EPA/600/R-06/129F 

 May 2009

METABOLICALLY DERIVED HUMAN VENTILATION RATES: A 

REVISED APPROACH BASED UPON OXYGEN CONSUMPTION RATES 

National Center for Environmental Assessment 

Office of Research and Development 

U.S. Environmental Protection Agency 

Washington, DC 20460 
DISCLAIMER

This document has been reviewed in accordance with U.S. Environmental Protection 

Agency policy and approved for publication. Mention of trade names or commercial products 

does not constitute endorsement or recommendation for use. 

ABSTRACT

The U.S. Environmental Protection Agency’s (EPA’s) National Center for Environmental 

Assessment (NCEA) publishes the Exposure Factors Handbook and the Child-Specific Exposure 

Factors Handbook to provide risk assessors with data on various factors that can impact an 

individual’s exposure to environmental contaminants. Both of these handbooks included 

estimates of ventilation rate (V&

E )—the volume of air that is inhaled by an individual in a 

specified time period. Previous approach to calculate V&

E is limited by its dependence on a 

“ventilatory equivalent” which, in turn, relies on a person’s fitness level. In this document, U.S. 

EPA presents a revised approach in which V&

E is calculated directly from an individual’s oxygen 

consumption rate. U.S. EPA then applies this method to data provided from more recent 

sources: the 1999−2002 National Health and Nutrition Examination Survey (NHANES) and 

U.S. EPA’s Consolidated Human Activity Database (CHAD). 

Preferred Citation:

U.S. Environmental Protection Agency (EPA). (2009) Metabolically derived human ventilation rates: a revised 

approach based upon oxygen consumption rates. National Center for Environmental Assessment, Washington, DC; 

EPA/600/R-06/129F. 

 ii
CONTENTS

LIST OF TABLES ...........................................................................................................................v 

LIST OF ABBREVIATIONS AND ACRONYMS ...................................................................... vi 

PREFACE ..................................................................................................................................... vii 

AUTHORS, CONTRIBUTORS, AND REVIEWERS ............................................................... viii 

EXECUTIVE SUMMARY ........................................................................................................... ix 

1. BACKGROUND AND OBJECTIVES ................................................................................. 1-1 

2. DATA SOURCES ................................................................................................................. 2-1 

2.1. SOURCE OF BODY WEIGHT DATA: 1999−2002 NHANES ................................. 2-1 

2.2. SOURCE OF BMR CALCULATION: SCHOFIELD (1985)..................................... 2-3 

2.3. SOURCE OF ACTIVITY AND METS DATA: CONSOLIDATED HUMAN 

ACTIVITY DATABASE (CHAD) .............................................................................. 2-4 

2.3.1. The National Human Activity Pattern Survey .................................................. 2-5 

3. APPROACH .......................................................................................................................... 3-1

3.1. STEP 1: GROUP NHANES AND NHAPS PARTICIPANTS BY AGE AND 

GENDER CATEGORIES ............................................................................................ 3-2 

3.2. STEP 2: CALCULATE BMR ESTIMATES FOR NHANES PARTICIPANTS ....... 3-2 

3.3. STEP 3: GENERATE A SIMULATED 24-HOUR ACTIVITY PATTERN 

FOR EACH NHANES PARTICIPANT ....................................................................... 3-2 

3.4. STEP 4: GENERATE A METS VALUE FOR EACH ACTIVITY WITHIN 

THE SIMULATED 24-HOUR ACTIVITY PATTERN FOR EACH NHANES 

PARTICIPANT............................................................................................................. 3-4 

3.5. STEP 5: CALCULATE ENERGY EXPENDITURE AND VO2 FOR EACH 

ACTIVITY WITHIN AN INDIVIDUAL’S SIMULATED 24-HOUR 

ACTIVITY PATTERN ................................................................................................. 3-6 

3.6. STEP 6: CALCULATE VENTILATION RATE FOR EACH ACTIVITY 

WITHIN THE SIMULATED 24-HOUR ACTIVITY PATTERN FOR EACH 

NHANES PARTICIPANT ........................................................................................... 3-7 

3.7. STEP 7: CALCULATE AVERAGE VENTILATION RATE FOR TIME 

SPENT PERFORMING ACTIVITIES WITHIN SPECIFIED METS 

CATEGORIES, AS WELL AS 24-HOUR AVERAGE VENTILATION RATE, 

FOR EACH NHANES PARTICIPANT ....................................................................... 3-9 

3.8. STEP 8: CALCULATE SUMMARY TABLES ACROSS INDIVIDUALS ............ 3-10 

4. RESULTS .............................................................................................................................. 4-1 

4.1. STRENGTHS AND LIMITATIONS ......................................................................... 4-11 

REFERENCES ............................................................................................................................R-1 

 iii
CONTENTS (continued)

APPENDIX A: EVISED VENTILATION RATE (VE) EQUATIONS FOR USE IN 

INHALATION-ORIENTED EXPOSURE MODELS ............................................................... A-1 

APPENDIX B: STATISTICAL DISTRIBUTIONS ASSIGNED TO ACTIVITY 

CODES FOR USE IN SIMULATING METS VALUES ............................................................B-1 

APPENDIX C: ADDITIONAL ANALYSIS TABLES .............................................................C-1 

APPENDIX D: RESPONSE PREPARED BY S. GRAHAM (U.S. EPA) TO PEER 

REVIEWER COMMENTS ON APPENDIX A ......................................................................... D-1 

 iv
APPENDIX A: 

Revised Ventilation Rate (VE) Equations for Use 

 in Inhalation-Oriented Exposure Models 

by 

S. Graham and T. McCurdy 

EPA/600/X-05/008
Disclaimer to Appendix A 

This document has been reviewed in accordance with U.S. Environmental Protection 

Agency policy and approved for publication. Mention of trade names or commercial products 

does not constitute endorsement or recommendation for use. 

Abstract to Appendix A 

Using data compiled from 32 clinical exercise studies, algorithms were developed to 

estimate body mass-normalized ventilation rate (VE, L/min-kg) for 4 age groups (<20, 20-<34, 

34-<61, 61+ years of age) and both genders. The algorithms account for differences in 

ventilation rate due to activity level, variability within age groups, and variation both between 

and within individuals. A multiple linear regression (MLR) model was first used to estimate 

significant explanatory parameters (p<0.01) following natural log (Ln) transformation of body 

mass (BM) normalized oxygen consumption rate (VO2). Log transformed age (Ln(age)), gender 

(-1 for males, 1 for females), and Ln(VO2/BM) served as independent variables and regressed on 

multiple VE measurements that were collected during incremental exercise to obtain regression 

parameter estimates. The (MLR) model showed marginal statistical improvement (R2

 +5%) in 

comparison with a previous simple linear regression model for estimating VE, however the MLR 

can estimate population VE with one-half the equations formerly used and can be used to address 

uncertainty in VE estimations. A mixed-effects regression (MER) model was then constructed 

utilizing the independent variables as fixed parameters and retaining individuals and study of 

origin as random effects variables. The MER model was used to allocate the random error (ε) to 

between-person residuals distributions (inter-individual variability) and within-person residuals 

distributions (intra-individual variability). Predictive equations were executed for 5,000 

iterations at a given age (e.g., 5 year olds) or age group classification (e.g., 45-55 years old) and 

estimated ventilation rates for each model were compared at their respective 50th, 95th and 99th

percentiles. U.S. EPA’s Air Pollution Exposure (APEX) model was used to estimate population 

ventilation rates using a variety of ventilation algorithms for comparison with the MLR and 

MER at individual years in age. VE estimations from the MLR and MER algorithms were 

similar across all ages and provided reasonable ventilation rates at all percentiles and ages, 

suggesting either approach is reasonable for stochastic modeling exercises where simulation of 

activity-specific person-oriented ventilation rates is desired. 

 A-ii 
Keywords / Acronyms 

APEX Air Pollution Exposure model (OAQPS) 

BMR Basal metabolism rate 

BM Body mass 

BMI Body mass index 

BSA Body surface area 

CHAD Consolidated Human Activity Database 

EE Energy expenditure 

EVR Equivalent ventilation rate [VE/BSA] 

Fi Conversion Factors 

HR Heart rate 

HT Height 

LBM Lean Body Mass (equivalent to fat-free mass) 

METS Metabolic equivalents of work 

NAAQS National Ambient Air Quality Standard 

NERL National Exposure Research Laboratory 

OAQPS Office of Air Quality Planning and Standards 

PaCO2 partial pressure of arterial carbon dioxide • •

RQ Respiratory quotient (VCO2 /VO2 ) 

SHEDS Stochastic Human Exposure and Dose Simulation model (NERL) •

VA Alveolar ventilation rate (due to formatting issues, VA is used in report) 

•

VCOs Carbon dioxide expiration rate 

VD Dead space volume of the lung 

•

VE Total ventilation rate (due to formatting issues, VE is primarily used here) 

VT Tidal volume of the lung 

•

VO2 Oxygen consumption rate (due to formatting issues, VO2 is primarily used here) 

• •

VQ Ventilatory equivalent (VE /VO2 ) 

 A-iii 
Acknowledgments 

 The authors are indebted to a number of people who invested time in improving this 

report. Special thanks are due our OAQPS colleagues who shared their expertise in human 

exposure modeling and risk assessment which helped focus our efforts; they are, in particular: 

John Langstaff, Ted Palma, and Harvey Richmond. Gratitude is also due to Ted Johnson of TRJ 

Environmental, who provided us with information on past practices regarding uptake dose 

modeling. Finally, we thank our U.S EPA colleague, Dr. James Starr who reviewed this report 

and discussed ventilation issues with us. 

