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Predicting Relative Workload During Construction Activities
Using Multiple Regression Techniques

presented by

Lili Xi

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PREDICTING RELATIVE WORKLOAD DURING CONSTRUCTION ACTIVITIES
USING MULTIPLE REGRESSION TECHNIQUES

By

Lili Xi

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Construction Management Program
School of Planning, Design and Construction

2005

ABSTRACT

PREDICTING RELATIVE WORKLOAD DURING CONSTRUCTION
ACTIVITIES USING MULTIPLE REGRESSION TECHNIQUES

By

Lili Xi

In this thesis, the method developed by Abdelhamid (1999) to predict relative
workload from in-situ collected sub—maximal oxygen uptake data is redeveloped for
100 experimental subjects from Michigan State University. A relative workload
prediction equation (RWP equation) is developed. The standard error of prediction for
"/oVOZmax and V02max are i7.6% and i065 liter- min’l, respectively.

In an effort to improve the predictive accuracy of the RW P equation, a number of
factors were considered in constructing a multiple linear regression (MLR) model.
The prediction capability was best when the Energy of Green‘s function, relative heart
rate, and body surface area were used as predictors. Using the regression model that
combined these predictors, the standard error of prediction for "/oVOzmax and V02max was
14.9% and $0.53 liter - min“, respectively.

All regression models have been validated using non-steady state oxygen uptake
and heart rate data measured for 100 validation subjects. The MLR model provides a
robust, efficient and reliable statistical methodology capable of predicting relative
workloads from submaximal exercises data collected in-situ. The prediction
technique would be critical to the success of many field studies and would greatly

enhance work study and exposure/risk assessment methods.

ACKNOWLEDGMENTS

I wish to thank my advisor, Dr. Tariq Sami Abdelhamid, for his encouragement,
guidance and kindness during my studies at Michigan State University. I would like
to express my gratitude to him for giving me the freedom to pursue this research, and
for the financial aid he provided to sponsor my graduate study. In particular, I want to
thank him for teaching me how to write research papers and proposals, and for assisting
me with the completion of this thesis. From him, I learned how to be a serious
researcher and how to take responsibilities and be patient. I am also thankful to Dr.
Mohammad Najafi and Dr. Joanne Westphal for their support and assistance during this
research.

I am grateful to my parents for taking care of my daughter Kelly for these two
years and for providing me moral and spiritual support. Finally, I can have free time
to play with her and answer her questions.

I also express my gratitude to Litian He and her husband Huaming Chen, my best
friends at MSU, who provided help and encouragement at my most difficult time at
MSU. Their friendship helped me to overcome the difficulties I faced when I was
pregnant, and when my daughter Kelly was born.

I am grateful to God for all the people around me. I could not have finished this
program without their kindness, encouragement and help. 1 was able to finish this
program successfully because of the love of my parents, family, and friends, and the

help and encouraging advice from Dr. Tariq. Thanks again to all of you.

iii

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................... VI
LIST OF TABLES ............................................................................................................ VII
LIST OF APPENDICES .................................................................................................... IX
CHAPTER I
INTRODUCTION .............................................................................................................. 1
1] Motivation ............................................................................................................... 1
1.2 Needs Statement ....................................................................................................... 4
13 Research goal and ObjeCtIVC .................................................................................... 5
1.4 Research scope ........................................................................................................ 6
[5 ThCSIS guide ............................................................................................................. 6
CHAPTER II
LITERATURE REVIEW .................................................................................................... 9
I] 1 Energy Expenditure in Humans ............................................................................. 9
111.1 Measuring Physiological Demands ....................................................... 10
11.1.2 Oxygen Uptake (VOz) and Heart Rate Measurements -------------------------- 11
".13 Maximum Oxygen Uptake .................................................................... 13
1114 Measurement 0f Maximum Oxygen Uptake ......................................... 16
11.1.5 Correlation Between Laboratory Test and Actual Output --------------------- 30
11.16 Relative worklOad ................................................................................. 31
11.1.7 Other Measurements of Physiological Demands ---------------------------------- 32
"2 Physical Perfomance ........................................................................................... 33
11.2.1 Respiration as a Limiting Factor in Exercise ---------------------------------------- 34
11.2.2 Smoke, Alcohol, Caffeine and Performance ---------------------------------------- 36
“3 Physical Fatigue ................................................................................................... 38
11.1] Classification of work ........................................................................... 4O
II..32 Dealing With Physical Fatigue ............................................................... 41
“4 Physical Demands ofconstmction work ............................................................ 43
”5 Conclusion ......................................................................................................... 47
CHAPTER III
MET}{ODOLOGY ........................................................................................................... 48
1“] ResearCh methods ............................................................................................... 48
[“2 Relation between the Green’s function and %VO;max --------------------------------------- 51
“I3 Hypothetical multiple linear regression mOdel ................................................... 54

iv

“[4 Summary ......................................................................................................... 5‘7

CHAPTER IV
RESULT ............................................................................................................................ 59
IV] Introduction ......................................................................................................... 59
IV.2 participants .......................................................................................................... 60
“1.3 Models analysis ................................................................................................... 61
IV.3.1 Part A: simple linear regression model development -------------------------- 62
“1.3.1.1 SLR model setup ................................................................... 62
IV.3.1.2 Normality and independence of error terms of SLR model -- 65
IV.3.1.3 Statistical properties of the SLR model -------------------------------- 69
“1.3.1.4 Summary ............................................................................... 73
“13.2 Part B: multiple regression models ...................................................... 74
IV...321 Factors for MLR mOdeiS ....................................................... 74
[v3.2.2 MLR model development ..................................................... 76
Model A: Ln(E(3) and heart rate (RHR) .................................. 80
Model B: Ln(Eg), RHR and Age ............................................ 88
Model CZ 1411036), RHR and BSA ........................................... 90
“(3.2.3 MLR models comparison ...................................................... 91
IVH33 Part C: Regression models validation .................................................. 95

CHAPTER V

CONCLUSION AND FUTURE WORK ........................................................................ 101
V1 Conclusion .......................................................................................................... 101
V2 ThCSIS contribution ............................................................................................. 102
V3 Limitation and Future work ................................................................................ 104
APPENDICES ................................................................................................................ 106
BIBLIOGRAPHY ........................................................................................................... 135

Figure 11.1
Figure 111.]

Figure 1112

Figure IV.1
Figure IV.2
Figure IV.3
Figure IV.4
Figure IV.5
Figure IV.6
Figure IV.7

Figure IV.8

Figure IV.9

Figure IV.9

Figure IV.10

Figure IV.11

LIST OF FIGURES
Factors influencing physical performance ability ------------------------------- 34
Oxygen uptake data for subject 78 and 98 (session 3) ----------------------- 49

Green’s function for subject 78 and 97 oxygen uptake data (session 3)

............................................................................................................. 50
Energy of the Green’s function and V023,.g/V02max ------------------------- 63
Transformed Energy of the Green’s function and VOhvg/VOZmax ------ 64
Normal probability plot for residuals .................................................. 66
Minitab residuals VCTSC OFCICI' Chart ..................................................... 6‘7
Minitab standardized residual plot ...................................................... 68
Minitab confidence interval & prediction intervals plot --------------------- 71
Minitab outputs for residual plots for "/oVOzmax ---------------------------------- 84

Minitab confidence Interval & prediction intervals plot for model A

............................................................................................................. 86
Main effects plot of predictors for O/OVOZmax (Z-D) ----------------------------- 87
Main effects plot of predictors for %VOzmax (3-D) ----------------------------- 87
Main effects plot ofpredictors for O/Ovozmax ....................................... 92

Individual value plot of "/oVOZmax for model C (actual VS prediction)
............................................................................................................. 98

vi

Table.Il.l

Table 11.2

Table.II.3a

Table.II.3b

Table 11.4

Table IV.l

Table IV.2

Table IV.3

Table IV.4

Table IV.5

Table IV.6

Table IV.7

Table IV.8

Table IV.9

Table IV. 1 0

Table IV.11

Table IV. 12

LIST OF TABLES
Equations used to predict VOgnm (Lynn A and Roberta L 1999) 23

Lung volumes from well-trained physical education students (Astrand
2003) ................................................................................................... 35

Prolonged physical VVOTk CiaSSIfication ............................................... 41
Work classification based on peak responses during manual work 41

Average energy expenditure by construction trade (Abdelhamid and
Everett 2002) ....................................................................................... 44

Descriptive Statistics and maximal exercise data for
experimental/validation Subjects ......................................................... 6]

Regression output for the 0/oVOzmax by Minitab ---------------------------------- 64
Regression output from Excel for regression slope and Intercept ------ 70
Sample of Minitab Output on C I &PI for subpopulation means -------- 72
Sample data for regression analysis results ......................................... 73
Minitab Regression output for Model A ............................................. 81

Descriptive statistics for the experimental subjects HR and Ln(E(;) by

Minitab ................................................................................................ 81
Minitab matrix of correlation between variables for model A ------------ 82
Sample of Minitab Running Output for 95%CI and 95%PI --------------- 86
Minitab Regression output of %V02max for Model B ---------------------- 89
Regression output for Model C ........................................................... 90
Minitab output of correlation between variables for model C ------------ 91

vii

Table 1V. 1 3

Table IV. 14

Table IV. 1 5

Table IV. 1 6

Table IV. 1 7

Table IV. 1 8

Table B.l

Table 8.2

Table B.3

Table B.4

Table 8.5

Table B.6

Minitab MLR Model running output for different variables to
prediction OfO/OVOZmaX ........................................................................ 92

Minitab outputs for MLR using unstandardized residual and Ln(EG)
............................................................................................................. 94

Sample for prediction results based on validation subjects data and

MSPR cheek ........................................................................................ 96
MSE and MSRP for %VOzmax and VOzmax for validation subjects ----- 97
Paired T—test and p-value for (yovozmx ............................................... 99
paired T—test and p-value for VOZmax ................................................. 100
Subject 78 and 97 raw daia on V02 and G}. ....................................... 109
Physiological data for 100 experimental subjects ---------------------------- 112
Physiological data for 100 validation subjects -------------------------------- 115

Actual/predicted values for %VOzmax &V02max for experimental
subjects .............................................................................................. 118

Actual/predicted values for ”/oVOZmax & VOZmax for validation subjects
........................................................................................................... 122

MSPR cheek and Jones’ equation comparison on validation subjects
........................................................................................................... 127

viii

LIST OF APPENDICES
A. Time series analysis ................................................................................... 105

B. Physiological data for all subjects .............................................................. 108

CHAPTER I
INTRODUCTION

1.1 Motivation

Construction work is physically demanding work. The culture of the
construction industry has evolved such that contractors rely heavily on hand labor with
small, relatively inexpensive and multipurpose tools. This reliance on hand labor may
explain why, in the Jobs Rated Almanac ranking of 250 jobs for physical demands,
construction trades account for 18 of the worst 50 jobs in the United States (Krantz
2000). The situation is not much different in other parts of the world. In the
early ’905, "3K", derived from "Kitsui" (physically hard work), "Kiken" (hazardous)
and "Kitanai" (dirty), became a fashionable term in Japan to describe the construction
industry (Everett and Saito 1996). Apparently, the construction industry has resigned
itself to the notion that a high level of physical effort is an inherent part of doing the
work.

A known fact about physically demanding work is that it leads to physical fatigue
that may lead to decreased productivity and motivation, inattentiveness, poor judgment,
poor quality work, job dissatisfaction, accidents, and injuries (Brouha 1967, Janaro
1982, Injury Facts 2003). Many investigators, dating back to Frederick W. Taylor (the
father of Scientific Management) in the early 19005, have argued that since physical

fatigue affects performance, performance can be improved by either identifying and

eliminating the causes of physical fatigue or by at least finding ways in which to
combat its effects (Aquilano 1968 and J anaro 1982).

Consequently, understanding the physical demands of construction work is of
paramount importance in protecting the workforce’s safety and health, and to improve
productivity. As suggested by Brouha (1967), such understanding is the key to the
solution of what a man can do safely.

The most common methods of measuring physical demand are those of
measuring the oxygen consumption or oxygen uptake, V02 (usually measured in liters
of oxygen per minute), during work or exercise, and/or recording the heart rate HR
(measured in beats per minute) associated with the performance of an activity.
Measured VOz has also been used to indirectly estimate energy costs of performing
various human activities, which in turn is used to assess potential for physical fatigue.

Earlier studies on the physical demands of construction activities date back to the
19503 and 19605. These studies were based on work physiology, and energy
expenditure values were collected for various trades. These investigations concluded
that accurate assessment of construction activities’ physiological demands is
particularly difficult. This difficulty was attributed to the variety of individual
operations involved in one activity, and to the lack of consistency among construction
workers in adopting a technique to carry out an activity, let alone its individual
operations (Astrand and Rodahl 2003).

Unfortunately, work physiology has been neglected in most contemporary
construction workforce research. Abdelhamid and Everett (1999) reversed this

situation and demonstrated the feasibility of measuring in-situ physical demands of

construction activities for a concrete placing and finishing operation, using work
physiology techniques.

Encouraged by these results, a larger study was conducted on construction sites to
measure the level of physiological effort at which construction workers work and to
evaluate if the effort exceeded physiologically-based standards and limits. Oxygen
uptake (V02) and heart rate (HR) data for 100 construction workers from 12 different
construction trades were collected. Data was collected over a period of 18 months.
The trades tested are Asbestos Workers, Bricklayers, Carpenters, Carpet Installers,
Cement Finishers, Drywall Installers, Electricians, Glaziers, Ironworkers, Laborers,
Pipe Fitters, and Sheet Metal Workers. The results of this study have been published
in Abdelhamid and Everett (2002).

The research findings of Abdelhamid and Everett (2002) indicated that the use of
any one physiological measurement does not present the entire story regarding the
physical workload affecting an individual worker. Wide differences were noted
among individual workers’ responses to strenuous work. Abdelhamid and Everett
(2002) concluded that:

“Future research should investigate not only the absolute energy expenditure,
oxygen uptake, or heart rate for individual workers, but how these values relate to the
individuals’ maximum values for each measure. Maximum values are difficult, if not
dangerous, to measure, but would lead to a better prediction of physical fatigue.”

This research is motivated by the need to better understand the physical demands
of construction work based on subject-specific measurements. Prior to accomplishing

this need, a technique that enables the assessment of subject-specific physical demands

needs to be developed.

1.2 Need Statement

Many work physiologists recommend expressing measured oxygen uptake as a
percentage of maximum oxygen uptake (VOZmax), commonly known as relative
workload (%V02ma, = VOmg/VOzmax), because it provides a subject-specific workload
(Astrand and Rodahl, Bonjer 1971, Rohmert 1973, Kamon 1979, Tomlinson and
Manenica 1977). In addition to accounting for individual differences in physiological
capacities among workers, relative workload also enables more accurate assessment of
potentials of physical fatigue.

As the expression for relative workload indicates, once a subject’s V02max is
known, the determination of %VO;Jnalx is arithmetically simple. Individuals vary
greatly in their respective V02max values beCause it can be greatly influenced by genetic
factors of age, gender and body dimension, as well as by other factors such as tobacco,
alcohol, caffeine usage, climate, and psychological factors. In general, determining
V03max is accomplished through the use of direct (exact) measurement or prediction
techniques. Exact measurement of V02max is impractical for applied research due to
its intensive and intricate laboratory procedures as well as the risks it poses for unfit
subjects. Prediction techniques offer an attractive alternative with numerous linear
and non-linear regression techniques available.

Abdelhamid (1999) developed a new method capable of such prediction. This
new prediction methodology was based on the hypothesis that oxygen uptake data are
serially dependent, and that by exploiting this dependence, using time series analysis
techniques, a regression model between relative workload (%V02max) and a statistical

characteristic of collected oxygen uptake data can be developed.

In Abdelhamid (1999), a time series-based metric called the Energy of Green’s
function (E(;) was found to be strongly linearly correlated to relative workload
(%V03max). Based on this finding, a simple linear regression model was developed
using data from 20 subjects. The regression model had a standard error in predicting
%VOzmax and V02max ofi 3.4% and i 0.5 liter - min", respectively.

Using data from five validation subjects, the standard error in predicting
‘VoVOZmax and V02max was i3.3% and i043 liter-min", respectively. The closeness
of these errors to those of the regression model indicated that the mean square error of
the regression equation is not seriously biased and that it provided an appropriate
indication of the predictive capability of the developed regression model.

These initial results are quite promising and establish a starting point for further

investigations. A few of the questions that could be explored include the following:

I Is this prediction method suitable for a larger pool of subjects?
I How will adding a subject’s height, weight, age, gender, and heart rate

affect the accuracy of the regression model?

Answers to the above questions will be very helpful in developing a non~invasive
technique for understanding the physical demands of construction work. Therefore,

these questions will be further investigated in this research.

[.3 Research Goal and Objectives

This research is motivated by the need to learn more about physical fatigue
resulting from work, and how to effectively reduce fatigue and improve work

productivity. In order to achieve this, it was clear that a measurement technique had

to be developed first. Hence, the goal of this research is to develop a technique for
predicting relative workload from sub-maximal physiological data collected in-situ.

The following are the primary objectives of this thesis:

I Validate the simple linear regression model developed in Abdelhamid
(1999) for 100 subjects performing a specified exercise regimen.
I Develop and validate a multiple linear regression model to predict the

relative workload from sub-maximal oxygen uptake (V02).

[.4 Research Scope

This research is an extension of previous work by Abdelhamid (1999) that was
aimed at developing a prediction technique for relative workload from in-situ collected
data. The primary aim of this research is to improve the accuracy of the simple linear
regression model developed by Abdelhamid (1999) through the development of a
multiple linear regression model. This research will use data collected from 200

subjects at Michigan State University.

[.5 Thesis Guide

This thesis is divided into five chapters. Chapter 1 presents the motivation behind
this research and the importance of measuring the physical demands of construction
work. A need statement is formulated and research goals and objectives are presented
along with the scope of the research.

Chapter 11 presents a background of work physiology and prior research on the
physical demands of construction work. Methods of measuring physiological

demands by measuring oxygen uptake and/or heart rate are also discussed. The chapter

then reviews earlier researches on the methods of predicting relative workload and
maximum oxygen uptake.

Chapter III outlines the methodology adopted to accomplish the research goal
through a detailed discussion of action items undertaken to achieve the two research
objectives. This chapter discusses in more detail the relative workload prediction
model developed in Abdelhamid (1999). It also discusses the development of
multiple regression models through a hypothetical multiple linear regression model,
used to demonstrate the research methodology and the expected results. Lastly, it
explains the method used to validate the regression models developed in this research.

Chapter IV presents results of redeveloping the simple regression model on a
larger pool of subjects. Development of the multiple linear regression (MLR) models,
with age, height, weight, and heart rate factors is also presented. Statistical properties
of the developed regression models are derived and analyzed against the basic
assumption upon which the models were constructed. The chapter concludes with a
validation of all the regression models on 100 validation subjects. The validation
results were used to find the best-fit MLR model.

Finally, Chapter V summarizes the conclusions and contributions of the thesis
work. It presents recommendations for future work which will improve accuracy of
the MLR model, especially its applicability for construction work. Appendix A
discusses time series analysis and serves as a foundation for understanding the
conceptual ideas and methods presented in Chapter III and 1V. Appendix B provides
the raw data for all measurements made in this research. Appendix C describes the

experimental protocol setup for data collection during the development and validation

experiments in this research.

CHAPTER II
LITERATURE REVIEW

11.1 Energy Expenditure in Humans

Humans typically expend energy through metabolic processing of foodstuffs
involving a complicated chain of chemical reactions that take place in various muscle
and body tissues. These metabolic processes are central in providing body
homeostasis and physical work. Body homeostasis refers to a state of physiological
equilibrium produced by maintaining vital functions of various body systems and
chemical composition of the human body. Body homeostasis must be maintained
regardless of being at rest or at work. At rest, the metabolic processes that guarantee
body homeostasis are termed in the literature “basic metabolism” (Astrand and Rodahl
2003). During work, body homeostasis is disturbed and various physiological
functions respond to maintain homeostasis and provide the musculoskeletal system
with the necessary energy to “operate”.

Measuring the energy expended by humans at rest or during work is very
important and is the cornerstone of many disciplines branching from human physiology
(e.g., exercise physiology and work physiology). The kilocalorie (kcal) is the unit
used for measuring energy and it is defined as the quantity of heat necessary to raise
the temperature of 1 kilogram (1 liter) of water 1° centigrade (McArdle, Katch, and
Katch 1996). It is familiar to dieters as the Calorie, and is equal to about 4 BTUs,
1.162 Watt-hours, or 4186 Joules. There are two main ways to measure the energy

humans expend: direct and indirect calorimetry.

11.1.1 Measuring Physiological Demands

Given that metabolic processes that take place in humans result in a production of
heat, the metabolic rate is indicated by the rate of heat production. This is the basic
idea behind measuring energy expended by humans through directly measuring the
heat produced from the metabolic processes. This measuring procedure is therefore
termed “direct calorimetry”.

Direct calorimetry can only be performed in a human calorimeter, which is an
airtight and thermally insulated chamber. A person can literally live in this chamber,
while the heat produced from metabolic processes can be accurately measured during
rest or work periods. The produced heat is measured by utilizing a heat-measuring
device. Many heat-measuring devices for human calorimeters have been deve10ped
over the years and are based on different operating principles (McArdle, Katch and
Katch 1996).

Measuring energy expenditure using direct calorimetry is extremely accurate.
However, human calorimeters are very expensive to build and operate and are
obviously not portable. These limitations restrict the use of direct calorimetry to
academic research performed in laboratory settings.

Earlier research has demonstrated that the total energy expended by a human can
be estimated by measuring the amount of oxygen consumed before, during, and after
performance of work or exercise activities. Because oxygen is used and carbon
dioxide is produced during energy-yielding reactions, the exhaled air contains less
oxygen and more carbon dioxide than the inhaled air. The difference in composition

between the inspired and expired air volumes reflects the body’s release of energy

10

through aerobic metabolic reactions (McArdle et a1. 1996). This technique is referred
to as “indirect calorimetry”. Indirect calorimetry provides a reasonably accurate,
portable, and relatively inexpensive method of measuring energy expenditure
compared to direct calorimetry.

Research has shown that for every liter of oxygen consumed 4.83 Kilocalories of
energy, on average, are produced. Thus, collected oxygen uptake data may be
converted to corresponding energy expenditure by multiplying it by 4.83 kcal per liter
of oxygen (Rodahl et a1. 1974, McArdle et a1. 1971, Astrand and Rodahl 1986). It
should be noted that the conversion multiplier varies slightly depending on a
physiological attribute termed the “Respiratory Quotient” (McArdle, Katch and Katch

1996)

11.1.2 Oxygen Uptake (VOz) and Heart Rate Measurements

Previous research showed that measuring heart rate (measured in beats per minute)
associated with the performance of an activity is another common method for
measuring physiological demands. Determining target exercise intensities by heart
rate is practical and useful, because it is easily and noninvasively obtained with heart
rate monitors during exercise. Many researchers, such as Wyndham et a1. (1962),
Poulsen and Asmussen (1962), McArdle et a1. (1971), Rodehl et a1, (1974) have used
this approach.

Researchers have found a linear relationship between heart rate and oxygen
uptake. As the body performs exercise. there is an increased demand for oxygen to be
delivered to the exercising muscles, and this demand is accompanied by an increase in

lung and heart function.

11

In the 19903, the validity of using this linear heart rate-oxygen uptake relation has
been called into question for non-dynamic and discontinuous exertions. Many argued,
for example, that a myriad of variables would affect the measured heart rate values and
the linear relation obtained for heart rate and oxygen uptake. It has been shown that
factors other than work or exercise may lead to increased heart rates. For example,
environmental conditions, emotions, fear, previous food intake, body position, muscle
groups used, continuity of the work, and whether muscles are acting statically or
dynamically (Mass et al. 1989), may all have an effect. Moreover, heart rates vary
greatly with individual characteristics such as age and weight. In addition, oxygen
consumption is dependent on the intensity of exercise, as well as age, gender, exercise
history or habits, hereditary factors and current health status (Lear et al 1999).

These examples indicate that inferences based on the linear relation between heart
rate and oxygen consumption may provide an inaccurate measure of metabolic stress
on the body. Despite criticism concerning the linear oxygen uptake heart rate relation
to predict energy expenditure for various activities, Astrand and Rodahl (2003) have
suggested, based on actual experimentation, that:

“In most cases, the reliability of the conversion is adequate for all practical
purposes of field investigation”... “It appears that the use of the recorded heart rate as a
basis for the estimation of work load may be acceptable even in many work situation
involving arm work or the use of small muscle groups.”

The reliability of indirect assessment of V02 by measuring HR has mainly been
limited to steady-state exercise. It would be a useful technique if it could be found
valid for non-steady-state activities, especially for understanding the physical demands

of construction work, and assist in developing prediction methods for relative workload

measurements.

12

Bot and Hollander (2000) studied the validity of using heart rate responses to
estimate oxygen uptake during varying non-steady activities, such as those found in
construction tasks. Dynamic and static exercises engaging large and small muscle
masses, and combinations of different muscle groups were conducted in four different
experiments. The individual regression equations disclosed significant linear
relationships between HR and V0; during dynamic, non-steady state arm and leg
exercises. Also, during non—steady state activities with different muscle groups
significant correlation coefficients (r) were established for all subjects. While the r
values were less compared to those in the steady state conditions, it can still be
concluded that estimation of V0; by measuring the HR is not limited to steady-state
exercise. This conclusion by Bot and Hollander (2000) is encouraging because in
most construction activities, the intensity varies constantly and no steady state is

reached.

11.1.3 Maximum Oxygen Uptake

The amount of oxygen supplied to a muscle is not unlimited and the limit varies
greatly between individuals due to the varying efficiency of peripheral and central
processes that occur in our bodies. The maximum supply of oxygen (and of energy)
has been reported in terms of the maximum oxygen utilization an individual can
achieve and has been termed as maximum oxygen uptake (McArdle et a1. 1996).
Maximum oxygen uptake or V02max is defined as the highest oxygen uptake per minute
that can be measured during dynamic exercise with large muscle groups.

Another common definition for VOZmax (maximal oxygen uptake, maximal

aerobic power) is that it’s the rate at which oxygen can be used by the body during

13

maximal work. VO;max is directly related to the capacity of the heart to deliver blood
to the muscles and is considered a good index of cardio-respiratory fitness and a good
predictor of performance capability in aerobic events such as distance running, cycling,
cross-country skiing, and swimming.

In general, V02max is accepted as one of the best single indicators of an
individual’s aerobic fitness. Aerobic fitness is frequently considered the most
important aspect of physical fitness. Shephard ( 1977) defined aerobic fitness as the:

“ability to maintain the various processes in metabolic exchange as close to the
resting state as is mutually possible during the performance of a strenuous and fully
learnt task for a moderate time, with a capacity to reach a higher steady rate of working

than the unfit and to restore promptly after exercise all equilibrium which were
disturbed.”

It should be noted, however, that VOZ.1m is only a predisposition for physical
performance. A high V02max does not guarantee good physical performance, since
technique and psychological factors may have influenced performance either positively
or negatively (Verma 1994).

Research has also shown that this measure is dependent on individual factors (e.g.,
sex, age, body dimensions, inheritance), environmental factors (e.g., intensity, duration,
and technique of exercise), and adaptation through training (J orgensen 1985).

Astrand (2003) et al., showed in their research on direct measurement of maximal
oxygen uptake in 350 individuals ranging in age from 4 to 65 years of age, that there is
in both sexes a peak in maximal oxygen uptake at 18 to 20 years of age, followed by a
gradual decline. At the age of 65, the mean value is about 70% of what it is for a 25
year-old individual. Maximal oxygen uptake for the average 65-year old man is the

same as for a typical 25-year old woman.

14

Changes in tissue and organ function due to age may explain the decline. As
people age, the decline in maximal heart rate is quite evident, and this lower heart rate,
coupled with other effects of age, may reduce the individual's maximal cardiac output
and hence the oxygen-transporting ability (Astrand and Rodahl 2003).

A study by Astrand (1967b) on 33 building workers (bricklayer, carpenters and
laborers) from 30 to 70 years of age showed that the mean heart rate during
occupational activity was correlated with the individual’s maximal heart rate. For
younger subjects, with a maximal heart rate of 185 beats/min, the mean heart rate
during occupational activity was 1 10, while those with a maximum of 150 had a mean
of 90 beats/min. Maximal oxygen uptake ranged from 2.2 to 3.6L/min. In general,
irrespective of maximal oxygen uptake, each worker used the same percentage of
his/her maximum in work operations. In other words, older workers with lower
maximal aerobic power kept a slower work tempo than younger ones, but relative load
was the same, about 40%. The person with a high maximal heart rate can do a day’s
work at a higher mean heart rate than a person with a lower maximum, but the relative
strain may be the same on the two persons.

