One hatched bar – every employee repeats the entire set of operations during a working day. Dark grey filled bars – every employee performs only one Mo marked as in Table 2, and repeats it multiple times during a working day.
Simple two task operations, characterized in Table 2, (Mo04, Mo06, Mo07, Mo19 – Mo30, Mo32) can be illustrated by real work of lifting plates. Based on the video recording of the work process, tasks can be identified and assigned specific body positions. The force exerted during each task, measured by its absolute or relative value, determines the RF that defines the task. Fig 8 illustrates the body positions assigned to two tasks involving the left upper limb. The first left upper limb task (tgrab) is to grab the plate, and the second task (tplace) is to put it down on the right hand. The force levels defined by the variable RF depend on the mass of the plate and the position of the upper limb. Both RF and task duration can correspond to those defining the above-mentioned operations.
[Figure omitted. See PDF.]
Task tgrab is to grab the plate, task tplace is to put it down on the right hand.
Daily work that consist of operations repeated many times with additional tasks (Mo01, Mo02, Mo03, Mo05, Mo08 – Mo15) can be projected into real work environments by including two additional tasks to those shown in Fig 8. The Mo then consists of few Bo (tasks tgrab and tplace) repeated multiple times, and additional tasks twalkright and twalkleft, during which the employee may walk with carrying plates. The force levels, the number of repetitions of the Bo and the duration of the individual tasks may vary.
The proposed WEI is dedicated to the assessment of the load/exposure associated with the work performance at real workplaces. To calculate WEI, the values of the primary variables must first be determined. The assessment of duration of each task is relatively easy. It can be done by video recording the subsequent tasks. The RF assessment is more demanding and time-consuming. The body position and applied force constitute the unit load associated with a particular task. RF corresponds to the relative unit load, i.e., the ratio between the applied force and the MVC exerted in the same body position. Commonly, under real working conditions, applied force is known. The MVC can be obtained using two different approaches.
The first approach involves measurement of employee’s MVC that align with each work task. Measurements of MVC must be taken in the same body posture in which the task is performed. Such measurements of MVC can be challenging due to the time-consuming nature of the measurements and the disruption to workflow. The second approach focuses on the values of the body angles linked with a task. The body angle values can be estimated from a photograph illustrating the body posture. However, estimating the angles in this manner can be a time-consuming process even when employing tools such as Kinovea [60,61]. Using sensors to measure employees’ body angles during work provides quantitative data and aids in determining angles values [62,63]. Such equipment can be safely used during work without disrupting the workflow. The estimated or measured angle values serve as input data for calculations of MVC. The MVC for general population can be calculated as a function of the angles that define the position of the body with application of the previously developed mathematical relationships [64,65]. Another way to calculate the RF is to express the load in body part (for example the lumbar back) as a function of the body position angles and the applied force, and subsequently relate this load to the maximum allowable load [66].
All calculations resulting in RF can be done with support of a software package containing the mathematical equations. The software package can also calculate the secondary variables and the WEI. Such approach will allow a relatively easy assessment of the exposure level due to a series of tasks that make up an operation or a working day. That will allow comparison of exposure among different workplaces. When WEI is supported by relevant and verified criteria it can be also used for assessment of risk for development of musculoskeletal disorders.
Discussion
The objective of this study was to establish and verify a predictive model that expresses exposure of performed task as a function of variables defining daily work and muscular fatigue as the logarithmic function of time with the exposure as a main coefficient. Muscle fatigue has been cited as a risk factor for injury in the workplace [59]. This leads to the assumption that decrease in fatigue through the application of tools that assess fatigue can be useful in a healthcare context. Models referring to fatigue or endurance time have already been established [22,67]. These were based on independent variables that characterized constant force [67] or, in very few cases, intermittent load according to a predetermined pattern [12,68]. The models were established based on fitted functions using muscular strength data from studies with a relatively small sample. The model presented in this study expresses exposure (equivalent to musculoskeletal load) as a function of ME, RT and SP, which makes it closer to real workplaces where work tasks are more complex. Additionally, the equation of exposure was verified based on data from 22 publications presenting 37 study cases, which makes it reliable for assessing load in real work environment.
Independent variables that refer to ME, relative time and the SP were chosen as most characteristic of a daily work. In spite of some degree of simplification in terms of exposure variables, they have been deemed to be the most critical variables for work exposure from one side and musculoskeletal load from the other [5]. Those variables refer to posture, force and time characteristics, taking into account differences between tasks. An early study has shown that those three factors are the main leading to the development of fatigue [69].
One of the decisions was about the number of study participants. Whether weighed or regular averages should be used was questioned. Studies differed in the number of participants, their sex and age, as well as the number of force measurements. All those features could have had an impact on the obtained results [39,44,45,49,54]. In addition, posture during measurement and the type of force may impact force capabilities [70]. Due to relative values that were under analysis, it has been decided that number of study participants will not be taken into consideration. This means that each study variant had the same weight in analysis of correlation between empirical and theoretical studies.
In the model presented here, force is expressed as a relative value. In calculating this value, both MVC and exerted force were considered for the same posture. In this way, posture could be ignored in subsequent analyses. Repetitiveness is determined by variables such as RT and SP. These characterize how often changes in RF take place and how similar tasks are, which are also crucial when work exposure is considered. The analysis was based on relative force measures presented in reviewed papers. This means that both individual factors related to sex and age, included in the measurements (type of force, engaged joint and posture), which had an impact on RF could have been ignored. As a consequence, the WEI index is not biased by individual factors and can be broadly applied.
The meta-analysis confirmed a strong correlation between the experimental studies and the calculations performed for the same variables characterizing a task. The Spearman’s correlation coefficient values were 0.72 with p < 0.001. Such a correlation is considered strong [71]. Thus, the presented model is a tool that may assist in quantifying exposure depending on the variables of task characteristics and then based on the exposure quantifying fatigue after a determined time of this exposure. Applying a model that allows for the assessment of fatigue after a predetermined period of time in industrial workplaces can lead to considerable improvements in terms of the avoidance of work-related disorders.
