By B. Kamalakannan, W. Groves and A. Freivalds
Balaji Kamalakannan, M.S., is currently employed by Algonquin Industries, Guilford, CT. He holds an M.S. degree in Industrial Engineering from the Pennsylvania State University.
William A. Groves, Ph.D., CSP, CIH, is an assistant professor in the Industrial Health and Safety program at Pennsylvania State University, University Park. He holds a B.S. in Chemical Engineering from Case Western Reserve University, and M.P.H. and Ph.D. degrees in Industrial Health from the University of Michigan. Groves is a member of ASSE and AIHA and serves on the editorial boards of the Journal of Occupational and Environmental Hygiene (JOEH) and the Journal of the International Society for Respiratory Protection (JISRP).
Andris Freivalds, Ph.D., is a professor in the department of Industrial and Manufacturing Engineering at Pennsylvania State University, University Park. He holds degrees in Bioengineering (Ph.D., M.S.), Computer, Information and Control Engineering (M.S.), and Science Engineering (B.S.E.) from the University of Michigan. Professor Freivalds initiated the Human Factors/Ergonomics Engineering program at Penn State and developed a human factors teaching and research laboratory. He is Fellow of the Ergonomics Society and is on the editorial boards for the International Journal of Industrial Ergonomics and for Applied Ergonomics.
Predictive equations were developed to estimate metabolic work rate (MWR) as a function of heart rate and physical characteristics. Thirteen subjects (5Female, 8Male) spanning a range of age (2255 yrs) and physical characteristics performed a series of “step” tests in which oxygen consumption and heart rate were recorded. Three stepping frequencies and two runs were considered. Physical workload was calculated for each subject based on the step height, stepping frequencies, and weight with results ranging from 1484 Watts (W). Corresponding estimates of MWR based on oxygen consumption ranged from 120745 W. Predictors considered for modeling were: heart rate (HR), resting heart rate (RHR), age (A), gender (G), height (H), weight (W), and body mass index (BMI). Four models were developed and evaluated using linear regression. The best results were achieved with a model that included predictor variable interactions and quadratic terms and the results of a single “calibration” steptest conducted prior to the sampling period to develop a simple linear prediction of workload as a function of heart rate specific to an individual. Validation through bootstrapping of residuals and Chow Tests suggest that the model can be generalized for prediction of MWR without the need for collecting metabolic work data.
Keywords: energy expenditure, work rate, pulse, hear rate, modeling
In the Final Rule of the Respiratory Protection Standard, the Occupational Safety and Health Administration (OSHA) estimates that approximately 35 million workers, representing roughly 20% of all establishments, wear respirators at some time for protection from airborne contaminants (OSHA, 1988). Given such widespread use it is important to have sufficient information to characterize respirator performance so that workers can be assured of adequate protection. However, there is limited data available for evaluating the performance of respiratory protection under actual workplace conditions. To address this problem, the National Institute for Occupational Safety and Health (NIOSH) funded this research project to develop a sampling system to measure contaminant concentrations inside respirators while worn.
Myers et al. (1983) defined workplace protection factor (WPF) as a measure of the actual protection provided in the workplace under the conditions of that workplace by a properly functioning respirator when correctly worn and used:
WPF = Co/Ci 
Eq. 1 
where Co is ambient contaminant concentration and Ci is the concentration inside the respirator face piece. Workplace performance of respirators is assessed by determining workplace protection factors. One of the factors likely to influence the effectiveness of respiratory protection is the work rateof the person wearing the respirator. Work rate is directly related to respiration rate and may also be correlated with respirator leakage; however, very little data exists on measurement of work rate while measuring WPF.
Energy expenditure can be defined as the amount of energy required by the body to perform a particular task. McArdle et al. (1991) defined daily energy expenditure as the sum total of the basal and resting metabolisms, thermogenic influences (particularly the thermic effect of food), and energy generated during physical activity. Though various factors affect a person’s metabolic rate, the greatest influence comes from physical activity. Several classification systems have been proposed for rating sustained physical activity in terms of its strenuousness. One recommendation is that work tasks be classified by the ratio of energy required for the task to the resting energy requirement. One of the systems used is the physical activity ratio, or PAR, to classify physical activities. Light work for men is defined as that eliciting an oxygen uptake (or energy expenditure) as great as three times the resting requirement; heavy work is categorized as that requiring six to eight times the resting metabolism; whereas maximal work is any task requiring an increase in metabolism to nine times or more above rest. As a frame of reference, most industrial tasks require less than three times the resting energy expenditure (McArdle et al.).