Another factor that is important to consider for the determination of maximum
oxygen uptake is body fat. Fatty tissue is metabolically fairly inert, but because it can
constitute a large proportion of the body weight, it may be important to exclude fatty
tissue when evaluating oxygen-transporting capacity (Astrand and Rodahl 2003).
This is especially important considering that women's body fat percentage and body
dimensions are different from those of men. For example, according to Wilmore

(1979), the average North American female at full maturity is approximately 13 cm.

shorter than the average male, 15 to 18 kg lighter in total weight, 18 to 23 kg lighter in
lean body weight and considerably fatter, i.e., 25% vs. 15% relative body fat. Hence,
it is not surprising that a woman's maximal oxygen uptake per kilogram of gross body
weight is a better expression of her potential to move her body than is the maximum

related to lean body weight.

11.1.4 Measurement of Maximum Oxygen Uptake

When does a person reach the maximum aerobic power level? If an individual
increases the intensity level of exercise, a corresponding increase occurs in heart rate,
respiration and oxygen intake, as well as in the activity levels of other parts of the
aerobic systems. At some point, however, oxygen intake cannot increase beyond a
specific level, even though more work is being performed. At this point, the individual
has reached a level that is commonly referred to as maximal oxygen uptake (VOzmax).
This measure is considered to be the best single indicator of aerobic fitness, because it
involves the optimal ability of three major systems of the body (pulmonary,
cardiovascular and muscular) to take in, transport and utilize oxygen. The higher an
individual's level of maximal oxygen uptake is, the greater the level of physical work
that can be performed (Bryant and Peterson 1997).

In the field of exercise physiology, when limiting factors for V02max are discussed,
it is usually with reference to human subjects, without metabolic disease, undergoing
maximal whole-body exercise, at sea level. Under these conditions, it is the ability of
the cardio-respiratory system (i.e. heart, lungs, and blood) to transport 0; to the
muscles, that limits VOan, not the ability of muscle mitochondria to consume 0;

(Bassett et a1. 2000).

16

Exact techniques for the determination of V03max require rigid and standardized
criteria to ensure that a true maximum has been reached. These techniques are
commonly performed on treadmills or cycle ergometers (CE) using an exercise
protocol that involves a gradual increase in the workload until the subject reaches
complete exhaustion and can no longer perform the exercise. Excellent discussions
on exact techniques to determine V02max can be found in Astrand and Rodahl (2003),
Kilbom (1995), and McArdle et a1. (1996).

But exact measurement of VOZmax requires well—equipped laboratory settings and
special equipment, and may be dangerous for unfit or untrained subjects. The
limitations of exact measurement have inspired the development of prediction
techniques to determine V03,” Examples of widely used prediction techniques are
the walking test (Cooper 1968, Kline et a1. 1987), endurance runs (Cooper 1968, Verrna
1994), the step test (as referenced in McArdle, Katch, and Katch 1996), nomograms
(Astrand 1960, Astrand and Rodahl 2003), and linear and non-linear regression
equations (Venna 1994).

Most of these prediction techniques use submaximal exercise tests to predict
maximal oxygen uptake (VOan) from an individual’s heart rate at a certain
submaximal workload. Maximal oxygen uptake is then predicted using an established
regression equation (Astrand 1956, ; Asmussen and Molbeck 1959, Maritz et a1. 1961,
and Margaria et a1. 1965). The submaximal tests are useful for estimating aerobic
fitness without undue stress to the subjects, and are more suited to the elderly or
individuals with known diseases. Submaximal tests are also more easily,

inexpensively and rapidly administered to larger numbers of subjects (ACSM 1995).

17

However, some researchers (Davies 1968, Glassford et al. 1965, Rowell et a1.
1964, McArdle et a1 1996) have pointed out serious limitations in the predictive
accuracy of using heart rate during submaximal work to evaluate VOzmax. The
percentage error in prediction values has been reported to be between 15-20%.

As summed in the classic textbook of work physiology by Astrand and Rodahl
(2003) the reliability of predicting maximal oxygen uptake from the submaximal heart
rate response to a given rate of exercise has to be studied in more detail.

One method of predicting an individual’s maximal oxygen uptake by use of
nomogram (P.O.Astrand and Ryhming 1954) has been critically studied over the years.
The standard error of this method for predicting maximal oxygen uptake from
submaximal exercise tests was 10% in individuals of the same age, but up to 15% in
subjects of different ages when the age correction factor of maximal oxygen uptake
was applied.

The validity of the nomogram has also been tested in other laboratories. In
some cases, there has been good agreement with other methods, but in other cases, it
has resulted in underestimations. Therefore it is suggested by Astrand and Rodahl
(2003) that an evaluation of the maximal effect of the oxygen uptake based on studies
at submaximal work rates or oxygen uptake should be done with great caution,
especially when persons of different age groups are considered.

To increase the accuracy of prediction, attempts have been made by Hermiston
and Faulkner (1971) and Mastropaolo (1970) to include more physiological variables in
the prediction equation. Predictive accuracy was further improved by Venna et a1.

(1977) by using a non-linear formula for estimating VOzmax from cardio-respiratory

18

strains. Jessup et a1. (1974) made an attempt to predict VOZmax from some
physiological as well as anthropometrical variables, and obtained a high multiple
correlation between observed and estimated VOZmax. Verrna et a1. (1980) suggested a
multiple linear regression equation for predicting VOzmax from anthropometric
variables. The equation has been considered a simple approach for predicting V02max
based on anthropometrics variables only.

Although some of the methods based on physiological variables have achieved
maximum precision for predicting VOzmax, these may not be of practical use in a field
situation for selecting personnel suitable for certain kinds of service and industrial
work, and for sports. This is due to the laborious and time-consuming procedures
required for measuring the physiological variables involved in the predictions. In
addition, the external validity of these techniques has been a topic of debate, i.e.,
whether the maximum oxygen uptake obtained from these techniques will be similar to
that during the actual activity under evaluation.

Wertheim et a1. (2002) performed a study on the measurement of maximal oxygen
uptake in moving environments. The study pointed out that in previous studies on
physical fatigue during simulated ship movements, the apparent exhaustion of subjects
after experimentation suggested that oxygen consumption, the traditional index of
physical workload, expressed as a percentage of peak oxygen consumption (VOZmax),
and measured in a separate graded exercise test (GXT), underestimates workload in a
moving environment.

They mentioned that the GXT tests were carried out in a stationary environment,

as is standard practice. To explain the underestimation, they hypothesized that V02max

l9

might have been less if the GXT had been carried out in a moving environment. Their
study employed three experimental tests of this hypothesis, performed with a ship
motion simulator aboard a ship at sea. In all three experiments, V02max was indeed
significantly reduced, the difference being between 6 and 10%, when the GXT was
carried out in a moving environment. Theoretical reasons for this phenomenon are
discussed and investigated, but a clear explanation is still lacking.

Though an explanation of the motion-induced decrease of V03amx was not given
by Wertheim et al., their research on maximum oxygen uptake under a moving
environment advanced research technologies for simulating a real dynamic situation for
measurement of V02...” It addressed the issue of how to measure or predict V03max
from an angle closer to real world conditions.

In sum, most of the methods for measuring or predicting VOan are generally
non-invasive and provide quick results, but are not necessarily the most accurate.
Some provide highly accurate results, but require the presence of a well-equipped
laboratory and trained personnel. Hereinafter some of these methods of predicting

V02max are reviewed in more detail.

A. HR-VO; Lir_rear Relationship
The most popular method for predicting V02max is the HR-VOZ linear relationship.

With an assumption of maximum heart rate, a corresponding value of oxygen uptake,
using the linear relationship, is developed between the two. This value is assumed to
be the VOZmax. The linear relationship has been explained in more detail in section

11.1.2. Therefore only some different views about this method will be mentioned here.

20

Several researchers argued that this method has an error of up to 8 percent
(McArdle et a1. 1996). The ACSM (1995) have reported variability of HRmax of up to
10—12 beats per minute in normal subjects when using the popular formula: HRmax =
220 — age. This suggests that HR may not be a valid measure of VOZmax,
Researchers have also argued that this method is only accurate for light to moderate
workloads, because at heavier workloads there is a larger than expected increase in the

V02 per unit increase in HR.

B. Time Series Agalysis

As previously mentioned, Abdelhamid (1999) developed a method capable of
directly predicting relative workload from in-situ collected sub-maximal oxygen uptake
data without the need to determine maximum oxygen uptake. A statistical analysis
technique called time series analysis was used to model oxygen uptake data. The
methodology is based on the hypothesis that oxygen uptake data are serially dependent,
and that by using time series analysis techniques, a regression model between relative
workload and statistical characteristics of collected oxygen uptake data can be
developed.

The result is a special kind of regression model, termed AutoRegressive Moving
Average model, ARMA(p,q). After arriving at an adequate ARMA(p,q) for the
observed time series, the Green’s function “Gj” was derived and used to make
inferences about the system that produced the data — the human body, in this case.
The Green’s function “Gj” was the strongest candidate because, by definition, it
quantitatively summarized how a system responded to disturbances and described the

system’s resistance to changes from a state of equilibrium.

21

Using the time series analysis package ITSM 2000 version 7.0 (Brockwell and
Davis 1996) on the data collected from subjects doing exercises on a treadmill, values
of the Green’s function were obtained and the value of the energy of the Green’s
Function, E6, was determined (based on the sum of squares of the individual G,- values).
The relationship between EG and %VOzmfllx exhibited a strong correlation. It was
analyzed using linear regression techniques to formally characterize this relationship,
and resulted in a simple regression model.

This research will utilize the mentioned time series analysis technique, along with
factors such as age, body dimensions and heart rate, to develop a multi-regression

model capable of predicting relative workloads.

C. Otthredictigr Methods and Linear/non linear Regression Models

Many researchers focus on different angles and methods of measuring VOZmax.
Except for direct measurement, most methods are based on linear or non-linear
regression models to predict VO;max values. These methods usually use data collected
from treadmill exercises.

Table 11.1 lists other researchers’ prediction methods, and equations currently
used for maximum oxygen uptake measurements. These equations use different
variables and different linear/non linear regression models to predict VOZmax_ The
characteristics of each equation, and some of the advantages and limitations, are
discussed further below. Jones’ equation is especially applied in the next chapters of
this thesis for validation purposes.

In 1973, Fox presented a prediction method based on a linear equation relating

VOZmax to submaximal heart rate during the 5th min of bicycle exercises at 150W. The

22

standard error of estimate (SEE‘) was i7.246ml/min (17.8% ofthe mean VOzmax) and

correlation coefficients (r2) was ($0.76). Though his method uses the submaximal

heart rate as a basis for the prediction of maximal aerobic power, it differs from the
previously mentioned HR-VOZ linear relationship in that it depends only on the
relationship that exists on a single submaximal heart rate determination. Whether or

not there is a linear increase in heart rate with oxygen consumption and workload is

 

 

 

inconsequential.
Fox VOZmaX (mL/min)== 6300- 19.26 x HR
(recorded at the 5th min of exercise @1 50W. b/min))
Jones V02max (L/min) = (0.046 x Ht (cm)) - (0.021 x age
(yrs)) — (0.62 x Sex) — 4.31 where for sex, men = 0,
women = l '
Storer V02max (mL/min) = (9.39 x max Watts) + (7.7 x BW

(Kg))- (5.88 x age (yrs) +136.7

Astrand-Rhyming V02max (L/min) = V025ubmax x ((220-age(yrs) —
bicycle ergometer 72/HRsubmax -72))

test where VOZSmeax (L/min) = (Power (watts) x 0.012)+ 0.3

Dobeln et al. _ L -0.00884 T where L is load in
VOZmax —l.29 We ’

 

 

kilo-pound-meters per minute at submaximal work, H is
heart rate after 5-6 mins at load L, and T is age in years.
Womack et a1. VOzpcak (mL/kg/min) = (0.00872 * maximal
claudication pain time [sec]) + (0.02839 * maximal
heart rate [b/min]) - (0.12034 * BMI) + 10.11411

Table 11.1 Equations used to predict V02...“ (Lynn A and Roberta L 1999)

 

 

 

 

 

Jones (1985) presented an equation that was derived from one hundred healthy

subjects (50 male and 50 female), selected to provide an even distribution of ages (15

 

' SEE: Standard Error of Estimation to measure of the accuracy of predictions.

2 r: called "Pearson's r”. It reflects the degree of linear relationship between two variables. It ranges from

+1 to - I. A correlation of +1 means that there is a perfect positive linear relationship between variables.

23

to 71 yr) and heights (165 to 194 cm in males and 152 to 176 cm in females). These
subjects underwent a progressively incremental (100 kpm/min each min) exercise test
up to a symptom-limited maximum. Measurements were made of 02 intake and C02
output, ventilation and breathing pattern, heart rate and blood pressure, and rating of
perceived exertion. See Table 11.1 for the equation. (SEE: 0.458; r: 0.869). Maximal
heart rate (HR) declined as a function of age: HRmax = 202 - 0.72 (Age) beats/min
(SEE: 10.3; r: 0.72). The researcher found that the V02 increased linearly with power
throughout the test. The one important aspect of this equation lies in that it showed a
possibility that, in an individual subject, the intercept of this relationship was positively
influenced by weight and height.

In 1990, Storer developed an equation based on the duration (an analog of
maximal work rate, Wmax) of a cycle ergometry3 (CE), hypothesizing that CE V02...“
could be accurately predicted due to its more direct relationship with work rate (W).
Thus, healthy, sedentary males (N = 115) and females (N = 116), aged 20-70 yr, were
given a 15 W - min" CE graded exercise test (GXT). His testing method results were
developed into a multiple linear regression equation which predicted V02max (ml-min")
from the independent variables of Wm. (W), body weight (kg), and age (yr) derived
from subjects:

Males: Y = 10.51 (W) + 6.35 (kg) - 10.49 (yr) + 519.3 ml-min'l

(SEE: 103 ml-min"; r: 0.939)
Females: Y = 9.39 (W) + 7.7 (kg) - 5.88 (yr) + 136.7 ml-min’l

(SEE: 147 ml-min"; r: 0.932)

 

3 Ergometry: Any method of measuring the amount of work done by an organism, usually during exertion.

Ergometry also includes measures of power.

24

Using the 95% confidence limits as examples of the worst-case errors, Storer’s
equations predict V02max to within 10% of its true value. lntemal (double
cross-validation) and external cross-validation analyses yielded r values ranging
between 0.920 and 0.950 for the male and female regression equations. These results
indicate that use of the equations generated in this study for a 15 W-min'l CE GXT
provides accurate estimates of V02nm.

The Astrand-Rhyming submaximal cycle ergometer test is designed to predict
V02max from a 6-minute exercise period. It is one of the most widely used
submaximal exercise tests. The testing procedure requires a steady heart rate at an
appropriately selected submaximal work rate (kpm/min or watts). This information,
together with a predicted maximal heart rate and an age correction factor, is used to
predict the subjects' V02m. (Astrand & Rodahl, 2003).

The main assumptions associated with this test are as follows (referred by Adams

1998):
I Subjects resting and maximum heart rates (RHR & MHR) may be
estimated according to age.
I MHR decreases by approximately 10 beats-min'l per decade after 30.
I A linear rise in HR up to MHR exists.
I V02max and work rate have a linear relationship.

I V02max occurs at the same work rate at which MHR occurs.

A number of researchers have referred to the errors associated with this and
similar submaximal tests in attempting to predict V02max. Some suggested that

regression equations derived from direct V02max data obtained from random samples of

25

specific populations should be used in the application of the Astrand test. It is
probably correct that the Astrand test tends to underestimate V02max in the unfit
subjects and to overestimate it in trained subjects.

Von Dobeln et a1. (1967) also developed a multiple regression method to predict
V02...“ Eighty-four male construction workers aged 30-70 years were tested once at
submaximal and maximal loads on a bicycle ergometer. Submaximal and maximal
heart rates and maximal oxygen uptake were measured. The prediction of V02max
from the other variables was analyzed by a fitting procedure using a modified
least-square criterion. The best equation gave an SEE of 8.4%. In this method, the
other variables such as body size (height and weight) were added to the regression
equation for the prediction of V02mam on the bicycle ergometer.

Womack et a1. (1998) developed a formula to predict peak oxygen consumption
using 157 patients with intermittent claudication, to estimate V02peak in peripheral
arterial occlusive disease (PAOD) patients and to determine independent predictors of
V02peak in this population. Medical history, height, weight, body mass index (BMI),
age, gender, smoking status, resting and post-exercise ankle/brachial systolic pressure
index (AB1), and time to maximal claudication pain and maximal heart rate from an
incremental graded exercise test (GXT) were used as potential independent predictors
of V02peak. Time to onset of maximal claudication pain, maximal heart rate, and
BMI were all independently associated with V02pwk. These variables were used to
estimate V02pcak. The r = 0.71, r2 = 0.50 for the developed formula and standard
error of estimate = 2.02 mL/kg/min, p < 0.0001. The coefficient of variation

between estimated and actual V02pea)< in this group was 18.3%. Results of this study

26

suggest that a multiple regression equation can be used to estimate V02pw)< in patients
with intermittent claudication by measuring time to maximal claudication pain and
maximal heart rate from a GXT and by measuring BMI.

The Womack et a1. (1998) research presents a good example of the multiple linear
regression model based on multiple independent variables to predict V02pcak, though
the test is done on a certain type of patient. The acceptable standard error level for
prediction results provides a promising method for this research; the concept of an
MLR model, which is promoted in this thesis for the prediction of physiological
demands of construction work.

Except for the above discussed equations or models on the prediction of V02nm
based on the data collected from exercises, George et a1. (1997) sought to develop a
maximal, oxygen consumption (V02nm) regression model derived strictly from
self-reported non-exercise (N-EX) predictor variables. The V02max (mean +/- SD;
44.05 +/- 6.6 ml-kg’l-min'l) of 100 physically active college students (50 females, 50
males), aged 18 to 29 years, was measured using a treadmill protocol and open circuit
calorimetry. Questionnaire-based predictor variables used in the N-EX regression
model included (a) the subject's perceived functional ability (PFA) to walk, jog, or run
given distances, (b) habitual physical activity (PA-R) data, (c) body mass index (BMI),
and ((1) gender. BMI (kg - m'z) was computed from self-reported body weight in pounds
and self-reported body height in feet and inches.

The questionnaire-based N-EX regression model (SEE = 3.44 ml - kg'1 - min", r =
0.85) developed in this study exceeded the accuracy of previously developed N-EX

regression models and is comparable to many exercise-based regression models in the

27

literature. Cross-validation using PRESS (predicted residual sum of squares) statistics
demonstrated minimal shrinkage (SEE = 3.60 ml - kg’1 -min”, r= 0.84,) of the present
regression model. The PFA data were useful in explaining observed V02"... variance
(squared partial r2 = 0.155, p < 0.0001) and enhanced the ability of the N-EX
regression model to accurately predict criterion V02max.

These results suggest that a questionnaire-based N-EX regression model provides
a valid and convenient method for predicting V02max in physically active college
students. And this method provides potentials for using non-exercise physical data
such as BMI, and habitual physical activity data, to develop a regression model to
predict V02max and challenges current research methods that rely on data collected
from real exercise.

Hermiston and Faulkner (1971) have used a stepwise multiple-regression
technique to develop equations for predicting maximal oxygen uptake of physically
active and physically inactive men, from data collected during a submaximal treadmill
walk. The most accurate prediction for physically active men was obtained from a
regression equation which included the subject’s age, lean weight, heart rate, factor of
carbon dioxide in expired gas, and tidal volume at a submaximum work level, in
addition to the rate of change in respiratory exchange ratio. For physically inactive
men, the equation included age, lean weight, respiratory exchange ratio, and tidal
volume at a submaximum work level. The coefficient of correlation was 0.91
between predicted maximal oxygen upake measure on two different occasions and 0.90
between the observed and predicted maximal oxygen uptake. The multiple regression

equations are as follows:

28

Active:
V02max =“ 2966-0031 (age) + 0.026 (FFW)-0.0l3(HR) +25.4(FEC02) + 0.330(V13)-8.77(AR)

Inactive:

V02max : 3.619 5 0.(.)22(age)-0.033(FFW) ~ 2.587 (R) +0.253(VT9)
where V02max is in liters per minute; age is in years; FFW is fat-free (lean) weight; HR
is the heart rate in beats per minute at the end of the 8% grade, FEco2 is the fraction of

expired carbon dioxide during the 8-9 min. gas collection; V12 is the tidal volume

during the 0% grade gas collection period; AR is the rate of change per minute of the

respiratory exchange ratio between the gas collection periods of 1-2 min and 8-9 min;
R is the respiratory exchange ratio during the 8-9 min gas collection; and VT.) is the
tidal volume during the 8% grade gas collection period.

The regression equations use a number of independent measures of physiological
responses at submaximal workloads. The equations presented above are appropriate
for the prediction of V02max from data collected on adult men during the 1St and 91" min
of a treadmill walk. The equations account for age, habitual level of physical activity,
and fat-free weight factors, etc. The technique of stepwise multiple-regression allows
inclusion of additional independent determinants if a more precise estimate of V02max
is required.

Astorino et a1. (2000) did research to better clarify the V02 response to exercise at
the V02max level by comparing data derived from different time averaging intervals and
exercise protocols. Sixteen active subjects completed three different VOZmax tests on a
cycle ergometer (a 25 Watt/min ramp protocol (R), a 75 Watt/3 min step protocol (S),

and a 25 Watt/min ramp protocol (H) under hypoxic conditions (F102 = 15 %, PB = 635

29

mm Hg) on separate days. All breath-by-breath data were smoothed using an
ll-breath moving average. These data were then time-averaged into 15-, 30-, and
60-second sampling intervals.

From their research, data of the change in V02 between VOzmax and the closest
neighboring data point revealed that variability was greatest for the longer
time-averaged data. This response was similar for each protocol. They conclude
that shorter sampling intervals (breath-by-breath and 15 s) are most suitable for the
detection of the V02 plateau during progressive exercise to V02nm. In addition, ramp
and step protocols produce similar results, and acute normobaric hypoxia does not
decrease the incidence of a V02 plateau at VOzmax using 11 breath or 15 s time
averaging procedures. Their research suggested a recommendation on the exercise

protocols to detect V02 plateau.

11.1.5 Correlation Between Laboratory Test and Actual Output

It is of great interest, both theoretically and practically, whether a correlation
exists between an individual's physiological working capacity as measured in the
laboratory on a bicycle, ergometer or treadmill, and actual work output in heavy
industry. It is also very important to know whether aerobic work capacity as
measured in the laboratory conforms to the occupational workload level on heart rate,
oxygen uptake and relative workload measurements. Several studies have been done
in this area, among which Astrand (1967) presented some explanations more closely
related to the construction industry.

In Astrand (1967), a definite relationship was established between aerobic work

capacity as measured in the laboratory and the occupational workload level voluntarily

30

chosen by the individual. It stated that such a correlation does exist among lumber
jacks, where a worker with a high work production also has a high physical capacity
for bicycling; that is, a large oxygen uptake capacity (Hansson 1965). In the
construction industry, information is unavailable on an individual’s specific production
(output) because most tasks are completed by teams of workers. If a correlation exists
between the laboratory test results and actual work output, measurements obtained in

the laboratory test could be used at least as an estimate of the workload.

11.1.6 Relative Workload

As mentioned in CH 1, numerous work physiologists advocate the use of relative
workloads to evaluate potentials of physical fatigue (Bonjer 1971, Bink et al. 1961,
Michael et a1. 1961, Petrofsky and Lind 1978, and Jorgensen 1985). After mean
oxygen uptake is determined for a particular task, relative workload is obtained by
expressing mean V02 as a fraction, or percentage, of the maximal (actual or predicted)
oxygen uptake (Kamon 1979).

Practical experience has shown that one cannot tax more than some 30% to 40%
of maximal aerobic power during an 8-hour working day without developing subjective
or objective symptoms of fatigue (Astrand and Rodahl 2003).

The percentage of relative workload is especially important for occupations with
intense physical demands and various demographic groups (old, young, male, and
female workers) such as construction and agriculture. If the burden placed on the
worker is too high in relation to the person’s capacity for sustained physical work,
fatigue invariably will develop. Christensen (1962) has concisely summarized the

importance of this percentage as follows:

31

“The determination of oxygen uptake or caloric output and a parallel
determination of maximal oxygen uptake of the worker can be valuable tools in our
effort to avoid overstrain of the worker at a given job.”

To ensure safety and health in the workplace, Brody (1945) first proposed that a
suitable safety margin would perhaps be needed in physically demanding jobs.
Several research results (e.g. Michael et al. 1961, Bink I962, Lehmann 1962, Ilmarinen
1992) suggested that 33% of the individual’s maximum aerobic capacity (V02nm)
should be used as the acceptable standard workload for a general 8-hour physical work
shift. Jurgensen (1985) also proposed that the general upper tolerance limit over an

8-hour workday, consisting of mixed physical work including manual—handling

operations, was 30-35%V02nm (based on bicycle legwork and treadmill testing).

11.1.7 Other Measurements of Physiological Demands

Although oxygen uptake and heart rate can be used to assess the physiological
demands of muscular work in general, sometimes we need to investigate the load on
single muscles as well as groups of muscles. For example, in construction, many
tasks require workers to change position. climb, lift, and bear heavy loads at certain
times. As Hanson and Jones (1970) pointed out, the recording of heart rate is a quite
sensitive index of muscular force and even responds significantly to minor changes in
posture. Currently, electromyographic recordings can perform load measurements on
single muscles, as well as on groups of muscles. A major advantage of this recording
methodology is that it can be used to visualize the effects of practical working
procedures on loads imposed on the involved muscles.

Some research has been performed to assess the level of stress imposed on a

worker by a given work situation (physical as well as psychological), which is

32

generally reflected by nervous and hormonal reactions, more or less proportional to the
degree of stress. Any stressful situation may trigger increases in heart rate and cardiac
output, increasing the oxygen uptake and the oxygen delivery to muscles. A lot of
research has also been done to observe hormonal and nervous responses and the

relationship between heart rate and stress reaction.

11.2 Physical Performance

To achieve top performance, the physiological demands of the event must be
perfectly matched to the individual ’5 capabilities. Some common factors can serve as
a frame of reference for demands versus individual capabilities. Undoubtedly an
individual's genetic factors play an important role in performance capability.
Sometimes the environment and geographic location are also important. This is very
typical for the construction industry, which is greatly influenced by weather, location,
and time. The intensity and duration of work activities also affect oxygen uptake. The
recovery time needed before oxygen uptake and rate of aerobic metabolism return to
pre-exercise levels differs too. In most of the exercises, oxygen uptake increases
roughly linearly with an increase in the rate of exercise.

Physical performance is affected not only by genes, age and sex, but also by
biological rhythms, sleep, nutrition, environment, and a number of other factors such as
use of alcohol and various drugs. Figure 11.1 is a schematic presentation of factors
influencing physical performance ability. The effects of the nature of exercise, sex,
age and body dimension on oxygen uptake and energy consumption have been
explored earlier. In this section, respiration as a limiting factor and the influence of

tobacco, alcohol and caffeine use will be discussed. Exploring these factors and their

33

effects on work performance will help us to better understand the physiological

performance ability of each worker.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Somatic factors Training Nutrition Tobacco Psychic factors
Sex/age/ health Adaptation Alcohol Attitude
Body dimensions Caffeine, etc Motivation
1 1
Nature of exercise Service functions Environment
Intensity 1. Fuel Altitude
Duration a) Intake b) Storage c) mobilization High gas
Technique F 2. Oxygen uptake H pressure
Position a) Pulmonary ventilation Heat
Rhythm b) cardiac output Cold
i. Stroke vol. ii. Heat rate
c) oxygen extraction

 

 

 

 

 

Energy yielding processes

 

 

A

1

Physical performance

 

 

 

 

 

Figure 11.] Factors influencing physical performance ability (Astrand 2003)

11.2.1 Respiration as a Limiting Factor in Exercise

Since oxygen uptake and energy expenditure have a close relationship with the
respiratory system of human beings, it is necessary in order to better understand
physical fatigue to explore prior research on the human body's mechanical system of
respiration, the relationship between physical fatigue and oxygen uptake, and
limitations of the respiration process during exercise.

Table 11.2 presents data on lung volumes, in liters, obtained from fairly
well-trained physical education students about 24 years old (Astrand 1952), who were

reinvestigated 21 and 32 years later (I.Astand, P.-0.Astrand et a1. 1973;Viljanen 1982).

34

From the table we can see that the lung volumes are about 10% smaller in women than
in men of the same age and size. The ratio of RV/TLC in the young individual is
about 20%, but for the 50 to 60 year-old individual, this ratio increases to about 30%,
an increase that can be accounted for almost entirely by changes in lung elasticity with

age (Viljanen 1982).

 

 

Females Males
Function 1949 1970 1982 1949 1970 1982
Vital capacity4 4.26 4.25 4.05 5.55 5.39 4.92
Residual volume 1.1 1.71 1.64 1.45 2.04 2.12
Total lung capacity 5.36 5.96 5.69 7.00 7.43 7.04
RV/TLC 20.52% 28.69% 28.82% 20.71% 27.46% 30.11%

Maximal tidal volume 2.24 2.26 2.23 3.38 3.31 3.23

Table 11.2 Lung volumes from well-trained physical education students (Astrand 2003)

 

From the Table 11.2, it can be inferred that effects of age and sex on the
respiratory system are visible and associated with a reduced vital capacity. Sex and
age factors differentiate individuals' capacity for respiration, which may affect the
ability of the person to deal with physical fatigue.