Limitations of the study and future studies
Limitations of the study refer mostly to the quantity of data available for verification, which was determined by results of review. Linear regression determined the relationship between computational and empirical outcomes on the available sample size, which was 37 cases. Jenkins [72] findings recommend sample sizes for linear regression and meta-regression analyses. For data with low variance, the sample size should be greater than 8 to perform a reliable regression analysis. For data with high variance, the sample size should be greater than 25 [72]. His study does not recommend the maximum sample size. A sample size calculation for a single study using linear regression with G*Power, assuming power (1-beta) of 0.8 and alpha error of 0.05, recommends a minimum sample size of 14 [73]. Calculations using the same tool suggest that increasing the sample size to 37 samples would increase the power to 0.99. This indicates that a larger sample size reduces the margin of error and increases the statistical power to detect true effects.
Increasing the sample size in experimental studies is not always cost-effective [74]. However, when analysing data from review studies, the sample size is predetermined. Furthermore, combining the results of different studies with a certain precision and accuracy of the data can improve accuracy and reduce bias compared to a single study. The analysis presented in this paper has a larger sample size than required. Running statistical analysis on a larger combined sample might ensure that the confirmed and accepted results are more reliable and accurate. The data analysed in this paper are based on papers published in scientific journals reported in significant databases. All are original studies, the results are not cited and are not derived from each other, indicating their reliability. The extent to which a predictive model reflects reality depends on the available validation options, in other word on available results from already completed studies. However, it should be kept in mind that what is accepted as fact today may be modified based on newly reported measurements.
This review focused only on cases of voluntary contractions because it assumed that electrical stimulation could influence the pattern of fatigue, as proven for example in Behm et al. [75], who showed that unilateral transcutaneous electrical nerve stimulation prolonged time to failure. Such attitude limited the number of studies eligible for verification and, at the same time, evaded additional factors that may seriously impact study results. However, optimal verification of the equation would be achieved when large numbers of groups and sets of dependent and independent variables are included in the process of equation verification.
Due to the limited number of studies, variables related to different types of force and different joints were pooled. This is somewhat of a simplification, given that Frey Law and Avin’s [76] study of static endurance time showed that different parts of the body have different fatigue rates for the same load. Such approach allowed to verify the equation that may refer to various types of force, formulated according to reviewed publications. The studies were conducted mostly on handgrip, knee flexion, elbow flexion and extension, and ankle dorsi and planar flexion. This can be considered as an advantage of this study because usually work processes requires various types of force, which may differ in the subsequent tasks. Focusing only on one of these during model verification would be a limitation in model applications. Due to such attitude the equation can be used in cases where a sequence of tasks with various types of force are performed.
Some limitation of the study is the fact that individual factors can cause metabolic changes in muscles, resulting in a decline of muscle power output that increases with fatigue and varies in nature. The influence of many of these factors was not analysed in this study. Only variables that define the performed task were taken as meaningful. Factors that influence strength, such as muscle fibre composition (slow or fast twitch fibres), posture, individual differences, strength, gender, age, motivation and training [24,77] were not taken into account in the analysis.
The majority of the reviewed studies participants were between 21 and 36 years old. The population aged 45 years or older was only about 7% of the total population. This suggests that the proposed equation appears to be biased towards younger workforce demographics, which can be considered a certain limitation to the application of the equation. Nevertheless, studies [44,45,77] show that effort at a specific level caused a lower decline in muscle strength in the older group compared to the younger group. This confirms that people become less prone to fatigue as they get older. As a consequence of that the index calculated from the equation is likely to overestimate the load on older employees, indicating that it can be safely applied to them.
Despite the existing limitations, the presented equation can be implemented for both the assessment of any existing workplace and in the process of workplace planning and development. The presented model undertakes a wholistic approach to daily work and calculations of exposure can be performed in relation to tasks, one operation, a set of operations or daily work. Expressing work exposure as a function of ME, RT and SP provides a simple and easy-to-use model for practical application. Further study should focus on determining criteria that influence the risk of developing musculoskeletal disorders, e.g., values of WEI that define risk as high, medium or low.
Conclusions
This study extends the knowledge on work process patterns by proposing a model of daily work exposure, defining tasks grouped into operations, and a mathematical equation that calculates exposure as a function of the variables defining each of daily work tasks. The verification of the model, based on data drawn from existing studies, showed a strong correlation between the experimental data obtained from the literature and calculations based on the model (0.72). The proposed equation can be used as a tool to determine occupational exposure during a specific set of tasks. It allows to monitor load associated to a performed work in any workplace, which would be beneficial for analyzing the risk of development of musculoskeletal disorders. The equation forms the basis for a computerized method for assessing the risk of developing musculoskeletal disorders. Assessing work-related exposure using the equation can lead to improved design of work processes.
Supporting information
S1 Table. Row data obtained from reviewed papers.
The table presents the raw results of the studies described in the papers that were the focus of the reviews. These data reflect the level of force applied and the corresponding time the load was held in each case. Muscle load (ML), which was significant in the ensuing analysis, was estimated using this information.
https://doi.org/10.1371/journal.pone.0324924.s001
References
1. 1. Silk A, Lenton G, Savage R, Aisbett B. Job task characteristics of Australian emergency services volunteers during search and rescue operations. Ergonomics. 2018;61(2):265–72. pmid:28738728
* View Article
* PubMed/NCBI
* Google Scholar
2. 2. Guerreiro MM, Serranheira F, Cruz EB, Sousa-Uva A. Self-reported variables as determinants of upper limb musculoskeletal symptoms in assembly line workers. Saf Health Work. 2020;11(4):491–9. pmid:33329916
* View Article
* PubMed/NCBI
* Google Scholar
3. 3. Rathore B, Pundir AK, Iqbal R. Ergonomic risk factors in glass artware industries and prevalence of musculoskeletal disorder. Int J Ind Ergon. 2020;80:1–11.