Another commonly used method for rating physical activity is measuring energy expenditure based on heart rate. For every individual, heart rate and oxygen uptake tend to be linearly related throughout a wide range of aerobic exercises. If this relationship is known, the exercise heart rate can be used to estimate oxygen uptake (and then to compute energy expenditure) during similar forms of physical activity. This approach has been used when the oxygen uptake could not be measured during the actual activity. It has been observed that of all the physiological variables, heart rate (HR) is the easiest to measure in the field (Acheson, 1980). The relationship between HR and energy expenditure was shown as early as 1907, when Benedict reported that changes in pulse rate were correlated with changes in heat production in any one individual. Bergen and Christensen (1950), and Booyens and Hervey (1960) have also described the use of hear rate as an estimator of metabolic rate.
Kaudewitz (1998) studied the assessment of a work standard using heart rate monitoring. The author performed heart rate analysis from data collected from a subject performing his normal work shift in a hospital. According to the author, heart rate monitoring is an ergonomic tool that can help assess the appropriateness of a work standard for jobs where energy expenditure and wholebody fatigue are primary concerns. Based on the results he concluded that the resting heart rate is critical to the validity of the work capacity calculation and work capacity can be significantly underestimated or overestimated if the resting heart rate is not accurate. This study underlines the importance of getting a good measure of the resting heart rate.
Bot and Hollander (2000) conducted a study to validate the use of heart rate responses to estimate oxygen uptake (VO2) during varying nonsteady state activities. Dynamic and static exercises engaging large and small muscles masses were studied in four different experiments. In the first experiment, 16 subjects performed an interval test on a cycle ergo meter, and 12 subjects performed a field test consisting of various dynamic leg exercises. Simultaneous heart rate and VO2 measurements were made. Linear regression analyses were done and the authors concluded that there is very high correlation between heart rate and VO2 during both the interval test and the field test.
These studies demonstrate the use of heart rate as a good measure of energy expenditure and generally confirm the linear relationship between oxygen consumption and heart rate. The objective of this research project was to identify an optimal protocol for estimating work rates for individuals wearing respirators based on heart rate data and physical characteristics. Heart rate was recorded by a multichannel datalogging unit that is an integral part of a personal sampling system developed for measuring WPF for gases and vapors. The complete system consists of a sampling pump, a pressure transducer circuit designed to sense differential pressure inside the respirator, and a multichannel datalogging unit for recording the output from the pressure transducer as well as a transducer for measuring heart rate. A “steptest” was used to simulate work rates in an actual work environment and heart rate was recorded when the subjects performed the step test. This heart rate, recorded after the subjects reached a steady state, was used as a measure of energy expenditure based on the linear relationship between heart rate and volume of oxygen consumption.
Thirteen Subjects (5Female,8Male) spanning a range of age (2255 yr) and physical characteristics (Table 1) performed step tests at three levels of exertion. Oxygen consumption and heart rate were recorded using a metabolic monitor and a commercially available heart rate monitor (Polar Electro Inc., Lake Success, NY). Physical workload (PWL) was calculated based on the step height (32.5 cm), stepping frequency (5, 10, and 15 steps/min), and body weight. Metabolic work rate (MWR) was calculated from oxygen consumption (VO2) as determined by the metabolic monitor. Two replicate runs per subject, for a total of 13 x 3 x 2 = 78 data points, were conducted during the same day/session after a 30 minute rest period.
The subjects were asked to complete a medical screening questionnaire and signed an informed consent form after being briefed about the experiment and the procedures involved. Subjects were then asked to sit in a chair for a approximately 15 minutes and resting heart rate was recorded with the help of the heart rate monitor. The metabolic monitor mask was donned by the subjects who then performed the first run which included 3 stepping rates – 5, 10 and 15 steps per minute. The VO2 values were read from a stripchart recorder and the digital display on the metabolic monitor. Each stepping rate was performed until the subjects reached a steady state that took a period of approximately 3 to 5 minutes depending on the age and physical fitness of the subject. VO2 and heart rate were the variables recorded. At the end of each stepping rate, the subjects were asked to rate their exertion using Borg’s RPE scale. This value was also recorded. At the end of each stepping frequency, the subjects were asked to rest on a chair for 2 to 3 minutes to allow them to return back to their resting heart rate. After completion of the first set of runs, the subjects were given a rest period of 30 minutes. At the end of this rest period, the procedure was repeated.
Seven variables (heart rate, resting heart rate, age, gender, height, weight, and body mass index) were used to develop four regression models for predicting work rates (Table 2). Model I was developed based on the significant variables obtained from stepwise regression of the seven predictor variables. Predictive equations for Model II were developed based on stepwise regression of predictor variables, interactions, and quadratic terms. Model III involved a single calibration step test to estimate a linear relationship between heart rate and work rate for each individual. Model IV is based on the stepwise regression of the variables obtained from Model II and III. Models were subsequently validated.