According to the research of Astrand and Rodahl (2003) in a group of about 190
individuals 7 to 30 years of age, a significant correlation was found between vital
capacity (VC) and maximal oxygen uptake. Individuals with a VC of approximately
4L may have a maximal oxygen uptake of about 2.0 to 3.5 L/min, and vital capacities

of 6.0 L/min. are associated with oxygen uptake capacities varying from about 3.5 to

 

4 The maximal volume of gas that can be expelled from the lungs following a maximal inspiration is called
the vital capacity (VC). When the respiratory muscles are relaxed, there is air still left in the lungs. This
air volume is the functional residual capacity (RV). The volume of gas moved during each respiratory

cycle is the tidal volume

35

5.5 L/min. This example shows that one function can appear closely related to
another if the data are derived from persons of greatly different size.

Additionally, pulmonary ventilation at rest and during exercise is totally different.
Pulmonary ventilation is the mass movement of gas in and out of the lungs. It is
regulated mainly to provide the gaseous exchange required for aerobic energy
metabolism. According to Astrand and Rodahl (2003), if pulmonary ventilation is
expressed in relation to the magnitude of oxygen uptake, it is 20 to 25 ml per liter of
oxygen at rest and during moderately heavy exercise, but it increases to 30 to 40 ml per
liter of oxygen during maximal exercise. Also in different age groups, the lower
ventilation in older individuals is associated with a reduced maximal oxygen uptake.
At rest, the respiratory muscles require from 0.5 to 1.0 m1 of oxygen per liter of

ventilation. During exercise, the oxygen cost per unit ventilation increases markedly.

11.2.2 Smoke, Alcohol, Caffeine and Performance

Smoke contains up to 4% by volume of carbon monoxide, which reduces the
oxygen-transporting capacity of the blood. This contributes to the reduced maximal
aerobic power and exercise perfomrance following smoking. The term “passive
smoking” is used when a person breathes air contaminated by tobacco smoke.
Long-term exposure to this environmental tobacco smoke increases the risk of lung
cancer and heart diseases.

The effect of cigarette smoking on work capacity is well known. Juurup and
Muiro (1946) demonstrated that during submaximal cycle exercise at a fixed oxygen
uptake, the heart rate was 10 to 20 beats/min higher when the work test was preceded

by smoking one or two cigarettes. Also, the higher the work rate the greater the

36

difference in heart rate between smokers and nonsmokers, as nicotine affects the
cardiovascular system.

Since smoking is a really common phenomenon in the construction industry, it is
meaningful to look at the metabolic effects of smoking. Wahren et a1. (1983)
examined the metabolic response to tobacco smoking in 11 healthy, habitual smokers.
The consumption of three cigarettes increased oxygen uptake by 11%, which was
sustained for more than an hour. In one subject who smoked 20 cigarettes during 11
hours, his energy expenditure was found to be 14% greater than on the following day
when he did not smoke. Food intake and physical activity were the same. Wahren et
a1. (1983) concluded that smoking significantly raises energy expenditure. So tobacco
smoking can contribute to earlier fatigue in smokers, compared with nonsmokers who
exercise at the same level. Similar effects on exercise tolerance are noted in those
who inhale environmental tobacco smoke (McDonough and Moffatt 1999). Women
who quit smoking and undergo a vigorous exercise training program demonstrate
improved exercise performance over those who continue to smoke.

The American College of Sports Medicine (1982), after conducting a
comprehensive analysis of alcohol and exercise, concludes the following:

1. Excessive ingestion of alcohol has a deleterious effect on many psychomotor
skills.

2. Alcohol consumption does not substantially influence physiological
functions crucial to physical performance.

3. Alcohol ingestion will not improve muscular work capacity and can decrease
performance levels.

4. Alcohol consumption can impair temperature regulation during prolonged

exercise in a cold environment.

37

Caffeine is a central nervous system stimulant and is known to have the most
apparent effects on cognitive functions of the fatigued subjects, by increasing alertness
and repelling drowsiness (Astrand and Rodahl 2003). There are a lot of arguments
about the effects of caffeine on perfromance. Moderate doses of caffeine (200-300
mg) may elevate mood and improve psychomotor and intellectual performance, while
larger doses can produce symptoms such as headache, irritability, tremors, etc. It may
be an effective short-temr ergogenic aid, but of the several studies that have been
conducted, most have failed to show any ergogenic effects of caffeine on muscle

strength and fatigue, work output and speed.

11.3 Physical Fatigue

Measuring the physiological demands of work is only one side of the story, the
other important side is evaluation. Astrand and Rodahl outlined the basic tasks in
measuring physiological demands as follows:

“A basic task for the work physiologist must be that of measuring the rate at
which the work is being done, i.e. the workload and matching this rate with the
worker’s ability to perform the wor .”

Evaluation of measured physiological demand of work and potential for physical
fatigue and the limitations it may have on worker productivity has attracted
physiologists for many years. The decrease in performance due to fatigue is widely
accepted, but no agreement has been reached in trying to quantify this decrease or in
setting acceptable limits for it (Christensen 1960; Oglesby, Parker, and Howell 1989).

As Astrand and Rodahl (2003) said, the main object of work physiology is to

make it possible for individuals to perform their work tasks without objectively or

subjectively developing feelings of physical fatigue.

38

The discussion in this chapter suggests that physical fatigue is closely associated
with oxygen uptake and could be greatly influenced by factors of age, gender and
cycles of work and rest. In the past thirty years, numerous evaluation techniques of
measuring physiological demands have been proposed such as classification of work
severity based on published tables for oxygen uptake and heart rate. Other techniques
evaluate physiological demands for potentials of physical fatigue using established
physiological limits.

Humans and animals can be viewed as machines that develop and store energy
from food, burn it with oxygen to sustain life and, on demand, create movement and
power through muscular contractions (Oglesby, Parker, Howell 1989). However,
factors such as physical dimensions and condition, weight and age impose limitations
on the body’s ability to perform certain tasks. Prolonged activity eventually leads to
the onset of physical fatigue, a decrease in performance and productivity, as well as the
potential for accidents and injuries (Kalsbeek 1971).

Studies of heart rates made over 50 years ago by EA. Muller (1950) have shown
that the heart rate of a worker is a very sensitive and reliable indicator of overexertion
and fatigue. Muller reported that in general, an hourly increase of six pulses
(heartbeats) per minute is a signal that a person is overexerting on a long-term basis.

Physical fatigue can also be assessed by measuring oxygen uptake and then
converting it produced energy (For every liter of oxygen used, 5 kilocalories of energy
are produced). Researchers have found that the average young male adult, 5 feet 8
inches tall, weighing 160 pounds and in good physical condition, can develop energy

over several hours at an average rate of about 5 kilocalories per minute. The energy

39

required to sustain life processes requires about 1 kilocalorie per minute. It follows
that occupations with energy demands less than 5 kilocalories per minute can be carried
on continually for an 8-hour shift or more, without being subject to human physical
limitation. However, if the energy expenditure is greater than this, intermittent rest is
required to recoup the energy taken from storage in the body and prevent the
development of physical fatigue (Oglesby et al 1989).

An acceptable workload requires a balance between physical workload and cardio
respiratory capacity during 8 hours of work (Aminoff et a1. 1998). When this balance
is maintained, V02 and HR will remain at steady-state with a constant work output.
After working a very prolonged time, an accumulation of lactic acid in the blood puts
an additional load on the cardiovascular system and causes a sudden increase in HR.
Thus, toward the end of a work shift, a markedly higher HR (about 10 beats/min. above
steady-state), as compared with the steady-state HR observed during the initial hours of
work, is a clear sign of fatigue. This criterion has been applied to determine the
acceptable workload for an 8-hour workday (Saha et a1. 1979).

With advanced technology, extremely heavy work can be eliminated quite easily.
Therefore the more important factor for workers is the manner in which the work is
performed, flexibility to govern one’s own job, the safety and general atmosphere of
the working environment, and the arrangement of work shifts. As summed by
Astrand and Rodahl (2003), a workload taxing 30% to 40% of the individual’s maximal
oxygen uptake is a reasonable average upper limit for physical work performed
regularly over an 8-h working day. No more than 40% of maximal muscle strength

should be applied in repetitious muscular work.

40

11.3 - 1 Classification of Work

Based on the measurement of oxygen uptake and heart rate, different direct
measurements or indirect prediction techniques, and all the other assessments on
somatic factors of age. sex, body dimension, psychic factors of stress, motivation,
tObacco, alcohol, caffeine usage, and environmental factors of heat cold, etc.,
prolonged physical work can be classified as to severity of workload and to
Cardiovascular response.

Table II.3a is a general guideline for identifying categories of prolonged physical
work. These figures refer to average individuals, 20 to 30 years of age. Table II.3b
(adapted from Christensen 1983) provides a guide to classify work severity based on

peak oxygen uptake and heart rate values.

 

 

Workload Oxygen uptake, L/min Heart rate, beats/min
Light work up to 0.5 up to 90

Moderate work 0.5-1.0 90-110

Heavy work 1.0-1.5 110-130

Very heavy work 1.5-2.0 130-150

Extremely heavy work over 2.0 150—1 70

 

Table 11.3a Prolonged physical work classification

 

 

Peak Oxygen uptake, Peak Heart rate
Workload L/min beats/min
Very light work Up to 0.5 Up to 75
Light work 0.5 - 1.0 75 — 100
Moderate work 1.0 - 1.5 100 — 125
Heavy work 1.5 - 2.0 125 — 150
Very heavy work 2.0 - 2.5 150 — 175
Extremely heavy work Over 2.5 Over 175

 

Table II.3b Work classification based on peak responses during manual work

41

11.3-2 Dealing with Physical Fatigue

As shown in Figure 11.1, the performance of physical work depends on the ability
of the muscle cell to transform chemical energy in the food into mechanical energy for
muscular work. This in turn depends on the capacity of the bodily functions that
deliver fuel and oxygen to the working muscle. That is, on the nutritional quality of
the food ingested; frequency of meals; oxygen uptake, including pulmonary ventilation,
Cardiac output and oxygen extraction; and the nervous and hormonal mechanisms that
regulate these function (Astrand 2003).

Additionally, many of these functions are influenced by age, gender, body
dimensions and health situation. At the same time, performance is influenced to a
great extent by motivation and attitude toward work. And from the previous section,
we know that alcohol also has a negative effect on performance.

Understandably, most studies of measurement of human fatigue are performed in
laboratory settings, which may vary greatly from situations encountered in real life.
And physical fatigue may include both muscle fatigue and fatigue caused by
non-biomechanical muscle activities. The challenge is, therefore, to relate the various
factors contributing to experimental fatigue to the fatigue encountered in the
workplace.

Literature on physical fatigue suggests several ways of improving these work
conditions. With the development of mechanization, automation, and many kinds of
labor-saving equipment, modern technology has eliminated much heavy physical work.
But the construction industry is still a typically labor-intensive industry, and some

heavy physical work is still obligatory. Also, sometimes the greatest problems in the

42

work environment are not the physical loads but rather mental stress and unfavorable
working conditions. Therefore, in order to reduce physical fatigue, the supervisor
making work assignments should plan to mix heavy and light work, schedule rest
periods, and match workloads to the worker’s ability to perform the task.

In sum, to deal with physical fatigue occurring during work cycles in different
industries, all the above factors have to be included, to find effective ways of
improving work conditions and performance. The major objective of the work
physiologist is to enable working individuals to accomplish their tasks without undue
fatigue, so that at the end of the working day they are left with sufficient vigor to enjoy

their leisure time (Astrand and Rodahl 2003).

11.4 Physical Demands of Construction Work

Physiological workload research has been well developed in industries such as
automobile manufacturing, where work is labor-intensive and workers often perform
their tasks repetitively and in poor working postures due to constrained work places.
One study (Min, K, Chung et a1. 1999) evaluated physiological workload during screw
driving tasks in the automobile assembly line.

The effects of load and work postures on heart rate, oxygen consumption during a
screw driving task with varying loads, leg postures (standing an squatting) and trunk
postures were studied, using nine male subjects. The effects of load, leg and trunk
posture were found to be significant on heart rate and oxygen consumption. Heart
rate, oxygen consumption and subjective discomfort rating all showed a significant
increase for heavy loads and for bent and twisted trunk postures, and a redesign of

work methods for screw driving was highly recommended.

43

These research studies document the necessity of exploring the physiological
demands of different types of work, the need to correctly measure these demands, and
to develop ergonomically designed work tools and methods of completing work tasks
efficiently. This certainly is true for construction work where it is known that workers
consume large amounts of energy in performing their work tasks. The high physical
demands of construction work can easily cause physical fatigue among workers. In
order for work physiology to achieve the target of eliminating physical fatigue and
improving worksite conditions, the physiological demands of work must be measured

and evaluated.

0.042

. 0

0. 9

Electrician 0.041

Glazi .045

0.04
0.055
. 3
0.04
Table 11.4 Average energy expenditure by construction trade (Abdelhamid and Everett 2002)

 

To illustrate the use of Table 11.4, assume that a person weighing 100 kg is
considering Bricklaying as a vocation. According to Table 11.4, this person should
expect to have average energy expenditures at 4.2 kcal/min (0.042 kcal/kg/minxlOOkg
= 4.2 kcal/min). Similarly, if this person is considering working as a Laborer, then
he/she should expect to have an energy expenditure of 5.5 kcal/min.

Data such as those in Table 11.4 are at a best a guide in assessing human ability to
carry out strenuous work tasks with or without intermittent rest. Among those of a

given age for the same trade, there are variations in overall body lean and fat weights,

44

lung capacity and blood-circulation rates. With age, heart-stroke volume and rate of
beating decrease and the oxygen transport system operates less effectively, reducing the
rate of oxygen intake by 20-25 percent between the ages of 25 and 60.

Also, nowadays more and more women work in trades and the construction
industry. On the average, women consume less energy in maintaining basic body
functions and expend less residual energy in performing heavy tasks. Compared with
males, the average female has less muscular strength. Measurements have shown that
on the average, women have 20 percent less body mass, 33 percent less lean body
(muscle) mass, and 14 percent more body fat. Body surface area for females averages
18 percent less than for males. These factors, coupled with a lower blood circulation
rate, explain why women on the average have more difficulty than do men in carrying
out heavy tasks and why they are less able to adjust to heat and cold but have more
endurance.

Measuring energy expenditure figures, such as the 4.2 and 5.5 kcal/min shown
above, only represent one side of the story. The other side is the evaluation of these
measurements for the potential of physical fatigue. A widely used rule of thumb is
that activities requiring less than 5 kcal per min can be performed continually for a
work shift without overly taxing the worker. An activity requiring more than 5 kcal
per min can be performed for a limited time before the worker needs rest to recoup
energy from stores within the body.

A more accurate assessment of physical fatigue potential is to express the
measured energy expenditure as a percentage of the maximum energy expenditure that

a person is capable of, which is affected by gender, age, height, weight, conditioning,

45

inheritance, and environmental factors. To illustrate this, let’s assume that two
different workers may be performing the same activity and expending energy at the
same rate of 4 kcal/min. If these two workers respectively have a 10 kcal/min and 15
kcal/min maximum energy expenditure, then the first is working at 40% (4/10) of
his/her max while the other is working at 27% (4/15) of his/her max. Clearly, the two
workers are taxing their bodies differently. Therefore, expressing the workloads as a
percentage, also known as “relative workload," is the only way to take into account
individual differences in physiological capacities among workers.

As mentioned previously, determining maximum energy expenditure values
requires actual testing procedures, which involve complicated and lengthy laboratory
procedures, and could even be dangerous for unfit construction workers. The specific
aim of this research is to develop a practical method to predict relative workload from
energy expenditure data collected during actual work activities. Another aim of this
research is to include factors of individual variability, such as variations in age, gender,
weight, etc., in the model for the prediction of relative workloads for the construction
industry.

For construction workers, a wide variety of tools and equipment are required in
carrying out construction tasks. Failure to have tools of the right kind in sufficient
quantity available at the workplace can be a major cause of lower productivity and
physical fatigue. To enable efficient use of tools, physical fatigue, awkward positioning
of the body, limbs, hands or fingers, and strenuous muscular movements, which may be
required to use the tools, have to be factored into the design of those tools, for

efficiency and to match them to the tasks and the workers’ needs.

46

11.5 Conclusion

This chapter provided a brief discussion of the literature relevant to this research,
regarding what is available and how to deal with and evaluate physical fatigue. Genetic
factors such as age, sex, body dimensions, psychic factors of stress and motivation,
tobacco and alcohol use, and external environment factors related to physical fatigue
and assessment of work performance are discussed as well, along with the
classification of work as to severity of workload.

The physical demands of construction work are briefly reviewed, followed by a
focus on several methods of measuring maximum oxygen uptake and relative
workloads to determine the physiological demands of work. Different equations for
V02max prediction have been discussed. And several factors such as age, gender,
weight, height and heart rate have been factored into the prediction techniques
developed by different researchers in linear/non linear multiple regression models.
All of these previous efforts provided a great resource for this ongoing research to
develop a multi-regression model to predict and measure the physical demands of
construction work based on the simple regression model developed in Abdelhamid
(1999). The next chapter describes the methodology used to achieve the goal of this

research.

47

CHAPTER III
METHODOLOGY

As mentioned previously, this research project is an extension of methods
developed in Abdelhamid (1999) to predict relative workload from in-situ collected
data. This method has been under validation as part of a grant from the National
Institute of Occupational Safety and Health (NIOSH). It is also expected that a
multiple linear regression model will increase the overall prediction accuracy of
relative workload because, as discussed in Chapter 11, factors such as age, gender,
hereditary factors, health condition, and exercise history have an established influence
on the maximal oxygen uptake (V02max) value that is central to the prediction method
developed in Abdelhamid (1999). The following sections will explain the

methodology that was adopted in this research.

11].] Relation the Between Green’s Function and %VO2.m

Figure 111.1 is a graph showing oxygen uptake data for two different subjects
while they were performing one of the treadmill exercise protocols used in Abdelhamid
(1999f. The two subjects were performing the same exercise protocol, and they were,
respectively, exercising at 36% and 64% of their individual maximum oxygen uptakes.
As Figure 111.1 shows, there is a clear difference between the two subjects in terms of

the recorded oxygen uptake data.

 

5 Details of the experimental protocol can be found in Abdelhamid (1999) and Appendix C of this thesis.
Data series for the whole plots in Figure 111.1 and 111.2 are listed in Table 8.1 in Appendix B.

48

+ Subject 78 -I— Subject 97

V02 (Liters/min)

O-INOO-bU’ICDV

l?

 

...
r
4.
,.

Time (minutes)

Figure 111.1 Oxygen uptake data for subject 78 and 98 (session 3)
The data in Figure 111.] was shown in Abdelhamid (1999) to have

auto-dependence or auto-correlation. This property was firrther exploited using a
statistical technique called time series analysis wherein data are auto-regressed to find a
linear statistical model that describes one observation in terms of earlier ones. Once
an adequate model is found, typically termed an Auto-Regresseive Moving Average
model [ARMA(p,q)], numerous statistical, and sometime physical, characteristics can
be derived regarding the system that produced the observed data.

Abdelhamid (1999) verified that the time series derived characteristic called the
Green’s function is positively correlated to %VO2max. Figure 111.2 shows a typical
plot of the Green’s function for the data shown in Figure 111.1. It should be noted that
the horizontal axis represents a time unit equal to the sampling interval at which
observations are measured, and the vertical axis is Gj, which is the value of the Green’s

function at a particular time unit j. To properly quantify the Green’s Function profile

49

and given its asymptotically limited property, the concept of ‘mathematical’ energy is

used, wherein the sum of squares for all individual data points is determined".

+ Sibj ect 78- sessi on3

1'2 , +8.1bj ect 97-session3

0.8
0.6 '
0.4

0.2

1 9 33 41 49 57 65 73 81 89 97

Figure 111.2 Green’s function for subject 78 and 97 oxygen uptake data (session 3)

Despite being subjected to the same exercise intensity, Figure 111.2 shows that the
two subjects have drastically different responses to the exercise. Recall that subjects
78 and 97 are, respectively, exercising at 36% and 64% of their individual maximum
oxygen uptakes. The value of the energy of the Green’s function (E0) was calculated
for the two subjects and found to be 4.79 and 14.16 for subjects 78 and 97, respectively.
Clearly, for these two different subjects under the same external effort level, the
difference in response is well captured using the Energy of Green’s function.

As mentioned in Chapter 11, time series analysis was used in Abdelhamid (1999)

to develop a simple linear regression model based on the relationship between

 

6 The Green’s function falls under non-periodic signals and is quantified using the concept of “energy”
(Abdelhamid 1999).

50

%VO2max and E0 on 20 subjects. Therefore in order to achieve the first objective of
this thesis, which is to verify the linear regression model on a larger pool of subjects,
the same treadmill experimental protocols and analytical procedures that were

performed in Abdelhamid (1999) were conducted for a pool of 100 subjects.

111.2 Research Methods

The goal of this research is to develop a multiple linear regression model to
predict the physiological demands of construction work. The model will incorporate
factors such as age, gender, and heart rate in addition to the factor established in the
simple linear regression model developed in Abdelhamid (1999).

To attain this goal the following objectives were established and accomplished:

I Validate the simple linear regression model developed in Abdelhamid
(1999) for 100 subjects performing a specified exercise regimen.
I Develop and validate a multiple linear regression model to predict the

relative workload from sub-maximal oxygen uptake (V02).

111.2.1 Objective 1

For the first objective, measurements will be conducted on subjects performing
the same treadmill experiment protocol that was performed in Abdelhamid (1999).
One hundred ‘development’ subjects will be tested. For each subject, oxygen uptake
and heart rate were measured during three different sessions requiring different levels
of effort. In addition, the maximum oxygen uptake was determined for each subject
using an exact technique termed the Harbor protocol (McArdle et a1 1996). Hence,

the exact relative workload for each subject could be determined at each level of effort.

51

Time series analysis was then performed for each data set collected to arrive at an
adequate ARMA(p,q) model from which the energy of the Green’s function was
obtained and related to the relative workload through regression analysis.

The V02000 Portable Metabolic System was used to measure oxygen uptake.
With this system, the subject wore a face mask and breathed ambient air. The subject
also wore a chest vest on which the measuring device was mounted. The Polar
Vantage XL was also used to measure heart rate.

A 4-session experiment was designed to investigate the E0 and %VO2max relation.
The experiment was designed such that all subjects were required to perform at the
same work intensity. During all sessions, oxygen uptake and heart rate data were
collected at 10-second intervals, the lowest possible setting by the V02000 Portable
Metabolic System. The following is a description of the 4-session experiment that
was performed on the 100 development subjects:

Session 1; Resting

The subject was instructed to assume a supine position for 20 minutes prior to
which the last food intake had at least been two hours.
Session 2; Treadmill walking (0% grade):

The subject was instructed to walk on the treadmill for twenty minutes at a speed
of 3 miles/hr (4.8 km/hr) and level grade. During the first two minutes, the speed was
gradually increased from 1.5 mile/hr to 3 miles/hr (2.4 km/hr to 4.8 km/hr). This
served both as a warm up period and a familiarization period. After finishing the

exercise, the subject was allowed to rest until oxygen uptake and heart rate values

52

returned to pre-exercise values (resting values). Data measurement was stopped after
this recovery period.
Session 3', Treadmill walking (1 2% grade):

The subject was instructed to walk on the treadmill for twelve minutes at a speed
of 3 miles/hr (4.8 km/hr) and 12% grade. The exercise started at 1.5 miles/hr (2.4
km/hr) and 0% grade, and during the first minute speed and grade were gradually
increased to 3 miles/hr (4.8 km/hr) and to 12% grade, respectively. After finishing the
exercise, the subject was allowed to rest until oxygen uptake and heart rate values
returned to pre-exercise values (resting values). Data measurement was stopped after
this recovery period.

Session 4; Harbor protocol for V02max measurement:

 

 

This session was performed to determine the exact value of maximum oxygen
uptake using the Harbor protocol. The subject was instructed to walk on the treadmill
for three minutes at a speed of 3.3 miles/hr (5.3 km/hr) and level grade. Then, the
grade was increased 2% every following minute. 1f the subject reached the 15% grade,
and was still able to continue, the speed was increased 0.5 miles/hr every following
minute. The exercise continued until the subject was unable to continue
walking/running. After finishing the exercise, the subject was allowed to rest until
oxygen uptake and heart rate values returned to pre-exercise values (resting values).
Data measurement was stopped after this recovery period. In order to determine if a
true V02max was achieved, a “peaking-over” in oxygen uptake was used as criteria

(McArdle et al 1996).

53

The collected data from the 100 development subjects was used to examine the

validity of the single linear regression model developed in Abdelhamid (1999).

[11.2.2 Objective 11

The second objective will be achieved by these following steps:

Conduct a literature review to understand contemporary methods of
predicting physiological demands of work.

Develop a multiple linear regression model to reflect the variables that
may affect the prediction of relative workload, such as body
dimensions (height and weight), age, gender and heart rate.

Assess the performance of the multiple linear regression model on a
pool of validation subjects performing random exercises, or working at
intensities ranging from light to heavy, as well as performing a
maximum oxygen uptake test to determine the actual %V02.,m at
which each subject was exercising/working.

Evaluate the predictive capability of the regression model by
predicting the %V02max from the validation subjects and comparing

results with the actual values.

111.3 Hypothetical Multiple Linear Regression Model

Building on the relation between Green’s function and %VO2max discussed in

section 111.1, this research will develop a multiple linear regression model to predict

and measure the physiological demands of physical work, such as construction work.

54

This research will focus on heart rate, age, body dimensions, and gender as the factors
that may affect the simple linear regression method and develop a multiple linear
regression model accordingly. Inclusion of these factors accounts for the inherent
inter-subject variability in terms of physical capacity and the type and length of the
activity performed.

The reason other factors, such as age and heart rate, need to be taken into account
is that inter-individual variability in terms of physical capacity exists in the real world,
especially in construction work. In addition, every worker is unique, and performs
different and sometimes unique work, due to variability of location, time and amount of
work. Also, as Christensen (1962) suggested, “we have to decide if the load of a
given job is reasonable or unreasonable for a given worker." Therefore, as many
relevant factors as possible should be incorporated in regression models used for
prediction of physiological demands.

To fit measured data to a certain model, one has to decide upon the form of the
model. For the prediction of relative workload, i.e. %V02nm, it is possible to make
an educated guess regarding the form of the model, rather than conducting a laborious
search process for the correct one. It has been well established that %VO2max can be
expressed linearly as a function of E0 as developed earlier by Abdelhamid (1999). It
has also been established by other researches that %VO2max has a linear relationship
with heart rate, weight, height, age, gender, and working power. So the basic multiple
linear regression model that will be investigated in this research will be generically
expressed in the following form:

%V02max = f (E3, HR, age, gender, height, weight) (Eq 3.1)

55

A hypothetical multi-regression model may take the following form:

%V02max = “1E6 + aZHR + a3Age + a4Height + asWeight + C (Eq 3.2)
where a1, a2, a3, a4 and a5 are the parameters of the model and C is a constant.
It is possible to combine the height and weight of a person using the Body Mass Index
(BMI) or the Body Surface Area(BSA). BMI is expressed as follows: BMI = [Weight
(kg) / Height2 (m)] while BSA is most commonly expressed as (Mosteller 1987): BSA
= ([Height (in) x Weight (lbs)]/ 3131) V’. As shown, either expression combines both
height and weight, which is an advantage when constructing the mathematical model.
So the Eq.3.2 may change to the following:

%VO2mam = alEG + azHR + aBAge + a4BMI(0rBSA) + C (Eq 3.3)
This equation of the model can be analyzed by the methods of multiple linear

regression (MLR) to estimate the parameters a), a2,..., an by minimizing the sum of

squared errors: minZgz , where g,- = y. _ y. and y. is the i-th predicted value and
. 1 1 l

l

y. is the i-th observed value. This is method is called the least squared errors and is

the method used in this research. It should be noted that using linear programming
may provide a better model because the actual deviations are minimized rather than the
square of the deviations.

The statistical properties of the model such as the standard error of estimation
(SEE), coefficient of determination (r2), and inferences about prediction of V02max will
be determined and analyzed. The effects of multi-collinearity will also be

investigated.

56

The developed multiple regression model will be verified on data collected for
100 subjects exercising/working during the validation sessions. The subjects were
instructed to perform random exercise or work at intensities ranging from light to heavy.
Subjects were allowed to choose the exercise equipment or the type of work at their
own discretion. These conditions were intended to match the random nature of work
that dominates real-world work situations. Maximum oxygen uptake was determined
for each subject using the Harbor protocol, as was done for the 100 development
subjects. The same time series analysis technique was applied to the validation
subjects’ oxygen uptake data sets to obtain the Green’s function and its energy. The
predictive capability of the multiple linear regression model will be evaluated by

calculating the mean squared prediction error.