* View Article
* Google Scholar
4. 4. Curti S, Mattioli S, Bonfiglioli R, Farioli A, Violante FS. Elbow tendinopathy and occupational biomechanical overload: A systematic review with best-evidence synthesis. J Occup Health. 2021;63(1):e12186. pmid:33534951
* View Article
* PubMed/NCBI
* Google Scholar
5. 5. da Costa BR, Vieira ER. Risk factors for work-related musculoskeletal disorders: A systematic review of recent longitudinal studies. Am J Ind Med. 2010;53(3):285–323. pmid:19753591
* View Article
* PubMed/NCBI
* Google Scholar
6. 6. Hooftman WE, van der Beek AJ, Bongers PM, van Mechelen W. Is there a gender difference in the effect of work-related physical and psychosocial risk factors on musculoskeletal symptoms and related sickness absence?. Scand J Work Environ Health. 2009;35(2):85–95. pmid:19337673
* View Article
* PubMed/NCBI
* Google Scholar
7. 7. Keyserling WM, Brouwer M, Silverstein BA. Effectiveness of a joint labor-management program in controlling awkward postures of the trunk, neck, and shoulders results of a field study. Int J Ind Ergon. 1993;11(1):51–65.
* View Article
* Google Scholar
8. 8. Chaffin DB. Localized muscle fatigue--definiton and measurement. J Occup Med. 1973;15(4):346–54. pmid:4348609
* View Article
* PubMed/NCBI
* Google Scholar
9. 9. Roman-Liu D. External load and the reaction of the musculoskeletal system – a conceptual model of the interaction. Int J Ind Ergon. 2013;43(4):356–62.
* View Article
* Google Scholar
10. 10. Enoka RM, Duchateau J. Translating fatigue to human performance. Med Sci Sports Exerc. 2016;48(11):2228–38.
* View Article
* Google Scholar
11. 11. Enoka RM, Stuart DG. Neurobiology of muscle fatigue. J Appl Physiol (1985). 1992;72(5):1631–48. pmid:1601767
* View Article
* PubMed/NCBI
* Google Scholar
12. 12. Roman-Liu D, Tokarski T, Kowalewski R. Decrease of force capabilities as an index of upper limb fatigue. Ergonomics. 2005;48(8):930–48. pmid:16147413
* View Article
* PubMed/NCBI
* Google Scholar
13. 13. Gallagher S, Schall MC Jr. Musculoskeletal disorders as a fatigue failure process: evidence, implications and research needs. Ergonomics. 2017;60(2):255–69. pmid:27376409
* View Article
* PubMed/NCBI
* Google Scholar
14. 14. Horton LM, Nussbaum MA, Agnew MJ. Effects of rotation frequency and task order on localised muscle fatigue and performance during repetitive static shoulder exertions. Ergonomics. 2012;55(10):1205–17. pmid:22849348
* View Article
* PubMed/NCBI
* Google Scholar
15. 15. Descatha A, Dale AM, Silverstein BA, Roquelaure Y, Rempel D. Lateral epicondylitis: new evidence for work relatedness. Joint Bone Spine. 2015;82(1):5–7. pmid:25553834
* View Article
* PubMed/NCBI
* Google Scholar
16. 16. Abate M, Di Carlo L, Salini V, Schiavone C. Risk factors associated to bilateral rotator cuff tears. Orthop Traumatol Surg Res. 2017;103(6):841–5. pmid:28578100
* View Article
* PubMed/NCBI
* Google Scholar
17. 17. Anwer S, Li H, Antwi-Afari M, Wong A. Associations between physical or psychosocial risk factors and work-related musculoskeletal disorders in construction workers based on literature in the last 20 years: A systematic review. Int J Ind Ergon. 2021;83:103113.
* View Article
* Google Scholar
18. 18. Motabar H, Nimbarte AD. The effect of task rotation on activation and fatigue response of rotator cuff muscles during overhead work. Appl Ergon. 2021;97:103461. pmid:34174574
* View Article
* PubMed/NCBI
* Google Scholar
19. 19. King J, Mattison M. An exploration of the effects of cycle time and force variations on muscle fatigue during submaximal intermittent isometric exertions. Ergonomics South Afr. 2017;29(1):36.
* View Article
* Google Scholar
20. 20. Mahdavi N, Dianat I, Heidarimoghadam R, Khotanlou H, Faradmal J. A review of work environment risk factors influencing muscle fatigue. Int. J. Ind. Ergon. 2020;80:103028.
* View Article
* Google Scholar
21. 21. Choi K, Lee S, Lee J, Kong Y. Development of thumb endurance curves associated with various exertion levels. Hum Ftrs & Erg Mfg Svc. 2017;27(5):249–55.
* View Article
* Google Scholar
22. 22. Rohmert W. Problems in determining rest allowances Part 1: use of modern methods to evaluate stress and strain in static muscular work. Appl Ergon. 1973;4(2):91–5. pmid:15677120
* View Article
* PubMed/NCBI
* Google Scholar
23. 23. Gamet D, Maton B. The fatigability of two agonistic muscles in human isometric voluntary submaximal contraction: an EMG study. I. Assessment of muscular fatigue by means of surface EMG. Eur J Appl Physiol Occup Physiol. 1989;58(4):361–8. pmid:2920714
* View Article
* PubMed/NCBI
* Google Scholar
24. 24. Hunter SK, Enoka RM. Changes in muscle activation can prolong the endurance time of a submaximal isometric contraction in humans. J Appl Physiol (1985). 2003;94(1):108–18. pmid:12391034
* View Article
* PubMed/NCBI
* Google Scholar
25. 25. van Dieën JH, Oude Vrielink HH. The use of the relation between relative force and endurance time. Ergonomics. 1994;37(2):231–43. pmid:8119257
* View Article
* PubMed/NCBI
* Google Scholar
26. 26. Elahrache K, Imbeau D, Farbos B. Percentile values for determining maximum endurance times for static muscular work. Int J Ind Ergon. 2006;36:99–108.