Predictive equations were developed based on the data collected from the 13 subjects. MINITAB 13.1, was used for developing the regression models and analysis of data. Models were validated using statistical resampling methods (bootstrapping) and crossvalidation tests (Chow Test). Resampling methods are a class of statistical techniques for drawing inferences based on the variability present within a dataset. They are typically used to calculate the confidence intervals and pvalues. The common concept underlying all resampling methods is that variability can be assessed by drawing a large number of samples from the observed data and then comparing the properties of the observed data to the properties of the resampled datasets. There are various resampling methods – a bootstrapping technique was employed for this study. Bootstrap methods are substantially more general than randomization methods, and involve resampling with replacement, i.e. a value from the original data may occur more than once in a resampled dataset (Efron 1979, 1983; Kohavi, 1995).
“Regressboot”, a bootstrapping macro in MINITAB was used to validate the models (Butler, 2003). This macro is used to fit a multiple regression model. The significance of the parameter for each predictor is computed, along with the overall significance of the regression. Regressboot computes the pvalues by bootstrapping of the residuals. The Chow test was used for crossvalidation of the predictive equations (Chow, 1960). This test determines if a regression model can be generalized between a training and validation data set. The entire data is split into two data sets and three separate regressions (complete, training, and validation sets) test whether the model applies to both subsets. The confidence intervals of the three subsets are compared and if there is no significant difference between the confidence intervals it is concluded that the data set can be generalized i.e. the results from the Chow test can be used to judge how well models developed based on the data collected from the subject population can also be used to predict metabolic work rate in an industrial population having similar characteristics.
Heart rate (HR), resting heart rate (RHR), and the physical characteristics age (A), gender (G), height (H), weight (W), and body mass index (BMI) were used as the predictor variables. Data were used to develop four models for correlating heart rate and metabolic work rate (MWR). A 5% level of significance was chosen as a criterion for statistical significance. A stepwise linear regression approach was adopted for finding the significant set of variables for the predictive equation. Models are summarized in Table 2.
Model I was developed to examine the correlation between work rate and predictor variables: age, gender, body mass index, height, weight, heart rate and resting heart rate. This regression model was developed based solely on the seven predictor variables. Interaction terms of physical characteristics and quadratic terms were not considered. Results are shown in Figure 3 and the following regression equation resulted:
MWR =  1967 + 8.58 HR + 25.1 HT + 4.50 A – 7.47 RHR + 67.8 G 
Eq. 2 
where MWR is metabolic work rate (W), HR is heart rate (bpm), HT is height (in.), A is age (yr), RHR is resting heart rate (bpm), and G is gender (M=0, F=1). The regression equation was significant (p<0.05) with an R2 value of 0.797.
This model included the original seven predictive variables as well as their interactions and quadratic terms as input variables for predicting MWR. Stepwise regression was used to select significant variables and a predictive equation was developed:
MWR =  37614 – 17.9*B2 + 698*B – 0.00170*HR*RHR*HT + 0.571*HR*A + 0.0544*RHR*HT*B + 0.0158*HR*A*B – 8.02*HT2 + 0.778*HR*B*G + 969*HT + 0.0510*WT2  0.132*HR*WT*G + 0.00109*HR*WT*HT – 0.00220*RHR*A*WT – 2.83*RHR*B 
Eq. 3 
The resulting equation included 14 variables and was significant (p<0.05) with an R2 value of 0.9741.
Model III was based on a single calibration step test. The results from the first stepping frequency (10 steps/min) were chosen for the 13 subjects and a slope (S) was calculated based on the change in heart rate and work rate (DHR/MWR). S was then used to predict the work rate for the remaining stepping frequencies (2 results from the first run and 3 results from the second run) for each subject. This model considers the effect of performing a single calibration step test in a workplace. There is no VO2 data and hence the metabolic work rate is calculated through an indirect method. Metabolic work rate is estimated based on the efficiencies obtained during laboratory experimentation. The efficiencies of the step test ranged from 7.29 % to 14.64%. The average efficiency was calculated to be 11%. The physical workload readings were used along with this overall efficiency to find the metabolic work rate, i.e., MWR = estimated physical work load / efficiency (0.11). This metabolic work rate was used along with the change in heart rate readings to estimate S. This value of the slope was then used to predict the metabolic work rate for the remaining energy expenditure results for each subject:
MWR = S * HRRHR 
Eq. 3 
This resulting regression equation was significant (p<0.05) with an R2 value of 0.886.