111.4 Summary

The construction industry differs from other industries in many unique ways.
An ever-changing job site under varying weather conditions and job demands are all
factors that make it critical to find a reliable technique for the accurate evaluation of
physical demands, and identify and eliminate potential causes of physical fatigue.

It is expected that the proposed multi-regression model will improve the accuracy
of relative workload predictions from sub-maximal oxygen uptake data collected
in-situ. The multi-regression model will include both the promising time series
analysis technique developed by Abdelhamid (1999) and other factors that affect
oxygen uptake such as age, body dimensions, heart rate, gender, etc.

If successful, the multiple linear regression model developed in this research will

be of great importance in better understanding physical demands on today’s workers.

57

This prediction method will be safer for unfit subjects and easier to use in general,
compared to maximal testing protocols and restrictive lab requirements. This
methodology will have widespread application in identifying excessively demanding
tasks so they can be better matched to the abilities of subjects. Women, older workers,
and workers who are partially disabled now can be placed in jobs according to their

capabilities.

58

CHAPTER IV
RESULTS

1V.l Introduction

The literature review in Chapter II reveals that typical influential factors in the
prediction of relative workload (%V02max) are heart rate, age, weight, height, and
gender. Combining these factors with the Energy of the Green’s function, as found in
Abdelhamid (1999), is expected to yield more accurate predictions of relative workload
from sub-maximal oxygen uptake and heart rate data collected in-situ. The current
research is limited to incorporating the factors of weight, height, age, and heart rate in
the development of a multiple linear regression model of %VO2,,m.

In this research, the same experimental protocol performed in Abdelhamid (1999)
was used on 100 subjects. The resulting data were analyzed to develop and validate a
simple linear regression model between %V02max and the Energy of the Green’s
function. In addition, multiple linear regression models were developed to include the
other influential variables discussed earlier. Validation of the multiple regression
models was undertaken on an additional 100 validation subjects. Comparison of the
multiple regression models with the simple linear regression model was performed and
the result revealed a significant improvement in the accuracy of prediction in %V02max
and the V02max, respectively.

This chapter presents the results of redeveloping the simple regression model on

the larger pool of subjects and the development of the multiple linear regression (MLR)

59

models, with age, height, weight, and heart rate factors. The statistical properties of
the developed regression models are derived and analyzed against the basic
assumptions upon which the models were constructed. The chapter concludes with a

presentation of the validation results for all the developed regression models.

IV.2 Participants

The study details were announced to students, staff and faculty from Michigan
State University. The target number of participants was 200, respectively divided into
100 development and 100 validation subjects. As the title implies, the data collected
for the development subjects were used to build the regression models, both simple and
multiple. Data collected for the validation subjects were used to verify the simple and
multiple linear regression models’ predictive accuracy. The validation compares
actual values observed for the validation subjects to predicted values for the same
subjects, using the developed regression equations.

Descriptive physical data and exercise data for the 200 experimental and
validation subjects are presented in Table IV.17. The age variable, with a range of 19
years for experimental subjects and 24 years for the validation subjects, seems to show
the least degree of variation among the other variables. Around 80% of the subjects
are 24-32 years old. The values for V02”, V02nm, %VO2max, HRavg, HRmax and
RHR are also very close for these two groups of subjects. HRmax is calculated by the

formula HRmax = 220-age.

 

7 The whole data series are listed in Appendix B Table 8.2 and B.3.

60

 

Development Subjects

 

 

 

 

 

Variable Mean SE Mean StDev Min Max Range
Height(inch) 681980.342 3.506 57.5 76.75 19.25
Weight(lb) 156.592.35 24.04 105.6 231 125.4
BSA( m2) 184340.017 0.1744 1.45 2.36 0.91
Age(yr) 24.438 0.45 4.614 18 37 19
VO2avg(liter/min) 1.0355 0.043 0.441 0.2758 2.0803 1.8045
VOzmax(liter/min) 339910.0754 0.7728 1.98 5.06 3.08
%VO2max 0.3095 0.0124 0.1272 0.1249 0.6578 0.5329
HRavg(Beat/min) 109.492.28 23.41 69.27 173.67 104.4
HRmax(Beat/min) 195.560.45 4.61 183 202 19
RHR 0.5599 0.0116 0.119 0.36 0.9 0.54
Validation Subjects
Variable Mean SE Mean StDev Min Max Range
Height(inch) 68.867 0.338 3.888 60.5 80.5 20
Weight(lb) 165.06 2.4 27.52 111 239 128
BSA(m’) 1.8928 0.0181 0.2085 1.47 2.39 0.92
Age(yr) 25.773 0.449 5.155 19 43 24
V02avg(1iter/min) 1.7137 0.0436 0.5014 0.84 2.87 2.03
VOzmainter/min) 3.5471 0.0761 0.8747 1,52 5.93 4.41
%V02max 0.49098 0.00919 0.10563 0.26 0.67 0.41
HRavg(Beat/min) 136.84 1.48 16.98 100.71 172.35 71.64
HRmax(BeaI/mln) 194.23 0.449 5.15 177 201 24
RHR 0.705 0.00768 0.0882 0.52 0.89 0.37

 

Note: V02max=maximal oxygen uptake, obtained from Harbor protocol for
V02max measurement; HRmax =maximal heart rate=220-age; %VO2max =
VO2avg/V02max; RHR=HRa,g/HRmax; BSA(m2)=([Height(in) x Weight(lbs) ]/

3131 )‘e (The Mosteller formula)

 

Table 1V.1 Descriptive Statistics and maximal exercise data for experimental/validation subjects

IV.3 Models Analysis

The models analysis is divided into three parts.

the single linear regression model is performed using the data from the 100

development subjects.

61

In Part A, the development of

This simple regression model is based on the relation

between the Energy of the Green’s function and relative workload (%V02max), which is
the method advocated by Abdelhamid (1999). Statistical properties of the simple
linear regression model are derived and illustrated. Part B discusses the motivation
for developing the multiple linear regression models and how the MLR models are set
up, with the accompanying statistical analysis to verify the suitability of the multiple
regression models. A comparison of a number of multiple linear regression models is
conducted to determine the best fit multiple linear regression model. Part C verifies
the simple linear and multiple linear regression models on the 100 validation subjects

for the appropriate applications.

1V 1 Part A: im 1e Linear Re r ssi n M (1 1D vel men

IV.3.1.1 SLR Model Setup

The simple linear regression model using the relationship between the Energy of
the Green’s function and %V02max is developed by Abdelhamid (1999). However, in
that research, the relation was developed based on data for 20 subjects and validated on
5 (Abdelhamid 1999). Therefore, this research begins with redeveloping this simple
linear regression relationship on 100 experimental subjects. This is also the part of
the research that involves the NIOSH project.

As explained in Ch 111, this research uses the same time series method to obtain
the Green’s function for each experimental subject on the treadmill exercises.
Because Session 1 exercise is a resting cycle, subjects are under less demanding
exertions. As a result, the Energy of the Green’s function doesn’t change significantly
for each subject. The trend is entirely different for Sessions 2 and 3, wherein

significant differences are observed in the values of the Energy of the Green’s function.

62

Values of the Energy of the Green’s function and %V02max for each experimental
subject are plotted in Fig.1V.1. As shown, the relation between the Energy of the
Green’s function and relative workload are strongly correlated. The solid line in
Figure IV.1 represents the best-fit curve (logarithmic) between the Energy of the
Green’s firnction and V02avg/V02max. This verifies that a non-linear relation exists

between the two variables for a larger pool of subjects.

    
 

Green's function VS %V02nmx
0.8
‘ 0.7 ‘r
l N 1
1 a 0.6
. 5 1
1 O 0.5 1 o 1
3°“ 1 y = 0.1603ln(x) + 0.2244
' g 0'3" R2=O.6456
>- 0.2 l
0.1 l
o 1. , _ _ _ .. .
o 2 4 6 8 10 12 14 16 18

E81

Figure 1V.1 Energy of the Green’s function and VOZavg/VOZmax

To allow using linear regression, the Energy of the Green’s function is
transformed using the natural logarithm (Ln). The result is shown in Figure IV.28.
Table IV.2 presents the running output from the Minitab software9 for the

regression of %V02max based on the Energy of the Green’s function. From the results,

 

8 All data plotted in Figure 1V.1 are listed in Appendix B Table 3.4.

9 In order to avoid exhausting calculations on the data, this thesis uses the software of Minitab, Excel and

SPSS for linear regression model running outputs.

63

we can also see the same linear regression equation between these two variables

derived from Figure IV.2.

Transformed Green's function VS %V02max

   

VOZavg/VOZmax
O
a

y = 0.1603x + 0.2244
4" 5’ o” R2 = 0.6456

N
1"
1J1
w

0 0.5 1 1.5
5&1

Figure IV.2 Transformed Energy of the Green’s function and vo,,,,,/vom,

 

lRegression Analysis: %VO2m,x versus Ln(E(;)
%VO2,mlx = 0.224 + 0.160 Ln(Eg)
S = 0.0760997 R-Sq = 64.6%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Predictor Coef SE Coef 11’ P
onstant 0.224405 0.00968 23.1 8 1)
1.11050) 0.1603 0.0117 13.7 0
Analysis of Variance
Source DF SS MS F P
Regression 1 1.0868 1.0868 187.66 0
Residual Error 103 0.5965 00058
Total 104 1.6833

 

 

 

 

 

 

 

Table IV.2 Regression output for the %VOZ,,,,, by Minitab

Therefore, the following single linear regression model results:

%v02m,, = 0.224 + 0.160 Ln(EG) + e (Eq N1)

64

The intercept and slope for the linear regression model are estimated as 0.224 and 0.160
respectively, with a standard deviationo, or standard error of estimation (SEE), of
i0.076.

IV.3.1.2 Normality and Independence of Error Terms of SLR Model

Several inferences from the SLR model in Eq IV.l such as the standard deviation,
and normality and independence of the error terms have to be validated to ensure the

developed model can be considered appropriate for its application.10

A. Star_rdard Deviation

In statistical theory, the deviations 8 in a simple linear regression model are

assumed to be independent and normally distributed random variables with mean 0 and
standard deviation 0' orx/MSE (MSE stands for mean squared error). For a simple

linear regression model, the 0, which measures the variation of the dependent variable,

in this case the %V02max, about the re ression line can be determined from:
g

(Eq IV.2)

 

The sum is averaged by dividing over 71-2 to make 5 an unbiased estimate of o.
The quantity n-2 is known as the degree of freedom for s. From the Minitab running
output (see Table IV.2), the estimated standard deviation ‘3 ' for the regression model to

analyze the relationship between %V02mu( and Ln(EG) is calculated as $0.076 or

 

'0 In order to make the illustration clear and easy to understand, some statistical background terminologies
are included in the analysis. For more detailed information regarding single and multiple linear regression

models, please refer to the referenced statistical textbooks.

65

17.60% for all the experimental subjects. This demonstrates that the standard error of

prediction for relative workload, i.e., %V02max, using the Eq 1V] is i7.60%.

B. Normality and Independence of Error Terng

The SLR model consists of the predicted mean of %V02max and deviations of the
data from the line of means, 8. As mentioned earlier, normality and independence of
the error terms have to be verified such that the developed model Equation IV.l using
linear regression is considered appropriate for its intended application.

The normality is verified using a normal probability plot of the residuals. A
normal probability plot is a plot of ordered residuals against their respective expected
values, which are assumed to follow a normal distribution. Figure IV.3 shows a plot
of the ordered residuals versus their expected value under normality by using the
Minitab software. The nearly linear plot indicates agreement with normality. i.e., the

distribution of the error terms can reasonably be assumed to be normal.

 

99.

99.

 

 

 

 

 

, E (ei)

 

Fig IV.3 Normal probability plot for residuals

66

 

 

 

 

 

1n linear regression, it is assumed that the residuals are independent of (not
correlated with) one another. If the independence assumption is violated, some model
fitting results may be questionable. The independence for the residuals e. was tested
using Minitab. The method used in Minitab involves graphing residuals versus the
ordered data. Once constructed, the graph provides a visual depiction of the residuals’
independence. A positive correlation is indicated by a clustering of residuals with the
same sign. A negative correlation is indicated by rapid changes in the signs of
consecutive residuals.

Figure IV.4 shows the plots of residuals versus ordered data for the single linear
regression Equation IV.1. From the plot, it is indicated that there are rapid changes in
the signs of consecutive residuals and there is no visible clustering of residuals with the
same sign. Therefore, there is no evidence of serial dependence in the observed

residual data, indicating independence of the residuals e1.

Residuals Versus the Order of the Data
(rsporse ls %V02max)

 

N
1

.—.
J.

 

O

r
H
1

 

Standardized Residual

 

11111 1%

 

 

 

 

 

Figure IV.4 Minitab residuals versus order chart

Residual analysis is not complete without considering whether there is a

possibility of residual outliers. Fig. IV.5 is a standardized residual plot generated by

67

the Minitab program. It reflects the relation of standardized residuals (8170') and the

independent variable X, in this case the Energy of the Green’s function.

 

 

l Residals Versus the Fitted Values
. (response is %V02max)

 

 

 

 

 

 

. O. C e
C . O.
O C
-2 .
.
o 2 03 0:4 0 s 0.6 07
rated Varue

 

Standardized Residual
. e 9 .
' I
"h’ '
0 b
, O
O
O
O
O
o 6.
o i
O
a)

 

Figure 1V.5 Minitab standardized residual plot

For a standardized residuals plot, outliers are considered as points, which are four
or more standard deviations from zero. Fig 1V.5 shows that most of the residuals are
scattered within a band of i2 standard deviations from zero. Therefore, there is not
sufficient evidence that outliers exist.

In sum, both the normality and independence of error terms have been checked
and they verify that the single linear regression model using the Energy of the Green’s
function to predict relative workload (%V02nm) is valid, and the linear relation
between the Energy of the Green’s function and %VO2max exists, even with a larger
pool of subjects. The developed equation using linear regression is considered
appropriate for the application.

The next step for the validation of the single linear regression model is to check

the statistical properties of the model equation to see how this model reflects the

68

capability of predicting %VO2max and how accurate is the model’s prediction of relative

workload.

1V.3.l.3 Statistical Properties of the SLR Model

A. Correlation coefficient, T value and P value

Table IV.2 indicates that the coefficient of determination for the regression
Equation IV] is r2=0.646 and the coefficient of correlation is r=0.80. In general,
values of r can range from -1 to +1, and fall between 0 (no correlation) and 1 (perfect
correlation). On the one hand, a positive value indicates that two variables tend to
increase together. On the other hand, a negative value indicates that one variable
tends to increase as the other decreases. In this model, an r-value of 0.8 indicates that
EU and %VO2max are highly correlated. In addition, an r2 value of 0.646 means that
around 64.6% variation in relative workload (%V02max) can be explained by Ln(E(-;).

However, the interpretation of r2 as the proportion of the total variation of
%VO2max explained by EU is frequently taken literally. A value of r2 close to 1 is not
an indication of perfect inference of %V02ma_, from EC, using the estimated regression
model. The usefulness of a regression model in predicting %VO2max from E0 depends
upon the width of the confidence or prediction intervals, which will be investigated
next

In order to check the significance of the predictors in the model, two other
reference values can be checked: t-value (T) and p-value (P). The t-value for testing
the regression coefficients is obtained by dividing the estimates by their standard errors.

The bigger the absolute value of the t-value, the more likely the predictor is significant.

69

The p-value is used in hypothesis testing to help decide whether to reject a null
hypothesis. The p-value is the probability of obtaining a test statistic that is at least as
extreme as the actual calculated value, if the null hypothesis is true. That is, the
p-value represents the probability of rejecting the null hypothesis when it is actually
true. The smaller the p-value, the smaller'the probability that rejecting the null
hypothesis would be a mistake. A commonly used cut-off value for the p-value is
0.05. The null hypothesis in this case would be that H0: ,6, =0, i.e., that there is no
straight-line relationship between EU and %VO2max and that linear regression of
%VO2max on E0 is of no value in prediction.

For the relation depicted here, between EU and %V02max, the t-value for the ,6,

is 13.70 (see Table IV.3), indicating that the significance of the predictor Ln(E(;). In

addition, Table IV.3 also shows that the p-value is equal to zero for Ho: ,6, =0, which

indicates that H0 is rejected. This verifies that the correlation between the Energy of

the Green’s function and relative workload exists and is valuable.

 

 

F’ 8:17;. 1,

 

 

 

 

 

 

 

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
'30 0.224405 0.009679691 23.18305 1.14E-42 0.205207 0.243602
[3‘ 0.1603 0.011701705 13.69886 6.08E-25 0.137092 0.183508

 

 

 

 

Table IV.3 Regression output from Excel for regression slope and Intercept

B. Inferences about ,8, and predicm of %V02M

In statistical analysis, a confidence interval refers to the range in which the

estimated mean response for a given set of predictor values is expected to fall. The

interval is defined by lower and upper limits, which Minitab calculates from the

confidence level selected and the standard error of the fitted values.

70

A prediction

 

interval refers to the range in which the predicted response for a new observation is

expected to fall. The interval is defined by lower and upper limits, which Minitab

calculates from the confidence level selected and a calculated standard error of

prediction. The prediction interval is always wider than the confidence interval

because of the added uncertainty involved in predicting a single response versus the

mean response. In this research, 95% intervals are considered appropriate.

From Table IV.3, the 95% confidence interval for ,8, is (O.l37,0.184). It means

we estimate with 95% confidence that an increase of 1 in the logarithm of the Eg is
associated with an increase of between 0.137 and 0.184 times of %V02max,

The fitted line plot for the predicted relative workload with 95% prediction

interval is illustrated in Figure IV.6 by Minitab software. Using the regression model

to predict %V02max, it is indicated from the chart that nearly all of the plots are falling

within the prediction intervals. In other words, using the simple linear regression

model is expected to have a reasonable prediction accuracy of %V02max.

 

Fitted Line Plot
%V02max = 0.2244 + 0.1603 Ln(Eg)

 

--- Regression
— — 95% Pl

'loVOZnax

---- 95% Pl

 

 

 

 

l I 1 l
0.0 0.5 1.0 1.5 2.0 2.5
“(511)

 

 

 

Figure IV.6. confidence interval & prediction intervals plot (Minitab)

71

 

Table IV.4 displays a sample Minitab confidence and prediction interval analysis
for specific values of Ln(E(,;). For example, for a subject with Ln(E(,)=0.06, the
predicted mean %VO2max is 0.23442 (practically 23%) with a standard error of 0.00923
(approximately 1%). The 95% confidence interval is (0.21612, 0.25272). In other
words, for this subject, we are 95% confident that the %V02max falls between 21.6%
and 25.3%. And if Ln(E(;) is 0.06, it is predicted with 95% confidence that the
%VO2.,m would fall between 8.24% and 38.65% for a new observation. Clearly, the
prediction interval is quite wide, underscoring the need to consider a multiple

regression approach.

 

 

 

 

 

 

 

 

 

 

 

 

ew

Obs Ln(Eo) Fit SE Fit 95% C1 95% PI

1 0.06 0.23442 0.00923 (0.21612, 0.25272) (0.08239, 0.38645)
2 0.09 0.23852 0.00905 (0.22056, 0.25647) (0.08653, 0.39051)
3 0.11 0.24218 0.0089 (022452025984)(009022039413)
4 0.21 0.25821 0.00832 (0.24172027470) (0.10639, 0.41004)

 

Table IV.4 Sample of Minitab Output on C1 &PI for four value of Ln(EG)

-m'g

 

As mentioned earlier, %V02m;,x = ; hence V02nm can be calculated easily.

a max

Table IV.5 lists sample results for the actual %V02ma(. V02max and predicted %V02max

and V02nm and their eis H respectively. Either using the equation

Ze.’ (Y, 41V . . . . .
of s: ——2—: ——————2—— , or usrng M1n1tab, we can easrly get the estimated
71— n—

standard en°or of prediction, ordMSE for maximum oxygen uptake (V02mm) for all
experimental subjects, which is estimated at i0.6523 liter-min'I (Recall that the

standard error of prediction, for %VO2max was i 7.60%).

 

H See Appendix B- Table 8.6 for all data ofTable IV.5.

72

3.132,

 

 

 

%V02max 0/0V()2max VOZmax VOZmax
exact predicted exact predicted B} [1-2] E.~2 [3-4]

0.214608 0.2339952 2.56 2.34791141 0.0003759 0.0449816
0.245296 0.2417408 2.35 2.38453749 1.264E-05 0.0011928
0.240882 0.2244656 2.8 3.00478113 0.0002695 0.0419353
0.229237 0.240296 2.84 2.70928355 0.0001223 0.0170868
0.169172 0.2380848 4.24 3.01275008 0.004749 1.5061424
0.204126 0.257744 3.19 252638277 0.0028749 0.4403878
0.197736 0.243864 3.61 2.92716432 0.0021278 0.4662646
0.211912 0.27412 3.31 2.55884284 0.0038698 0.5642371
.263785 0.2352752 3.21 3.59897686 0.0008128 0.151303

Table 1V.5 Sample data for regression analysis results

 

 

 

 

 

 

 

 

 

IV.3.1.4 Summary

In this section, time series analysis techniques are used to determine the Green’s
function values, from which the Energy of the Green’s function is calculated as the sum
of squared values of individual Green’s function values. A linear regression equation
is constructed between the Energy of the Green’s function and relative workload

(%V02max). The standard error of prediction for %VO2max and V02"),x are i7.6% and

350.6523 liter-min", respectively. In Abdelhamid (1999), this equation was termed
Relative Workload Prediction equation - RWP equation. In this thesis, this term RWP
will still be used hereafter to refer to Equation IV]. The statistical properties of the
equation have been analyzed and the results indicate that the regression model has
merit in predicting relative workload from sub-maximal oxygen uptake data.
Further steps taken to develop a multiple regression model that improves the
accuracy of the prediction as well as validating all models are discussed in the

following sections, Parts B and C.

73

 

 

 

 

1V .2 P rt B: Multi 1e R ressi 11 Models

This section focuses on the development of a multiple regression model (MLR) to
predict relative workload from sub-maximal oxygen uptake (V02), which is the second
objective of this thesis. The section begins with a discussion of the motivation behind
developing the MLR and the factors to include in the MLR model. Then the section
focuses on the model setup and statistical properties analysis, and concludes with a

comparison of the MLR model to the SLR model developed in Part A.

IV.3.2.1 Factors for MLR Models
The analysis performed in Part A indicates that using the RWP equation has a

standard error of prediction for relative workload (%V02max) equal to i7.60%. This is
higher than the 25.0% of value reported’in Abdelhamid (1999), which was based on 20
development subjects. This difference indicates the need to consider other factors in
addition to the Energy of the Green’s function, which could potentially improve
predictive accuracy.

In the RWP equation, there is only one predictor—the Energy of the Green’s
function. As discussed in Chapter 11, several researchers have investigated the
development of multiple regression models to include predictors of V02max such as
heart rate, age, gender, physical dimension, and work duration. The inclusion of such
factors along with the Energy of the Green’s function in a multiple regression model
was investigated in this research. This was expected to increase predictive accuracy

for relative workload derived from sub-maximal oxygen uptake data.

74

 

A. Heart Rate

In many types of exercise, heart rate increases linearly with exercise intensity.
In most test procedures, the evaluation, from submaximal rates of exercise, of an
individual’s maximal oxygen uptake or capacity to perform work involves measuring

the heart rate during steady state and then extrapolating to a fixed heart rate or to an

assumed maximal heart rate. As mentioned in Chapter 11, there are many pitfalls with

this method of predicting V02max from HR.

Despite criticism concerning the linear oxygen uptake/heart rate relationship,

heart rate still remains a very important factor in reflecting the feeling of strain during

an exercise. While the use of submaximal heart rate as a basis for the prediction of

maximal oxygen uptake is not new, this factor will be used in developing the multiple

linear regression (MLR) model. This is possible to investigate because the treadmill

tests have recorded the heart rate for both the experimental and validation subjects in

- -1
beats-mm .

B. Age

Jones (1985) and Von Dobeln et a1. (1967) all considered the age factor in their

V02max prediction equations. This is primarily because of the typical effect of the

aging process on various body functions, such as circulatory and pulmonary capacity in

older individuals (Astrand and Rodahl 2003). Thus, age will be included in the MLR

models to verify its influence on the prediction accuracy of the models.

C. Body Surface Area (BSA)
As mentioned earlier in chapter 111, Body Surface Area (BSA) is the total surface

area of the human body. Jones (1985) developed a prediction equation for V02max

75

that accounts for this factor. Differences in body size are as important as age in
V02max prediction because of the effects on the circulatory capacity, heart rate, stroke
volume, and cardiac output. It is especially important to consider the influence of the
body size factor in construction fieldwork where many tasks require workers to lift,
rotate, climb up and down, and walk, etc. In this research, the BSA factor is
considered as a candidate for the MLR model.

In sum, based on the simple linear regression model developed in the previous
section, this part of the thesis will focus on developing a multi-regression model that
incorporates the Energy of the Green’s function, heart rate, age, and BSA for the
prediction of %V02max. The independent and combined effects of heart rate, age, and
BSA will be investigated in terms of their contribution to the accuracy of predicting
%VO2max. Statistical properties of the developed models, such as the coefficient of

determination and prediction accuracy, will be presented.

1V.3.2.2 MLR Model Development

For single regression models, it is assumed that there is a linear relationship
between a response variable Y and a single explanatory variable X. With multiple
linear regression, more than one explanatory variable explains or predicts a single
response variable. The introduction of more explanatory variables may lead to a more
complicated situation, with many additional factors. As with single linear regression,
multiple-regression can be utilized for forecasting purposes.

In multiple regression, the response Y depends on X1, X2,..., Xk explanatory

variables, which will be denoted by Xk. The statistical model for multiple linear

regression is

76

”2-..?

 

 

Y,=,BO+,B,X“+,63X,.,+...,B,X,, (Eq 1V.S)
for i=1, 2, ...,.n The mean response Y is a linear function of the explanatory
variables:

Y 2,60 + ,8le + AA”, + “,6ka (Eq IV.6)
The deviation 8.- is assumed to be an independent and normally distributed random
variable with mean 0 and standard deviation (5. The coefficients of the model are [30,
[11, B2,..., 131-, and o. It implies that the mean response Y can be predicted from

estimates of the coefficients [3. To the extent that this model is accurate, it is a useful

tool for describing how Y varies with the Xk’s.

For the simple linear regression, the least square method is used to obtain
estimates of the intercept and slope of the regression model. The multiple linear
regression model uses a similar method but details are more complicated. Assume b0,
12., b2, bk denote the estimators of the coefficients BO, 131, B2, ..., 131,. The predicted
response for the ith observation is:

Y“, = b, +b,X, +b,X, +...b,x,, (Eq IV.7)
The ith residual or the difference between the observed and predicted response is
calculated by:
g,=11—19,=Y,—bO—h,x,,—b,X,,—...—h,,X,.p (EqIV.8)
For the least square method, the values of b’s are obtained by minimizing the sum

of the squares of the residuals, i.e., the coefficients [20, h), [22, bk by minimizing the

quantity: Z(Y1 “b0 ‘ban -b2X12 _"‘_ka17()2

77

 

 

The Minitab program performs these calculations based on the least square
method. In a similar fashion to simple linear regression, the parameter 02, which

measures the variation of the responses about the regression model, is estimated by an

average of the squared residuals as,

e.2 Y—f’. 2
52 = Z ’ =Z(’ ‘) (EqIV.9)
n—k—l n-k—l

where n—k—l is the degrees of freedom related with 52. The degrees of freedom

are equal to the sample size n minus the number of [3’s used to fit the model. When
k=l , the multiple regression model is reduced to the single regression one.

For simple linear regression, the coefficient of determination r2 is equal to the
ratio of SSM (model sum of squared errors) to SST (SST = SSE +SSM — where SSE is

the sum of squared errors) and is interpreted as the proportion of variation in Y

explained by X. A similar calculation is applicable for multiple regression models and

is calculated as follows:

2-172
r2=SSM=Z(’ _), (EqIV.10)
SST 207—1”)-

In the case of multiple regression. r2 is interpreted as the proportion of the
variation observed in the response Y that is explained by the dependent variables X 1,
X2, ..., Xp. Usually, r2 is multiplied by 100 and expressed as a percent. It is also

called multiple correlation coefficient and is the correlation between the observation Y,

A

and the predicted Y, .

In this research, a series of physiological data and subject characteristics were

collected for 100 experimental and 100 validation subjects during specified as well as

78

 

 

 

random exercise protocols. This data and the four factors discussed earlier (Energy of
the Green’s function, HR, Age, and BMI) were analyzed using multiple regression to

develop a number of multiple-regression models. The three best models are presented

next.

To enable easy comparisons between all of these models, the RWP model and the

three best MLR models are listed together. With the help of Minitab, the standard
deviation or VMSE and coefficient of correlation r2 for each equation has been

calculated and presented as well.