* View Article
* Google Scholar
27. 27. Rashedi E, Nussbaum MA. Mathematical models of localized muscle fatigue: sensitivity analysis and assessment of two occupationally-relevant models. PLoS One. 2015;10(12):e0143872. pmid:26656741
* View Article
* PubMed/NCBI
* Google Scholar
28. 28. Iridiastadi H, Nussbaum MA. Muscle fatigue and endurance during repetitive intermittent static efforts: development of prediction models. Ergonomics. 2006;49(4):344–60. pmid:16690564
* View Article
* PubMed/NCBI
* Google Scholar
29. 29. Masuda K, Masuda T, Sadoyama T, Inaki M, Katsuta S. Changes in surface EMG parameters during static and dynamic fatiguing contractions. J Electromyogr Kinesiol. 1999;9(1):39–46. pmid:10022560
* View Article
* PubMed/NCBI
* Google Scholar
30. 30. Yassierli, Nussbaum MA. Muscle fatigue during intermittent isokinetic shoulder abduction: age effects and utility of electromyographic measures. Ergonomics. 2007;50(7):1110–26. pmid:17510825
* View Article
* PubMed/NCBI
* Google Scholar
31. 31. Dickerson CR, Meszaros KA, Cudlip AC, Chopp-Hurley JN, Langenderfer JE. The influence of cycle time on shoulder fatigue responses for a fixed total overhead workload. J Biomech. 2015;48(11):2911–8. pmid:26117074
* View Article
* PubMed/NCBI
* Google Scholar
32. 32. Seghers J, Spaepen A. Muscle fatigue of the elbow flexor muscles during two intermittent exercise protocols with equal mean muscle loading. Clin Biomech (Bristol). 2004;19(1):24–30. pmid:14659926
* View Article
* PubMed/NCBI
* Google Scholar
33. 33. Garg A, Kapellusch JM. The Cumulative Lifting Index (CULI) for the Revised NIOSH lifting equation: quantifying risk for workers with job rotation. Hum Factors. 2016;58(5):683–94. pmid:26896406
* View Article
* PubMed/NCBI
* Google Scholar
34. 34. Koyuncu A, Bates MN, Petrin Z, Cope M, McCoy SI, Prata N, et al. Heavy load carrying and musculoskeletal health: An exploratory study of biomechanical risk factors among sand miners in Pokhara, Kaski District, Nepal. Int. J. Ind. Ergon. 2021;85:103187.
* View Article
* Google Scholar
35. 35. Padula RS, Comper MLC, Sparer EH, Dennerlein JT. Job rotation designed to prevent musculoskeletal disorders and control risk in manufacturing industries: A systematic review. Appl Ergon. 2017;58:386–97. pmid:27633235
* View Article
* PubMed/NCBI
* Google Scholar
36. 36. Roman-Liu D. Repetitive task indicator as a tool for assessment of upper limb musculoskeletal load induced by repetitive task. Ergonomics. 2007;50(11):1740–60. pmid:17972200
* View Article
* PubMed/NCBI
* Google Scholar
37. 37. Mathiassen SE, Winkel J. Quantifying variation in physical load using exposure-vs-time data. Ergonomics. 1991;34(12):1455–68. pmid:1800110
* View Article
* PubMed/NCBI
* Google Scholar
38. 38. Allman BL, Rice CL. Perceived exertion is elevated in old age during an isometric fatigue task. Eur J Appl Physiol. 2003;89(2):191–7. pmid:12665984
* View Article
* PubMed/NCBI
* Google Scholar
39. 39. Ansdell P, Thomas K, Howatson G, Hunter S, Goodall S. Contraction intensity and sex differences in knee-extensor fatigability. J Electromyogr Kinesiol. 2017;37:68–74. pmid:28963937
* View Article
* PubMed/NCBI
* Google Scholar
40. 40. Armatas V, Bassa E, Patikas D, Kitsas I, Zangelidis G, Kotzamanidis C. Neuromuscular differences between men and prepubescent boys during a peak isometric knee extension intermittent fatigue test. Pediatr Exerc Sci. 2010;22(2):205–17. pmid:20567042
* View Article
* PubMed/NCBI
* Google Scholar
41. 41. Benwell NM, Mastaglia FL, Thickbroom GW. Changes in the functional MR signal in motor and non-motor areas during intermittent fatiguing hand exercise. Exp Brain Res. 2007;182(1):93–7. pmid:17549462
* View Article
* PubMed/NCBI
* Google Scholar
42. 42. Birtles DB, Minden D, Wickes SJ, M Puxley KP, A Llewellyn MG, Casey A, et al. Chronic exertional compartment syndrome: muscle changes with isometric exercise. Med Sci Sports Exerc. 2002;34(12):1900–6. pmid:12471294
* View Article
* PubMed/NCBI
* Google Scholar
43. 43. Boccia G, Dardanello D, Tarperi C, Festa L, La Torre A, Pellegrini B, et al. Fatigue-induced dissociation between rate of force development and maximal force across repeated rapid contractions. Hum Mov Sci. 2017;54:267–75. pmid:28595134
* View Article
* PubMed/NCBI
* Google Scholar
44. 44. Callahan DM, Foulis SA, Kent-Braun JA. Age-related fatigue resistance in the knee extensor muscles is specific to contraction mode. Muscle Nerve. 2009;39(5):692–702. pmid:19347926
* View Article
* PubMed/NCBI
* Google Scholar
45. 45. Chung LH, Callahan DM, Kent-Braun JA. Age-related resistance to skeletal muscle fatigue is preserved during ischemia. J Appl Physiol (1985). 2007;103(5):1628–35. pmid:17690199
* View Article
* PubMed/NCBI
* Google Scholar
46. 46. Egaña M, Green S. Intensity-dependent effect of body tilt angle on calf muscle fatigue in humans. Eur J Appl Physiol. 2007;99(1):1–9. pmid:17013590
* View Article
* PubMed/NCBI
* Google Scholar
47. 47. Fulco CS, Cymerman A, Muza SR, Rock PB, Pandolf KB, Lewis SF. Adductor pollicis muscle fatigue during acute and chronic altitude exposure and return to sea level. J Appl Physiol (1985). 1994;77(1):179–83. pmid:7961231
* View Article
* PubMed/NCBI
* Google Scholar
48. 48. Gonzales JU, Scheuermann BW. Absence of gender differences in the fatigability of the forearm muscles during intermittent isometric handgrip exercise. J Sports Sci Med. 2007;6(1):98–105. pmid:24149231
* View Article
* PubMed/NCBI
* Google Scholar
49. 49. Hamada T, Sale DG, MacDougall JD, Tarnopolsky MA. Interaction of fibre type, potentiation and fatigue in human knee extensor muscles. Acta Physiol Scand. 2003;178(2):165–73. pmid:12780391
* View Article
* PubMed/NCBI
* Google Scholar
50. 50. Mitsukawa N, Sugisaki N, Kanehisa H, Fukunaga T, Kawakami Y. Fatigue-related changes in fascicle-tendon geometry over repeated contractions: difference between synergist muscles. Muscle Nerve. 2009;40(3):395–401. pmid:19705427
* View Article
* PubMed/NCBI
* Google Scholar
51. 51. Morse CI, Pritchard LJ, Wüst RCI, Jones DA, Degens H. Carbon monoxide inhalation reduces skeletal muscle fatigue resistance. Acta Physiol (Oxf). 2008;192(3):397–401. pmid:17970829
* View Article
* PubMed/NCBI
* Google Scholar
52. 52. Muthalib M, Jubeau M, Millet GY, Maffiuletti NA, Ferrari M, Nosaka K. Biceps brachii muscle oxygenation in electrical muscle stimulation. Clin Physiol Funct Imaging. 2010;30(5):360–8. pmid:20618357
* View Article
* PubMed/NCBI
* Google Scholar
53. 53. Ordway GA, Kearney JT, Stull GA. Rhythmic isometric fatigue patterns of the elbow flexors and knee extensors. Res Q 1977;48(4):734–40.