 A-iv 
Table of Contents 

1. Introduction ............................................................................................................................ A-1 

2. Methods.................................................................................................................................. A-3 

Data Set Description ........................................................................................................... A-3 

Statistical Analysis .............................................................................................................. A-3 

Algorithm Evaluation .......................................................................................................... A-5 

3. Results and Discussion .......................................................................................................... A-6 

Statistical Analysis .............................................................................................................. A-6 

Extrapolation Issues and Assumptions ............................................................................... A-9 

Performance Evaluation .................................................................................................... A-11 

4. Recommendations ................................................................................................................ A-15 

5. Future Research ................................................................................................................... A-15 

6. References ............................................................................................................................ A-16 

Attachment A1 ........................................................................................................................ A-199 

Attachment A2 .......................................................................................................................... A-31 

Attachment A3 ........................................................................................................................ A-355

List of Tables 

Table A-1. Parameter estimates used to estimate activity-specific VO2 for males and 

 females of different age groups ....................................................................... A-5 

Table A-2. Parameter and residuals distribution estimates derived from two different 

 statistical techniques and reported from Johnson (2002) for use in predictive 

 equation (1) or (2) ........................................................................................... A-7 

Table A-3. Ventilation parameter estimates (bi), standard errors (se), and residual 

 distributions standard deviation estimates (ei) using Adams data and 

 assuming equation (3) or (4) ........................................................................... A-9 

Table A-4. Residual distributions standard deviation estimates (eb and ew) using 

 data characterized by percentage of maximum VO2 (VO2m) assuming 

 equation (3) ................................................................................................... A-10 

Table A-5. Residual distributions standard deviation estimates (eb and ew) using 

 data categorized by percentage of maximum VO2 (VO2m) assuming 

 equation (4) ................................................................................................... A-10 

Table A-6. Recommended inhalation rates (L/min) from U.S. EPA (1997) Table 5-23 A-12 

Table A1-1. Total subjects for each study, gender, and exercise ergometry used ............ A-20 

 A-v 
 A-vi 

List of Figures 

Figure A-1. Pathways for estimating various ventilation parameters and metrics ............. A-1 

Figure A-2. Ventilatory quotient (VQ) as a function of age during exercise ..................... A-8 

Figure A-3. Estimated ventilation rates (VE, L/min) for females (left) and males 

 (right) while performing low-level (top), moderate (middle), and 

 vigorous (bottom) activities .......................................................................... A-13 

Figure A-4. Estimated population ventilation rates (VE, L/min) for 20,000 persons 

 using APEX and the mixed effects regression (MER) algorithm 

 (Equation 4 and Table 3) ............................................................................... A-14

Figure A2-1. Relationship between total ventilation rate (VE) and oxygen 

 consumption rate (VO2) during exercise ....................................................... A-33 

Figure A2-2. Relationship between body mass normalized total ventilation rate 

 (VE/BM) to oxygen consumption rate (VO2/BM) during exercise ............... A-33 

Figure A2-3. Relationship between the natural logarithm of total ventilation rate 

 Ln(VE) and oxygen consumption rate Ln(VO2) during exercise .................. A-34 

Figure A2-4. Relationship between body mass normalized total ventilation rate 

 Ln(VE/BM) to oxygen consumption rate Ln(VO2/BM) during exercise ...... A-34 

Figure A3-1. Comparison of selected percentiles of estimated event-based 

 ventilation rates from 20,000 person APEX model simulation using 

 different ventilation algorithms ..................................................................... A-37 

Figure A3-2. Comparison of estimated event-based ventilation rate percentiles from 

 20,000 person APEX model simulation using mixed effects regression 

 (MER-left) and Johnson (2002) (right) ventilation algorithms ..................... A-38 

Figure A3-3. Percent difference of estimated event-based ventilation rate percentiles 

 from 20,000 person APEX model simulation using mixed effects 

 regression (MER-left) and Johnson (2002) (right) ventilation algorithms ... A-39 
1. Introduction 

 The use of population-based probabilistic exposure models in risk assessments has 

increased over the past few decades, largely due to their ability to simulate human activities more 

realistically than previous models that used mostly static but conservative estimates of 

physiologic parameters such as ventilation rate (VE, commonly in L min-1). Some of the early, 

more advanced human exposure models were developed by U.S. EPA’s Office of Air Quality 

Planning and Standards (OAQPS) in the 1980s, each containing an inhalation dose metric since 

their inception (Johnson, 1995; McCurdy, 1994a, 1995). The first series of these models were 

known as NAAQS Exposure Model NEM and probabilistic NEM (pNEM) models. The 

ventilation algorithm became more detailed over time, culminating with equivalent ventilation 

rate (EVR; VE normalized to body surface area (BSA)) and alveolar ventilation rate (VA) 

estimations used by a number of the pNEM models that are described in numerous 

OAQPS-sponsored papers and reports (Johnson, 2002; Johnson and Adams, 1994; Johnson and 

Capel, 2002; Johnson et al., 1995, 1996; Johnson and McCoy, 1995; McCurdy, 1994b; and 

McCurdy, 1997a). More recently, the National Exposure Research Laboratory (NERL) has 

developed the Stochastic Human Exposure and Dose Simulation (SHEDS) model, essentially 

adopting the ventilation algorithm used in OAQPS’s Air Pollution Exposure (APEX) model, 

itself a variant of the pNEM models. The impact of using advanced procedures for dose rate 

metrics has been evaluated by McCurdy (1997b, c); however an integrated approach for 

estimating multiple ventilation parameters has not yet been developed. 

 To estimate inhalation exposure and dose in these fairly complex models, a standard but 

flexible algorithm is required. One that not only addresses variability in breathing rates but can 

simulate differences in the site of action of pollutants within the respiratory system (e.g., ozone, 

particulate matter deposition) and variable chemical uptake characteristics (e.g., absorption 

across the alveolar membrane versus total absorption). Using current U.S. EPA exposure model 

approaches for approximating ventilation rates and considering the need to address ventilation 

for multiple classes of pollutants, a framework of activity-specific ventilation parameters was 

constructed and is depicted in Figure A-1. 

BMR METS

VQ

* * =

BM

HT

BSA

EVR

CHAD

VD/VT

VE

.

F1

(EE Æ VO2)

VA

.

VO2

.

RQ/PaCO2

F2

BMR METS

VQ

* * =

BM

HT

BSA

EVR

CHAD

VD/VT

VE

.

F1

(EE Æ VO2)

VA

.

VO2

.

RQ/PaCO2

F2

Figure A-1. Pathways for estimating various ventilation parameters and metrics. 

 A-1 
 Central to the framework is the U.S. EPA’s Consolidated Human Activity Database 

(CHAD), a database of nearly 23,000 person-days of time-location-activity data useful for 

exposure modeling purposes (McCurdy et al., 2000). Distributions of metabolic equivalents 

(METS) are assigned in CHAD to every activity that respondents participated in. These METS 

distributions have been developed from a review of the exercise physiology and clinical nutrition 

literatures (McCurdy, 2000) and represent the ratio of the energy needed for the activity 

performed to the energy needed to sustain life (basal metabolism). The METS are fundamental 

to simulating an individual’s breathing rate while the person is performing a variety of activities 

(e.g., running, walking, sleeping). 

 To estimate activity-specific ventilation rates, first a prediction equation for basal 

metabolic rate (BMR, in kilocalories min-1) is used to estimate the simulated individual’s resting 

metabolic rate from their body mass (BM), or from BM and height (HT) together. Then activityspecific METS (METSA) are sampled via Monte-Carlo techniques and multiplied by a person’s 

estimated BMR to obtain a single realization of the energy expenditure rate (EE, kilocalories 

min-1). This rate of energy expenditure is retained over the duration of the activity (termed here 

as an “event”), which can be as short as 1 minute or as long as one hour (due to the structure of 

CHAD). 

 Thus mathematically, event-specific EE for an individual (EEEi) is defined as: 

EEEi = BMRi * METSA

 Estimated EEEi can then be converted to an activity-specific oxygen consumption rate 

(VO2Ei) using a gender-specific relationship expressed as a uniform distribution (F1i,

L-O2/kilocalorie) (McCurdy, 2000) as follows: 

VO2Ei = EEEi * F1i

VO2, however, is not the final physiological process to be simulated since most air pollution 

clinical studies do not use it as the end-point ventilation metric. Most of these studies use VE or 

EVR, and some exposure models, particularly OAQPS’s APEX model for carbon monoxide 

(APEX-CO), need VA (commonly in L min-1) for their inhalation modeling approach. By 

definition, VA is a fraction of VE and is important in estimating respiratory uptake of gases 

(e.g., O2, CO, CO2) and chemicals that likely act as gases (e.g., benzene, 1-3-butadiene 

[Lin, et al., 2001]). Regardless, all three mentioned ventilation metrics (VE, EVR, VA) can be 

obtained from VO2, either directly or indirectly, thus VO2 is fundamental to the development of 

each of these ventilation algorithms. 

 The pathway from VO2 to VE can be direct or indirect, with the indirect approach itself 

having a few options: from VO2 to VA and then to VE, or from VO2 to VE using the ventilatory 

quotient (VQ or alternatively, the ventilatory equivalent). VQ is simply the unitless ratio of VE

to VO2 when both metrics are in the same units. This ratio is non-linear with work rate however, 

varying between 20 and 32 in healthy people at low-to-moderate work rates while higher at more 

extreme exercise levels (McArdle et al., 1991). While there are nuances among the many ways 

 A-2 
that VE and EVR have been estimated over the years, in general the approach taken has been the 

VQ pathway depicted in Figure A-1. VA has been estimated by Johnson (2002) using a direct 

relationship between VO2 and VA originally described by Galletti (1959). For a more complete 

discussion of how ventilation rate has been modeled by OAQPS, see Section 9 of Johnson 

(2002). 