Model IV is a combination of Models II and III. The slope and predicted work rate calculated from Model III were used as input variables along with the variables from Model II and a regression model was developed. A stepwise regression was performed to identify the significant variables and the following equation resulted:
MWR =  145 + 0.0249*RHR*PWR + 67.7*A*G*S – 0.172 A*G*RHR – 0.560*PWR + 0.230*A*G*B – 0.101*A2 + 0.0978*A*HT – 0.0288*W*S*PWR 
Eq. 3 
where PWR (W) and S (D bpm / W) are the predicted work rate and slope from Model III. The equation was significant (p<0.05) with an R2 value of 0.9764 (Figure 3). A summary of all modeling results is presented in Table 3.
The Regressboot Minitab macro fits a multiple regression model and the significance of the parameter for each predictor is computed, along with the overall significance of the regression. Regression pvalues in these cases should be less than 0.05. In the case of the Chow test, the null hypothesis is that these models could be generalized to predict metabolic work rate without the actual collection of metabolic work data. If we obtain a pvalue greater than 0.05, the null hypothesis can be accepted. Validation tests were conducted for Model II and IV (Models I and III were not validated due to the lower R2 and larger prediction errors). The validation tests were run and the pvalues for prediction of the metabolic work rate obtained. Tables 4 and 5 shows the results of the bootstrap evaluation of Models II and IV. All regression parameters and the overall regression equations were found to be significant. CrossValidation was done using the Chow test. Fifteen runs of the Chow test were completed for each model to estimate the range of pvalues. In all cases, results were well over a pvalue of 0.05 indicating that the models could be generalized.
Model I is the simplest approach for estimating work rate and performs reasonably well in terms of the percent of the variability explained. However the model exhibits a significant bias as demonstrated by the slope of the regression line (Fig. 3a). The results obtained are dependent on the subject population to a great extent and the results may vary when a different set of subjects are used for experimentation. In an effort to reduce this bias and for better prediction, interaction terms and quadratic terms were considered to develop the next Model II. Stepwise linear regression was conducted and 14 significant variables were identified. The resulting model had a higher R2 value and reduced errors (Table 3). However, the model is relatively complicated in terms of the number of variables in the predictive equation and the ability to generalize well to larger populations is uncertain.
The previous models considered heart rate and physical characteristics of the subjects. Model III is based on the change in heart rate and a slope (S) calculated based on a single calibration step test. The regression equations for this model gave R2 values of 0.886 and average percentage error for predicting the metabolic work rate of 11.06%. Model III is computationally simple and is likely to be the most robust in predicting work rate since it employs a “calibration” step test and is not dependent on the characteristics of the 13 subject steptest. However, the calculated slope (S) is based on an estimate of efficiency which is in turn based on the characteristics of the steptest. If the characteristics of the calibration test employed do not accurately reflect the actual work activities of the subject, the resulting model may not give a good prediction of work rate. Though validation runs indicate that this model can be generalized to predict metabolic work rate without collection of actual metabolic work data, error levels and R2 values were superior for Model II.
Model II was developed based on predictor variables and their interactions and Model III was based on a single calibration step test. To optimize the favorable results from these models, Model IV was developed as a combination of these two models with the predictor variables, interactions, and the slope and predicted work rate obtained from Model III as input variables. Stepwise linear regression was conducted and eight significant variables were identified. The regression equation based on these significant variables gave an R2 value of 0.976 for metabolic work rate.
Model IV has the best R2 value of all the four models and a low average percentage error for predicting the metabolic work rate  0.72%. Though slightly higher than Model II, Model IV incorporates a calibration step test which eliminates potential bias and dependency on the subject population shown by Models I and II. Model IV combines the features of Model II and Model III resulting in a more accurate and less biased estimate of work rate. This approach is expected to be more robust than Model II as a result of the calibration step test. Validation techniques performed on Model IV yielded results that indicate that this model can be generalized to predict metabolic work rate without actual collection of metabolic work data.
The results of this project suggest that work rates can be estimated without collection of metabolic work data. Physical characteristics such as age, gender, height, and weight can be used to improve the accuracy of predicted work rates. Model I is the simplest approach to estimating MWR and performs reasonably well in terms of the portion of the variability explained (~80%) and the percent error. However, the model exhibits a significant bias as demonstrated by the slope of the regression line (Fig. 3a). Model II yields excellent, unbiased results that explain 97% of the variability in MWR with the lowest average absolute % error. However, the model contains 14 parameters and should be applied with caution. Models I and II do not require the “calibration” steptest and would be easier to implement in a field protocol; however, it is assumed that the subjects used to develop the models fully represent the industrial workplace population. Model III is computationally simple and is likely to be the most robust in predicting MWR for individuals since it employs a “calibration” steptest and is not dependent on the characteristics of the 13 subject testset. Model IV combines the features of Models II and III resulting in an accurate, unbiased estimate of MWR (Fig 3b). This approach is expected to be more robust than Model II as a result of including the “calibration” step test.