* View Article
* Google Scholar
54. 54. Saito Y, Iemitsu M, Otsuki T, Maeda S, Ajisaka R. Gender differences in brachial blood flow during fatiguing intermittent handgrip. Med Sci Sports Exerc. 2008;40(4):684–90. pmid:18317376
* View Article
* PubMed/NCBI
* Google Scholar
55. 55. Saugen E, Vøllestad NK, Gibson H, Martin PA, Edwards RH. Dissociation between metabolic and contractile responses during intermittent isometric exercise in man. Exp Physiol. 1997;82(1):213–26. pmid:9023519
* View Article
* PubMed/NCBI
* Google Scholar
56. 56. Thomas CK, del Valle A. The role of motor unit rate modulation versus recruitment in repeated submaximal voluntary contractions performed by control and spinal cord injured subjects. J Electromyogr Kinesiol. 2001;11(3):217–29. pmid:11335152
* View Article
* PubMed/NCBI
* Google Scholar
57. 57. Wallström A, Nordenskiöld U. Assessing hand grip endurance with repetitive maximal isometric contractions. J Hand Ther. 2001;14(4):279–85. pmid:11762728
* View Article
* PubMed/NCBI
* Google Scholar
58. 58. White C, Dixon K, Samuel D, Stokes M. Handgrip and quadriceps muscle endurance testing in young adults. Springerplus. 2013;2:451. pmid:24052933
* View Article
* PubMed/NCBI
* Google Scholar
59. 59. Enoka RM, Duchateau J. Muscle fatigue: what, why and how it influences muscle function. J Physiol. 2008;586(1):11–23. pmid:17702815
* View Article
* PubMed/NCBI
* Google Scholar
60. 60. https://www.kinovea.org/
* View Article
* Google Scholar
61. 61. Sarraf F, Abbasi S, Varmazyar S. Self-management exercises intervention on text neck syndrome among university students using smartphones. Pain Manag Nurs. 2023;24(6):595–602. pmid:37173200
* View Article
* PubMed/NCBI
* Google Scholar
62. 62. Merino G, da Silva L, Mattos D, Guimarães B, Merino E. Ergonomic evaluation of the musculoskeletal risks in a banana harvesting activity through qualitative and quantitative measures, with emphasis on motion capture (Xsens) and EMG. Int J Ind Ergon. 2019;69:80–9.
* View Article
* Google Scholar
63. 63. Zhang T, Li X, Sun S, Lan H, Du P, Wang M. Determination of lignin in marine sediment using alkaline cupric oxide oxidation-solid phase extraction-on-column derivatization-gas chromatography. J Ocean Univ China. 2013;12(1):63–9.
* View Article
* Google Scholar
64. 64. Roman-Liu D. Maximum handgrip force in relation to upper limb posture--a meta-analysis. AIHA J (Fairfax, Va). 2003;64(5):609–17. pmid:14521433
* View Article
* PubMed/NCBI
* Google Scholar
65. 65. Roman-Liu D, Tokarski T. Upper limb strength in relation to upper limb posture. Int J Ind Ergon. 2005;35(1):19–31.
* View Article
* Google Scholar
66. 66. Tokarski TM, Roman-Liu D. Assessment of load on the lumbar spine using two computerised packages and REBA method. Acta Bioeng Biomech. 2020;22(3).
* View Article
* Google Scholar
67. 67. Kinali G, Kara S, Yıldırım MS. Electromyographic analysis of an ergonomic risk factor: overhead work. J Phys Ther Sci. 2016;28(6):1924–7. pmid:27390448
* View Article
* PubMed/NCBI
* Google Scholar
68. 68. Bazzucchi I, Marchetti M, Rosponi A, Fattorini L, Castellano V, Sbriccoli P, et al. Differences in the force/endurance relationship between young and older men. Eur J Appl Physiol. 2005;93(4):390–7. pmid:15578202
* View Article
* PubMed/NCBI
* Google Scholar
69. 69. Beck B, Ham DJ, Best SA, Carstairs GL, Savage RJ, Straney L, et al. Predicting endurance time in a repetitive lift and carry task using linear mixed models. PLoS One. 2016;11(7):e0158418. pmid:27379902
* View Article
* PubMed/NCBI
* Google Scholar
70. 70. Sommerich CM, McGlothlin JD, Marras WS. Occupational risk factors associated with soft tissue disorders of the shoulder: a review of recent investigations in the literature. Ergonomics. 1993;36(6):697–717. pmid:8513776
* View Article
* PubMed/NCBI
* Google Scholar
71. 71. Akoglu H. User’s guide to correlation coefficients. Turk J Emerg Med. 2018;18(3):91–3. pmid:30191186
* View Article
* PubMed/NCBI
* Google Scholar
72. 72. Jenkins DG, Quintana-Ascencio PF. A solution to minimum sample size for regressions. PLoS One. 2020;15(2):e0229345. pmid:32084211
* View Article
* PubMed/NCBI
* Google Scholar
73. 73. G * Power 3.1 manual June 1, 2023. https://www.psychologie.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf
* View Article
* Google Scholar
74. 74. Faber J, Fonseca LM. How sample size influences research outcomes. Dental Press J Orthod. 2014;19(4):27–9. pmid:25279518
* View Article
* PubMed/NCBI
* Google Scholar
75. 75. Behm DG, Colwell EM, Power GMJ, Ahmadi H, Behm ASM, Bishop A. Transcutaneous electrical nerve stimulation improves fatigue performance of the treated and contralateral knee extensors. Exp Brain Res. 2019;182:193–7.