 This NERL Research Report describes an approach to estimating VE directly from VO2

using a series of regression-based equations derived from 25 years of clinical studies conducted 

by Dr. William C. Adams of the University of California at Davis. Much of the work cited 

above has been predicated upon past work and data provided by Dr. Adams, particularly Adams 

(1993) and Adams et al. (1995). OAQPS and NERL at different times acquired independent 

(non-overlapping) data sets from his laboratory at the University of California-Davis. These data 

have been extensively analyzed by OAQPS contractors, particularly Ted Johnson of TRJ 

Environmental (and previously with IT Technology). In addition to the citations noted above 

regarding analysis of Dr. Adams’ data, see also Johnson et al. (1998). 

 OAQPS requested that staff in the Exposure Modeling Research Branch of NERL review 

the literature on calculating VA since a previous review of the algorithms used in pNEM/CO 

indicated that a constant in the equation possibly varied non-linearly with exercise rate. That 

review has not been completed as of this date, but as an outgrowth of this work NERL staff 

decided to first investigate a VE algorithm for use in both the APEX and SHEDS inhalation 

modules. It is this work that is described below. 

2. Methods 

Data Set Description 

 The data set acquired is listed and briefly described in communication memos authored 

by Dr. Adams and provided in Attachment A1. Data from 32 panel studies collected over a 

25-year period by the same laboratory were obtained in electronic format. The number of 

subjects included within these studies was nearly one-thousand, undoubtedly one of the largest 

datasets of its kind. The data set used was a Microsoft ® Excel (.xls) file obtained from a disk 

labeled “Converted Adams Data”. The file used in this analysis (adam2.xls) was considered as 

the raw data file, since also on this disc was included an ASCII text version of the file and the 

memo from Dr. Adams describing the data set. 

 The raw data required physical manipulation and mathematical transformation to allow 

for statistical analyses. Details of the procedures used as part of this research are described 

further in Attachment A2. Briefly, due to the format of the original study data sets, a file was 

created containing a single vector for each individual ventilation parameter. Data were then 

screened for erroneous and potentially extreme values. Ventilation parameters (VE and VO2) 

were normalized to body mass and followed with a natural logarithm (Ln) transformation. 

Statistical Analysis 

 All statistical analyses were performed using SAS® software, version 8.2.1 (SAS 

Institute, Cary, NC). Parameters considered useful in model simulations (i.e., those that could 

capture a significant degree of variability and are consistent with current exposure modeling 

 A-3 
structure) were first evaluated for statistical significance (p<0.01) using an analysis of variance 

(ANOVA). Then, a simple linear regression (SLR) model was developed of the form yi = b0 + 

b1xi + εi to estimate parameter coefficients for use in predictive equations: 

 Ln(VE/BM)i = b0 + (b1 * Ln(VO2/BMi)) + ei Eq. (1) 

where b0 = the regression intercept, b1 = the regression slope coefficient, and ei representing 

individual variability in ventilation rate. The coefficient of determination (R2

) was used in 

evaluating the regression model since it represents the proportion of total variance of the 

dependent variable “explained” by the independent variables. 

 The approach was modified slightly for predictive purposes to reflect additional test 

factors contributing to variance in the ventilation rate. The model presented here was given as 

Equation 9-6 in Johnson (2002) and interpreted as follows, where b0 = the intercept and b1 = the 

slope regression coefficient: 

 Ln(VE/BM)i = b0 + (b1 * Ln(VO2/BMi)) + ebi + ewi Eq. (2) 

 It was assumed here that the predictive regression equation represents a mixed-effects 

regression (MER) model containing both fixed and random effects variables. VO2 was 

considered a fixed parameter and subject and study were random effects variables used to 

estimate the between-person (inter-individual variability) residuals distribution (eb) and withinperson (intra-individual variability) residuals distribution (ew) rather than simply random error 

(ε) alone. Each of the residuals are normally distributed, with a mean of 0 and an estimated 

standard deviation of σ

2

 (i.e., N{0, σ

2

}). Statistical significance of estimated coefficients and the 

regression model was assessed at p<0.01. The purpose of this regression analysis was to 

duplicate the model presented by Johnson (2002) and provide standard errors associated with the 

parameter estimates. 

Finally, multiple linear regression (MLR; yi = b0 + b1xi1 + b2xi2 +...+ bixip + εi) was 

implemented to include both age and gender as independent variables: 

 Ln(VE/BM)i = b0 + (b1 * Ln(VO2/BMi)) + (b2 * Ln(agei)) + (b3 * genderi) + ei Eq. (3)

The age of each study subject was transformed by the natural logarithm. Gender was used as a 

classification variable, with males represented by -1 and females represented by 1. The 

regression was set in this manner to provide for reasonable estimation of ventilation rates even if 

gender was unknown (gender=0). Random error (ε) can also be allocated to two variance 

components as described above for equation (2) using a MER model that includes age and 

gender as additional variables. This new model is represented as: 

 Ln(VE/BM)i = b0 + (b1 * Ln(VO2/BMi)) + (b2 * Ln(agei)) + (b3 * genderi) + ebi + ewi Eq. (4) 

Statistical significance of estimated coefficients and the regression model was assessed at 

p<0.01. 

 A-4 
 Modification of the age groupings originally developed by Johnson (2002) was 

performed to determine if the statistical performance of the predictive equations could be 

improved. Criteria for the model development included individual regression coefficient 

significance (p- or t-value), total model explanatory power (R2), and stability of the regression 

coefficients. For this last criterion, it was desired that coefficients neither greatly increase nor 

decrease in the individual regression equations compared with previous coefficient estimates 

while expanding/compressing age classifications. Age groupings were varied by one-year 

increments until the evaluation criteria described above was optimized, that is, models containing 

the greatest R2, with statistically significant coefficients that varied minimally were retained. 

Algorithm Evaluation 

 Each of the algorithms for estimating ventilation were evaluated using one or both 

methods described below to determine the range possible outcomes for individuals and a 

population. Selected evaluations for the MLR and MER (using equations 3 and 4, respectively) 

are presented in the main text, while additional evaluations are provided in Attachment A3. 

 Ventilation rates were first estimated using Crystal BallTM software (Decisioneering, Inc., 

Denver Colorado). Age- and gender-specific body weights for simulated individuals were 

estimated by probabilistic sampling of distributions provided by Burmaster and Crouch (1997). 

Basal metabolic rate was estimated using age- and gender-specific equations presented in 

Schoefield (1985), with age itself being sampled from uniform distributions within the age 

groupings used in our analyses. Activity-specific VO2 was generated using METS distributions 

for low, moderate, and vigorous intensity activities combined with the unit conversions given in 

Table A-1. Ventilation rates were estimated for 5,000 hypothetical persons within each age (or 

age grouping) and gender category using predictive equations (3) and (4) and their respective 

parameters. To estimate variability in ventilation rates, each of the residuals distributions were 

probabilistically sampled while the intercept and coefficients held as constants, thus each 

estimated ventilation rate is representative of one activity performed by one hypothetical 

individual. Median (p50), 95th (p95), and 99th (p99) percentiles of the hypothetical population 

distribution of estimated ventilation rates were compiled by age. The output represents the 

possible range of expected ventilation rates across the population at a moment in time. 

Table A-1. Parameter estimates used to estimate activity specific VO2 for males and females 

of different age groups.1

Age group Gender 

METS-Activity Level2 Conversion Factors 

Low Moderate Vigorous 

Energy to 

Oxygen 

(L-O2/kcal) 

Unit 

(MJ/kcal)/ 

(min/day) 

Child 

(0-18 yrs) 

Male N{2.0,0.34} N{5.0,0.85} N{9.0,1.5} U{0.20-0.22} 

239/1440 Female N{1.5,0.26} N{4.5,0.77} N{8.0,1.4} U{0.19-0.21} 

Adult 

(>18 yrs) 

Male N{2.5,0.43} N{6.5,1.1} N{10,1.7} U{0.20-0.22} 

Female N{2.0,0.34} N{5.0,0.85} N{9.0,1.5} U{0.19-0.21} 

1

 Distribution type and parameters used: N=normal {arithmetic mean, standard deviation}; U=Uniform 

{min,max}. 

2

 It was assumed that the relative standard deviation of the METS for each distribution was 17% (see 

McCurdy and Graham, 2004) 

 A-5 
 A second method for evaluation was conducted using OAQPS’s APEX model, version 

4.0 (see U.S. EPA, 2005 for details on the model algorithms). Twenty thousand individuals were 

simulated for one day to allow for the comparison of selected ventilation algorithms developed 

as would be used in an actual exposure model. Activity-specific ventilation rates were generated 

by APEX using human activity diaries from CHAD and the general approach described above 

and outlined in Figure A-1. Diaries in CHAD are at a minimum disaggregated to hourly 

components, that is, the maximum time step for an activity or location inhabited could be one 

hour, thus up to 24 events in a day. However much of the data are further divided such that 

within one hour there may be multiple activities performed or multiple locations inhabited, 

upwards to 1 minute in duration. Since every simulated individual had multiple estimations for 

ventilation rate depending on their activities performed (generally ranging from 30-40 events in a 

day), distributions were first calculated for each person followed by an estimate of the population 

distribution at each age (generally between 1 and 400 persons were simulated for each year of 

age). The median (p50), 95th (p95), and 99th (p99) percentiles and maximum ventilation rates 

estimated with the APEX model represent the variability in the mid-upper range of ventilation 

rates for individuals within a population. It should be noted that the maximum for all individuals 

is the same as the 99th percentile unless there was more than 99 events (rare if occurs at all). 

3. Results and Discussion 

Statistical Analysis 

 Both age and gender were used in the development of several regression equations 

derived from the Adams data set and summarized in Table 9-1 of Johnson (2002); however 

significance of these variables was not reported there. An analysis of variance was performed 

here on VE, utilizing the 4 age groups (i.e., <18, 18-44, 45-64, >65 years old) and two genders as 

classification variables indicated by Johnson (2002). VO2 normalized to body mass was 

included as an additional independent variable. Age group, gender, their interaction term (age 

group by gender), and VO2 were each significant explanatory parameters (all p<0.003). 