 

%voz..,,, = 0.224 + 0.160 Ln(E(;)
(s = 0.076 r2 = 64.46%) (RWP)
%V02m., = - 0.0891 + 0.0832 Ln(EG) + 0.633 RHR

(s = 0.0503065 r2 = 84.7%) (Model A)
%voz...., = - 0.0879 + 0.0831 Ln(E(;) + 0.633 RHR - 0.00005 Age

(3 = 0.0505543 r2: 84.7%) (Model B)
%voz.,,,, = - 0.232 + 0.0792 Ln(EG) + 0.662 RHR + 0.0699 BSA

(8 = 0.049086 r2: 85.5%) (Model C)

 

 

A detailed description of each model is explained separately in the following
sections. Independent variables (IVs) considered for possible inclusion in the multiple
regression models A, B, and C include the combination of factors of the Energy of the
Green’s function, age, body surface area (BSA), and heart rate.

The Pearson Product Moment correlation values (r) are computed between

observed and predicted %VO2max. In addition, paired t-test, MSE, and analysis of

79

“Tum-inure“?
‘ , Jamal."
. i- .11

 

variance are considered in the analysis. A comparison between the four models is

performed to evaluate the predictive ability of each model and the contribution of each

predictor. Based on the results, the final best fit MLR model that provides the most

accurate predictions of the relative workload is selected and verified on the 100

validation subjects.

Model A: Ln(EQLand Heart Rate (RHR)

Model A uses the E0 and heart rate to predict %V02 max. Because heart rate

responses to the same exercise or work vary individually, using it as a predictor
requires expressing it as a percentage of maximum heart rate, or as termed here, RHR,

Relative Heart Rate. RHR is calculated as RHR = HRan/HRmat. where Hng is the

average heart rate and HR,“ax is maximum heart rate which is calculated by using the

formula HRma, = (220-age). Minitab is used to construct the MLR equation,

determine its properties, and conduct the necessary statistical analysis. The model
takes the following form:
%VO2max = - 0.0891 + 0.0832 Ln(EG) + 0.633 RHR (HRavg/HRmax);
(Eq IV.11)

r2: 84.7%; SD: :0050;

Other results are tabulated in Table IV.6.

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[Regression Analysis: %VO2m,, versus Ln(EG), RHR

/oV02m;,x = - 0.0891 + 0.0832 Ln(E(;) + 0.633 RHR

S= 0.0503065 R-Sq = 84.7%

Predictor Coef SE Coef T P VIF
Constant -0.08914 0.02786 -3.2 0.002
Ln(Ec,) 0.08316 0.01022 8.14 0 1.7
RHR 0.6331 0.05475 11.56 0 1.7
Analysis of Variance

Source DF SS MS F P
Regression 2 1.42512 0.71256 281.56 0
Residual Error 102 0.25814 0.00253

Total 104 1.68325

 

 

 

sen—u --r——
,4

 

‘_

Table IV.6 Minitab regression output for model A

In model A, the response variable is the %V02max. The explanatory variables
are the Ln(Eg) and RHR. The first step in analyzing this model is to carefully
Means, standard deviation and minimum and

examine each of the variables.

maximum values appear in Table IV.7.

 

 

 

 

 

 

 

 

 

 

 

 

ariable Mean SE Mean StDev Minimum aximum Range
11ng 109.49 2.28 23.41 69.27 173.67 104.4
HRm,x 195.56 0.45 4.61 183 202 19
RHR 0.5599 0.0116 0.119 0.36 0.9 0.54
LN(EG) 0.5305 0.0622 0.6377 0.00018 2.7654 2.7652

 

 

 

Table IV.7 Descriptive statistics for the experimental subjects HR and Ln(Ec) by Minitab

The heart rate data shows that the average and standard deviation for the three
variables HRavg, HRmax, and RHR are 109.49 i23.4l (beat-min"), 195.56 3: 4.61
(beat - min"), and 0.5599 i 0.119, respectively. The minimum value for the Ln(EG)
variable appears to be rather extreme with a minimum value of 0.00018 and maximum
value of 2.7654, range =2.7652. The mean of Ln(E(-;)=0.5305:0.6377. The big

standard deviation value may be caused by the wide range of the Ln(EG) data. As

81

mentioned earlier, the Green’s function reflects the system’s response to a change until
it returns to equilibrium. It is inferred here that each subject’s response to the
treadmill exercise varied greatly.

The second step in the analysis is to assess the correlation between the dependent
and individual independent variables. This can be accomplished by applying the
Pearson Correlation Coefficient (r) to each independent variable, which would indicate
how much of the change in dependent variable can be explained by the change in the
independent one. Those independent variables with a high r2 should then be used for
multiple regression. The same correlation coefficient can be applied to multiple
independent variables to ascertain how much of the change in dependent variables can
be explained by changes in all the independent variables.

The correlations matrix using Minitab software appears in Table IV.8. The
output includes the p-value resulting from testing the null hypothesis that the
population correlation is 0 versus the two-sided alternative for each pair. Thus, the
correlation between %VO2max and RHR is 0.8643 with a p-value of 0, whereas the
correlation between %V02mam and Ln(E(-;) is 0.80351 with a p-value of 0 too. From
the output we can infer that both are statistically significant and the RHR and Ln(EG)

are useful predictors for the MLR model A.

 

 

 

 

 

Correlations: %V02max, RHR, Ln(EG)
P Value %V02max RHR Ln(Gj)
%V02max 1 0.8643 0.80351
0 0 0
HRavg/HRmax 0. 8643 1 0.65311
0 0 0
Ln(Gj) 0.80351 0.65311 1
0 b 0

 

 

 

 

 

 

Table IV.8 Minitab matrix of correlation between variables for model A

82

 

The relationship between the independent variables Ln(E(;) and RHR and the

dependent variable %VO2max is explored in the next sections.

A. Standard Deviation_

Table IV.6 indicates that the standard error of prediction for relative workload
using the model A is i 5%. Compared with the standard error of prediction of the
RWP equation, with a value of i 7.60%, the new MLR model A provides a significant

improvement in the prediction of %V02max. In addition, the estimated standard error
of prediction, orJMSE , for maximum oxygen uptake (V02max) for model A is i050

liter- min". Again, compared with the RWP model, this standard error of prediction

value is smaller, which indicates an improvement in accuracy of the prediction method

of model A.

B. Correlation Coefficient, t-value and_p-va1u_e

From Table IV.6, the coefficient of determination r2 is 0.847 (r=0.92). That is,
84.7% of the observed variation in the %V02max is explained by the linear regression
with Ln(EG) and RHR. In other words, model A is better than the RWP equation,
which had a coefficient of correlation F 0.80, in showing how closely %V02nm is
related to the variables. Hence, by adding the RHR as a predictor, the MLR model A
has improved the prediction ability of %VO2max from submaximal data.

For model A, the t-value for Ln(EG) and RHR are 8.14 and 11.56, respectively.

The p-value for both was equal to zero. Therefore, the null hypothesis: H0: 6. =
,6, = 0 can be rejected, indicating that the regression coefficients for LII(E(‘.) and RHR

achieves statistical significance. This result gives confidence that %V02max, Ln(E(,),

and RHR are indeed correlated.

83

C. Normality and independenrce of error terms

Similar to simple linear regression, the residuals should always be examined as
aids to determining whether the multiple regression model is appropriate. Because
there are several explanatory variables, several residual plots must be examined. It is
typical to plot the residuals versus the predicted value and also versus each of the
independent variables, and to look for outliers, influential observations, evidence of a
curved (rather than linear) relation and anything else unusual. Again, Minitab is used
to generate these plots.

Using the same analysis methods used with the RWP equation, Figure IV.7
illustrates the residual plot for MLR Model A. The plot indicates that most of the
residuals are scattered within a band of i2 standard deviations from zero. Hence,
there is not sufficient evidence of outliers or serial dependence in the observed residual

data. which means that the residuals ei can be considered normally distributed.

 

_.__ _ _—

Residual Plots for %V02max

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values
99.9 .-
994
u 90‘
i .. r
11 8 -
0'1 -4 -2 o 2 4 02 0'3 0'4 0'5 0'6
Standardized Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data
244 FT - .
r— 3 ’ . 1
31‘ 1 ~1 .1'1
E J g 04 4‘ ‘l ll.l 1‘ l‘ J J... . [1" i
g 12 I1 (11110 (Pt) 1 "1111 '11
a a -11 l 1 l
a -2.
0-2 -10 i a 1102030405060708090100
Standardized Residual Observation Order

 

 

 

Figure IV.7 Minitab outputs for residual plots for %V02m,

84

—!_74- ‘ twvsr.‘ -
a . M
' h

I.

From the preceding normality and residual analysis, it is inferred that the multiple
linear regression model using the Energy of the Green’s function and relative heart rate
(RHR) to predict the relative workload (%V02nm) is valid and the linear relation
between the predictors and the dependence variable exists. In other words, the

developed equation using linear regression is considered appropriate for the prediction.

D. Inferefles abop;_ ,6, and predictionL of %VO2Em

The confidence intervals and significance tests for each of the regression

coefficients ,31’5 are performed similar to how it is performed in simple linear

regression. The standard errors of the ,6 (’s have more complicated formulas, but all

are multiples of the overall model standard deviation. Again, the calculations are
performed using Minitab, which in this case allows performing these rather complex
calculations without an intimate knowledge of all of the computational details.
Basically, the same commands to construct confidence and prediction intervals for
simple linear regression are also used for multiple linear regression models. The only
difference is that a list of explanatory variables is specified rather than just a single
variable.

Table IV.9 shows a sample output from Minitab running output for model A for
three subjects. For example, for subject 2 the predicted mean %VO2max is 0.37049
with a standard error of 3:0.00555. The 95% confidence interval for this predicted
mean is (035947038150), i.e., it is estimated with 95% confidence that %V02max lies
between 35.95% and 38.15%. The 95% prediction interval of (0.27010, 0.47088) is

interpreted in a very similar manner to the confidence interval. The fitted line plot for

85

‘mymfi " Luci-1'11"! w
.. 4

the predicted relative workload using model A with the 95% prediction interval is

shown in Figure IV.8.

95% Cl 95% Pl
381 10 47088)

47 45

 

12 19 1 18480
Table IV.9 Sample of Minitab running output for 95%C1 and 95%P1

 

 

 

 

 

 

 

 

 

Fiuied Line Plot
%V02max (actual) = 0.02687 + 0.9619 °/d/02max (Model A)
0.8— — Regres‘on
— — 95% c1
95% P1
0.7-
5 0.0606727
R Sq 67.3%
a 0.6- RSQtadJ) 610%
x 0.5-
E
> 0.4-
a
0.3-
0.2-
1 1 l l I
0.3 0.4 0 5 0.6 0.7

°ldI02nnx (W A)

 

 

 

Figure IV.8. Minitab confidence Interval & prediction intervals plot for model A

E. Main Effects Plots for %V02max
The main effects plot chart of Ln(E(;) and RHR have been displayed in the 2-D

and 3-D surface in Figure IV.9. The plots provide visual evidence that using both
variables in Model A as predictors of %V02nm is better compared to the RWP model.
For example, the 2-D chart shown in Figure IV.9(a), indicates that both RHR and
Ln(EG) have a positive relation with %V02mz“, i.e., an increase in Ln(Eg) and RHR is

associated with an increase in %V02max. This trend is expected because of the nature

86

of the two variables. On the one hand, EU reflects the system’s response from
excitation back to the state of equilibrium, hence, a high value of EC, is expected to
reflect a high value of V02nm. On the other hand, high values of RHR will be
associated with high values of V021,“, and vice versa, because of the
increased/decreased demands that are placed on the cardio-vascular system. Figure
IV.9(b) is a 3-D plot showing again the positive relationship between the predictors and

response variable.

1 Main Effects Plot (data mans) for %V02max
131(9)) l'Ravg/i-RMax

 

 

 

 

 

 

l 311; n

 

 

 

 

IVIIIVTIIIIIIIIIII1111111111111llITIIIIIIII

 

(a)

 

Figure IV.9 Main effects plot of predictors for %V02max

 

lvlain effeds of predctnrs for %VOZnax

o/oVOZmaxé

0.6 s

0.4 ..

0
MM
02. . -3
l

"(9.1)
0?\Q'\ 0

n8

 

 

 

 

 

HRavg/HRmax

 

 

(b)

 

Figure IV.9 Main effects plot of predictors for %V02max

87

To sum it all, the regression model A has a standard error of prediction of i 5%
and i0.5 liter- min‘1 for %VOZmax and VOZmax, respectively. Compared to the RWP
equation, model A generates better results for the prediction of %V02max and V02max

from the two predictors Ln(EG) and RHR as derived and measured from sub-maximal

V02 and HR data.

Model B: Ln(Eg), RHR and Age_

As previously discussed, the age of an individual typically has an effect on
maximum oxygen uptake. The effect of this factor on the prediction of %V02max, and
subsequently VOan, is investigated using multiple regression in a manner similar to

how model A was developed and analyzed. The following model results:

%vom, = - 0.0879 + 0.0831 LN(gi)l + 0.633 RHR - 0.00005 Age (Eq 4.12)

Table IV. 1 0 shows the Minitab outputs for model B. As shown, r2 for this model
is 84.7% and the standard deviation, 0, is estimated at i 0.05%. Compared with the
previous running outputs of model A, the value of r2 has not considerably changed. In
other words, adding the age factor to the model resulted in almost no change to the
explanatory/prediction power of the model. The measurements of variation about the
fitted equation are also nearly identical between model B and model A. The p-value
for the individual regression coefficients indicate that Ln(Eo) and RHR are still
significant with p=O. However, the regression coefficient for age is 0.00005, which is
a very small figure, with no statistical significance for the prediction of %VOzmax

(p-value =0.96l ).

88

 

[Regression Analysis: %VOZmn versus Ln(Eg), RHR and Age
%VOZmax = - 0.0879 + 0.0831 Ln(EG) + 0.633 RHR - 0.00005 Age

 

 

 

 

 

 

 

 

 

 

S=0.050554 R-Sq = 84.7%

Predictor Kioef SE Coef T P VIF
Constant L0.08788 0.03805 ~23] 0.023

Ln(Eg) 0.08312 0.01029 8.08 0 1.8
RHR 0.63318 0.05505 11.5 0 1.7
Age —5.3OE-05 0.001077 ~0.05 0.961 1

 

Analysis of Variance

 

 

 

 

 

 

Source DP ss Ms F P
Regression 3 1.42512 0.47504 185.87 0
Residual Error 101 0.25813 0.00256

Total 104 1.68325

 

 

 

 

 

 

Table IV.10 Minitab Regression output of %V02max for Model B

The results of model B indicate that age does not contribute in any significant
way in the prediction of %V02max. However, V02max and heart rate will decrease with
age and some researchers have developed MLR models that incorporate age as a
variable. The insignificant effect of age on the prediction of %V02max is primarily an
artifact of the subject population used in this research. Recall that the subjects in this
research are recruited from the student and staff population at Michigan State
University. While the range of subjects participating in the study is between the ages
of 19 and 43, approximately 80% of the subjects were in the age group 28-32. Clearly,
inclusion of this important factor requires the involvement of more subjects over a
wider age group. Such an effort is outside both the research scope and available funds.
In sum, for the subject population included in this research, age doesn’t show a

significant effect on the prediction of %V02max,

89

Model C: Ln(EQLRHR and BSA

Body Surface Area (BSA) is combined with Ln(Eg) and RHR to form the
multiple regression model C. The following model is created:
%V02max = - 0.232 + 0.0792 Ln(EG) + 0.662 RHR + 0.0699 BSA (Eq 4.13)
Table IV.11 shows the Minitab outputs for model C. r2 for this model is 85.5% and

the standard deviation, 0‘, is estimated at i 0.049%. The estimated standard error of

prediction of model C is :4.9% and i0.5 liter-min‘l for %VOzmax and VOZmax,

respectively. By adding BSA to Model A, a change is observed in the regression
coefficients of the variables and the intercept. This phenomenon occurs generally in
multiple regression. Individual regression coefficients, their standard errors, and
significance tests are meaningful only when interpreted in the context of the other
explanatory variables in the model. By adding the BSA as a predictor, the MLR

model achieves a slight improvement over model A.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ilTegression Analysis: %VOZM,‘ versus Ln(EG), RHR and BSA
%VOZmax = - 0.232 + 0.0792 Ln(EG) + 0.662 RHR + 0.0699 BSA

8: 0.049087 R-Sq = 85.5%

Predictor Coef SE Coef T P VIF
Constant -0.232 0.0638 -3.64 0

LN(gj) 0.0792 0.0101 7.84 0 1.8
HRavg/HRMax 0.6617 0.0547 12.11 0 1.8
BSA 0.07 0.0282 2.48 0.015 1
Analysis of variance

Source F SS MS F 1’
Regression 3 1.4399 0.48 199.2 0
Residual Error 101 0.2434 0.0024

Total 104 1.6833

 

 

 

 

 

 

 

90

Table lV.11 Regression output for Model C

 

The correlations matrix, as calculated in Minitab, is shown in Table IV.12. The
matrix indicates that the individual regression coefficients for Ln(EG) and RHR are still
significant with p=0. The individual regression coefficient of BSA with its response
variable %VOZmax (p-value:0.l44>0.05) does not achieve statistical significance,

similar to what is found with the age factor.

 

 

 

 

 

 

 

 

Correlations:%V02max, RHR, Ln(EG, and BSA

P Value %V02max RHR Ln(Gj) BSA

%V02max 1 0.864 0.8041 0.017
0 0 0 0.862

HRavg/HRmax 0.8643 1 0.65311 -0.143
0 0 0 0.144

Ln(Gj) 0.80351 0.65311 1 0.025
0 0 0 0.798

BSA 0.017 , -0.143 0.025 1
0.862 0.144 0.798 0

 

 

 

 

 

Table IV.12 Minitab output of correlation between variables for model C

As discussed above, adding BSA as a predictor for %VOZmam was only expected
to have a slight increase in the accuracy of the model. This finding is in agreement
with that of Von Dobeln et al. (1967). The most likely explanation for this is that the
relationship between body surface area and %VOzmax is accounted for in both the V0;
and HR data. It is worth noting that the Body Mass Index (BMI), which is a more
common body dimension measurement, was considered but yielded an r2: 84.8%.
Hence, the BSA measurement was used instead.

IV.3.2.3 MLR Models Comparison

The main effects of Ln(Ea) and RHR, Age, BSA on the prediction of %VOzmax
are plotted as shown in Figure IV.10. Careful examination of the plots indicates that
BSA has a slight influence on the prediction of %V02max, with age having hardly any

impact.

91

Table IV.13 lists all the attempted regression models, with the resulting r2 and 5,
based on the variables Ln(E(.). RHR, Age. and BSA. The results show a significant
improvement of r2 and s when Ln(E(;) and RHR are incorporated in any of the models.
The precision is reduced when BSA is omitted. Age had no significant association
with %V02max. The results from Figure IV.9 and Table IV.13 indicate that the most

accurate prediction of %VOgnm is achieved when Ln(Eg), RHR, and BSA are used.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Main Effects Plot (data means) for %V02max
0.6
0.
E
0.2
§
3*
h
2 Age BSA "
N
g 0.6«
0.4.
‘ A'A'A'Hm‘ Rn¥ n AVA LA
0.2T v VFXVV U V V in
Figure IV.10 Main effects plot of predictors for %V02max
Variables Regression Model for %V02max r2 R S
Ln(EG) %VOan 0.224 r 0 160 Ln(E(;) 64.60% 0.8037 0.0761
Ln(EU), Age %VOgnm ; 0.217 + 0 I60 Ln(E(;)+ 0.00032 Age 64.60% 0.8037 0.0766
Ln(E(,~), BSA %VOgmu‘ : 0.229 + 0 I60 Ln(E(,)-0.0023BSA 64.6 "A. 08037 0.0765
RHR VnVOgmu. * -0.208 . 0.924 RHR 74.70% 0.8643 0.0643
RHR. Age “Nomi“ ,, - 0.192 + 0.924 RHR - 0.00065 Age 74.80% 0.8649 0.0645
RHR. BSA %VOgnm '~' - 0.414 + 0.946 RHR + 0.105 BSA 76.70% 0.8758 0.062

 

Ln(EG). RHR %vom. : -0.089l ~ 0.633 RHR +0.0832 Ln(EG) 84.70% 0.9203 .0503
Ln(EG),RHR. yovognm 7 . 0,0879 . 0.633 RHR + 0.0831 Ln(EG) -

 

 

 

84.7 % 0.9203 0.0506

 

Age 0.00005 Age

.RHR, . -. - _ z _ ,
Ln(EG) /oV02.mx 0 232 O 662 RHR + O 0792 Ln(EG) +85.50% 09247 0049]
BSA 0.0699 BSA

 

 

 

 

 

 

 

Table IV.13 Minitab MLR Model running output for different variables to prediction of %Vozmu

92

While model C appears to be the clear favorite in terms of prediction accuracy,
the model development assumes the independence of the model variables, namely,
Ln(E(-,), RHR, and BSA. If this assumption does not hold, i.e., the independent
variables are highly correlated themselves, then this will lead to high variance in the
estimation of the model Bi’s. This problem is known as “Multi-colinearity” of the
multiple regression model, which significantly compromises the forecasting power of
the developed model. In addition, extremely high correlations can terminate the
model development procedure altogether. For this reason, the independence of the
variables Ln(EG) ,RH R and BSA was investigated.

Multi-colinearity can be checked by finding the r2 between the independent
variables. As a rule-of-thumb, r-values higher than 0.5 between the two variables
being tested indicate that some level of dependence exists. Another measure of
multi-colinearity is known as the Variance Inflation Factor (VIF), which measures how
much the variance of an estimated regression coefficient increases if the predictors are
correlated. A VIF = 1 indicates no relation among predictors, a VIF > 1 indicates that
the predictors are correlated, and a VIF> 5 indicates that the regression coefficients are
poorly estimated.

The values of VIF for model C are listed in Table IV.l 1. As shown, the VIFs for
Ln(Eg), RHR and BSA are 1.8, 1.7 and 1, respectively. The results indicate that there
is no correlation between BSA and the other two independent variables. However, the
VlF values indicate that a correlation exists between Ln(Eg) and RHR. This means

that using both of these predictors in a multiple regression equation may undermine the

93

prediction accuracy of the resulting model. Therefore, the effect of this correlation on
the prediction accuracy of the model must be further investigated.

The basic idea is to enter Ln(E(;) and also the component of RHR that is unrelated
to Ln(EU) into the MLR regression model as predictors. The component of RHR that
is unrelated to Ln(EG) is derived by creating a multiple regression model, where RHR
is the dependent variable and LII(E(;) is the independent variable. From the running
output, the “unstandardized residuals” can be obtained. These residuals form the
component of RHR that is unrelated to Ln(EG). Consequently, these residuals are
used with Ln(Eg) to form the multiple regression model with RHR as the dependent

variable. The analysis results are listed in Table IV.14.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

egression Analysis: %VOZmam versus Ln(EG),Unstandardresidue
%V02mam = - 0.224405 + 0.1603 Ln(Eg) + 0.633 1 unstandardresidue
S: 0.0503063 R-Sq = 84.7%
Predictor Coef SE Coef T P VIF
Constant 0.224405 0.006399 35.07 0
LN(gj) 0.1603 0.007736 20.72 0 l
Unstandardresidue 0.6331 0.05475 11.56 0 1
Analysis of Variance
Source DF SS MS F P
Regression 2 1.42512 0.71256 281.56 0
Residual Error 102 0.25813 0.00253
Total 104 1.68325

 

 

 

 

 

 

 

 

Table IV.14 Minitab outputs for MLR using unstandardized residual and Ln(Ec)
The VIF values shown in Table IV.14 indicate that all the independent variables

for the multiple regression model using Ln(EG) and the “unstandardized residuals” are
not correlated. Comparing Table IV.16 results with those in Table IV.5 for model A, it

becomes evident that the r2 and s for the prediction of %VOZmax are almost the same.

94

Therefore, it can be concluded that the degree of correlation between Ln(EG) and RHR
does not undermine the prediction ability of model C. In other words, the
multicolinearity between Ln(EG) and RHR can be ignored.

In sum, the MLR prediction model C generated based on the variables of Ln(EG),
RHR and BSA is valid for the prediction of relative workload and maximum oxygen

uptake. The estimated standard error of prediction of model C is i4.9% and i0.5

liter- min"1 for %VOZmax and vow... respectively. The next step is to validate this
model against the results of 100 validation subjects who performed random exercise

protocols as described before in Chapter III.

IV Part ' R res i n Models Validation

Validation of the regression modelswas performed through the collection of new
oxygen uptake data for 100 validation subjects, including a limited number of
construction workers. The subjects were instructed to perform random exercise or
work at intensities ranging from light to heavy. Maximum oxygen uptake was
determined for each subject using the same Harbor protocol used for the development
subjects. The time series analysis techniques discussed in Chapter III and IV are used
to calculate the Energy of the Green’s function (EU). The RHR and BSA for each
validation subject were also determined. The final step is to use this data, i.e., EU,
RHR, age and BSA to predict the %VOgmax and V02max for each subject using the

regression model C '2.

 

'2 See Appendix B-Table B.5 for all the data.

95

For comparison purposes, the validation of RWP equation and multiple linear
regression models A and C is combined. For a limited number of subjects”, actual
and predicted values for %V02max and V02max have been tabulated in Table IV.15,.
Jones’s equation (referred to as J in the table) is also applied on the validation subjects

for reference to predict %V02max and VOZmax.

 

 

 

O/OVOZmax V02max

# (actual) RWP A C J (actual) RWPA C J

l 0.38 ' 0.33 0.36 0.35 0.44 3.22 3.73 3.42 3.53 2.8
2 0.3 0.41 0.4 0.38 0.29 3.06 2.2 2.29 2.37 3.14
3 0.43 0.4 0.35 0.34 0.38 2.52 2.75 3.1 3.2 2.9
4 0.35 0.4 0.38 0.4 0.38 4.52 3.92 4.15 3.91 4.07
8 0.5 0.35 0.41 0.39 0.36 2.09 2.99 2.56 2.66 2.86
10 0.4 0.39 0.36 0.39 0.53 4.96 5.11 5.54 5.14 3.79

11 0.56 0.49 0.53 0.55 0.58 3.35 3.89 3.54 3.42 3.23
12 0.57 0.42 0.49 0.48 0.45 2.27 3.14 2.67 2.7 2.9

13 0.38 0.51 0.48 0.47 0.36 2.75 2.07 2.19 2.23 2.92
14 0.42 0.53 0.46 0.45 0.39 2.86 2.26 2.63 2.67 3.09
15 0.26 0.35 0.34 0.35 0.37 5.04 3.77 3.81 3.75 3.58

Table IV.15 Sample for MSPR check and Jones’ equation comparison on validation subjects

 

 

 

 

 

AgMSPR Check

For the validation process, the prediction capability of a regression model is
measured by calculating the mean squared prediction error, denoted as MSPR, and
calculated as follows (Neter et al. 1990):

Z<Y _ Y,“ [)2

MSPR = "=' (Eq 4.14)

[1*

 

where Y, is the value of the response variable in the ith validation case, 1’. is the

I

predicted value for the ith validation case based on the original model, and n* is the

 

'3 See Appendix B-Table 8.6 for all the data.

96

number of cases in the validation data set. After MSPR is calculated, it is then
compared to the MSE value from the original regression model. If the two are close,
then MSE is not seriously biased and gives an appropriate indication of the predictive
capability of the selected regression model. If MSPR is much larger than MSE, the
MSPR should be used as an indicator of the prediction capability of the original model
and not its MSE (Neter et al.1990).

Using the data available for the validation subjects, the MSPR for %V02max and
V02max can be readily derived from Eq IV.14 for each regression model, i.e., the RWP
equation, and Model A and C. The MSE values for these models were given earlier in
this Chapter. Table IV.16 lists the MSE and MSRP values for relative workload

%V02max and V02max for available validation subjects’ data.