* View Article
* Google Scholar
76. 76. Frey Law LA, Avin KG. Endurance time is joint-specific: a modelling and meta-analysis investigation. Ergonomics. 2010;53(1):109–29. pmid:20069487
* View Article
* PubMed/NCBI
* Google Scholar
77. 77. Hunter SK, Critchlow A, Enoka RM. Muscle endurance is greater for old men compared with strength-matched young men. J Appl Physiol (1985). 2005;99(3):890–7. pmid:15879165
* View Article
* PubMed/NCBI
* Google Scholar
Citation: Roman-Liu D, Kamińska J, Tokarski T (2025) A knowledge-based equation of daily work exposure. PLoS One 20(6): e0324924. https://doi.org/10.1371/journal.pone.0324924
About the Authors:
Danuta Roman-Liu
Roles: Conceptualization, Data curation, Formal analysis, Writing – review & editing
E-mail: [email protected]
Affiliation: Central Institute for Labour Protection – National Research Institute (CIOP-PIB), Warsaw, Poland
ORICD: https://orcid.org/0000-0001-7836-8516
Joanna Kamińska
Contributed equally to this work with: Joanna Kamińska, Tomasz Tokarski
Roles: Data curation, Formal analysis, Writing – original draft
¶These authors also contributed equally to this work
Affiliation: Central Institute for Labour Protection – National Research Institute (CIOP-PIB), Warsaw, Poland
Tomasz Tokarski
Contributed equally to this work with: Joanna Kamińska, Tomasz Tokarski
Roles: Data curation, Formal analysis
¶These authors also contributed equally to this work
Affiliation: Central Institute for Labour Protection – National Research Institute (CIOP-PIB), Warsaw, Poland
ORICD: https://orcid.org/0000-0003-3572-6939
1. Silk A, Lenton G, Savage R, Aisbett B. Job task characteristics of Australian emergency services volunteers during search and rescue operations. Ergonomics. 2018;61(2):265–72. pmid:28738728
2. Guerreiro MM, Serranheira F, Cruz EB, Sousa-Uva A. Self-reported variables as determinants of upper limb musculoskeletal symptoms in assembly line workers. Saf Health Work. 2020;11(4):491–9. pmid:33329916
3. Rathore B, Pundir AK, Iqbal R. Ergonomic risk factors in glass artware industries and prevalence of musculoskeletal disorder. Int J Ind Ergon. 2020;80:1–11.
4. Curti S, Mattioli S, Bonfiglioli R, Farioli A, Violante FS. Elbow tendinopathy and occupational biomechanical overload: A systematic review with best-evidence synthesis. J Occup Health. 2021;63(1):e12186. pmid:33534951
5. da Costa BR, Vieira ER. Risk factors for work-related musculoskeletal disorders: A systematic review of recent longitudinal studies. Am J Ind Med. 2010;53(3):285–323. pmid:19753591
6. Hooftman WE, van der Beek AJ, Bongers PM, van Mechelen W. Is there a gender difference in the effect of work-related physical and psychosocial risk factors on musculoskeletal symptoms and related sickness absence?. Scand J Work Environ Health. 2009;35(2):85–95. pmid:19337673
7. Keyserling WM, Brouwer M, Silverstein BA. Effectiveness of a joint labor-management program in controlling awkward postures of the trunk, neck, and shoulders results of a field study. Int J Ind Ergon. 1993;11(1):51–65.
8. Chaffin DB. Localized muscle fatigue--definiton and measurement. J Occup Med. 1973;15(4):346–54. pmid:4348609
9. Roman-Liu D. External load and the reaction of the musculoskeletal system – a conceptual model of the interaction. Int J Ind Ergon. 2013;43(4):356–62.
10. Enoka RM, Duchateau J. Translating fatigue to human performance. Med Sci Sports Exerc. 2016;48(11):2228–38.
11. Enoka RM, Stuart DG. Neurobiology of muscle fatigue. J Appl Physiol (1985). 1992;72(5):1631–48. pmid:1601767
12. Roman-Liu D, Tokarski T, Kowalewski R. Decrease of force capabilities as an index of upper limb fatigue. Ergonomics. 2005;48(8):930–48. pmid:16147413
13. Gallagher S, Schall MC Jr. Musculoskeletal disorders as a fatigue failure process: evidence, implications and research needs. Ergonomics. 2017;60(2):255–69. pmid:27376409
14. Horton LM, Nussbaum MA, Agnew MJ. Effects of rotation frequency and task order on localised muscle fatigue and performance during repetitive static shoulder exertions. Ergonomics. 2012;55(10):1205–17. pmid:22849348
15. Descatha A, Dale AM, Silverstein BA, Roquelaure Y, Rempel D. Lateral epicondylitis: new evidence for work relatedness. Joint Bone Spine. 2015;82(1):5–7. pmid:25553834
16. Abate M, Di Carlo L, Salini V, Schiavone C. Risk factors associated to bilateral rotator cuff tears. Orthop Traumatol Surg Res. 2017;103(6):841–5. pmid:28578100
17. Anwer S, Li H, Antwi-Afari M, Wong A. Associations between physical or psychosocial risk factors and work-related musculoskeletal disorders in construction workers based on literature in the last 20 years: A systematic review. Int J Ind Ergon. 2021;83:103113.
18. Motabar H, Nimbarte AD. The effect of task rotation on activation and fatigue response of rotator cuff muscles during overhead work. Appl Ergon. 2021;97:103461. pmid:34174574
19. King J, Mattison M. An exploration of the effects of cycle time and force variations on muscle fatigue during submaximal intermittent isometric exertions. Ergonomics South Afr. 2017;29(1):36.
