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Twenty ergonomic tasks were evaluated in which human operators performed mixed static work and dynamic work. Steady-state physiological data are the input into a model as regressor variables, which are then multiplied by the respective regressor coefficients. The resultant physiological state model output is a single response variable that represents the workload. Mixed stepping regression techniques were utilized to calculate the regressor coefficients. Ten physiological state model equations resulted. A lower order equation (with three regressor variables) accounted for 80% of the observed variance. The highest order equation (with ten regressor variables) accounted for 89% of the variance.

Workload has been defined by Phillips [1] as the reaction of the human body when performing external work. When the external work is physical work, the bodily reactions consist of physiological adjustments and adaptations required for the performance of that external physical work. When these physiological adjustments and adaptations can be measured and quantified, the ergonomic engineer has an analytical basis for the quantitative assessment of human physical workload. The acquisition of physiological data with respect to the neuromuscular system and the cardiopulmonary system is necessary [2]. The quantification of such physiological data and the application of these quantitative relationships represents a physiological state model for human workload. Most work performed during ergonomic tasks is a combination of static work (muscle generates internal force, but without external movement) and dynamic work (muscles generate force that results in external movement). With static work, then no external work is accomplished in the environment. Dynamic work, however, occurs when external work is accomplished in the environment. Consequently, it is helpful to briefly review the physiological reactions to both static work and dynamic work. 1.1. Physiological background The cardiopulmonary responses associated with static work reflect the human reaction to isometric muscle contraction as described by Petrofsky and Phillips [3]. When isometric contractions are sustained at muscle forces that are non-fatiguing (forces that are below 10% to 15% of the muscle's maximum strength), heart rate and blood pressure rise to a certain level and are then maintained throughout the duration of the static work. This represents a steady-state response in which the blood pressure will rise 10–View the MathML source, and the heart rate will rise 10–20 beats per minute. However, there is a dramatic rise in blood pressure (both the systolic pressure and the diastolic pressure) during the time course of the fatiguing isometric muscle contractions (see below). The cardiopulmonary responses to fatiguing static work are not only of greater magnitude, but also of a different pattern than of those observed during dynamic work. For example, during dynamic work, Asfraud and Rodahl [4] observed that the systolic pressure will increase, but the diastolic pressure will decrease, and the peripheral resistance will decrease during the time course of the fatiguing dynamic work. By contrast, during the course of fatiguing static work, both the systolic pressure and the diastolic pressure will increase and there will also be a boost in the peripheral resistance. Cardiac output increases modestly during fatiguing static work. A resting cardiac output of View the MathML source will usually only become boosted to about View the MathML source over the duration of fatiguing static work. The heart rate response during fatiguing static work is much more modest than during dynamic work. The heart rate may augment to a level above View the MathML source (during dynamic work). However, during static work the heart rate rarely exceeds View the MathML source. Oxygen consumption View the MathML source during fatiguing static work also intensifies modestly. However, ventilation View the MathML source can increase markedly. Some individuals will actually experience a distinct hyperventilation. Although heart rate and blood pressure continuously rise throughout the time course of fatiguing static work, there is little change in View the MathML source or View the MathML source until approximately halfway into the duration of fatiguing static work. After that, these parameters increase and may become enhanced markedly. When an individual performs moderate dynamic work, vasoactive metabolites are produced and accumulate in the working muscles [5]. This results in a dramatic dilation of the blood vessels in the working skeletal muscle. As a result, the blood flow through the working skeletal muscle advances to amounts from 10 to 20 times that of the resting (non-working) state. Venous return to the right side of the heart can also be augmented due to the enhanced contraction of skeletal muscles around the veins returning blood to the right side of the heart. This occurs because of compression of the veins and the subsequent one-way displacement of the blood toward the thorax. The enhancement in body temperature (which is produced by the dynamic work) will further dilate blood vessels in the skin in order to offload heat. The net effect of this vasodilation of skeletal muscle