Directions for future research include an examination of the performance of the predictive models and field protocols for their implementation using a larger industrial population and an evaluation of model applicability for subjects who are in good physical shape versus subjects who do not exercise regularly.
Support by the National Institute for Occupational Safety and Health (NIOSH) is gratefully acknowledged (SERCA 5K01OH00177). This project was approved by the Pennsylvania State University Institutional Review Board (IRB Approval # 15194).
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Table 1. Subject's Physical Characteristics
SUBJECT 
AGE 
Gender 
HEIGHT 
WEIGHT 
BMI 
A 
41 
Male 
76.0 
203 
25 
B 
55 
Male 
72.5 
193 
26 
C 
32 
Male 
69.0 
127 
19 
D 
22 
Male 
70.5 
135 
20 
E 
39 
Female 
65.0 
143 
24 
F 
52 
Male 
73.0 
170 
22 
G 
45 
Male 
74.0 
187 
24 
H 
33 
Female 
64.0 
117 
20 
I 
29 
Male 
72.5 
234 
31 
J 
50 
Male 
70.0 
179 
26 
K 
22 
Female 
68.5 
168 
25 
L 
22 
Female 
67.5 
132 
20 
M 
26 
Female 
65.5 
154 
25 
Mean (SD) 
36 (12) 

69.8 (3.7) 
165 (34) 
23.6 (3.4) 
Table 2. Model Descriptions
Model 
Description 
I 
Stepwise regression of seven predictor variables vs. MWR 
II 
Stepwise regression of predictor variables, interactions, and quadratic terms vs. MWR 
III 
“Calibration” step test to establish relationship between heart rate and MWR for each individual 
IV 
Models II and III combined, stepwise regression of variables vs. MWR 
Table 3. Summary of Modeling Results for Prediction of MWR
Model 
Significant Terms 
R2 
Average % Error 
Average Absolute % Error 
I 
5 
0.797 
2.77 
16.46 
II 
14 
0.974 
0.42 
5.99 
III 
1 
0.886 
11.06 
15.36 
IV 
8 
0.976 
0.72 
6.96 
Table 4. Bootstrap Results for Model II  Metabolic Work Rate
Row 
coef 
SE coef 
F 
normal p 
ran p 
1 
17.936 
1.622 
122.340 
0.0000000 
0.0009990 
2 
698.004 
60.597 
132.683 
0.0000000 
0.0009990 
3 
0.002 
0.000 
31.678 
0.0000005 
0.0009990 
4 
0.571 
0.047 
146.396 
0.0000000 
0.0009990 
5 
0.054 
0.011 
26.716 
0.0000027 
0.0009990 
6 
0.016 
0.002 
70.487 
0.0000000 
0.0009990 
7 
8.021 
1.124 
50.952 
0.0000000 
0.0009990 
8 
0.778 
0.152 
26.131 
0.0000033 
0.0009990 
9 
968.799 
145.267 
44.477 
0.0000000 
0.0009990 
10 
0.051 
0.009 
31.027 
0.0000006 
0.0009990 
11 
0.132 
0.023 
32.086 
0.0000004 
0.0009990 
12 
0.001 
0.000 
94.460 
0.0000000 
0.0009990 
13 
0.002 
0.000 
93.086 
0.0000000 
0.0009990 
14 
2.827 
0.699 
16.361 
0.0001473 
0.0009990 
Overall Fratio for regression 166.24  
Pvalue using normality 0.0000  
Pvalue using randomization 0.0010 
Table 5. Bootstrap Results for Model IV
Row 
coef 
SE coef 
F 
normal p 
ran p 
1 
0.0249 
0.0023 
114.955 
0.0000000 
0.0009990 
2 
67.7477 
12.3878 
29.909 
0.0000011 
0.0009990 
3 
0.1724 
0.0456 
14.297 
0.0003867 
0.0029970 
4 
0.5599 
0.1386 
16.310 
0.0001682 
0.0009990 
5 
0.2296 
0.0952 
5.820 
0.0192113 
0.0229770 
6 
0.1008 
0.0295 
11.640 
0.0012167 
0.0009990 
7 
0.0978 
0.0310 
9.990 
0.0025589 
0.0039960 
8 
0.0288 
0.0065 
19.351 
0.000504 
0.0009990 