20. Mahdavi N, Dianat I, Heidarimoghadam R, Khotanlou H, Faradmal J. A review of work environment risk factors influencing muscle fatigue. Int. J. Ind. Ergon. 2020;80:103028.
21. Choi K, Lee S, Lee J, Kong Y. Development of thumb endurance curves associated with various exertion levels. Hum Ftrs & Erg Mfg Svc. 2017;27(5):249–55.
22. Rohmert W. Problems in determining rest allowances Part 1: use of modern methods to evaluate stress and strain in static muscular work. Appl Ergon. 1973;4(2):91–5. pmid:15677120
23. Gamet D, Maton B. The fatigability of two agonistic muscles in human isometric voluntary submaximal contraction: an EMG study. I. Assessment of muscular fatigue by means of surface EMG. Eur J Appl Physiol Occup Physiol. 1989;58(4):361–8. pmid:2920714
24. Hunter SK, Enoka RM. Changes in muscle activation can prolong the endurance time of a submaximal isometric contraction in humans. J Appl Physiol (1985). 2003;94(1):108–18. pmid:12391034
25. van Dieën JH, Oude Vrielink HH. The use of the relation between relative force and endurance time. Ergonomics. 1994;37(2):231–43. pmid:8119257
26. Elahrache K, Imbeau D, Farbos B. Percentile values for determining maximum endurance times for static muscular work. Int J Ind Ergon. 2006;36:99–108.
27. Rashedi E, Nussbaum MA. Mathematical models of localized muscle fatigue: sensitivity analysis and assessment of two occupationally-relevant models. PLoS One. 2015;10(12):e0143872. pmid:26656741
28. Iridiastadi H, Nussbaum MA. Muscle fatigue and endurance during repetitive intermittent static efforts: development of prediction models. Ergonomics. 2006;49(4):344–60. pmid:16690564
29. Masuda K, Masuda T, Sadoyama T, Inaki M, Katsuta S. Changes in surface EMG parameters during static and dynamic fatiguing contractions. J Electromyogr Kinesiol. 1999;9(1):39–46. pmid:10022560
30. Yassierli, Nussbaum MA. Muscle fatigue during intermittent isokinetic shoulder abduction: age effects and utility of electromyographic measures. Ergonomics. 2007;50(7):1110–26. pmid:17510825
31. Dickerson CR, Meszaros KA, Cudlip AC, Chopp-Hurley JN, Langenderfer JE. The influence of cycle time on shoulder fatigue responses for a fixed total overhead workload. J Biomech. 2015;48(11):2911–8. pmid:26117074
32. Seghers J, Spaepen A. Muscle fatigue of the elbow flexor muscles during two intermittent exercise protocols with equal mean muscle loading. Clin Biomech (Bristol). 2004;19(1):24–30. pmid:14659926
33. Garg A, Kapellusch JM. The Cumulative Lifting Index (CULI) for the Revised NIOSH lifting equation: quantifying risk for workers with job rotation. Hum Factors. 2016;58(5):683–94. pmid:26896406
34. Koyuncu A, Bates MN, Petrin Z, Cope M, McCoy SI, Prata N, et al. Heavy load carrying and musculoskeletal health: An exploratory study of biomechanical risk factors among sand miners in Pokhara, Kaski District, Nepal. Int. J. Ind. Ergon. 2021;85:103187.
35. Padula RS, Comper MLC, Sparer EH, Dennerlein JT. Job rotation designed to prevent musculoskeletal disorders and control risk in manufacturing industries: A systematic review. Appl Ergon. 2017;58:386–97. pmid:27633235
36. Roman-Liu D. Repetitive task indicator as a tool for assessment of upper limb musculoskeletal load induced by repetitive task. Ergonomics. 2007;50(11):1740–60. pmid:17972200
37. Mathiassen SE, Winkel J. Quantifying variation in physical load using exposure-vs-time data. Ergonomics. 1991;34(12):1455–68. pmid:1800110
38. Allman BL, Rice CL. Perceived exertion is elevated in old age during an isometric fatigue task. Eur J Appl Physiol. 2003;89(2):191–7. pmid:12665984
39. Ansdell P, Thomas K, Howatson G, Hunter S, Goodall S. Contraction intensity and sex differences in knee-extensor fatigability. J Electromyogr Kinesiol. 2017;37:68–74. pmid:28963937
40. Armatas V, Bassa E, Patikas D, Kitsas I, Zangelidis G, Kotzamanidis C. Neuromuscular differences between men and prepubescent boys during a peak isometric knee extension intermittent fatigue test. Pediatr Exerc Sci. 2010;22(2):205–17. pmid:20567042
41. Benwell NM, Mastaglia FL, Thickbroom GW. Changes in the functional MR signal in motor and non-motor areas during intermittent fatiguing hand exercise. Exp Brain Res. 2007;182(1):93–7. pmid:17549462
42. Birtles DB, Minden D, Wickes SJ, M Puxley KP, A Llewellyn MG, Casey A, et al. Chronic exertional compartment syndrome: muscle changes with isometric exercise. Med Sci Sports Exerc. 2002;34(12):1900–6. pmid:12471294
43. Boccia G, Dardanello D, Tarperi C, Festa L, La Torre A, Pellegrini B, et al. Fatigue-induced dissociation between rate of force development and maximal force across repeated rapid contractions. Hum Mov Sci. 2017;54:267–75. pmid:28595134
44. Callahan DM, Foulis SA, Kent-Braun JA. Age-related fatigue resistance in the knee extensor muscles is specific to contraction mode. Muscle Nerve. 2009;39(5):692–702. pmid:19347926
45. Chung LH, Callahan DM, Kent-Braun JA. Age-related resistance to skeletal muscle fatigue is preserved during ischemia. J Appl Physiol (1985). 2007;103(5):1628–35. pmid:17690199
46. Egaña M, Green S. Intensity-dependent effect of body tilt angle on calf muscle fatigue in humans. Eur J Appl Physiol. 2007;99(1):1–9. pmid:17013590
47. Fulco CS, Cymerman A, Muza SR, Rock PB, Pandolf KB, Lewis SF. Adductor pollicis muscle fatigue during acute and chronic altitude exposure and return to sea level. J Appl Physiol (1985). 1994;77(1):179–83. pmid:7961231
48. Gonzales JU, Scheuermann BW. Absence of gender differences in the fatigability of the forearm muscles during intermittent isometric handgrip exercise. J Sports Sci Med. 2007;6(1):98–105. pmid:24149231
49. Hamada T, Sale DG, MacDougall JD, Tarnopolsky MA. Interaction of fibre type, potentiation and fatigue in human knee extensor muscles. Acta Physiol Scand. 2003;178(2):165–73. pmid:12780391
50. Mitsukawa N, Sugisaki N, Kanehisa H, Fukunaga T, Kawakami Y. Fatigue-related changes in fascicle-tendon geometry over repeated contractions: difference between synergist muscles. Muscle Nerve. 2009;40(3):395–401. pmid:19705427
51. Morse CI, Pritchard LJ, Wüst RCI, Jones DA, Degens H. Carbon monoxide inhalation reduces skeletal muscle fatigue resistance. Acta Physiol (Oxf). 2008;192(3):397–401. pmid:17970829
52. Muthalib M, Jubeau M, Millet GY, Maffiuletti NA, Ferrari M, Nosaka K. Biceps brachii muscle oxygenation in electrical muscle stimulation. Clin Physiol Funct Imaging. 2010;30(5):360–8. pmid:20618357
53. Ordway GA, Kearney JT, Stull GA. Rhythmic isometric fatigue patterns of the elbow flexors and knee extensors. Res Q 1977;48(4):734–40.