 Results of the simple linear regression analysis, the simple mixed model addressing fixed 

and random effects, and parameter coefficients reported by Johnson (2002) assuming equations 

(1) or (2) are presented in Table A-2. Regression model intercept and slope were statistically 

significant parameters in each of the regression models. 

 There were marginal differences between the simple regression coefficients and the 

simple mixed model coefficients developed in this work; both the intercepts and slopes were 

systematically lower for the simple regression. The results from the simple mixed model and 

Johnson (2002) were nearly identical with the most notable differences seen in the residuals 

distributions, albeit at a minimal level. 

 Following this single variable model comparison, age and gender were investigated as 

additional independent variables for use in a multiple linear regression model. Gender was 

already deemed significant based on the ANOVA and, since its use as a parameter in a multiple 

linear regression would halve the number of equations needed for ventilation simulations, was to 

be included as a parameter in the regression model. For age, it was hypothesized that it would 

 A-6 
have a statistically significant effect on the relationship between VE and VO2, not just among the 

different age groups but also within a given age group. Figure A-2 shows the relationship 

between VQ and age, with the most notable variation of VQ for those under age 18. These data 

(age<18) were not analyzed by Johnson (2002) due to lack of availability. Age, when included 

in a preliminary multiple regression model, was determined to be a significant explanatory 

parameter for both genders where age<18 and for males only within the other age groups (data 

not shown here). Estimated coefficients for the females, although not statistically significant, 

were generally consistent with those of the males. 

 When VQ was plotted by age (Figure A-2), it was observed that a few of the subjects 

contained excessive VQ values, such that further culling of the data set was warranted. 

Observations of VQ in excess of 50 were removed based on a review of the relevant literature 

undertaken as part of the work documented by McCurdy and Graham (2004). Based on this 

criterion, 13 data points were removed. No single subject had more than one data point 

removed. The impact of the additional culling was negligible (not reported). 

Table A-2. Parameter and residuals distribution estimates derived from two different 

statistical techniques and reported from Johnson (2002) for use in predictive 

equation (1) or (2).

Age 

group n Gender Methoda

Ln(VO2/BM) Residuals

R2 b0 seb0 b1 seb1 eb ew

<18 

315 F 

SLR 3.214 0.089 0.941 0.022 0.1609 0.8504 

MER 3.263 0.050 0.950 0.012 0.1427 0.0735 

Johnson Not Performed

288 M 

SLR 3.054 0.103 0.913 0.026 0.1715 0.8069 

MER 3.180 0.052 0.941 0.012 0.1600 0.0722 

Johnson Not Performed

18-44 

1473 F 

SLR 4.021 0.040 1.182 0.011 0.1736 0.8790 

MER 4.358 0.034 1.276 0.009 0.1351 0.1176 

Johnson 4.357 1.276 0.1351 0.1182 

3145 M 

SLR 3.758 0.023 1.130 0.007 0.1826 0.8965 

MER 3.983 0.022 1.194 0.006 0.1219 0.1382 

Johnson 3.991 1.197 0.1228 0.1395 

45-64 

60 F 

SLR 3.360 0.239 0.998 0.055 0.1401 0.8498 

MER 3.462 0.153 1.023 0.034 0.1152 0.0774 

Johnson 3.454 1.021 0.1106 0.0769 

641 M 

SLR 3.824 0.060 1.117 0.016 0.1584 0.8884 

MER 4.019 0.047 1.166 0.012 0.1172 0.1073 

Johnson 4.018 1.165 0.1107 0.1112 

65+ 

45 F 

SLR 2.687 0.297 0.846 0.068 0.0960 0.7820 

MER 2.958 0.143 0.908 0.032 0.0920 0.0341 

Johnson 2.956 0.908 0.0886 0.0338 

317 M 

SLR 3.686 0.090 1.060 0.023 0.1280 0.8729 

MER 3.731 0.055 1.071 0.013 0.1092 0.0632 

Johnson 3.730 1.071 0.1082 0.0632 

a SLR: simple linear regression model (PROC REG in SAS) when using equation (1); MER: mixed 

effects regression model (PROC MIXED in SAS) when using equation (2); Johnson: data reported in 

Johnson (2002) for use with equation (2)

 A-7 
Figure A-2. Ventilatory quotient (VQ) as a function of age during exercise. 

 To determine optimum age groups for the final multiple linear regression model, the 

boundary values of the age groups--i.e., the youngest and oldest age groups determined by 

Johnson (2002) (<18 and 65+ years of age, respectively) were first evaluated. Based on the 

criteria described above, the lower and upper age groups were redefined to be <20 years old and 

>60 years old. Two “inner” age groupings (20 to <34; 34 to <61) were also optimized based on 

their fit with each other and with the lower and upper boundaries. The group comprising ages 

34 to <61 could have been further subdivided (e.g., 34 to <45, 45 to <61 groups provided a good 

statistical fit based on the semi-quantitative criteria), however the regression coefficients for the 

intercept and age variables were dramatically altered for the 34-<45 age group (decreased and 

increased, respectively) in comparison with the other age groups. It is not apparent whether this 

response is physiologically representative of this age group, or that it is a function of the data set 

itself; therefore, the larger age grouping was retained. 

 Final ventilation parameter estimates for use in equations (3) or (4) following age group 

optimization are presented in Table A-2. Slightly improved explanatory power was achieved 

with the new models (as measured by the multiple linear regression model, about 90% of total 

variance is now explained) compared with the earlier analyses (on average 85%). Each of the 

regression models and all estimated coefficients were statistically significant (p<0.01) except 

where noted. 

 A-8 
Table A-3. Ventilation parameter estimates (bi), standard errors (se), and residual 

distributions standard deviation estimates (ei) using Adams data and assuming 

equation (3) or (4).

Age 

group n Methoda

Ln(VO2/BM) Ln(age) Gender Residuals 

R2 b0 se b0 b1 se b1 b2 se b2 b3 se b3 eb ew

<20 1085 

MLR 4.4329 0.0579 1.0864 0.0097 -0.2829 0.0124 0.0513 0.0045 0.1444 0.9250 

MER 4.3675 0.0650 1.0751 0.0087 -0.2714 0.0190 0.0479 0.0077 0.0955 0.1117 

20-<34 3646 

MLR 3.5718 0.0792 1.1702 0.0067 0.1138 0.0243 0.0450 0.0031 0.1741 0.8927 

MER 3.7603 0.1564 1.2491 0.0061 0.1416 0.0493 0.0533 0.0061 0.1217 0.1296 

34-<61 1083 

MLR 3.1876 0.1271 1.1224 0.0120 0.1762 0.0335 0.0415 0.0095 0.1727 0.8925 

MER 3.2440 0.2578 1.1464 0.0088 0.1856 0.0674 0.0380b 0.0172 0.1260 0.1152 

61+ 457 

MLR 2.4487 0.3646 1.0437 0.0195 0.2681 0.0834 -0.0298 0.0100 0.1277 0.8932 

MER 2.5826 0.7013 1.0840 0.0122 0.2766 0.1652 -0.02081c 0.0149 0.1064 0.0676 

a MLR: multiple linear regression model (PROC REG in SAS) when using equation (3); MER: mixed-effects regression 

(PROC MIXED in SAS) when using equation (4); b p=0.0286; c p = 0.1656. 

Extrapolation Issues and Assumptions 

 Prior to algorithm evaluation, an analysis of the residuals distributions was first 

undertaken in a manner that mimicked the way the equations would be applied in human 

exposure modeling simulations. Note that all of the data were collected while individuals were 

performing exercise; however exposure modelers will commonly extrapolate the data to activity 

situations outside of the sample collection range. For example, when estimating a typical 

person’s daily exposure, there is not a significant time spent exercising but more spent 

performing less strenuous activities such as sleeping. Since resting measurements were not 

collected by Dr. Adams for most of his subjects, an evaluation of the data bracketed by percent 

of maximum VO2 (VO2m) was decidedly appropriate in determining whether the data could be 

extrapolated downward to reasonably simulate low energy-expenditure activities. Typically VO2

reserve (VO2res) is used; however, this was not measured in the Adams’ studies. A tripartite 

categorization of the measured VO2 for a step relative to the VO2m of each subject was 

undertaken using <33.3%, 33.3-66.6%, >66.6% of VO2m as the category boundary values. This 

categorization has been done previously based on intervals of low, moderate, and vigorous 

exercise and recently summarized from the exercise physiology literature (McCurdy and 

Graham, 2004). Residuals distributions were estimated using the multiple linear regression and 

mixed models as was done above [equations (3) and (4)], but now accounting for the tripartite 

categorization. 

 Residuals for the MLR model using equation (3) and the tripartite categorization (Table 

A-4) were generally lower at the lower and moderate level exercise levels compared with the 

estimated total residuals in Table A-3. This indicates there is less variability in ventilation rate at 

the low and moderate exercise levels. 

 A-9 
Table A-4. Residual distributions standard deviation estimates (eb and ew) using data 

categorized by percentage of maximum VO2 (VO2m) assuming equation (3). 

Age 

Group 

<33.3% V02m 33.3-66.6% V02m >66.6% V02m 

ei x n ei x s ei x s 

<20 0.1233 123 2.0 0.1007 179 2.5 0.1523 137 2.8 

20-<34 0.1486 127 1.9 0.1184 428 2.9 0.1734 521 4.1 

34-<61 0.1954 74 1.8 0.1568 144 3.2 0.1592 139 3.5 

61+ 0.0974 9 1.9 0.1144 78 2.7 0.1344 67 3.4 

x is the number of subjects in given age group and tripartite categorization where measurements were 

collected. 

n is the average number of V02 samples subjects had within each age group and tripartite 

categorization.

 For the mixed model, between-person residuals (eb) were generally higher and the withinperson variability was lower for all age groups using the tripartite breakdown (Table A-5) 

compared to the residuals distributions estimated using all of the data combined (Table A-3). 