 

 

 

 

 

MOdCI , %V02max VOZmax
Equation

Type MSE MSRP MSE MSRP

RWP %V02ma.=0.224+0.160 Ln(EG) 0.58 0.69 0.43 0.44
%VOZma. = - 0.0891 + 0.0832

A Ln(E(;)+0.633 RHR 0.25 0.37 0.25 0.25
%Voznw. = - 0.232 + 0.0792

C Ln(Eo) + 0.662 RHR + 0.0699
BSA 0.24% 0.35% 0.28 0.22
V02...“ (L/min) = (0.046 x Ht

Jone’s (cm)) - (0.021 x age (yrs)) — (0.62
x Sex) ~ 4.31 where for sex, men
l=0,women=1 N/A 1.3% N/A 0.56

 

 

 

 

 

 

Table IV.16 MSE and MSRP for %VOZm“ and VOzma,‘ for validation subjects
The MSE and MSRP values listed in Table IV. 16 indicate that both of these errors

are close. For the %VOgmax figures, the difference is within the range of 0.1 and for
the absolute V02max value, the gap is around 0.01. It would, therefore, appear that the

MSE for each respective model is providing an appropriate indication of how well the

97

model can predict %V02max and VOZmax. It is also clear that Model C provides the
least MSE and MSRP values compared to the other models, which confirms the
expectation that Model C would outperform the other models in the prediction of
%V02max and VOZmax. While the the MSE value for Iones’s model for the original
model is not available, the MSRP for the validation subjects was calculated as 1.3% for
%V02max and 0.56 for V02max value, respectively. Compared to the values from the
RWP and MLR models, it is clear that the MLR model provides better prediction.
Figure IV.11 shows the individual value plot of %V02max for both the actual
values and predictions from Model C. From the displayed plots, it is visibly clear that

no significant difference exists between the predicted values and the actual

 

 

 

 

 

 

measurements.
Individual Value Plot of %V02max (actual), %V02max (Model C)
0.7
O O
a. ’0. ° . '
0.6+ o .‘ i. .
0.5- 1 "
3 C; C . }
3 a I § 0
°-4‘ «pan: ,I-c
as}. '4'-
0.34 o ' 5 5 ' ’
‘0
O
0.2- . ,
%V02max (actual) %V02max (Model C)

 

 

 

Figure IV.11 Individual value plot of %V02max for Model C (actual VS prediction)

B. p-valge Validation

To complete the analysis, it is imperative to determine the statistical significance

of the prediction produced by model C, i.e., whether the difference between the MSE

98

and the MSRP of Model C is statistically significant. The p-value for the application
at hand involves the use of the 2-sample t-test, with the null and alternative hypotheses
being the following:
0 H0: %V02max (MLR) ~ %VOgnm (Actual) = 0
. Ha: O/OVOZmax (MLR) 7‘ 0/0V02ma\ (ACtual) ¢ 0
Here, the %VOgmax (MLR) means the predicted %VOZmax value obtained from
Model C and %V02max_ (Actual) means the actual value measured for the validation
subjects. The null hypothesis means that there is no significant difference between
the predicted value and the actual value (note that HU is rejected when P-value S a).

Table IV.17 shows the paired t-test results from Minitab.

 

Two-sample T for %V02max (actual) vs %V02max (Model C)

 

 

 

N Mean StDev SE Mean
%V02max (actual) 132 0.491 0.106 0.0092
%V02max (MOdel C) 132 0.486 0.0897 0.0078

 

 

 

 

 

Difference = mu (%V02max (actual)) - mu (%V02max (Model C))

Estimate for difference: 0.004937

95% CI for difference: (-0.018821, 0.028694)

T-Test of difference = 0 (vs not =): T—Value = 0.41 P-Value = 0.683 DF = 255

 

 

 

Table [v.17 Paired T-test and P value for %VOzmam

The paired t-test results in a t-value and a p-value of 0.41 and 0.683, respectively.
Consequently, the null-hypothesis cannot be rejected (p-value >005), indicating that
there is no significant difference in the actual and predicted values of %V03max for the

validation subjects.

99

A similar t-test was perfomted for the V02max values. The test reveled a t-value of
—0.08, and a p-value of 0.938. Again, the p-value > 0.05, indicates that the null
hypothesis cannot be rejected. Hence, it can be concluded that there is no significant
difference in the prediction value and actual measurements of V02max for the validation

subjects.

 

Two-sample T for VOZmax (actual) vs VOZmax (Model C)

 

N Mean StDev SE Mean

 

VOZmax (actual) 132 3.547 0.875 0.076

 

VOZmax (Model C) 132 3.556 0.893 0.078

 

 

 

 

 

Difference : ’4 (VOZmax (actual)) " l1 (VOZmax (Model C))
Estimate for difference: -0.008423

95% CI for difference: (0.222630, 0.205784)
T—Test of difference = 0 (vs not =): T-Value = -0.08 P-Value = 0.938
DF = 261

 

 

 

Table IV.18 Paired T-test and P value for VON,“

The validation results indicate that the multiple regression model C produces
acceptable prediction values for both relative and maximum oxygen uptake values. It
also greatly improves the accuracy of the prediction results compared to the model

described by the RWP equation.

100

CHAPTER V
CONCLUSION AND FUTURE WORK

V.l Conclusion

This research introduced a methodology for predicting relative workload from
sub-maximal oxygen uptake data collected in-situ, using multiple linear regression
models and without the need to determine maximum oxygen uptake. In this research,
the method developed by Abdelhamid (1999) to predict relative workload from in-situ
collected sub-maximal oxygen uptake data was reconstructed for 100 experimental
subjects from Michigan State University. As in the original technique, a strong linear
relation was found between the Energy of the Green’s fiinction and relative workload
(%V02max). A relative workload prediction equation (RWP equation) was developed
based on the collected data. The standard error of prediction for %VOZmax and V02max
was estimated at ”57.6% and $0.65 liter - min", respectively.

In an effort to improve the accuracy of predictions using the RWP equation,
multiple linear regression modeling was considered. This led to the development of a
number of regression models, which incorporated the Energy of the Green’s function,
relative heart rate, body surface area, and age as explanatory variables. A statistical
comparison between the different MLR models indicated that the best prediction results
would be attained when the Energy of the Green’s function, relative heart rate, and
body surface area were used as predictors. Using multiple regression methods to

combine these predictors resulted in a model with a standard error of prediction for

%VO;max and VOzmalx equal to i4.9% and i053 liter- min], respectively.

101

All regression models have been validated using non-steady state oxygen uptake
and heart rate data measured for 100 validation subjects. No significant differences
between measured and predicted %V02max (or VOW, ) are found. The validation
results indicated that the multiple regression model developed in this research produced
acceptable prediction values for both relative and maximum oxygen uptake values and
greatly improves the accuracy of the prediction results compared to the single

regression model developed by Abdelhamid (1999).

V.2 Thesis Contribution

This thesis makes the following important contributions:

1. Validating the time series analysis technique developed by Abdelhamid (1999)
on a larger pool of subjects.

2. Improving the accuracy of the technique developed by Abdelhamid (1999)
through the development and validation of a multiple regression model that
includes heart rates and body dimensions.

3. Preserving the benefits of the single regression model advanced by
Abdelhamid (1999), such as subject safety and ease of application.

4. Developing a model that provides acceptable prediction values in comparison
with other quantitative prediction methods.

5. Providing a robust, efficient and reliable statistical methodology capable of
predicting relative workloads from submaximal oxygen uptake and heart rate

data collected in-situ.

102

V.2.l Contributions to Construction

Construction work is physically demanding work. The construction industry has
assumed that a high level of physical effort is an inherent part of doing the work. In
fact, the culture of the construction industry has evolved such that contractors rely
heavily on hand labor with small, relatively inexpensive, multipurpose tools.
Contractors seldom consider the physical demands of work or a worker’s physical
qualifications to perform a given task.

Understanding the physical demands of construction work is of great importance
in protecting the workforce’s safety, health. and productivity. It is key to solving the
problem of designing jobs that workers can safely perform. Improvements in
performance can be attained when the workload is matched to the abilities of the
individual worker, because this matching prevents the development of physical fatigue.

By using the methods developed and results advanced in this research and by
promoting and applying concepts of work physiology at the workplace, many
improvements will find their way to the occupational health and safety of the
construction workforce. The methods described in this research will be critical to the
success of many field studies focusing on:

1) Reliable evaluation of workloads to which workers are subjected, so that
engineering or administrative interventions may be more effectively
implemented by management to reduce workloads and injuries.

2) Expanding job opportunities for women, older workers, and workers who are

partially disabled, by placing them in jobs according to their capabilities.

l ()3

3) Evaluation of the effectiveness of rehabilitation programs for construction

workers who previously suffered overexertion injuries.

V.3 Limitations and Future Work

Maximum oxygen uptake values are difficult, if not dangerous, to measure, but
would lead to a better assessment of physical fatigue. Much research is needed to
arrive at simple and reliable ways to achieve such measurements. The multiple
regression model developed in this research proved promising in predicting relative
workload. However, the model has some limitations which are worth noting. Firstly,
the model was developed for a relatively homogeneous college-age group of
predominantly white males. The effects of a wider range of ages, different racial
backgrounds, and gender on the accuracy of the developed regression model need to be
investigated. Secondly, many factors such as general health conditions, smoking
habits, alcohol intake, and conditioning are explanatory variables that may increase the
accuracy of the prediction.

Thirdly, because real construction environments and tasks were quite difficult to
simulate in the lab, the results and findings of this study lose ecological (external)
validity. Hence, the higher or lower limits of the prediction intervals as estimated by
the model should not be respectively used to justify critical decisions regarding a
worker’s suitability for a particular work activity.

Additional development of the model presented in this research will be of great
importance in better understanding the physical demands on today’s workforce doing

today’s work. It will have widespread application in identifying excessively demanding

104

tasks so they can be better matched to the abilities of subjects. Future research efforts
should consider the following:
' Investigating the effects of gender, age, racial background, and overall health
condition (smoking, fitness, stress, etc) on the model's accuracy.
I Validating the model on subjects from construction trades while performing
various types of construction work.

' Investigating the use of other techniques/models to predict relative workload.

105

APPENDIX A
TIME SERIES ANALYSIS

A.l Introduction14

When a sequence of data is observed with respect to time and space, the collected
data is called a time series. In statistical theory, an observed time series is considered
as one possible realization of a stochastic process (Pandit and Wu 1993, Anderson
1971). An observed stochastic process or time series is called strictly stationary when
the probability distribution and all of its moments, i.e., mean, variance, etc., are
independent of the origin. However, when the first and second moments are only
assumed to be independent of the origin, the series is called wide sense stationary.
Series that do not satisfy the mentioned conditions are considered to be non-stationary
and are caused by trends or seasonalities in the data (Anderson 1971, Brockwell and
Davis 1996).

The basic idea of time series analysis is to find a regression model that can
represent an observation in time t, denoted as X., as the sum of two uncorrelated and
independent parts: one dependent on preceding observed data and the other an

independent sequence of unmeasured inputs (Pandit and Wu 1993).

A.2 Fitting and Finding Adequate ARMA(p,q) Models

Discrete or continuous Autoregressive Moving Average models, denoted as
ARMA(p,q) models, are the family of regression models that can be fitted to time

series data. The variables p and q describe the order of the ARM A(p,q) model to be

 

'4 Most content of this appendix is from Abdelhamid (1999).

106

used. The value of p represents how many preceding observations Xl depends on, and
the value of q represents how many preceding disturbances affect X..
A general discrete Autoregressive Moving Average model, ARMA(p,q), has a

linear stochastic difference equation of the form:

Xl-(ple-(pzxtq - ...-(prt-p = at-Glam ~923(-2 - 0an (A.1) Th6

left-hand side of A.l is the autoregressive part, and the right hand side is the moving
average part. The basic assumptions of the ARMA(p,q) model represented by (Al)
are as follows: 31 = NID (0,032).i.e. a. are normally and identically distributed random
variables, i.e., a1 is independent of app, a,-p_],. . .,and of X.-p-], X.-p-2. . ..

Given that ARMA(p,q) models are considered as conditional regression models,

the parameterstpl, (pzmtpp andOl, 02 ,,,,, Gq can be estimated using the methods of least

squares. Minimizing the nonlinear function S is performed in a stepwise fashion.
Initial values of the parameters obtained through rough algorithms are used to compute
at’s recursively and to obtain the value of S. The direction along which S will be
smaller is then found by methods of linearization and/or steepest descent. The new
values of parameters with this smaller S are then taken as initial values and the routine

continues until the minimum S is obtained (Pandit and Wu 1993).

A.3 Time Series Analysis
For each subject in this research, ARMA(p,q) models were fitted to oxygen

uptake data collected during sessions 1,2 and 3, and the random sessions using the time
series analysis packages ITSM 2000 version 7.0 (Brockwell and Davis 1996). Final

model parameters were obtained using maximum likelihood methods of estimation.

107

After the adequate model was chosen, values of the Green’s function were obtained.
From the Green’s function, the value of E0 was determined by sum the square of the

Green’s function.

A.4 Interpretation of the Green’s Function

When a system is affected by disturbances a., it is important to understand how
the system response or output at time t is affected by or depends on previous values of
these disturbances. The Green’s function summarizes the dependence or memory of an
observed value X on previous as In essence, the Green’s function characterizes how
long a disturbance that affected the system at time t will be “remembered” by the
system; or equivalently, how much time would the system require to “forget” the
disturbance that affected it at time t. The shorter the time, the better the system is in
coping with the disturbance and the more resistant it is to change. Therefore, by
plotting the Green’s function, an understanding of the “memory dynamics” or
resistance to change from equilibrium in the system will be more easily visualized and

quantified.

108

APPENDIX B

PHYSIOLOGICAL DATA FOR ALL SUBJECTS

The Green’s function GJ- and oxygen uptake data collected for subject 78 and 97

during the exercise session 3 discussed in Figure 111.1 and 1112 are shown in Table B.1.

The Energy of the Green’s function is to sum the square of all the Gj for each subject.

 

 

 

 

 

 

 

Subject 78 Subject 97 Subject 78 Subject 97
V02 (L/min) VOz (L/min) Gj"2 Gj"2

0.16 0.1 5 1 .000000 1.000000
0.57 0.24 0.232247 0.929412
0.88 0.44 0.382493 0.863 803
1.07 0.46' 0.488573 0.802816
1.27 0.61 0.533104 0.746133
1.3 0.73 0.518083 0.693473
1.59 1.04 0.457341 0.644520
1.88 1.31 0.369688 0.599014
1.7 1.16 0.273560 0.556725
1.75 1.23 0.183724 0.517421
1.77 1.28 0.109700 0.480901
1.98 1.44 0.055734 0.446946
1.53 1.52 0.021744 0.415393
1.75 1.38 0.004683 0.386076
1.69 1.42 0.000001 0.358813
1.16 1.44 0.002878 0.333483
2 1.4 0.009092 0.309948
1.73 1.38 0.015500 0.288068
1.81 1.4 0.020181 0.267734
1.6 1.38 0.022308 0.248831
1.85 1.39 0.021901 0.231265
1.8 1.5 0.019505 0.214934
1.53 1.35 0.015901 0.199764
1.55 1.22 0.011870 0.185658

 

Table 8.] Subject 78 and 97 raw data on V0; and G,

109

 

 

Subject 97

 

 

 

 

 

Subject 78 Subject 97 Subject 78
V02 (L/min) V02 (L/min) Gj"2 Gj"2

1.66 1.31 0.008053 0.172557
1.78 1.5 0.004871 0.160376

1.6 1.49 0.002522 0.149050
1.65 1.45 0.001018 0.138533

1.6 1.37 0.000240 0.128752

1.8 1.48 0.000002 0.119661
1.69 1.56 0.000100 0.111216
1.69 1.56 0.000354 0.103362
1.87 1.43 0.000627 0.096069
1.63 1.41 0.000832 0.089281
1.59 1.31 0.000933 0.082979

1.5 1.52 0.000925 0.077123
1.59 1.46 0.000831 0.071679
1.74 1.52 0.000683 0.066621
1.78 1.45 0.000515 0.061916
1.73 1.39 0.000353 0.057547
1.51 1.46 0.000216 0.053481
1.48 1.46 0.000114 0.049707
1.75 1.45 0.000047 0.046199
1.64 1.4 0.000012 0.042936
1.71 1.51 0.000000 0.039904
1.58 1.49 0.000003 0.037087

1.5 1.51 0.000014 0.034470
1.57 1.53 0.000025 0.032037
1 .66 1.62 0.000034 0.029774

1.7 1.49 0.000039 0.027672‘
1.51 1.51 0.000023 0.025719
1.68 1.2 0.000026 0.023904
1.57 1.4 0.000015 0.022216
1.82 1.62 0.000017 0.020647
1.62 1.51 0.000010 0.019191
1.59 1.53 0.000011 0.017836
1.61 1.47 0.000006 0.016577
1.73 1.52 0.000007 0.015406
1.48 1.42 0.000004 0.014319
1.64 1.58 0.000005 0.013308
1.56 1.5 0.000003 0.012368

 

 

 

 

Table 3.] Subject 78 and 97 raw data on V0; and G,- (continued)

110

 

 

 

 

 

 

 

 

 

 

 

 

 

Subject 78 Subject 97 Subject 78 Subject 97
V02 (L/min) V02 (L/min) Gj"2 Gj"2

1.66 1.39 0.000003 0.011496

1.61 1.55 0.000002 0.010683

1.8 1.65 0.000002 0.009930

1.64 1.54 0.000001 0.009229

1.44 1.55 0.000001 0.008577

1.57 1.49 0.000001 0.007971

1.68 1.46 0.000001 0.007410

1.64 1.49 0.000001 0.006886

1.4 1.5 0.000001 0.006400

1.71 1.53 0.005947

1.6 1.6 0.005528

1.83 1.52 0.005138

1.73 1.46 0.004775

1.69 1.47 0004438

1.55 1.54 0.004124

1.7 1.41 0.003834

1.5 1.36 0.003563

1.67 1.37 0.003311

1.6 1.69 0.003078

1.24 1.66 0.002860

1.38 1.61 0.002658

1.69 1.62 0.002471

1.64 1 .49 0.002296

1.72 1.46 0.002134

1.51 1.31 0.001984

1.85 1.42 0.001844

1.47 1.55 0.001713

1.51 1.57 0.001593

1.57 1.45 0.001480

1.64 1.45 0.001376

1.62 1.33 0.001279
VOzavg 1.5758696 1.404915
VOzmax 4.46 2.18
%V02max 0.353334 0.644457

F5 4.79 14.16

 

Table 3.] Subject 78 and 97 raw data on V0; and G, (continued)

111

 

actual oxygen uptake data collected in Session 2, 3 for the 100 experimental subjects

The physiological data including height, weight, BSA, age, heart rate, and

discussed in Chapter IV Table IV.1 are shown in Table B215

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Section 2 Section 3
%
I-[R V02 HR V02 V02 HR V02 %V02

Sub H W BSA Age max max avg avg max lan avg max
5 68 129 1.7 20 200 2.56 110.96 0.55 0.21 N/A N/A N/A
6 63 135 1.64 19 201 2.35 88.47 0.58 0.25 N/A N/A N/A
7 68.5 137 1.75 20 200 2.8 88.26 0.67 0.24 133.8 1.33 0.47
9 66.5 162 1.84 18 202 2.84 101.26 0.65 0.23 N/A N/A N/A
10 65.5 146 1.74 24 196 4.24 81.83 0.72 0.17 110.63 1.49 0.35
12 61.5 105.6 1.45 21 199 2.36 N/A N/A N/A 159.1 0.89 0.38
13 65 126 1.63 20 200 2.91 N/A N/A N/A 139.6 1.29 0.44
14 68 147 1.79 32 188 3.19 83.04 0.65 0.2 N/A N/A N/A
15 70.5 150.7 1.86 29 191 3.61 83.45 0.71 0.2 137.77 1.42 0.39
16 67 160 1.84 28 192 3.31 101.29 0.7 0.21 N/A N/A N/A
18 71.25 176.66 2.01 18 202 321 98.21 0.85 0.26 138.26 1.92 0.6

22 70.5 181.06 2.01 20 200 2.63 99.01 0.57 0.22 N/A N/A N/A
23 74 212 2.23 18 202 4.87 99.99 0.99 0.2 114.05 2.08 0.43
26 69 131 1.73 l 199 3.05 97.71 0.58 0.19 146.45 1.32 0.43
27 67.25 160 1.84 37 183 2.74 101.35 0.77 0.28 N/A N/A N/A
28 62.5 123 1.56 22 198 2.4 92.62 0.52 0.22 N/A N/A N/A
30 65.5 154 1.78 20 200 3.31 92.6 0.74 0.22 N/A N/A N/A
31 67.25 125 1.66 23 197 2.61 95.98 0.61 0.23 141.78 1.32 0.51
33 68 175 1.93 25 195 3.51 109.61 0.74 0.21 N/A N/A N/A
36 67 126 1.66 21 199 2.22 N/A N/A N/A 152.22 1.29 0.58
38 71.25 176.5 2 90 200 4.73 76.47 0.85 0.18 110.27 1.67 0.35
39 67 142.78 1.75 24 196 2.32 101.9 0.48 0.21 N/A N/A N/A
40 64.5 121 1.59 19 201 2.89 92.65 0.53 0.18 N/A N/A N/A
41 67.5 133 1.71 20 200 2.95 87.79 0.64 0.22 N/A N/A N/A
42 70 147 1.83 21 199 1.98 95.04 0.28 0.14 N/A lN/A N/A

 

 

Table 3.2 Physiological data for 100 experimental subjects

 

'5 The table does not include subjects’ with missing data due to experimental errors or machine

malfunctions.

112

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Section 2 Section 3

% %
HR V02 HR V02 V02 HR V02 V02
Sub H NV BSA Age max max avg avg max avg avg max
44 71.75 160 1.93 20 200 4.6 94.25 .83 0.18 128.65 1.68 0.37
45 67 163 1.85 32 188 4.1 80.18 0.71 0.17 N/A N/A N/A
46 62.5 141 1.66 20 200 2.22 99.34 0.53 0.24 N/A N/A N/A
48 63 126 1.59 19 201 2.16 108.32 0.62 0.29 N/A N/A N/A
H9 76.75 214 2.3 22 198 4.07 N/A N/A N/A 121.5 1.99 0.49
50 68.5 187 2 23 197 4.11 92.59 11.91 0.22 131.78 1.77 0.43
51 72.5 157.7 1.94 20 200 5.06 93.5 0.63 0.12 125.36 1.41 0.28
52 69.5 150 1.84 25 195 3.86 N/A N/A N/A 108.93 1.3 0.34
53 68 167 1.89 21 199 2.42 118.11 0.71 0.29 157.85 1.59 0.66
54 69.25 176 1.96 21 199 2.78 108.4 0.8 0.29 148.47 1.65 0.59
56 76 231 2.36 28 192 4.67 90.7 0.96 0.21 N/A N/A N/A
57 65 133 1.66 21 199 2.78 98.78 0.55 0.2 N/A N/A N/A
58 69 163 1.89 19 201 3.75 98.71 0.81 0.22 N/A N/A N/A
60 74 192 2.14 30 190 4.74 69.27 0.7 0.15 95.14 1.69 0.36
62 69 203 2.08 27 193 4 79.86 0.86 0.21 N/A N/A N/A
63 66 145 1.74 28 192 3.21 92.36 0.68 0.21 125.54 1.39 0.43
66 69.25 176 1.96 21 199 4.27 108.4 0.85 0.2 N/A N/A N/A
67 57.5 140 1.56 2 198 2.9 98.45 0.69 0.24 N/A N/A N/A

69 66 172 1.88 20 200 3.31 113.01 0.9 0.27 147.48 1.65 0.5
70 68.5 147 1.8 21 199 4.15 89.2 0.71 0.17 121.07 1.52 0.37
72 63 140 1.66 28 192 2.61 108.88 0.6 0.23 173.67 1.45 0.56
73 66.5 165 1.85 27 193 3.33 99.96 0.73 0.22 132.55 1.62 0.49
74 68.25 198 2.04 25 195 3.92 81.74 1.01 0.26 124.91 1.93 0.49
76 73 161 1.96 24 196 3.49 138.86 1.6 0.46 140.89 1.59 0.46
77 64.5 118 1.57 26 194 3.07 78.69 0.6 0.2 110.44 1.21 0.39
78 73.5 176 2.05 27 193 4.46 78.91 0.82 0.18 95.61 1.59 0.36
79 62.5 127 1.59 28 192 2.65 97.26 0.68 0.26 142.01 1.29 0.49
80 64 155 1.76 34 186 2.99 95.24 0.65 0.22 152.71 1.46 0.49
81 72.5 168 1.99 34 186 3.98 74.97 0.88 0.22 101.69 1.51 0.38
82 64 141 1.69 27 193 2.67 99.07 0.7 0.26 127.95 1.19 0.44
83 67 135 1.71 25 195 2.47 88.06 0.56 0.23 137.42 1.35 0.55
84 73.5 199 2.16 26 194 3.86 90.58 0.79 0.2 124.37 1.71 0.44
85 65 139 1.69 34 186 3 85.6 0.61 0.2 N/A N/A N/A
88 69 134 1.74 24 196 3.37 101.91 0.61 0.18 140.83 1.4 0.42

 

 

Table 3.2 Physiological data for 100 experimental subjects (Continued)

113

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Section 2 Section 3
% %
HR V02 HR V02 V02 HR V02 V02
Sub H W BSA Age max max Iavg vag max tavg vag max
89 69.5 142 1.8 25 195 3.81 99.27 0.75 0.2 93.55 1.44 0.38
90 66 149 1.76 24 196 2.71 103.13 0.75 0.28 N/A N/A N/A
91 72 167 1.97 22 198 4.36 90.33 0.77 0.18 121.98 1.57 0.36
93 70.5 163 1.92 24 196 3.42 106.14 0.77 0.22 155.36 1.43 0.4
94 64.5 137 1.67 24 196 4.02 l81.96 0.64 0.16 142.89 1.72 0.5
95 69 150 1.83 27 193 2.86 110.37 0.7 0.24 162.43 1.46 0.51
96 66.5 158 1.82 25 195 3.4 l81.51 0.9 0.27 N/A N/A N/A
97 69 150 1.83 37 183 2.18 101.33 0.6 0.27 N/A N/A N/A
98 67.5 162 1.86 37 183 3.36 8.03 0.75 0.22 N/A N/A N/A
100 68.5 171 1.92 25 195 3.9 E536 0.99 0.25 128.96 1.84 0.47

 

 

Table 3.2 Physiological data for 100 experimental subjects (Continued)

114

 

 

The physiological data including height, weight, BSA, age, heart rate, and
actual oxygen uptake data for the 100 validation subjects discussed in Chapter IV Table

IV.1 are shown in Table B.3”.

 

Random exercise
test VOzmax test
% %
HR V02 HR V02 V02 HR V02 V02
SubH W BSA Age max max Iavg avg max avg avg max
1 65 1341.67 23 197 3.22 122.9 1.24 0.38 N/A N/A N/A
2 67.75 1241.66 22 198 3.06 121.25 0.91 0.3 143.371.62 0.53
3 68.5 1321.72 38 182 2.52 100.711.09 0.43 N/A N/A N/A
4 75.5 1942.18 21 199 4.52 117.961.57 0.35 149.94 2.6 0.57
5
8

 

 

71.5 155 1.9 24 196 3.52 N/A N/A N/A 136.37 1.72 0.49
65.5 116 1.58 23 197 2.09 134.281.04 0.5 152.58 1.27 0.61
10 74 200 2.26 26 194 4.96 111.26 1.99 0.4 143.52 2.8 0.56
11 70.5 195 2.08 33 187 3.35 143.971.89 0.56 140.29 1.94 0.58
12 65.5 140 1.71 21 199 2.27 150.4213 0.57 145.6 1.45 0.64
13 68 139 1.75 34 186 2.75 123.571.05 0.38 N/A N/A N/A
14 66.75 155 1.81 19 201 2.86 122.1 1.2 0.42 127.66 1.64 0.57
15 71.5 161 1.93 22 198 5.04 115.22 1.31 0.26 151.86 2.58 0.51
16 64 125 1.6 23 197 3.11 140.141.07 0.34 166.35 1.67 0.54
17 73 188 2.1 23 197 4.23 118.15 1.69 0.4 158.39 2.52 0.6
18 70 145 1.82 25 195 3 134.131.28 0.43 156.43 1.73 0.58
23 67 185 1.96 24 196 4.05 147.471.79 0.44 155.63 2.32 0.57
24 63 140 1.66 27 193 2.27 159.661.06 0.47 N/A N/A N/A
25 68 142 1.77 21 199 4.07 N/A N/A N/A 166.71 2.21 0.54
26 67 166 1.87 22 198 3.05 156.491.55 0.51 153.35 1.75 0.57
28 70 152 1.86 22 198 4.24 110.24 1.2 0.28 143.28 2.15 0.51
29 80.5 209 2.35 21 199 4.64 119.81 1.64 0.35 144.85 2.58 0.56
30 73 182 2.07 26 194 4.01 112.97 1.46 0.37 147.83 2.35 0.59
31 68 160 1.86 22 198 4.32 N/A N/A N/A 139.47 2.31 0.54
33 68.5 152 1.83 27 193 239 136.471.08 0.45 139.7 1.45 0.61
34 69.5 174 1.96 21 199 5.05 107.661.55 0.31 141.51 2.78 0.55
35 66.5 150 1.78 30 190 3.01 121.3 1.36 0.45 147.86 1.93 0.64
Table B.3 Physiological data for 100 validation subjects

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'6 Same as notes 14.