and skin blood vessels is to dramatically reduce the systemic peripheral resistance (R). However, there is marked vasoconstriction in the viscera (stomach, intestines, kidneys, etc.) so that blood flow to these organs is abated. This tends to somewhat offset the marked reduction in systemic peripheral resistance which occurs during moderate dynamic work. The pronounced increase in heart rate during moderate dynamic work contributes to a dramatic enhancement in cardiac output. This effect is partially offset by a reduction in stroke volume due to a shortening of R–R interval. However, there is still a significant upsurge in cardiac output. The end result is a rise in the mean systemic arterial pressure with moderate dynamic work. This augmentation in mean arterial pressure is accompanied by an increase (or widening) of the pulse pressure (ΔP). The systolic pressure rises in relation to the enhancement in cardiac output. The pulmonary response to mild, moderate, and heavy dynamic work is progressive and proportional to the level of the dynamic work [6]. For a young healthy adult male, the tidal volume is approximately View the MathML source and the respiratory rate is View the MathML source at rest. This results in a minute ventilation of approximately View the MathML source. With very heavy dynamic work, the tidal volume can enlarge up to View the MathML source and the respiratory rate can increase up to View the MathML source so that the minute ventilation with very dynamic work can be View the MathML source. 1.2. Objective Mixed work occurs when the human operator performs tasks that require both a component of static work and also a component of dynamic work. Mixed work represent the interaction of static work physiology with dynamic work physiology (as discussed separately above). The resultant workload (WL) is then a function of the relative proportions of the static work and the dynamic work with respect to the total work effort (see Methods). In practical ergonomic applications, it is usually difficult or impossible to physically measure and quantify the actual workload value for mixed static and dynamic work. First, the tasks can be somewhat complex, and it is difficult to separate the specific static work proportion from the specific dynamic work proportion. Second, there is interaction between the two types of work, such that the proportion of static work can affect the portion of dynamic work and vice versa. The objective of this paper is to develop the general and specific form of a physiological state model that addresses these problems. As a human operator performs an ergonomic task, basic physiological data can be obtained relatively simply and non-invasively. Steady-state values of such data are then input into the model as regressor variables (both directly measured and/or directly calculated), which are then multiplied by the respective regressor coefficients (i.e., much like “weighting” factors), which are statistically determined as non-different from zero. The resultant physiological state model output is a single response variable that represents the workload value for the mixed static and dynamic work.

Mixed step-wise regression of the 12 physiological variables has resulted in an array of physiological state models that utilize from one to 10 of the physiological parameters considered (see Table 3). It is interesting that a model with only one to two parameters, WL(1) and WL(2) account for 52% and 67% of the total variance, respectively. Respiratory rate (F Resp) rather than the more commonly monitored heart rate (F HR) is the more significant physiological variable. Heart rate (RR) correlates well with predominantly dynamic work effort, ranging between 85 and View the MathML source for tasks 1–11. However, heart rate changes are rather minimal to modest with predominantly static work effort, varying between 82 and 110 for tasks 12–20. The significant increases in systolic and diastolic blood pressure during predominantly static work will trigger a reflex slowing of heart rate through the carotid baroreceptor mechanism. Clearly respiratory rate (RR) is the better single indicator of mixed static and dynamic work effort, since the increased oxygen demand of both types of work is met through increasing the respiratory rate. Peripheral resistance (PR) is a calculated, non-linear variable that first appears as the second parameter in WL(2). PR will then appear as a model parameter in every subsequent model through the 10-parameter model. This does not occur for any other of the 11 parameters. This fact can be interpreted physiologically and demonstrates the usefulness of step-wise regression models to create parsimonious models (with good data fit). Recall that there is little a priori knowledge about the physiological state when mixed static and dynamic work effort is analyzed. PR is defined by Eq. (45) as mean pressure (P Mean) divided by cardiac output (CO). Note, however, the CO (a calculated, non-linear variable) does not individually appear until the WL(6) model and P Mean (a calculated linear variable) until the WL(7) model. The underlying significance of PR is that fundamentally it represents the interaction of four (of the five) directly measured variables. More specifically, P Mean is calculated from the systolic pressure (PS) and diastolic pressure (PD) as per Eq. (42). CO is calculated from the tidal volume (VA) and respiratory rate (RR) as per Eq. (43). PR is the quotient of a PS and PD numerator and a VA and RR denominator. Two different physiological state models were developed that utilize three parameters. [WL(3A)] utilizes F Resp and PR [as per WL(2)] and adds FHR to account for 75% of the total variance. WL(3B) retains only PR from WL(2) and adds FHR and SV in order to account for 80% of the total variance. Based upon R2, then WL(3B) clearly is the superior three-parameter model, and leads to some interesting physiological insights into mixed static and dynamic work. WL(3A) improves model prediction (over a two-parameter model) by utilizing two directly monitored physiological variables (RR and HR) combined with a third calculated, non-linear variable (PR). Alternatively, WL(3B) provides still further improvement by utilizing only one directly monitored linear variable (RR) and two calculated, non-linear variables (SV and PR). This shift between linear variables to non-linear variables will continue into the higher parameter models through WL(7) where two parameters are calculated, linear (P Delta, P Mean), and five parameters are calculated non-linear (CO, SV, PR, SW, S Pow). At this point, the seven-parameter model will account for 89% of the variance (and an r=0.942). A major finding of the physiological state model is that calculated, non-linear parameters must be included in any model for physiological assessment of workload effort. As a corollary to this finding, this study also indicates that an entirely linear model of both directly measured linear variables and calculated linear variables will not be as effective (as a non-linear model) in the physiological assessment of workload effort. To support this finding, five quasi-physiological models were derived by step-wise regression of 12 linear variables (five directly measured and seven calculated). Only five quasi-physiological state models were derived by step-wise regression (see Table 5). The interesting result is that a single parameter model WL(1) using MRP2 (defined as one-half F Resp plus one-half of P Dias) accounted for 65% of the total variance. This is much better than the single parameter, View the MathML source, physiological model accounting for only 52% of the total variance. A two-parameter quasi-physiological model, View the MathML source was comparable to a two-parameter physiological model WL(2), each accounting for 66% of the total variance. Subsequent, quasi-physiological state models of three, four, and five parameters, only accounted for 67% or 68% of the total variance, however. There are some limitations to the physiological state model as developed to date. First, it is a steady-state model. The five directly measured physiological parameters (regressor variables 1–5) must all be relatively constant (within a defined co-efficient of variation) over a continuous 1-min period. This is because the relevant calculated linear and non-linear physiological parameters (regressor variables 6–12) are derived from steady-state approximations of the cardiopulmonary and systemic vascular adjustments to human workload. Experience indicates that the data are best acquired during the middle one-third of the sustained human workload effort. Therefore, the current version of the physiological state model will not adequately predict human operator workload during initial (warm-up) periods and final (end-fatigue) periods. This will be true even though the actual human work (mixed static and dynamic work) is constant throughout the ergonomic task period. Second, the current version of the model is limited by the nature of the mixed static and dynamic work that was analyzed. The 20 ergonomic tasks represent mixed work, but predominantly dynamic or static. The 11 predominantly dynamic tasks are estimated to be a mix of 75% or greater dynamic work with 25% or lesser static work. The nine predominantly static tasks are estimated to be a mix of 75% or greater static work with 25% or lesser dynamic work. Since human physiological reaction to mixed static and dynamic work is dependent upon the relative proportion of each type of work, the ultimate robustness of the physiological state model as applied in this paper will be determined by a larger sampling of human ergonomic tasks and those that include less disparity between the relative proportion of each type of work. Summary Twenty ergonomic tasks were evaluated in which human operators performed mixed static work and dynamic work. This paper describes the development of both the general form and various specific forms of a physiological state model to describe the human ergonomic workload. Ten physiologycal state model equations resulted from step-wise regression of the data table. Mixed stepping regression techniques were utilized to calculate the regressor coefficients. A lower order equation (with three regressor variables) accountef for 80% of the observed variance. The highest order equation (with ten regressor variables) accounted for 89% of the variance. Five quasi-physiological state model equations resulted from step-wise regression of the data table. The highest order equation (with five regressor variables) accounted for 68% of the variance.