This indicates that there is greater variability in ventilation between persons and less variability 

within a person than would be simulated when an individual is performing low-level activities. 

One may expect this to occur intuitively since the tripartite breakdown basically restricts the total 

number of measurements for an individual while the number of individuals for the most part has 

remained the same. There was a small difference in the total number of subjects in each exercise 

category because some of the individuals did not attain a level of exercise >66.6% VO2m; 

however, this was not the principal reason for the observed residual differences since 

consistently even fewer individuals were measured at exercise <33.3% VO2m (Tables 4 and 5). 

In addition, more measurements were consistently obtained for exercise >66.6% VO2m on 

average per person than at the low or moderate levels of exercise. 

Table A-5. Residual distributions standard deviation estimates (eb and ew) using data 

categorized by percentage of maximum VO2 (VO2m) assuming equation (4).

Age Group 

<33.3% V02m 33.3-66.6% V02m >66.6% V02m 

eb ew eb ew eb ew

<20 0.1217 0.0506 0.0951 0.0456 0.1637 0.0741 

20-<34 0.1291 0.0728 0.1088 0.0524 0.2190 0.0740 

34-<61 0.1522 0.0938 0.1444 0.0581 0.1936 0.0710 

61+ 0.1244 0.0164 0.1112 0.0362 0.1422 0.0563 

Numbers of individuals and samples collected per individual are the same as indicated in Table A-4. 

 These results in Tables A-4 and A-5 imply that activity-level specific equations may be 

warranted to better simulate an individual’s ventilation rate over all ranges of exercise levels. 

However, given the sample size of the data set analyzed, further subclassification of the data 

would likely lead to greater instability of the regression coefficients and prevent reasonable 

 A-10 
ventilation estimations for all exercise levels, age groups, or genders. Using the data provided in 

Table A-3 and implementation of either equation (3) or equation (4) should not have a large 

impact on a population-based exposure analyses. 

 It should be noted that in extrapolating lower than the age range of the original data 

(e.g., <3.6 years old), it is assumed that regression equations are suitable for these children and 

infants. The trend for VQ illustrated in Figure A-2 is likely to be continued upward for younger 

children and infants due to the anticipated reduction in efficiency (i.e., underdevelopment) of 

their respiratory systems. However, since the natural log for age <1 is negative [i.e., ln(1)=0; for 

x<1, ln(x)<0], the equations are inappropriate for infants <1. 

Performance Evaluation 

 The algorithms underwent a probabilistic evaluation using either representative 

distributions of exposure model input parameters (evaluation method 1) and/or by using the 

algorithm in an actual exposure model (evaluation method 2). When simulating multiple 

activities for one individual and for a population, alternative sampling strategies are 

recommended below for estimating variability and uncertainty. Ventilation rates estimated using 

the general input parameter distributions (evaluation method 1) are summarized in Figure A-3 

for females and males separately from using either the MLR or MER models. 

 Ventilation estimates for both the MLR and MER models are comparable to one another, 

particularly for young persons at each of the exertion levels and at the various mid to upper 

percentiles, however some trends were noted. Even though each simulation is independent, 

comparisons of the average percent difference at selected percentiles for each of the 5,000 person 

simulations are considered appropriate. Female ventilation rates estimated using the MLR 

tended to be slightly higher on average at each of the percentiles (average percent difference of 

between 3.5-4.0%) than those estimated using the MER for low exertion activities. This trend 

was also consistent with the results for males, whereas the MLR estimated ventilation rates were 

on average 1.6-2.9% higher than those estimated using the MER algorithm. Moderate exertion 

activities yielded the most similar results in both males and females (-0.6 to 0.1% and -0.1 

to 0.9%, respectively). However, ventilation rates associated with vigorous activity levels were 

1.3-1.8% lower in females, and 1.8-2.3% lower in males when comparing the MLR with the 

MER algorithm. These results suggest that either approach is acceptable for use in estimating 

ventilation rate, but that the MER model may be slightly more responsive to changes in activity 

level and better capture variability in ventilation rates, specifically when using the intra- and 

inter-personal residuals. Overall female ventilation rates ranged from 5 to 20 L/min, 

20 to 50 L/min, and 40 to 100 L/min for low, moderate, and vigorous exertion activities, 

respectively using either algorithm. Ventilation rates for males ranged higher for the varying 

activities, with 10 to 35 L/min, 25 to 110 L/min, and 50 to 175 L/min estimated for low, 

moderate and vigorous exertion, respectively using either algorithm. 

 Additional evaluations were performed on the MER algorithm by estimating potential 

population-based ventilation rates with the APEX model. Results for the 20,000 person 

simulation of both genders are presented in Figure A-4. At any given percentile, ventilation rates 

increase rapidly with age for persons less than 20 years old, stabilize from ages 20 to about 60, 

then gradually decline with further increases in age. The distribution of these selected mid to 

upper percentiles for ventilation rate in individuals spans by about a factor of 5 or more, 

 A-11 
 A-12 

depending primarily on age. Values at older ages are compressed, possibly biased by the small 

number of persons simulated (10-50 persons for each year in age 80 to 90; 1-10 for each year in 

age >90). Rarely did the upper percentile ventilation rate exceed 100 L/min, the majority of 

simulated persons performed activities requiring less than 50 L/min, with most breathing about 

10 L/min throughout the day. 

 Results are also compared to those summarized by U.S. EPA (1997), but much of the 

data presented here are in fact approximations to that report utilizing similar approaches. 

Table 5-6 in U.S. EPA (1997) contains somewhat comparable data disaggregated by age and 

gender, adults only, for average inhalation rates. The origin of the U.S. EPA (1997) data, 

however, is Adams (1993), which is used extensively in this report. Recommended inhalation 

rates from Table 5-23 in U.S. EPA (1997), based on measured and approximated data, are 

presented in Table A-6 and are assumed to be reflective of "average" or likely inhalation rates 

and are generally comparable to the medians reported here in Figures 3 and 4. 

Table A-6. Recommended inhalation rates (L/min) from U.S. EPA (1997) Table 5-23.

Rest Sedentary Low Medium High 

Children 5.0 6.7 16.7 20 31.7 

Adults 6.7 8.3 16.7 26.7 53.3 
Percentiles of Estimated VE for Females Performing Low-Exertion Activities Using Selected 

Parameter Distributions

0

5

10

15

20

25

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Percentiles of Estimated VE for Males Performing Low-Exertion Activities Using Selected 

Parameter Distributions

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Percentiles of Estimated VE for Females Performing Moderate-Exertion Activities Using 

Selected Parameter Distributions

0

25

50

75

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Percentiles of Estimated VE for Males Performing Moderate-Exertion Activities Using Selected 

Parameter Distributions

0

25

50

75

100

125

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Percentiles of Estimated VE for Females Performing Vigorous-Exertion Activities Using 

Selected Parameter Distributions

0

25

50

75

100

125

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Percentiles of Estimated VE for Males Performing Vigorous-Exertion Activities Using Selected 

Parameter Distributions

0

25

50

75

100

125

150

175

0 20 40 60 80 100

Age (years)

VE (L/Min)

p50-MLR

p95-MLR

p99-MLR

p50-MER

p95-MER

p99-MER

Figure A-3. Estimated ventilation rates (VE, L/min) for females (left) and males (right) while 

performing low-level (top), moderate (middle), and vigorous (bottom) activities. 

Median (p50), 95th (p95) and 99th (p99) percentiles are given for a 5,000 person 

simulation for each of the multiple parameter regression models. 

 A-13 
p99 VE using 20,000 persons from APEX and using Mixed Model

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

Age (years)

VE (L/min)

p99mean

p99p50

p99p95

p99p99

p99max

p99p5

p99p1

p99min

p95 VE using 20,000 persons from APEX and using Mixed Model

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

Age (years)

VE (L/min)

p95mean

p95p50

p95p95

p95p99

p95max

p95p5

p95p1

p95min

p50 VE using 20,000 persons from APEX and using Mixed Model

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Age (years)

VE (L/min)

p50mean

p50p50

p50p95

p50p99

p50max

p50p5

p50p1

p50min

Figure A-4. Estimated population ventilation rates (VE, L/min) for 20,000 persons using APEX 

and the mixed effects regression (MER) algorithm (Equation 4 and Table A-3). The 

full distribution of the median (p50-top), 95th (p95-middle) and 99th (p99-bottom) 

percentiles are represented for each age. 

 A-14 
4. Recommendations 

 We recommend that for inhalation exposure modeling purposes, the regression equation 

coefficients listed in Table A-3 be used with equation (3) or (4) to estimate activity-specific body 

mass-adjusted VE for simulated individuals in the age groups listed. Estimated regression 

coefficients and output from each of the algorithms were very similar, however gender within the 

MER algorithm was not considered statistically significant for the older age group compared 

with the MLR. 

 To obtain estimates of VE in units of L min-1, the antilog of the predicted value multiplied 

by the subject’s body mass (BM in kg) would be taken. Ages less than one year old are not to be 

approximated (i.e., persons with age<1 can be estimated as one year old or using an alternative 

approximation). In addition, we suggest that individual variability be addressed by “fixing” the 

regression parameter estimates and using random sampling from each of the residual 

distributions {N: 0, sd} to account for individual variability, with the MER model used when 

addressing inter- and intra-individual variability. Inter-individual variability is addressed 

through selection of between-person residuals (eb) once per simulated individual. Intraindividual variability is addressed through selection of within-person residuals (ew) every time an 

individual undertakes an activity. To address uncertainty, we recommend that additional 

simulations should be undertaken using the standard errors (se) of the regression coefficients 

themselves to address measurement error and unobserved variability. 