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Random exercise

test V02"...x test

% %
HR V02 HR V02 V02 HR V02 V02
Sub H W BSA Age max max avg avg max Iavg avg max

36 64 112 1.53 31 189 2.54 127.82 0.84 0.33 137.9 1.27 0.5
39 73 204 2.17 24 196 4.16 114.9 1.47 0.35 137.812.29 0.55
40 72 175 2.01 23 197 3.78 109.75 1.42 0.38 131.03 2.02 0.54
41 65.5 152 1.77 20 200 3.75 121.24 1.24 0.33 143.27 2.11 0.56
42 72.5 222 2.24 26 194 3.23 128.31 1.65 0.51 135.44 2.04 0.63
44 76 204 1.58 22 198 2.78 121.91 0.97 0.35 141 1.43 0.52
45 63 125 2.05 28 192 4.23 125.18 1.4 0.33 N/A N/A N/A
46 61 111 1.47 23 197 1.69 151.22 0.93 0.55 154.65 1.11 0.66
47 64 126 1.61 35 185 2.75 111.09 1.06 0.38 N/A N/A N/A
48 62 146 1.67 21 199 2.95 130.05 1.34 0.45 134.36 1.66 0.56
49 68 157 1.48 31 189 3.98 126.461.16 0.29 147.6 2.1 0.53
50 68 149 1.8 21 199 5.93 N/A N/A N/A 140.95 2.67 0.45
51 71.5 155 1.9 24 196 3.76 124.17 1.43 0.38 146.06 2.21 0.59
52 69 179 1.97 36 184 4.95 100.94 1.55 0.31 141.12 2.78 0.56
53 72 173 2 27 193 4.24 109.4 1.49 0.35 140.24 2.41 0.57

54 72 170 1.99 22 198 4.12 132.79 1.55 0.38 158.55 2.47 0.6
55 64 148 1.72 20 200 1.74 N/A N/A N/A 161.72 1.17 0.67
56 63 130 1.63 23 197 2.71 122.39 1.02 0.38 144.14 1.55 0.57
57 72 182 2.05 23 197 4.31 N/A N/A N/A 167.71 2.47 0.57
58 71.5 183 2.04 27 193 3.92 133.37 1.54 0.39 161.87 2.38 0.61
59 66.5 136 1.71 29 191 2.77 127.2 0.98 0.35 146.49 1.69 0.61

60 67 180 1.93 37 183 3.23 122.67 1.52 0.47 151.54 1.93 0.6
62 76 239 2.39 34 186 4.68 124.99 1.99 0.43 154.77 2.87 0.61
64 67.5 154 1.91 43 177 2.38 142.22 1.56 0.66 N/A N/A N/A
65 66 180 1.75 39 181 2.64 117.96 1.26 0.48 128.83 1.62 0.61

66 70 173 1.96 25 195 3.64 138.461.94 0.53 165.6 2.19 0.6
67 71 192.5 2.07 28 192 2.9 151.9 1.64 0.57 164.2 1.87 0.64
68 67.5 166 1.88 32 188 3.42 127.67 1.4 0.41 140.99 1.95 0.57
69 70.25 151 1.86 25 195 3.55 121.7 1.05 0.3 145.8 1.91 0.54
70 69 200 2.07 28 192 3.85 120.05 1.81 0.47 N/A N/A N/A
71 60.5 133 1.58 35 185 1.52 159.84 0.94 0.62 156.25 0.92 0.61
72 66 156 1.8 23 197 3.42 129.05 1.31 0.38 145.96 1.87 0.55
74 71 177 2 21 199 3.83 109.13 1.39 0.36 128.91 2.08 0.54
76 70 166 1.93 24 196 4.19 N/A N/A N/A 127.84 2.38 0.57

 

 

Table B.3 Physiological data for 100 validation subjects (Continued)

116

 

 

Random exercise
test V02max test

 

% %
HR V02 HR V02 V02 HR V02 V02
Sub H W BSA Age max max iavg avg max lan avg max

 

77 72 216 2.2 21 199 4.21 103.612.03 0.48 N/A N/A N/A
78 155.5 1451.74 19 201 2.72 138.351.26 0.46 153.061.55 0.57
82 77 205 2.26 31 189 4.25 124.3415 0.35 N/A N/A N/A
83 67 1491.78 24 196 2.73 137.881.27 0.46 150.661.66 0.61
5 695166192 22 198 3.98 111.1316 0.4 141.78 2.3 0.58
6 70.5 202 2.11 28 192 4.37 107.091.73 0.4 141.73 2.69 0.62
8 71 1842.04 29 191 2.58 N/A N/A N/A 129.181.72 0.67
89 68 1821.96 34 186 3.31 134.921.31 0.4 144.881.93 0.58
90 71 1912.07 26 194 5.11 109.881.39 0.27 146.95 2.87 0.56
91 73.5194 2.13 22 198 4.49 104.691.78 0.4 133.54 2.52 0.56
94 73 1912.11 21 199 4.18 124.781.37 0.33 149.65 2.28 0.55
95 63 1541.73 30 190 3.33 N/A N/A N/A 168.581.69 0.51
96 66 1341.69 24 196 2.89 N/A N/A N/A 163.891.61 0.56
97 70.51541.88 27 193 3.97 N/A 151/A N/A 172.35 2.12 0.53
98 65 1711.85 29 191 3.55 143.531.57 p.44 157.412 0.56
100 69 1671.91 0 200 3.93 111.911.32 0.34 146.44 2.15 0.55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B.3 Physiological data for 100 validation subjects (Continued)

117

Table 3.4 lists the data used to depict Figure IV.1 between EG and %V02max,
and to generate the RWP and Model A and C based on the predictors of E5, RHR and
BSA from the experimental subjects, and the predicted %VO;mam and V02max values

based on these models. Table 3.4 (a) refers to section 2 exercise and (b) to section 3.

 

/..V02 %V02 l%vo2 %voz vo2 vo2 v02
RH max max max max max max max
Sub [E(G) Ln(EG)BSA R (actual) (RWP) (A) (C) (RWP) (A) (C)
1.06 0.06 1.7 0.55 0.21 0.23 0.26 0.26 2.35 2.08 2.15
1.12 0.11 1.64 0.44 0.25 0.24 0.20 0.18 2.38 2.90 3.16
7 1.00 0.00 1.75 0.44 0.24 0.22 0.19 0.18 3.00 3.56 3.71
1.11 0.10 1.84 0.5 0.23 0.24 0.24 0.24 2.71 2.76 2.76
10 1.09 0.09 1.74 0.42 0.17 0.24 0.18 0.17 3.01 3.90 4.11
14 1.23 0.21 1.79 0.44 0.20 0.26 0.21 0.20 2.53 3.15 3.24
15 1.13 0.12 1.86 0.44 0.20 0.24 0.20 0.20 2.93 3.57 3.58
16 1.37 0.31 1.84 0.53 0.21 0.27 0.27 0.27 2.56 2.57 2.58
18 1.07 0.07 2.01 0.49 0.26 0.24 0.23 0.24 3.60 3.73 3.55
22 1.02 0.02 2.01 0.5 0.22 0.23 0.23 0.24 2.51 2.49 2.37
23 1.13 0.13 2.23 0.5 0.20 0.24 0.24 0.26 4.07 4.18 3.76
26 1.10 0.09 1.73 0.49 0.19 0.24 0.23 0.22 2.45 2.56 2.65
27 1.00 0.00 1.84 0.55 0.28 0.22 0.26 0.26 3.45 2.98 2.97
28 1.57 0.45 1.56 0.47 0.22 0.30 0.25 0.22 1.77 2.13 2.33
30 1.28 0.25 1.78 0.46 0.22 0.26 0.22 0.22 2.80 3.31 3.40
31 1.00 0.00 1.66 0.49 0.23 0.22 0.22 0.21 2.73 2.76 2.93
33 1.12 0.12 1.93 0.56 0.21 0.24 0.27 0.28 3.05 2.69 .62
38 1.22 0.20 2 0.38 0.18 0.26 0.17 0.18 3.33 5.07 4.87
39 1.01 0.01 1.75 0.52 0.21 0.23 0.24 0.24 2.14 2.01 2.05
40 1.18 0.17 1.59 0.46 0.18 0.25 0.22 0.20 2.11 2.44 2.68
41 1.30 0.26 1.71 0.44 0.22 0.27 0.21 0.20 2.39 3.01 3.19
42 1.11 0.11 1.83 0.48 0.14 0.24 0.22 0.22 1.14 1.23 1.24
44 1.74 0.55 1.93 0.47 0.18 0.31 0.25 0.26 2.67 3.28 3.23
45 1.37 0.31 1.85 0.43 0.17 0.27 0.21 0.21 2.58 3.38 3.42
46 1.69 0.53 1.66 0.5 0.24 0.31 0.27 0.26 1.71 1.94 2.05
48 1.40 0.34 1.59 0.54 0.29 0.28 0.28 0.26 2.23 2.20 2.35
50 2.96 1.08 2 0.47 0.22 0.40 0.30 0.30 2.28 3.04 2.98
51 1.04 0.04 1.94 0.47 0.12 0.23 0.21 0.22 2.75 2.99 2.90
53 1.18 0.17 1.89 0.59 0.29 0.25 0.30 0.30 2.83 2.38 2.34
Table 3.4 (a) Actual/predicted values for %VOZm“ & VOZmax for experimental subjects

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

%voz I0/..vo2 10/..V02 1%V02 vo2 vo2 vo2

max max max max max max max
Sub 113(0) Ln(EG) BSA RHR (actual) (RWP) (A) (C) (RWP) (A) (C)
54 1.14 0.14 1.96 0.54 0.29 0.25 0.26 0.27 3.25 3.02 2.92
56 1.09 0.08 2.36 0.47 0.21 0.24 0.22 0.25 4.05 4.47 3.84
57 1.14 0.13 1.66 0.5 0.20 0.25 0.24 0.23 2.25 2.31 2.44
58 1.26 0.23 1.89 0.49 0.22 0.26 0.24 0.24 3.13 13.39 3.36
60 1.17 0.16 2.14 0.36 0.15 0.25 0.15 0.17 2.79 4.58 4.13
62 1.25 0.22 2.08 0.41 0.21 0.26 0.19 0.20 3.30 4.53 4.23
63 1.04 0.04 1.74 0.48 0.21 0.23 0.22 0.21 2.96 3.13 3.24
66 1.63 0.49 1.96 0.54 0.20 0.30 0.29 0.30 2.81 2.89 2.82
67 1.07 0.07 1.56 0.5 0.24 0.24 0.23 0.21 2.93 2.96 8.23
159 1.13 0.12 1.88 0.57 0.27 0.24 0.28 0.29 3.69 3.19 3.14
70 1.01 0.01 1.8 0.45 0.17 0.23 0.20 0.19 3.13 3.60 3.67
72 1.27 0.24 1.66 0.57 0.23 0.26 0.29 0.28 2.30 2.06 2.15
73 1.54 0.43 1.85 0.52 0.22 0.29 0.28 0.28 2.50 2.65 2.65
74 1.03 0.03 2.04 0.42 0.26 0.23 0.18 0.19 4.43 5.65 5.30
76 1.89 0.63 1.96 0.71 0.46 0.33 0.41 0.43 4.90 3.86 3.75
77 1.11 0.11 1.57 0.41 0.20 0.24 0.18 0.16 2.50 3.36 3.82
78 1.12 0.11 2.05 0.41 0.18 0.24 0.18 0.19 3.40 4.57 4.29
79 1.17 0.16 1.59 0.51 0.26 0.25 0.25 0.23 2.73 2.76 .97
80 1.01 0.01 1.76 0.51 0.22 0.23 0.23 0.23 2.85 2.75 2.81
81 1.07 0.07 1.99 0.4 0.22 0.23 0.17 0.18 3.76 5.21 4.98
82 1.01 0.01 1.69 0.51 0.26 0.22 0.23 0.22 3.10 2.98 3.11
83 1.18 0.16 1.71 0.45 0.23 0.25 0.21 0.20 2.25 2.68 2.83
84 1.21 0.19 2.16 0.47 0.20 0.25 0.22 0.25 3.08 3.50 3.20
85 1.11 0.11 1.69 0.46 0.20 0.24 0.21 0.20 .53 2.89 3.06
88 1.42 0.35 1.74 0.52 0.18 0.28 0.27 0.26 2.18 2.26 2.33
89 1.21 0.19 1.8 0.51 0.20 0.25 0.25 0.25 2.94 3.00 3.03
90 1.38 0.32 1.76 0.53 0.28 0.28 0.27 0.27 2.73 2.75 2.81
91 1.19 0.17 1.97 0.46 0.18 0.25 0.22 0.22 3.04 3.54 3.42
93 1.01 0.01 1.92 0.54 0.22 0.23 0.25 0.26 3.40 3.03 2.95
94 1.56 0.44 1.67 0.42 0.16 0.29 0.21 0.20 2.17 3.00 3.24
95 1.07 0.07 1.83 0.57 0.24 0.24 0.28 0.28 2.96 2.51 2.50
96 1.02 0.02 1.82 0.42 .27 0.23 0.18 0.17 3.98 5.07 5.17
97 1.19 0.17 1.83 0.55 0.27 .25 0.27 0.27 2.36 2.18 2.17
8 1.11 0.10 1.86 0.48 0.22 .24 0.22 0.22 3.10 3.34 .33
100 1.17 0.16 1.92 0.49 0.25 0.25 0.23 0.24 3.95 4.21 4.12

 

 

119

Table 3.4 (a) Actual/predicted values for %V02max & VOzm“ for experimental subjects (continued)

 

 

 

I%vo2 'o/ov02 %V02 %voz V02 vo2 vo2
max max max max max max max
Sub 13(0) Ln(EG) BSA RHR (actual) (RWP) (A) (C) (RWP) (A) (C)
7 1.79 0.58 1.75 0.67 0.47 0.32 0.38 0.38 4.18 3.46 3.49
10 1.22 0.20 1.74 0.56 0.35 0.26 0.28 0.28 5.81 5.28 5.39
12 1.86 0.62 1.45 0.8 0.38 0.32 0.47 0.45 2.77 1.91 2.00
13 2.02 0.70 1.63 0.7 0.44 0.34 0.41 0.40 3.83 3.12 3.21
15 1.35 0.30 1.86 0.72 0.39 0.27 0.39 0.40 5.22 3.63 3.57
18 6.65 1.89 2.01 0.68 0.60 0.53 0.50 0.51 3.65 3.86 3.78
23 1.60 0.47 2.23 0.56 0.43 0.30 0.30 0.33 6.95 6.83 6.27
26 1.65 0.50 1.73 0.74 0.43 0.30 0.42 0.42 4.33 3.13 3.14
31 4.55 1.51 1.66 0.72 0.51 0.47 0.49 0.48 2.84 2.68 2.75
36 7.47 2.01 1.66 0.76 0.58 0.55 0.56 0.55 2.36 2.30 2.35
38 1.41 0.35 2 0.55 0.35 0.28 0.29 0.30 5.96 5.79 5.57
44 4.01 1.39 1.93 0.64 0.37 0.45 0.43 0.44 3.77 3.90 3.86
49 6.44 1.86 2.3 0.61 0.49 0.52 0.45 0.48 3.81 4.40 4.14
50 1.23 0.20 2 0.67 0.43 0.26 0.35 0.37 6.90 5.03 4.82
51 1.18 0.17 1.94 0.63 0.28 0.25 0.32 0.33 5.64 4.37 424
52 1.84 0.61 1.84 0.56 0.34 0.32 0.32 0.32 4.04 4.11 4.12
53 15.89 2.77 1.89 0.79 0.66 0.67 0.64 0.64 2.39 2.48 2.48
54 9.78 2.28 1.96 0.75 0.59 0.59 0.58 0.58 2.80 2.87 2.83
69 2.02 0.70 2.14 0.5 0.36 0.34 0.29 0.30 5.03 5.92 5.57
63 2.65 0.98 1.74 0.65 0.43 0.38 0.40 0.40 3.67 3.45 3.51
69 4.76 1.56 1.88 0.74 0.50 0.47 0.51 0.51 3.49 3.25 3.22
70 1.50 0.40 1.8 0.61 0.37 0.29 0.33 0.33 5.27 4.60 4.62
72 6.61 1.89 1.66 0.9 0.56 0.53 0.64 0.63 2.76 2.28 2.31
73 3.78 1.33 1.85 0.69 0.49 0.44 0.46 0.46 3.71 3.53 3.52
74 5.53 1.71 2.04 0.64 0.49 0.50 0.46 0.47 3.87 4.20 4.10
76 1.89 0.63 1.96 0.72 0.46 0.33 0.42 0.43 4.90 3.80 3.69
177 2.51 0.92 1.57 0.57 0.39 0.37 0.35 0.33 3.25 3.46 3.68
78 4.79 1.57 2.05 0.5 0.36 0.47 0.36 0.37 3.36 4.45 4.35
79 12.31 2.51 1.59 0.74 0.49 0.63 0.59 0.57 2.06 2.19 2.27
80 3.15 1.15 1.76 0.82 0.49 0.41 0.53 0.52 3.57 2.77 2.77
81 1.07 0.07 1.99 0.55 0.38 0.23 0.26 0.28 6.43 5.70 5.46
82 1.37 0.31 1.69 0.66 0.44 0.27 0.35 0.35 4.33 3.35 3.41
83 4.58 1.52 1.71 0.7 0.55 0.47 0.48 0.47 2.89 2.81 2.87
84 2.05 0.72 2.16 0.64 0.44 0.34 0.38 0.40 5.04 4.55 4.28
Table B.4 (b) Actual/predicted values for %V02mu & V02...“ for experimental subjects (continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

120

V02 V02 V02 V02 02 02 02

G actual WP A WP A
.25 .22 .74 .72 .42 .26 .39 .38 .4 .64 .65
.96 .78 .8 .48 .38 .51 .36 .35 .83 .97 .09
.46 .38 .97 .62 .36 .29 .34 .35 .51 .69 .53
45 .90 .69 .83 .40 .37 .51 .51 .90 .80 .83
48 .91 .92 .73 .50 .37 .45 .46 .66 .84 .77
.70 .55 .83 .84 .51 .47 .57 .57 .10 .56 5
00 .53 .71 1.92 .66 .47 .50 .47 .47 .70 .91 .88

Table B.4 (b) Actual/predicted values for %V02max & VOzmu for experimental subjects (continued)

 

121

Table 85 lists the actual %VOzmax and the predictecd %VOzmax and absolute
VOzmax values of validation subjects using the developed RWP and MLR model A and
C. Table 8.5 (a) refers to validation subjects doing the random exercise test and (b)

refers to the VOzmax test.

 

I%voz %V02 %V02 %voz vo2 vo2 v02
max max max max max max max
Sub 13(0) Ln(EG)BSARHR(actua1)(RWP) (A) (C) (RWP) (A) (C)
1.96 0.67 1.67 0.62 0.38 0.33 0.36 0.35 3.73 3.42 3.53
3.30 1.19 1.66 0.61 0.30 0.41 0.40 0.38 2.20 2.29 2.37
.95 1.08 1.72 0.55 0.43 0.40 0.35 0.34 2.75 13.10 3.20
3.00 1.10 2.18 0.59 0.35 0.40 0.38 0.40 3.92 4.15 3.91
2.17 0.77 1.58 0.68 0.50 0.35 0.41 0.39 2.99 2.56 2.66
10 2.82 1.04 2.26 0.57 0.40 0.39 .36 0.39 5.11 5.54 5.14
11 6.12 1.63 2.08 0.77 0.56 0.49 0.53 0.55 3.89 3.54 3.42
12 3.31 1.20 1.71 0.76 0.57 0.42 0.49 0.48 3.14 2.67 2.70
13 5.89 1.77 1.75 0.66 0.38 0.51 0.48 0.47 2.07 2.19 2.23
14 6.86 1.93 1.81 0.61 0.42 0.53 0.46 0.45 2.26 2.63 2.67
15 2.16 0.77 1.93 0.58 0.26 0.35 0.34 0.35 3.77 3.81 3.75
16 3.06 1.12 1.60 0.71 0.34 0.40 0.45 0.44 2.66 2.36 2.44
17 2.48 0.91 2.10 0.60 0.40 0.37 0.37 0.38 4.58 4.62 4.41
18 2.29 0.83 1.82 0.69 0.43 0.36 0.42 0.42 3.60 3.09 3.09
23 .48 1.25 1.96 0.75 0.44 0.42 0.49 0.50 4.22 3.64 3.56
24 2.73 1.00 1.66 0.83 0.47 0.38 0.52 0.51 2.76 2.05 2.08
26 5.79 1.76 1.87 0.79 0.51 0.50 0.56 0.56 3.08 2.79 2.77
28 2.86 1.05 1.86 0.56 0.28 0.39 0.35 0.35 3.06 3.42 3.43
29 2.73 1.00 235 0.60 0.35 0.38 0.38 0.41 4.28 438 .01
30 1.63 0.49 2.07 0.58 0.37 0.30 0.32 0.34 4.85 4.57 4.35
33 2.44 0.89 1.83 0.71 0.45 0.37 0.43 0.43 2.94 2.49 2.48
34 1.77 0.57 1.96 0.54 0.31 0.31 0.30 0.31 4.92 5.16 15.03
35 3.26 1.18 1.78 0.64 0.45 0.41 0.41 0.41 3.28 B.28 3.32
36 4.59 1.52 1.53 0.68 0.33 0.47 0.47 0.44 1.80 1.81 1.90
39 5.70 1.74 2.17 0.59 0.35 0.50 0.43 0,45 2.92 3.44 3.30
40 2.12 0.75 2.01 0.56 0.38 0.34 0.33 0.34 4.12 4.36 4.22
41 1.88 0.63 1.77 0.61 0.33 0.33 0.35 0.34 3.82 3.58 3.62
Table 13.5 (a) Actual/predicted values for %VOZmu & V02"...ll for validation subjects

 

 

 

 

 

OOhleQt—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sub E(G) Ln BSA RHR %VOz %V02 %V02 %VO; V02 V02 V02
(EG) max max max max max max max

(actual) (RWP) (A) (C) (RWP) (A) (C)

42 4.48 1.50 2.24 0.66 0.51 0.46 0.45 0.48 3.56 3.63 3.43
44 5.96 1.79 1.58 0.62 0.35 0.51 0.45 0.43 1.91 2.17 2.28
45 1.94 0.66 2.05 0.65 0.33 0.33 0.38 0.40 4.24 3.69 3.54
46 6.64 1.89 1.47 0.77 0.55 0.53 0.55 0.53 1.77 1.68 1.77
47 1.75 0.56 1.61 0.60 0.38 0.31 0.34 0.32 3.37 3.13 3.28
48 5.68 1.74 1.67 0.65 0.45 0.50 0.47 0.46 2.66 2.85 2.94
49 2.30 0.83 1.48 0.67 0.29 0.36 0.40 0.38 3.25 2.88 3.05
51 1.49 0.40 1.90 0.63 0.38 0.29 0.35 0.35 4.97 4.15 4.07
52 1.68 0.52 1.97 0.55 0.31 0.31 0.30 0.31 5.06 5.16 5.01
53 2.03 0.71 2.00 0.57 0.35 0.34 0.33 0.34 4.41 4.53 4.39
54 4.30 1.46 1.99 0.67 0.38 0.46 0.46 0.47 3.38 3.38 3.31
56 6.07 1.80 1.63 0.62 0.38 0.51 0.45 0.44 1.99 2.25 2.34
58 2.86 1.05 2.04 0.69 0.39 0.39 0.44 0.45 3.92 3.52 3.40
59 2.31 0.84 1.71 0.67 0.35 0.36 0.40 0.39 2.74 2.44 2.48
60 4.86 1.58 1.93 0.67 0.47 0.48 0.47 0.47 3.19 3.26 3.23
62 1.67 0.51 2.39 0.67 0.43 0.31 0.38 0.42 6.51 5.25 4.73
64 6.10 1.81 1.91 0.80 0.66 0.51 0.57 0.58 3.04 2.74 2.71
65 3.92 1.37 1.75 0.65 0.48 0.44 0.44 0.43 2.85 2.88 2.93
66 3.45 1.24 1.96 0.71 0.53 0.42 0.46 0.47 4.59 4.18 4.09
67 4.73 1.55 2.07 0.79 0.57 0.47 0.54 0.56 3.47 3.03 2.93
68 6.66 1.90 1.88 0.68 0.41 0.53 0.50 0.50 2.65 2.81 2.80
69 2.77 1.02 1.86 0.62 0.30 0.39 0.39 0.39 2.72 2.70 2.69
70 4.35 1.47 2.07 0.63 0.47 0.46 0.43 0.44 3.93 4.21 4.07
71 3.57 1.27 1.58 0.86 0.62 0.43 0.56 0.55 2.21 1.67 1.71
72 7.39 2.00 1.80 0.66 0.38 0.54 0.49 0.49 2.40 2.66 2.69
74 2.25 0.81 2.00 0.55 0.36 0.35 0.33 0.34 3.92 4.26 4.14
77 3.73 1.32 2.20 0.52 0.48 0.43 0.35 0.37 4.66 5.79 5.47
78 2.92 1.07 1.74 0.69 0.46 0.40 0.44 0.43 3.19 2.90 2.94
82 2.45 0.90 2.26 0.66 0.35 0.37 0.40 0.43 4.07 3.72 3.46
83 2.06 0.72 1.78 0.70 0.46 0.34 0.42 0.42 3.73 3.04 3.05
85 2.07 0.73 1.92 0.56 0.40 0.34 0.33 0.33 4.71 4.91 4.84
86 1.70 0.53 2.11 0.56 0.40 0.31 0.31 0.33 5.62 5.63 5.31
89 2.52 0.93 1.96 0.73 0.40 0.37 0.45 0.46 3.53 2.94 2.86
90 2.31 0.84 2.07 0.57 0.27 0.36 0.34 0.35 3.88 4.09 3.92

 

Table B.5 (a) Actual/predicted values for %V0;..,., & V02...“ for validation subjects (Continued)

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sub E(G) Ln BSA RHR %V02 %V02 %V02 %V02 V02 V02 V02
(E0) max max max max max max max

(actual) (RWP (A) (C) (RWP (A) (C)

) )

91 1.95 0.67 2.13 0.53 0.4 0.33 0.3 0.32 5.37 5.9 5.55
94 2.60 0.96 2.11 0.63 0.33 0.38 0.39 0.41 3.64 3.54 3.38
98 1.38 0.32 1.85 0.75 0.44 0.28 0.41 0.42 5.70 3.80 3.73
100 1.69 0.53 1.91 0.56 0.34 0.31 0.31 0.31 4.30 4.29 4.22

 

Table 3.5 (a) Actual/predicted values for %VOZmu & V02...“ for validation subjects (Continued)

124

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sub 13(6) Ln BSA RHR %V02 %V02 %V02 %V02 V02 V02 V02
(EG) max max max max max max max

(actual) (RWP) (A) (C) (RWP) (A) (C)

2 2.95 1.08 1.66 0.72 0.53 0.40 0.46 0.45 4.08 3.53 3.61
4 10.88 2.39 2.18 0.75 0.57 0.61 0.59 0.61 4.29 4.43 4.27
5 3.00 1.10 1.90 0.70 0.49 0.40 0.44 0.45 4.31 3.89 3.84
8 4.41 1.48 1.58 0.77 0.61 0.46 0.52 0.51 2.74 2.41 2.49
10 7.73 2.05 2.26 0.74 0.56 0.55 0.55 0.58 5.07 5.09 4.84
11 6.27 1.84 2.08 0.75 0.58 0.52 0.54 0.56 3.75 3.61 3.50
12 7.71 2.04 1.74 0.73 0.64 0.55 0.54 0.54 2.64 2.67 2.72
14 12.96 2.56 1.81 0.64 0.57 0.63 0.53 0.52 2.59 3.12 3.17
15 7.15 1.97 1.93 0.77 0.51 0.54 0.56 0.57 4.78 4.60 4.55
16 8.61 2.15 1.60 0.84 0.54 0.57 0.62 0.61 2.94 2.68 2.75
17 5.66 1.73 2.10 0.80 0.60 0.50 0.56 0.58 5.02 4.46 4.31
18 5.32 1.67 1.82 0.80 0.58 0.49 0.56 0.56 3.52 3.11 3.10
23 5.81 1.76 1.96 0.79 0.57 0.51 0.56 0.57 4.60 4.15 4.08
25 6.83 1.92 1.77 0.84 0.54 0.53 0.60 0.60 4.15 3.67 3.68
26 5.16 1.64 1.87 0.77 0.57 0.49 0.54 0.54 3.59 3.25 3.23
27 6.85 1.92 1.81 0.82 0.50 0.53 0.59 0.59 3.81 3.42 3.42
28 5.07 1.62 1.86 0.72 0.51 0.48 0.50 0.51 4.44 4.27 4.25
29 8.03 2.08 2.35 0.73 0.56 0.56 0.54 0.58 4.63 4.73 4.45
30 12.35 2.51 2.07 0.76 0.59 0.63 0.60 0.62 3.76 3.91 3.82
31 10.84 2.38 1.86 0.70 0.54 0.61 0.56 0.55 3.82 4.17 4.18
33 6.56 1.88 1.83 0.72 0.61 0.52 0.53 0.52 2.77 2.76 2.77
34 4.96 1.60 1.96 0.71 0.55 0.48 0.49 0.50 5.78 5.62 5.53
35 5.63 1.73 1.78 0.78 0.64 0.50 0.55 0.54 3.85 3.52 3.54
36 5.24 1.66 1.53 0.73 0.50 0.49 0.51 0.49 2.59 2.48 2.59
39 4.96 1.60 2.17 0.70 0.55 0.48 0.49 0.51 4.76 4.67 4.47
40 6.59 1.89 2.01 0.67 0.54 0.53 0.49 0.50 3.85 4.14 4.06
41 6.77 1.91 1.77 0.72 0.56 0.53 0.52 0.52 3.99 4.03 4.08
42 12.39 2.52 2.24 0.70 0.63 0.63 0.56 0.59 3.25 3.62 3.48
44 6.47 1.87 1.58 0.71 0.52 0.52 0.52 0.50 2.74 2.77 2.88
46 12.35 2.51 1.47 0.79 0.66 0.63 0.62 0.59 1.77 1.80 1.88
48 7.57 2.02 1.67 0.68 0.56 0.55 0.51 0.49 3.03 3.27 3.37
49 6.65 1.90 1.48 0.78 0.53 0.53 0.56 0.54 3.99 3.74 3.91
50 5.25 1.66 1.80 0.71 0.45 0.49 0.50 0.49 5.45 5.36 5.40
51 6.93 1.94 1.90 0.75 0.59 0.53 0.54 0.55 4.15 4.07 4.04