54. Saito Y, Iemitsu M, Otsuki T, Maeda S, Ajisaka R. Gender differences in brachial blood flow during fatiguing intermittent handgrip. Med Sci Sports Exerc. 2008;40(4):684–90. pmid:18317376
55. Saugen E, Vøllestad NK, Gibson H, Martin PA, Edwards RH. Dissociation between metabolic and contractile responses during intermittent isometric exercise in man. Exp Physiol. 1997;82(1):213–26. pmid:9023519
56. Thomas CK, del Valle A. The role of motor unit rate modulation versus recruitment in repeated submaximal voluntary contractions performed by control and spinal cord injured subjects. J Electromyogr Kinesiol. 2001;11(3):217–29. pmid:11335152
57. Wallström A, Nordenskiöld U. Assessing hand grip endurance with repetitive maximal isometric contractions. J Hand Ther. 2001;14(4):279–85. pmid:11762728
58. White C, Dixon K, Samuel D, Stokes M. Handgrip and quadriceps muscle endurance testing in young adults. Springerplus. 2013;2:451. pmid:24052933
59. Enoka RM, Duchateau J. Muscle fatigue: what, why and how it influences muscle function. J Physiol. 2008;586(1):11–23. pmid:17702815
60. https://www.kinovea.org/
61. Sarraf F, Abbasi S, Varmazyar S. Self-management exercises intervention on text neck syndrome among university students using smartphones. Pain Manag Nurs. 2023;24(6):595–602. pmid:37173200
62. Merino G, da Silva L, Mattos D, Guimarães B, Merino E. Ergonomic evaluation of the musculoskeletal risks in a banana harvesting activity through qualitative and quantitative measures, with emphasis on motion capture (Xsens) and EMG. Int J Ind Ergon. 2019;69:80–9.
63. Zhang T, Li X, Sun S, Lan H, Du P, Wang M. Determination of lignin in marine sediment using alkaline cupric oxide oxidation-solid phase extraction-on-column derivatization-gas chromatography. J Ocean Univ China. 2013;12(1):63–9.
64. Roman-Liu D. Maximum handgrip force in relation to upper limb posture--a meta-analysis. AIHA J (Fairfax, Va). 2003;64(5):609–17. pmid:14521433
65. Roman-Liu D, Tokarski T. Upper limb strength in relation to upper limb posture. Int J Ind Ergon. 2005;35(1):19–31.
66. Tokarski TM, Roman-Liu D. Assessment of load on the lumbar spine using two computerised packages and REBA method. Acta Bioeng Biomech. 2020;22(3).
67. Kinali G, Kara S, Yıldırım MS. Electromyographic analysis of an ergonomic risk factor: overhead work. J Phys Ther Sci. 2016;28(6):1924–7. pmid:27390448
68. Bazzucchi I, Marchetti M, Rosponi A, Fattorini L, Castellano V, Sbriccoli P, et al. Differences in the force/endurance relationship between young and older men. Eur J Appl Physiol. 2005;93(4):390–7. pmid:15578202
69. Beck B, Ham DJ, Best SA, Carstairs GL, Savage RJ, Straney L, et al. Predicting endurance time in a repetitive lift and carry task using linear mixed models. PLoS One. 2016;11(7):e0158418. pmid:27379902
70. Sommerich CM, McGlothlin JD, Marras WS. Occupational risk factors associated with soft tissue disorders of the shoulder: a review of recent investigations in the literature. Ergonomics. 1993;36(6):697–717. pmid:8513776
71. Akoglu H. User’s guide to correlation coefficients. Turk J Emerg Med. 2018;18(3):91–3. pmid:30191186
72. Jenkins DG, Quintana-Ascencio PF. A solution to minimum sample size for regressions. PLoS One. 2020;15(2):e0229345. pmid:32084211
73. G * Power 3.1 manual June 1, 2023. https://www.psychologie.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf
74. Faber J, Fonseca LM. How sample size influences research outcomes. Dental Press J Orthod. 2014;19(4):27–9. pmid:25279518
75. Behm DG, Colwell EM, Power GMJ, Ahmadi H, Behm ASM, Bishop A. Transcutaneous electrical nerve stimulation improves fatigue performance of the treated and contralateral knee extensors. Exp Brain Res. 2019;182:193–7.
76. Frey Law LA, Avin KG. Endurance time is joint-specific: a modelling and meta-analysis investigation. Ergonomics. 2010;53(1):109–29. pmid:20069487
77. Hunter SK, Critchlow A, Enoka RM. Muscle endurance is greater for old men compared with strength-matched young men. J Appl Physiol (1985). 2005;99(3):890–7. pmid:15879165
© 2025 Roman-Liu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.