5. Future Research 

 As mentioned earlier, a method for estimating VA to remain consistent with the VE

estimation is currently being investigated by both NERL and OAQPS. Currently, the pathway 

from VO2 to VA is considered as a direct linear proportionality (i.e., a constant value of 19.63) 

and estimated independently from VE. A preliminary literature review indicates that the 

approximation is reasonable and may be linear for low to moderate exercise levels, but at a 

minimum, there is variability in VA at all exercise levels that is not accounted for by the point 

estimate used to modify VO2. Further investigation is needed to determine if the VO2 to VA

relationship is maintained for vigorous activity levels. In addition, the lack of a direct 

computational link with VE potentially can lead to simulated values of VA in excess of VE, a 

physiological impossibility. 

 One potential method would be to estimate VA from VE by using another physiological 

relationship: the ratio of dead space volume-to-tidal volume (VD/VT, see Figure A-1). 

Physiological dead space is the volume of the lung that does not take part in gas exchange and is 

comprised of basic anatomic dead space (e.g. volume of trachea and bronchioles) and areas of 

lung with reduced functionality (e.g., damaged alveolar regions, increased dead space due to 

bronchiole expansion during exercise). Tidal volume is the total amount of air breathed upon 

inspiration, not all of which comes in contact with the alveolar region of the lung due to the 

presence of physiologic dead space. It has been found that VD/VT does not remain constant over 

varying exercise levels, with VT increasing at a greater rate than VD during increasing exercise 

level. The effect of this non-linear relationship in simulating VA (does VA increase linearly with 

increasing VO2 at all exercise levels?) has not yet been determined. The relationships of VE, 

 A-15 
VD/VT, and VO2 with VA and other ventilation parameters (e.g., the respiratory quotient or RQ) 

will be explored in greater detail and integrated in a second report. 

6. References 

Adams WC. 1993. Measurement of Breathing Rate and Volume in Routinely Performed Daily 

Activities. Davis CA: University of California. 

Adams WC, Shaffrath JD and Ollison WM. 1995. The relation of pulmonary ventilation and 

heart rate in leg work alone, arm work alone, and in combined arm and leg work. Paper WA84A.04 presented at the Annual Meeting of the Air & Waste Management Assoc. 

Baba R, Mori E, et al. 2002. Simple exponential regression model to describe the relation 

between minute ventilation and oxygen uptake during incremental exercise. Nagoya J Med 

Sci. 65: 95-102. 

Burmaster DE and Crouch EAC. 1997. Lognormal distributions for body weight as a fucntion of 

age for males and females in the United States, 1976-1980. Risk Anal. 17(4): 499-505. 

Galletti PM. 1959. Les echanges respiratoires pendant l'exercice musculaire. Helv Physiol 

Acta. 17:34-61. 

Johnson T. 1995. Recent advances in the estimation of population exposure to mobile source 

pollutants. J Exp Anal Environ Epidemiol. 5: 551-571. 

Johnson T. 2002. A Guide to Selected Algorithms, Distributions, and Databases Used in 

Exposure Models Developed by the Office of Air Quality Planning and Standards. Chapel 

Hill: TRJ Environmental. 

Johnson T and Adams WC. 1994. An algorithm for determining maximum sustainable 

ventilation rate according to gender, age, and exercise duration. Unpublished paper. 

Johnson T and Capel J. 2002. User’s Guide: Software for Estimating Ventilation (Respiration) 

Rates for Use in Dosimetry Models. Chapel Hill NC: TRJ Environmental. 

Johnson T, Capel J, McCoy M, and Warnasch J. 1996. Estimation of Ozone Exposures 

Experienced by Outdoor Children in Nine Urban Areas Using a Probabilistic Version of 

NEM. Durham NC: IT Corporation. 

Johnson T and McCoy M. 1995. A Monte Carlo Approach to Generating Equivalent 

Ventilation Rates in Population Exposure Assessments. Washington DC: American 

Petroleum Institute (API Publication # 4617). 

Johnson T, McCoy Jr. M, and Ollison W. 1995. A Monte Carlo approach to generating 

equivalent ventilation rates in population exposure assessments.” Paper 95-TA42.05 

presented at the annual meeting of the Air & Manage. Waste Assoc.; San Antonio TX. 

 A-16 
Johnson T and Mihlan G. 1998. Analysis of clinical data provided by Dr. William Adams and 

revisions to proposed probabilistic algorithm for estimating ventilation rate in the 1998 

version of pNEM/CO. Memo to A. Rosenbaum, Systems Applications International. 

Lin Y-S, Smith TJ, et al. 2001. Human physiologic factors in respiratory uptake of 1,3-

butadiene. Environ Health Perspect. 109(9):921-926. 

McArdle WD, Katch FI, and Katch VL. 1991. Exercise Physiology. 3rd Ed. Philadelphia: Lea 

& Febiger. 

McCurdy T. 1994a. Human exposure to ambient ozone. pp. 85-127 in: D.J. McKee (ed.) 

Tropospheric Ozone. Ann Arbor MI: Lewis Publishers. 

McCurdy T. 1994b. Repackaging Adams (1993) breathing rate data. U.S. EPA memo, 

Research Triangle Park NC (April 20). 

McCurdy T. 1995. Estimating human exposure to selected motor vehicle pollutants using the 

NEM series of models: Lessons to be learned. J Exp Anal Environ Epidemiol. 5: 533-550. 

McCurdy T. 1997a. Comparison of cumulative inhaled ozone dose estimates using a 

disaggregated, sequential approach and alternative recommended approaches. Paper 

presented at the 7th Annual Meeting of the International Society of Exposure Analysis. 

McCurdy T. 1997b. Human activities that may lead to high inhaled intake doses in children 

aged 6-13. Environ Tox Pharm. 4: 251-260. 

McCurdy T. 1997c. Modeling the dose profile in human exposure assessments: ozone as an 

example. Rev Tox: In Vivo Tox Risk Assess. 1: 3-23. 

McCurdy T. 2000. Conceptual basis for multi-route intake dose modeling using an energy 

expenditure approach. J Expos Anal Environ Epidemiol. 10: 86-97. 

McCurdy T. 2001. Research Note: Analyses to understand relationships among physiological 

parameters in children and adolescents aged 6-16. RTP: U.S. Environmental Protection 

Agency (being reviewed). 

McCurdy T, Glen G, Smith L, and Lakkadi Y. 2000. The National Exposure Research 

Laboratory’s Consolidated Human Activity Database. J Exp Anal Environ Epidemiol. 10: 

566-578. 

McCurdy TR and Graham SE. 2004. Analyses to understand relationships among physiological 

parameters in children and adolescents aged 6-16. EPA/600/X-04/092. 

Nieman DC. 1999. Exercise Testing and Prescription. A Health-Related Approach. 4th edition. 

Mayfield Publishing Company, Mountain View, CA. 

 A-17 
 A-18 

Schofield WN. 1985. Predicting basal metabolic rate, new standards and review of previous 

work. Human Nutrition: Clinical Nutrition. 39C(Supp1):5-41. 

U.S. EPA. 1997. Exposure Factors Handbook. National Center for Environmental Assessment, 

Office of Research and Development, Washington D.C. EPA/600/P-95/002Fa. 

http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=12464 

U.S. EPA. 2005. Total Risk Integrated Methodology (TRIM) Air Pollutants Exposure Model 

Documentation (TRIM.Expo / APEX, Version 4) Volume I: User’s Guide. Office of Air 

Quality Planning and Standards, US EPA. November 2005. 

http://www.epa.gov/ttn/fera/data/apex/APEX4UG120505.pdf 
Attachment A1 to Appendix A 

First memo from Dr. Adams to T. McCurdy describing major data set

 21 August 1998 

Dear Tom: 

Enclosed is a diskette which includes the electronic data base containing data my graduate 

students and I have collected over the last 25 years on a large number of subjects of varying ages 

that includes VE, VO2, and other physiological data that should be very useful for estimating VE 

and respiratory intake dose. It is in an Excel (5.0a) spread sheet format, as well as an ASCII 

format, blank delimited file with headings. 

A description of the subjects for which data were potentially available was detailed in a list of 37 

studies (pages 5-8) in my proposal dated 28 April 1998. Table A1-1 details the 31 studies for 

which valid physiologic data were available, together with the total number of subjects, their 

gender, and whether they were tested on a cycle ergometer or on a motor driven treadmill. 

Missing study numbers from the original proposal list denotes that no valid body composition 

and multi-stage VO2max data were available. In Study 21, 16 male subjects exercised on a cycle 

ergometer (21.1), while 22 male subjects exercised on a treadmill (21.2). 

The total number of subjects with multi-stage, steady-state corresponding VO2 and VE values, 

including those at VO2max, was 521 males and 224 females. Most were obtained on a cycle 

ergometer test (262 males and 158 females), with the remainder on a treadmill, utilizing a 

walking and/or running protocol. In addition, steady-state VO2 and VE values at several 

submaximal workloads on the treadmill were available on 211 other subjects as described in 

Study 30, above. Time at each work level was usually two or three minutes, except at the 

maximal work level, which sometimes was as short as 15 sec. (with the physiologic data 

extrapolated to per minute values). A variety of progressive increment protocols were used on 

both the cycle ergometer and the treadmill. However, each (except for Study 30) was designed 

to obtain at least near steady-state physiologic response at progressively intensified work rates 

ranging from light, or moderate, through very heavy, ending with voluntary exhaustion. 

In the electronic data base, the array of data for each subject is arranged horizontally in the 

following order: 

1. study ID number (1=Study 1, 2=Study 2, etc.) 