 

 

 

 

 

 

 

 

 

 

 

 

125

Table 8.5 (b) Actual/predicted values for %vomx & VOZmu for validation subjects

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sub 13(0) Ln BSA RHR %V02 %V02 %V02 %V02 V02 V02 V02
(EG) max max max max max max max

(actual) (RWP) (A) (C) (RWP) (A) (C)

52 9.79 2.28 1.97 0.77 0.56 0.59 0.59 0.59 4.73 4.75 4.69
53 9.58 2.26 2.00 0.73 0.57 0.59 0.56 0.57 4.11 4.30 4.24
54 4.86 1.58 1.99 0.80 0.60 0.48 0.55 0.56 5.17 4.49 4.39
55 7.15 1.97 1.72 0.81 0.67 0.54 0.59 0.58 2.17 1.99 2.02
56 12.41 2.52 1.63 0.73 0.57 0.63 0.58 0.57 2.47 2.66 2.74
57 5.54 1.71 2.05 0.85 0.57 0.50 0.59 0.61 4.96 4.17 4.05
58 10.64 2.36 2.04 0.84 0.61 0.60 0.64 0.65 3.95 3.73 3.64
59 6.04 1.80 1.71 0.77 0.61 0.51 0.55 0.54 3.31 3.10 3.15
60 5.30 1.67 1.93 0.83 0.60 0.49 0.57 0.58 3.93 3.36 3.30
62 8.27 2.11 2.39 0.83 0.61 0.56 0.61 0.65 5.10 4.67 4.39
65 6.68 1.90 1.75 0.71 0.61 0.53 0.52 0.51 3.07 3.12 3.17
66 12.70 2.54 1.96 0.85 0.60 0.63 0.66 0.67 3.48 3.32 3.28
67 4.08 1.40 2.07 0.86 0.64 0.45 0.57 0.59 4.16 3.28 3.16
68 12.08 2.49 1.88 0.75 0.57 0.62 0.59 0.59 3.12 3.28 3.28
69 10.30 2.33 1.86 0.75 0.54 0.60 0.58 0.58 3.20 3.30 3.30
71 5.90 1.77 1.58 0.84 0.61 0.51 0.59 0.58 1.81 1.55 1.59
72 10.82 2.38 1.80 0.74 0.55 0.60 0.58 0.57 3.08 3.23 3.26
74 5.68 1.74 2.00 0.65 0.54 0.50 0.47 0.47 4.15 4.48 4.40
76 6.00 1.79 1.93 0.65 0.57 0.51 0.47 0.48 4.66 5.03 4.99
78 4.05 1.40 1.74 0.76 0.57 0.45 0.51 0.50 3.45 3.04 3.07
83 4.78 1.57 1.78 0.77 0.61 0.47 0.53 0.53 3.51 3.15 3.17
85 10.65 2.37 1.92 0.72 0.58 0.60 0.56 0.56 3.82 4.10 4.08
86 3.15 1.15 2.11 0.74 0.62 0.41 0.47 0.50 6.60 5.68 5.43
88 12.93 2.56 2.04 0.68 0.67 0.63 0.55 0.56 2.72 3.12 3.07
89 4.17 1.43 1.96 0.78 0.58 0.45 0.52 0.53 4.27 3.70 3.62
90 4.07 1.40 2.07 0.76 0.56 0.45 0.51 0.53 6.40 5.66 5.47
91 4.42 1.49 2.13 0.67 0.56 0.46 0.46 0.48 5.47 5.47 5.25
94 7.59 2.03 2.11 0.75 0.55 0.55 0.56 0.57 4.17 4.11 3.98
95 3.50 1.25 1.73 0.89 0.51 0.42 0.58 0.58 3.98 2.93 2.93
96 5.85 1.77 1.69 0.84 0.56 0.51 0.59 0.58 3.19 2.75 2.78
97 4.44 1.49 1.88 0.89 0.53 0.46 0.60 0.61 4.59 3.54 3.49
98 4.74 1.56 1.85 0.82 0.56 0.47 0.56 0.57 4.23 3.56 3.53
100 8.82 2.18 1.91 0.73 0.55 0.57 0.56 0.56 3.76 3.87 3.85

 

Table 8.5 (b) Actual/predicted values for %V02max & V02...“ for validation subjects (Continued)

126

 

 

 

l0/..vo2 V02

max max

(actual) RWP A C J (actual) RWP A C J
0.38 0.33 0.36 0.35 0.44 3.22 3.73 3.42 3.53 2.80
0.30 0.41 0.40 0.38 0.29 3.06 2.20 2.29 2.37 3.14
0.43 0.40 0.35 0.34 0.38 2.52 2.75 3.10 3.20 2.90
0.35 0.40 0.38 0.40 0.38 4.52 3.92 4.15 3.91 4.07
8 0.50 0.35 0.410.390.362.09 2.99 2.56 2.66 2.86
10 0.40 0.39 0.36 0.390.53 4.96 5.11 5.54 5.14 3.79
11 0.56 0.49 0.53 0.55 0.58 3.35 3.89 3.54 3.42 3.23
12 0.57 0.42 0.49 0.48 0.45 2.27 3.14 2.67 2.70 2.90
13 0.38 0.51 0.48 0.47 0.36 2.75 2.07 2.19 2.23 2.92
14 0.42 0.53 0.46 0.45 0.39 2.86 2.26 2.63 2.67 3.09
15 0.26 0.35 0.34 0.35 0.37 5.04 3.77 3.81 3.75 3.58
16 0.34 0.40 0.45 0.44 0.40 3.11 2.66 2.36 2.44 2.68
17 0.40 0.37 0.37 0.38 0.45 4.23 4.58 4.62 4.41 3.74
18 0.43 0.36 0.42 0.42 0.38 3.00 3.60 3.09 3.09 3.34
23 0.44 0.42 0.49 0.50 0.59 4.05 4.22 3.64 3.56 3.01
24 0.47 0.38 0.52 0.51 0.43 2.27 2.76 2.05 2.08 2.48
26 0.51 0.50 0.56 0.56 0.51 3.05 3.08 2.79 2.77 3.06
28 0.28 0.39 0.35 0.35 0.35 4.24 3.06 3.42 3.43 3.41
29 0.35 0.38 0.38 0.41 0.35 4.64 4.28 4.38 4.01 4.65
30 0.37 0.30 0.32 0.34 0.40 4.01 4.85 4.57 4.35 3.67
33 0.45 0.37 0.43 0.43 0.34 2.39 2.94 2.49 2.48 3.13
34 0.31 0.31 0.30 0.31 0.46 5.05 4.92 5.16 5.03 3.37
35 0.45 0.41 0.41 0.41 0.483.01 3.28 3.28 3.32 2.83
36 0.33 0.47 0.47 0.44 0.33 2.54 1.80 1.81 1.90 2.52
39 0.35 0.50 0.43 0.45 0.40 4.16 2.92 3.44 3.30 3.72
40 0.38 0.34 0.33 0.34 0.39 3.78 4.12 4.36 4.22 3.62
fll 0.33 0.33 0.35 0.34 0.43 3.75 3.82 3.58 3.62 2.92
42 0.51 0.46 0.45 0.48 0.46 3.23 3.56 3.63 3.43 3.61
44 0.35 0.51 0.45 0.43 0.24 2.78 1.91 2.17 2.28 4.11
45 0.33 0.33 0.38 0.40 0.57 4.23 4.24 3.69 3.54 2.46
46 0.55 0.53 0.55 0.53 0.401.69 1.77 1.68 1.77 2.33

Table 13.6 (a)'7 MSPR check and Jones’ equation comparison on validation subjects

 

hWN—‘lli:

 

 

 

 

 

 

'7 Table B.6 (a) refers to the random exercise test and (b) refers to VOzmax test for all validation subjects.

127

 

 

612(0/0)

2
61

 

RWPACJ

RWPA C

J

 

thu—Ilt

8
10
11
12
13
14
15
16
17
18
23
24
26
28
29
30
33
34
35
36
39
40
41
42
44
45
46

 

0.00
0.01
0.00
0.00
0.02
0.00
0.01
0.02
0.02
0.01
0.01
0.00
0.00
0.01
0.00
0.01
0.00
0.01
0.00
0.00
0.01
0.00
0.00
0.02
0.02
0.00
0.00
0.00
0.03
0.00

 

0.00

0.00 0.00 0.00
0.01 0.01 0.00
0.01 0.01 0.00
0.00 0.00 0.00
0.01 0.01 0.02
0.00 0.00 0.02
0.00 0.00 0.00
0.01 0.01 0.01
0.01 0.01 0.00
0.00 0.00 0.00
0.01 0.01 0.01
0.01 0.01 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.02
0.00 0.00 0.00
0.00 0.00 0.00
0.01 0.00 0.01
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.01
0.00 0.00 0.02
0.00 0.00 0.00
0.02 0.01 0.00
0.01 0.01 0.00
0.00 0.00 0.00
0.00 0.00 0.01
0.00 0.00 0.00
0.01 0.01 0.01
0.00 0.00 0.06
0.00 0.00 0.02

0.26
0.75
0.05
0.37
0.81
0.02
0.29
0.76
0.47
0.37
1.62
0.21
0.12
0.36
0.03
0.24
0.00
1.40
0.13
0.70
0.30
0.02
0.07
0.55
1.53
0.12
0.01
0.11
0.76
0.00

 

0.01

0.04 0.10
0.59 0.47
0.34 0.47
0.14 0.37
0.22 0.32
0.33 0.03
0.03 0.00
0.16 0.19
0.31 0.27
0.05 0.04
1.51 1.67
0.57 0.45
0.16 0.03
0.01 0.01
0.17 0.24
0.05 0.04
0.07 0.08
0.68 0.66
0.07 0.40
0.32 0.11
0.01 0.01
0.01 0.00
0.07 0.10
0.54 0.41
0.52 0.75
0.33 0.19
0.03 0.02
0.16 0.04
0.38 0.25
0.29 0.48
0.00 0.01

0.18
0.01
0.14
0.20
0.59
1.37
0.01
0.40
0.03
0.05
2.13
0.18
0.24
0.12
1.07
0.05
0.00
0.69
0.00
0.11
0.54
2.82
0.03
0.00
0.20
0.03
0.68
0.15
1.76
3.12
0.42

 

Table 3.6 (a) MSPR check and Jones’ equation comparison on validation subjects (Continued)

128

 

 

 

%VO; V02

max max

# (actual) RWP A C J (actual) RWP A C J

47 0.38 0.31 0.34 0.32 0.43 2.75 3.37 3.13 3.28 2.43
48 0.45 0.50 0.47 0.46 0.54 2.95 2.66 2.85 2.94 2.49
49 0.29 0.36 0.40 0.38 0.39 3.98 3.25 2.88 3.05 2.98
51 0.38 0.29 0.35 0.35 0.40 3.76 4.97 4.15 4.07 3.54
52 0.31 0.31 0.300.310.524.95 5.06 5.165.01 3.00
53 0.35 0.34 0.33 0.34 0.42 4.24 4.41 4.53 4.39 3.54
54 0.38 0.46 0.46 0.47 0.42 4.12 3.38 3.38 3.31 3.64
56 0.38 0.51 0.45 0.44 0.40 2.71 1.99 2.25 2.34 2.57
58 0.39 0.39 0.44 0.45 0.44 3.92 3.92 3.52 3.40 3.48
59 0.35 0.36 0.40 0.39 0.34 2.77 2.74 2.44 2.48 2.85
60 0.47 0.48 0.47 0.47 0.56 3.23 3.19 3.26 3.23 2.74
62 0.43 0.31 0.38 0.42 0.52 4.68 6.51 5.25 4.73 3.86
64 0.66 0.51 0.57 0.58 0.58 2.38 3.04 2.74 2.71 2.67
65 0.48 0.44 0.44 0.43 0.49 2.64 2.85 2.88 2.93 2.58
66 0.53 0.42 0.46 0.47 0.58 3.64 4.59 4.18 4.09 3.34
67 0.57 0.47 0.54 0.56 0.48 2.90 3.47 3.03 2.93 3.40
68 0.41 0.53 0.50 0.50 0.48 3.42 2.65 2.81 2.80 2.90
69 0.30 0.39 0.390.390.313.55 2.72 2.70 2.69 3.37
70 0.47 0.46 0.43 0.44 0.57 3.85 3.93 4.21 4.07 3.16
71 0.62 0.43 0.56 0.55 0.47 1.52 2.21 1.67 1.71 2.02
72 0.38 0.54 0.49 0.49 0.45 3.42 2.40 2.66 2.69 2.92
74 0.36 0.35 0.33 0.34 0.39 3.83 3.92 4.26 4.14 3.54
77 0.48 0.43 0.35 0.37 0.55 4.21 4.66 5.79 5.47 3.66
78 0.46 0.40 0.44 0.43 0.43 2.72 3.19 2.90 2.94 2.94
82 0.35 0.37 0.40 0.43 0.37 4.25 4.07 3.72 3.46 4.04
83 0.46 0.34 0.42 0.42 0.42 2.73 3.73 3.04 3.05 3.01
85 0.40 0.34 0.33 0.33 0.48 3.98 4.71 4.91 4.84 3.35
86 0.40 0.31 0.31 0.33 0.52 4.37 5.62 5.63 5.31 3.34
89 0.40 0.37 0.45 0.46 0.45 3.31 3.53 2.94 2.86 2.92
90 0.27 0.36 0.34 0.35 0.40 5.11 3.88 4.09 3.92 3.44
91 0.40 0.33 0.30 0.32 0.47 4.49 5.37 5.90 5.55 3.82
94 0.33 0.38 0.390.410.364.18 3.64 3.543.38 3.78
98 0.44 0.28 0.41 0.42 0.59 3.55 5.70 3.80 3.73 2.68
100 0.34 0.31 0.31 0.31 0.40 3.93 4.30 4.29 4.22 3.33

Table 13.6 (a) MSPR check and Jones’ equation comparison on validation subjects (continued)

 

 

 

 

 

 

129

 

 

#

612(0/0)

Ci

2

 

RWPACJ

RWPA C

J

 

47
48
49
51
52
53
54
56
58
59
60
62
64
65
66
67
68
69
70
71
72
74
77
78
82
83
85
86
89
90
91
94
98
100

 

0.00
0.00
0.00
0.01
0.00
0.00
0.01
0.02
0.00
0.00
0.00
0.02
0.02
0.00
0.01
0.01
0.01
0.01
0.00
0.04
0.03
0.00
0.00
0.00
0.00
0.01
0.00
0.01
0.00
0.01
0.00
0.00
0.03
0.00

 

0.00 0.00 0.00
0.00 0.00 0.01
0.01 0.01 0.01
0.00 0.00 0.00
0.00 0.00 0.04
0.00 0.00 0.01
0.01 0.01 0.00
0.01 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.01
0.00 0.00 0.01
0.01 0.01 0.01
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.01
0.01 0.01 0.01
0.01 0.01 0.00
0.00 0.00 0.01
0.00 0.00 0.02
0.01 0.01 0.00
0.00 0.00 0.00
0.02 0.01 0.01
0.00 0.00 0.00
0.00 0.01 0.00
0.00 0.00 0.00
0.01 0.00 0.01
0.01 0.01 0.01
0.00 0.00 0.00
0.00 0.01 0.02
0.01 0.01 0.00
0.00 0.01 0.00
0.00 0.00 0.02
0.00 0.00 0.00

0.38
0.08
0.53
1.47
0.01
0.03
0.55
0.51
0.00
0.00
0.00
13.33
0.44
0.04
0.90
0.33
0.59
0.68
0.01
0.47
1.04
0.01
0.20
0.22
0.03
0.99
0.53
1.55
0.05
1.52
0.77
0.29
4.61
0.13

 

0.15
0.01
1.22
0.15

0.28
0.00
0.86
0.10

0.04 0.00

0.08
0.54
0.21
0.16
0.11
0.00
0.33
0.13
0.06
0.29
0.02
0.37
0.73
0.13
0.02

0.02
0.65
0.14
0.27
0.08
0.00
0.00
0.11
0.08
0.20
0.00
0.38
0.74
0.05
0.04

0.59 0.54
0.19 0.10
2.49 1.58
0.03 0.05
0.28 0.63
0.10 0.10
0.86 0.74
1.59 0.88
0.14 0.20
1.04 1.41
1.98 1.13
0.41 0.64
0.06 0.03
0.13 0.09

0.10
0.21
0.99
0.05
3.82
0.50
0.23
0.02
0.20
0.01
0.24
0.68
0.09
0.00
0.09
0.25
0.27
0.03
0.47
0.25
0.25
0.08
0.30
0.05
0.05
0.08
0.40
1.06
0.15
2.79
0.45
0.16
0.76
0.36

 

130

Table 8.6 (a) MSPR check and Jones’ equation comparison on validation subjects (continued)

 

 

V02
%V02 max
max (actua
(actual)RWP A C J l) RWP A C J

 

#
2 0.53 0.40 0.46 0.45 0.52 3.06 4.08 3.53 3.61 3.14
4 0.57 0.61 0.59 0.61 0.644.52 4.29 4.43 4.27 4.07
15 0.49 0.40 0.44 0.45 0.49 3.52 4.31 3.89 3.84 3.54
8 0.61 0.46 0.52 0.51 0.442.09 2.74 2.41 2.49 2.86
10 0.56 0.55 0.55 0.58 0.74 4.96 5.07 5.09 4.84 3.79
11 0.58 0.52 0.54 0.56 0.60 3.35 3.75 3.61 3.50 3.23
12 0.64 0.55 0.54 0.54 0.50 2.27 2.64 2.67 2.72 2.90
14 0.57 0.63 0.53 0.52 0.53 2.86 2.59 3.12 3.17 3.09
15 0.51 0.54 0.56 0.57 0.725.04 4.78 4.60 4.55 3.58
16 0.54 0.57 0.62 0.61 0.623.11 2.94 2.68 2.75 2.68
17 0.60 0.50 0.56 0.58 0.67 .23 5.02 4.46 4.31 3.74
18 0.58 0.49 0.56 0.56 0.52200 3.52 3.11 3.10 3.34
23 0.57 0.51 0.56 0.57 0.774.05 4.60 4.15 4.08 3.01
25 0.54 0.53 0.60 0.60 0.694.07 4.15 3.67 3.68 3.19
26 0.57 0.49 0.54 0.54 0.573.05 3.59 3.25 3.23 3.06
27 0.50 0.53 0.59 0.59 0.614.02 3.81 3.42 3.42 3.31
28 0.51 0.48 0.50 0.51 0.63 4.24 4.44 4.27 4.25 3.41
29 0.56 0.56 0.54 0.58 0.55 4.64 4.63 4.73 4.45 4.65
30 0.59 0.63 0.60 0.62 0.64 4.01 3.76 3.91 3.82 3.67
31 0.54 0.61 0.56 0.55 0.73 4.32 3.82 4.17 4.18 3.17
33 0.61 0.52 0.53 0.52 0.46 2.39 2.77 2.76 2.77 3.13
34 0.55 0.48 0.49 0.50 0.82 5.05 5.78 5.62 5.53 3.37
35 0.64 0.50 0.55 0.54 0.68 3.01 3.85 3.52 3.54 2.83
36 0.50 0.49 0.510.49 0.50 2.54 2.59 2.48 2.59 2.52
39 0.55 0.48 0.49 0.51 0.62 4.16 4.76 4.67 4.47 3.72
40 0.54 0.53 0.49 0.50 0.563.78 3.85 4.14 4.06 3.62
41 0.56 0.53 0.52 0.52 0.723.75 3.99 4.03 4.08 2.92
42 0.63 0.63 0.56 0.59 0.563.23 3.25 3.62 3.48 3.61
44 0.52 0.52 0.52 0.50 0.55 2.78 2.74 2.77 2.88 2.59
46 0.66 0.63 0.62 0.59 0.471.69 1.77 1.80 1.88 2.33
48 0.56 0.55 0.510.49 0.66 2.95 3.03 3.27 3.37 2.49
49 0.53 0.53 0.56 0.54 0.703.98 3.99 3.74 3.91 2.98
50 0.45 0.49 0.50 0.49 0.83 5.93 5.45 5.36 5.40 3.19
51 0.59 0.53 0.54 0.55 0.62 3.76 4.15 4.07 4.04 3.54

 

 

 

 

 

 

Table 3.6 (b) MSPR check and Jones’ equation comparison on validation subjects

131

 

6120/0)

Ciz

 

RWPACJ

RWPA C J

 

01-51041:

8
10
11
12
14
15
16
17
18
23
25
26
27
28
29
30
31
33
34
35
36
39
40
41
42
44
46
48
49
50
51

 

0.02
0.00
0.01
0.02
0.00
0.00
0.01
0.00
0.00
0.00
0.01
0.01
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

 

0.00

0.00 0.01 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.01 0.01 0.03
0.00 0.00 0.03
0.00 0.00 0.00
0.01 0.01 0.02
0.00 0.00 0.00
0.00 0.00 0.04
0.01 0.00 0.01
0.00 0.00 0.01
0.00 0.00 0.00
0.00 0.00 0.04
0.00 0.00 0.02
0.00 0.00 0.00
0.01 0.01 0.01
0.00 0.00 0.01
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.04
0.01 0.01 0.02
0.00 0.00 0.08
0.01 0.01 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.03
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.03
0.00 0.00 0.01
0.00 0.00 0.03
0.00 0.00 0.15
0.00 0.00 0.00

1.05 0.22 0.31 0.01
0.05 0.01 0.06 0.20
0.62 0.14 0.10 0.00
0.43 0.10 0.16 0.59
0.01 0.02 0.01 1.37
0.16 0.07 0.02 0.01
0.14 0.16 0.20 0.40
0.07 0.07 0.10 0.05
0.07 0.19 0.24 2.13
0.03 0.18 0.13 0.18
0.63 0.05 0.01 0.24
0.28 0.01 0.01 0.12
0.30 0.01 0.00 1.07
0.01 0.16 0.15 0.77
0.30 0.04 0.03 0.00
0.04 0.36 0.35 0.50
0.04 0.00 0.00 0.69
0.00 0.01 0.03 0.00
0.06 0.01 0.04 0.11
0.25 0.02 0.02 1.32
0.14 0.14 0.15 0.54
0.54 0.32 0.23 2.82
0.70 0.26 0.28 0.03
0.00 0.00 0.00 0.00
0.36 0.26 0.09 0.20
0.00 0.13 0.08 0.03
0.06 0.08 0.11 0.68
0.00 0.16 0.06 0.15
0.00 0.00 0.01 0.04
0.01 0.01 0.04 0.42
0.01 0.10 0.18 0.21
0.00 0.06 0.01 0.99
0.23 0.32 0.28 7.49

 

0.15 0.10 0.08 0.05

 

Table 3.6 (b) MSPR check and Jones’ equation comparison on validation subjects (continued)

132

 

 

 

lo/..vo2 vo2

max max

# (actual) RWP A C J (actual) RWP A C J
52 0.56 0.59 059059093495 4.73 4.754.69 3.00
53 0.57 0.59 0.560.570.68424 4.11 4.304.24 3.54
55 0.67 0.54 0.590.580.431.74 2.17 1.992.02 2.75
56 0.57 0.63 058057060271 2.47 2.662.74 2.57
57 0.57 0.50 0.590.610.684.31 4.96 4.174.05 3.62
58 0.61 0.60 064065068392 3.95 3.733.64 3.48
59 0.61 0.51 0.550.540.59277 3.31 3.103.15 2.85
60 0.60 0.49 0.570.580.703.23 3.93 3.363.30 2.74
62 0.61 0.56 0.610.650.744.68 5.10 4.674.39 3.86
65 0.61 0.53 052051063264 3.07 3.123.17 2.58
66 0.60 0.63 0.660.670.66364 3.48 3.323.28 3.34
67 064 0.45 0.570.590.55290 4.16 3.283.16 3.40
68 0.57 0.62 0.590.590.673.42 3.12 3.283.28 2.90
69 0.54 0.60 058058057355 3.20 3.303.30 3.37
71 0.61 0.51 059058045152 1.81 1.551.59 2.02
72 0.55 0.60 0.580.570.643.42 3.08 3.233.26 2.92
74 0.54 0.50 0.470.470.59383 4.15 4484.40 3.54
76 0.57 0.51 0.470.480.714.19 4.66 5,034.99 3.36
78 0.57 0.45 0.510.500.53272 3.45 3.043.07 2.94
83 0.61 0.47 053053055273 3.51 3.15317 3.01
85 0.58 0.60 056056069398 3.82 4.104.08 3.35
86 0.62 0.41 047050081437 6.60 5685.43 3.34
88 0.67 0.63 055056051258 2.72 3.12307 3.38
89 0.58 0.45 052053066331 4.27 3.70362 2.92
90 0.56 0.45 0.510.530.845.11 6.40 5.665.47 3.44
91 0.56 0.46 0.460.480.664.49 5.47 5.475.25 3.82
94 0.55 0.55 0.560.570.604.18 4.17 4.113.98 3.78
95 0.51 0.42 058058070333 3.98 2.932.93 2.42
96 0.56 0.51 059058056289 3.19 2.752.78 2.90
97 0.53 0.46 060061063397 4.59 3543.49 3.36
98 0.56 0.47 056057075355 4.23 3.563.53 2.68
1000.55 0.57 056056065393 3.76 3873.85 3.33

Table 3.6 (b) MSPR check and Jones’ equation comparison on validation subjects (continued)

 

 

 

 

 

 

133

 

 

Ci2(°/o) Biz

# RWP A C J RWP A C J
52 0.00 0.00 0.00 0.14 0.05 0.04 0.07 3.82
53 0.00 0.00 0.00 0.01 0.02 0.00 0.00 0.50
54 0.02 0.00 0.00 0.01 1.11 0.14 0.07 0.23
55 0.02 0.01 0.01 0.06 0.19 0.06 0.08 1.02
56 0.00 0.00 0.00 0.00 0.06 0.00 0.00 0.02
57 0.01 0.00 0.00 0.01 0.43 0.02 0.07 0.48
58 0.00 0.00 0.00 0.01 0.00 0.04 0.08 0.20
59 0.01 0.00 0.01 0.00 0.29 0.11 0.15 0.01
60 0.01 0.00 0.00 0.01 0.49 0.02 0.01 0.24
62 0.00 0.00 0.00 0.02 0.18 0.00 0.09 0.68
65 0.01 0.01 0.01 0.00 0.19 0.23 0.28 0.00
66 0.00 0.00 0.00 0.00 0.03 0.10 0.13 0.09
67 0.04 0.01 0.00 0.01 1.59 0.15 0.07 0.25
68 0.00 0.00 0.00 0.01 0.09 0.02 0.02 0.27
69 0.00 0.00 0.00 0.00 0.13 0.06 0.06 0.03
71 0.01 0.00 0.00 0.02 0.09 0.00 0.01 0.25
72 0.00 0.00 0.00 0.01 0.11 0.04 0.03 0.25
74 0.00 0.01 0.00 0.00 0.11 0.42 0.32 0.08
76 0.00 0.01 0.01 0.02 0.22 0.71 0.65 0.68
78 0.01 0.00 0.00 0.00 0.54 0.10 0.12 0.05
83 0.02 0.01 0.01 0.00 0.61 0.18 0.19 0.08
85 0.00 0.00 0.00 0.01 0.03 0.01 0.01 0.40
86 0.05 0.02 0.02 0.03 4.97 1.71 1.13 1.06
88 0.00 0.01 0.01 0.03 0.02 0.29 0.24 0.63
89 0.02 0.00 0.00 0.01 0.92 0.15 0.10 0.15
90 0.01 0.00 0.00 0.08 1.67 0.31 0.13 2.79
91 0.01 0.01 0.01 0.01 0.95 0.96 0.57 0.45
94 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.16
95 0.01 0.00 0.00 0.03 0.42 0.16 0.16 0.83
96 0.00 0.00 0.00 0.00 0.09 0.02 0.01 0.00
97 0.00 0.00 0.01 0.01 0.38 0.19 0.23 0.37
98 0.01 0.00 0.00 0.04 0.46 0.00 0.00 0.76
100 0.00 0.00 0.00 0.01 0.03 0.00 0.01 0.36
28.9

>: 0.91 0.49 0.46 1.71 57.90 32.81 6 73.36
[MSRP 0.69% 037% 0.35% 1.30% 0.44 0.25 0.22 0.56

Table 3.6 (b) MSPR check and Jones’ equation comparison on validation subjects (continued)

 

 

 

 

 

 

 

 

134

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