2. subject ID number 

3. subject gender (0=male, 1=female) 

4. subject age (years) 

5. special characteristics of the subject (e.g., 1= trained athlete, 2= trained non-athlete, 3= 

normally active, 4= sedentary, and 5= obese) 

6. subject height (cm) 

7. subject body mass (kg) 

8. subject lean body mass (kg) 

 A-19 
9. machine used (1= cycle ergometer, 2= treadmill) 

10. total test time (min) 

11. observed VO2max (l/min, STPD) for the test 

12. for each step of the test for each subject, the following sequence was used: 

a. cumulative test time at end of step 

b. machine setting (cycle ergometer in Watts, treadmill in speed (m/min) and percent 

grade) 

c. VE (l/min BTPS) measured during the last minute of each step 

d. VO2 (l/min, STPD) measured during the last minute of each step 

e. HR (b/min) measured during the last minute of each step 

Table A1-1. Total subjects for each study, gender, and exercise ergometry used. 

Cycle Ergometer Tests Treadmill Tests

Study Total Subjects Males Females Males Females Males Females

1 148 148 0 0 0 148 0

2 42 42 0 0 0 42 0

5 60 30 30 0 0 30 30

6 12 6 6 0 0 6 6

7 4 0 4 0 4 0 0

8 6 6 0 6 0 0 0

9 10 10 0 10 0 0 0

10 8 8 0 8 0 0 0

12 10 10 0 10 0 0 0

13 8 8 0 8 0 0 0

14 32 0 32 0 32 0 0

16 10 10 0 10 0 0 0

18 25 25 0 25 0 0 0

19 15 0 15 0 15 0 0

20 39 18 21 18 21 0 0

21.1 16 16 0 16 0 0 0

21.2 22 22 0 0 0 22 0

23 17 9 8 9 8 0 0

24 13 13 0 13 0 0 0

25 37 37 0 37 0 0 0

26 13 13 0 13 0 0 0

27 21 11 10 0 0 11 10

28 40 20 20 20 20 0 0

29 11 0 11 0 11 0 0

30 211 105 106 0 0 105 106

31 20 0 20 0 0 0 20

32 10 10 0 10 0 0 0

33 40 20 20 20 20 0 0

34 10 6 4 6 4 0 0

35 6 3 3 3 3 0 0

36 12 6 6 6 6 0 0

37 28 14 14 14 14 0 0

Total 956 626 330 262 158 364 172

Consistent units of measurement for all entries were used throughout the file. For machine 

setting, two columns were needed for treadmill tests, one each for speed and percent grade, while 

 A-20 
only one (work rate in Watts) was required for Quinton electronically braked cycle ergometer 

tests. A Monark cycle ergometer was used in Studies 9 and 33-37. Calibration of the Monark 

device displayed on the ergometer itself only accounts for braking force produced by the 

flywheel friction strap, and does not include internal friction produced in the drive train. 

Therefore, work rate values displayed on the ergometer were converted to Watts and then 

increased by 9% in order to obtain corrected values (E. Harman, Medicine and Science in Sports 

and Exercise 21(4):487, 1989). 

Quality assurance of the basic data, including that from handwritten records and computer print 

outs, was initiated by my review of each subject’s data. Where apparent spurious data appeared, 

or notably aberrant subject responses were identified, they were eliminated from transfer to the 

electronic data base. I also noted any missing data for any subject, so that it was clear to the 

graduate student transferring the data which were valid and what data were missing. The 

graduate student transferring data to the electronic data base was thoroughly trained as to what 

data were to be entered and the format that they were to be entered in. After data were entered 

for a study, the graduate student read the data appearing on the original data record for each 

subject’s protocol, while another graduate student verified that what was being said was what 

appeared on the spreadsheet. Errors identified by this procedure proved to be relatively small in 

number, non-systematic, and easily correctable. I have great confidence that the data furnished 

you are a valid representation of what appears in our original handwritten or computer print-out 

records. 

A list of subjects who participated in more than one study is given below in ascending Study 

Number (and subject number) for the first study they participated in, and then the other 

study(ies), with their subject number(s), that they participated in. 

Study 1 

Subject #2 also subject #2 in study 2. 

Subject #6 also subject #10 in study 18. 

Subject #25 also subject #7 in study 2, and #3 in study 5. 

Subject #29 also subject #18 in study 18. 

Subject #30 also subject #23 in study 18. 

Subject #43 also subject #3 in study 18. 

Subject #52 also subject #2 in study 18. 

Subject #54 also subject #17 in study 18. 

Subject #55 also subject #20 in study 2. 

Subject #56 also subject #19 in study 2, and #5 in study 19. 

Subject #60 also subject #13 in study 2. 

Subject #61 also subject #19 in study 18. 

Subject #63 also subject #18 in study 2, and #5 in study 8. 

Subject #69 also subject #16 in study 18. 

Subject #88 also subject #21 in study 18. 

Subject #89 also subject #14 in study 18. 

Subject #91 also subject #22 in study 18. 

Subject #97 also subject #11 in study 18. 

 A-21 
Study 2 

Subject #17 also subject #6 in study 18. 

Subject #32 also subject #30 in study 5. 

Subject #33 also subject #26 in study 5. 

Subject #34 also subject #1 in study 8. 

Subject #35 also subject #3 in study 8. 

Study 5 

Subject #18 also subject #1 in study 6. 

Subject #19 also subject #3 in study 6. 

Subject #21 also subject #6 in study 6, #1 in study 9, #1 in study 12, #2 in study 20, #17 in 

study 21.2, and #23 in study #25. 

Subject #27 also subject #2 in study 9. 

Subject #43 also subject #10 in study 6. 

Subject #48 also subject #11 in study 6. 

Study 9 

Subject #9 also subject #15 in study 21.2. 

Study 10 

Subject #1 also subject #7 in study 13, #3 in study 20, and #34 in study 25. 

Subject #2 also subject #4 in study 13 and #1 in study 20. 

Subject #7 also subject #8 in study 13. 

Study 12 

Subject #10 also subject #5 in study 20. 

Study 13 

Subject #2 also subject #5 in study 16. 

Study 20 

Subject #7 also subject #16 in study 21.1 and #8 in study 25. 

Study 21.1 

Subject #3 also subject #3 in study 24 and #33 in study 25. 

Study 21.2 

Subject #18 also subject #18 in study 25. 

Study 23 

Subject #1 also subject #10 in study 28. 

Subject #5 also subject #12 in study 24. 

Study 24 

Subject #13 also subject #21 in study 25. 

 A-22 
 A-23 

Study 28 

Subject #12 also subject #3 in study 32. 

Subject #28 also subject #20 in study 31. 

Study 31 

Subject #10 also subject #40 in study 33. 

Subject #15 also subject #3 in study 34. 

Study 32 

Subject #2 also subject #12 in study 33. 

Study 33 

Subject #3 also subject #7 in study 34. 

Subject #7 also subject #4 in study 35. 

Subject #9 also subject #10 in study 34, and #5 in study 35. 

Subject #35 also subject #4 in study 34. 

Study 34 

Subject #1 also subject #2 in study 35. 

Study 35 

Subject #3 also subject #3 in study 36. 

Study 36 

Subject #12 also subject #26 in study 37. 

I believe that this final report letter contains additional information beyond the electronic data 

base that you wanted and clarifies the format that was used. If you have questions, however, 

please do not hesitate to give me a call or drop me a note by FAX. I look forward to hearing from 

you and working with you and Ted on developing a publishable paper or two. 

Best regards, 

William C. Adams 

Professor 
Second memo from Dr. Adams to T. McCurdy describing additional data from 

study #30

8 October 2001 

Dear Tom: 

Pursuant to the U.S. EPA Order for Supplies and Services, No. 1D-5590-NATX, approved for 

the period, 1 August - 1 November 2001, I believe that I have now completed all professional 

services stipulated. Specifically, it was requested that I provide certain “raw” data on a group of 

children and adolescents who were part of the subject pool utilized in a California State Air 

Resources Board sponsored study, entitled: Measurement of Breathing Rate and Volume in 

Routinely Performed Daily Activities (Adams, 1993). The professional services stipulated 

included: 1) providing a complete listing of all variables that were obtained during the study in 

accordance with the attached Statement of Work; 2) the development of an electronic data base 

of selected physiological information for children and adolescents from the aforementioned 

study, again in accordance with the attached Statement of Work; and 3) the submittance of a 

transcribed data file for the aforementioned study in ASC II format, together with a description 

of data quality objectives that were established in accordance with the attached Statement of 

Work. 

The subject pool of interest included 132 individuals, half female and half male, including 12 

young children, age 3.6-5.8 yrs., 80 children, age 6.0-12.9 yrs., and 40 adolescents, age 13.2-18.9 

yrs. All subjects were apparently healthy. In all cases, subject identification, including age and 

gender, as well as body weight, height, and activity habitus, were obtained. Body composition, as 

assessed by gender/age specific skinfold formulae, were used to calculate lean body mass. All 

subjects completed a laboratory treadmill walk (usually three different speeds, i.e., steps) and 

jog (ranging form 1 to 3 different speeds) protocol. The treadmill grade was horizontal 

throughout. Each subject completed a laboratory resting protocol (40 of the children did only 

sitting and standing, while the others also rested in a lying position). The 12 young children each 

did two spontaneous play protocols of 20 minutes duration, while 40 children also did two 

spontaneous play protocols, but of 30 minutes duration. The other 40 children did a single 

spontaneous play protocol of 35 minutes duration. The 40 adolescent subjects were not asked to 

perform a spontaneous play protocol. In addition, each subject (or their parent/guardian) 

completed an 11-item health history questionnaire. 

Enclosed is a 3.75 ZIP disk which includes the electronic data base containing data described in 

general above. It is in an Excel (5.0a) spread sheet format produced on a Macintosh Performa 

6214CD hard drive, as well as an ASCII format, blank delimited file with headings. Consistent 

units of measurement for all entries were used throughout this file. In the electronic data base, 

the array of data for each subject is separated into five distinct files: 1) active (treadmill) 

protocol; 2) resting protocol; 3) spontaneous play protocol; 4) health history responses to 

selected questions; and 5) predicted VO2max values from measured submaximal HR and VO2

values contained in File #1. Details of what items, variables, time periods, etc., and their order, 

which are arranged horizontally in each file, is as we agreed on via my FAX of 22 August 2001, 

 A-24 
with minor modifications we agreed on by phone the next day. The order for each file is given 

below: 

ACTIVE (File #1) 

1. File ID number (#1) 

2. subject ID number (same number for each subject as identified for Study #30 in 1998 

data base) 

3. subject gender (0=male, 1=female) 

4. subject age (years) 

5. special characteristics of the subject (viz., 1= trained athlete, 2= trained non-athlete, 3= 

normally active, 4= sedentary, and 5= obese) 

6. subject height (cm) 

7. subject body mass (kg) 

8. subject lean body mass (kg) 

9. machine used (1= cycle ergometer, 2= treadmill) - NOTE: TREADMILL ONLY 

USED IN THIS STUDY. 

10. total test time (min) 

11. observed VO2max (l/min, STPD) for the test - NOTE: VO2max NOT MEASURED IN 

THIS STUDY.

12. for each step of the test for each subject, the following sequence was used: 

a. cumulative test time at end of step 

b. machine setting (two columns: one for treadmill in speed (m/min) and one for 

percent grade). The latter was always zero. 

c. VE (l/min BTPS) measured during the last two minutes of each step 

d. VO2 (l/min, STPD) measured during the last two minutes of each step 

e. HR (b/min) measured during the last two minutes of each step 

RESTING (File #2) 

1. File ID number (#2) 

2. subject ID number (same number for each subject as identified for Study #30 in 1998 

data base) 

3. subject’s body surface area in square meters; from measured body height and body mass, 

using the standard DuBois and DuBois formula 

4. for each resting posture for each subject, the following sequence was used: 

a. VE (l/min BTPS) measured during the 5 minutes of each test 

b. VO2 (l/min, STPD) measured for the 5 minute of the test 

c. average of five HR (b/min) measurements taken each minute of the 5 minute test 

d. average of five breathing frequency (breaths/min) measurements taken each 

minute of the 5 minute test 

SPONTANEOUS PLAY (File #3) 

1. File ID number (#3) 

2. subject ID number (same number for each subject as identified for Study #30 in 1998 

data base) 

 A-25 
3. for each 5 minutes data collection period for each subject, the following sequence was 

used: 

a. VE (l/min BTPS) measured during the 5 minutes 

b. average of five HR (b/min) measurements taken each minute of the 5 minute 

period 

c. average of five breathing frequency (breaths/min) measurements taken each 

minute of the 5 minute period. NOTE: Because these data were obtained on a tape 

cassette that rather routinely malfunctioned, valid data were obtained in only 

~75% of the subject 5-minute time periods 

d. activity intensity rating by the technician. NOTE: There was some confusion 

among the technicians as to what they were to indicate in the comments column; 

e.g., any problems with the equipment, what the subject was playing, and/or an 

estimation of the intensity of activity. The occasional noted problems with 

equipment were dealt with as described on pp. 38-39 of the CARB Final Report 

(Adams, 1993). While the play activity was occasionally recorded, it was not 

systematic (i.e., estimated at between 15-20%). Intensity of play was recorded 

~55% of the time. The intensity scale devised and used for the first time in the 

enclosed data base was: 1 = standing, or just “hanging out”; 2 = moderate 

intensity, i.e., walking, swinging an implement, kicking or throwing a ball, etc.; 

and 3 = vigorous, or very active. Ratings of 1.5 and 2.5 were used to indicate 

activity intensity somewhere in-between the absolute number categories. The 

mean value for each 5-minute period was near 2.0, moderate, which closely 

agrees with the observed VE estimated intensity discussed on p. 110 of the CARB 

Final Report. 

HEALTH HISTORY (File #4) 

1. File ID number (#4) 

2. subject ID number (same number for each subject as identified for Study #30 in 1998 

data base) 

3. Re question #1, how often do you exercise? Numerals in column 3 correspond to which 

of 5 choices were circled. 

4. Re question #2, describe the intensity of your exercise. Numerals in column 4 correspond 

to which of 5 choices were circled. In six cases, two adjoining numbers (e.g., 2 and 3) 

were circled, and the mean entered (in this case, 2.5). 

5. Re question #3, what types of exercise do you engage in? Numerals in column 5 

correspond to which of 9 choices were circled. No one circled No. 1 (none). Most 

subjects circled more than one choice, which is reflected by the numerals 2 through 8 in 

column 5 for each subject. If the subject circled 9 (other), the following numerals were 

entered in column 5 to indicate which other activities they engaged in (10, play; 11, 

dance; 12, horseback riding; 13, gymnastics; 14, rollerblading; 15, karate; 16, ice skating; 

17, aerobics (high impact); 18, aerobics (machines at fitness club); 19, hockey; and 20, 

boxing 

6. Re question #7, any medical complaints? 1 = yes; 2 = no. If yes, 1 was not entered, but 

what “caused” the yes answer was entered in column 6 as follows: 3, asthma; 4, ear, 5, 

scoliosis; 6, cerebral palsy; 7, allergies 

 A-26 
7. Re question #11, do you have, or have you ever had, any of the following? Numerals 

from 1 through 12 in column 7 indicate that only one choice was circled. If more than one 

choice was indicated, higher numbers were used as follows: 13, choices 7, 9, and 10; 14, 

choices 9, 10, and 11; and 15, choices 10 and 11. 

 A-27 
PREDICTION OF VO2MAX FROM SUBMAXIMAL MEASURED HR AND VO2 VALUES 

OBTAINED FROM FILE #1 (File #5) 

1. File ID number (#5) 

2. subject ID number (same number for each subject as identified for Study #30 in 1998 

data base) 

3. subject body mass (kg) 

4. subject age (years) 

5. estimated HRmax

6. VO2max y intercept 

7. VO2max b exponent 

8. predicted VO2max (l/min) 

9. predicted VO2max (l/min/kgBM) 

The rationale for predicting percent VO2max at any given percent HRmax is developed in brief on 

p. 403 of McArdle et al.’s exercise physiology text (4th ed., 1996) and in more detail in Astrand 

and Rodahl’s Textbook of Work Physiology (2nd ed., 1977), pp. 344-348. Using data from both 

sources, I calculated very closely similar submaximal % VO2max values as a function of % 

HRmax values (i.e., never more than 2%, and usually the same or only 1% difference). To get a 

clear visual perspective overview of the estimated VO2max prediction from measured 

submaximal HR and VO2, see Fig.10-4 (line A), p. 346, in Astrand and Rodahl. To use this 

procedure, it is first necessary to obtain a valid HRmax value which decreases an average of 1 

b/min each year of age from 10 years on. The best data I’m aware of on young children and 

adolescents that had HR and VO2 measured in both submaximal and maximal treadmill exercise 

is that of Astrand (Experimental Studies of Physical Working Capacity in Relation to Sex and 

Age, 1952, Ejnar Munksgaard, Copenhagen). Between the ages of 4 and 10 years, there was no 

significant relationship between HRmax and age for either sex, averaging 205 b/min. Thereafter, 

up to 33 years, there was the now widely accepted decrease of 1 b/min per year of age for both 

males and females, with 10 year-old boys and girls averaging 210 b/min. Accordingly, in File #5, 

the estimated HRmax in column 5 is 205 b/min for subjects less than 10 years of age and 220 

minus age in years for subjects 10 to 18.9 years of age. The y intercept and b exponent values for 

predicting VO2max were obtained by calculating, via simple regression analyses, individual 

subject values from measured submaximal HR and VO2 values taken from File #1. Predicted 

VO2max (in l/min), given in column 8 for each subject, was obtained by multiplying the b 

exponent value (column 7) times the estimated HRmax value (column 5) for each subject, and 

then subtracting their y intercept value (column 6). Each subject’s VO2max value in ml/min/kg 

(column 9) was calculated by dividing the column 8 value by body mass (column 3). 

Accuracy of the data in the enclosed electronic files began with data management and quality 

control procedures employed in the original CARB study, and which are described in detail on 

pages 38-39 of the Final Report (Adams, 1993). In summary, very few problems were 

encountered in the acquisition of active and resting protocol data. Accuracy assurance 

procedures for the transfer of the data from handwritten records to master data sheets, and 

 A-28 
subsequently to electronic spreadsheet data bases, is described in the aforementioned Final 

Report. The retrospective quality control program for all field protocol data bases, including 

spontaneous play, revealed that 5 children needed to repeat a protocol. Elimination of aberrant 

bits of data obtained during the play protocols (due to the result of momentary saliva blockage in 

the Harvard respirometer, Heart Watch heart rate artifacts, etc.), which rarely included more than 

one or two 1-min "glitches" in any one protocol, were part of the aforementioned quality control 

program. When this was done, the remaining data for the 5-min period was used to calculate an 

average for the full time period (i.e., 20, 30, or 35 min). A significant number of play protocols 

(~35%) were completed with incomplete, or no, fB data. This occurred because there was no 

way to determine whether the expiration electronic pulse from the Harvard respirometer was 

being recorded on the tape cassette until after the protocol was completed. However, since these 

were random occurrences, and fB was not of such prime concern as HR and VE, these protocols 

were not repeated. 

Per the Statement of Work for this project, to ensure that an accurate translation of the data was 

accomplished, all data entries were checked by me. The data quality objectives described in 

detail below were developed before data were translated to the enclosed electronic data files. 

These objectives were applied against 100% of the entries transcribed, including file column 

headings, for the first 500 datum points. In each of the five files, this objective was met, and 

double-checking procedures described in detail below were employed to achieve the highest 

accuracy possible. I have great confidence that the data furnished you are a valid representation 

of what appears in our original CARB study computer data files and the original handwritten 

records used to transfer data to electronic files for the first time in this project. 

The specific procedures used for each of the five files differed somewhat and are described in 

detail here. For the active file, a copy of the 1998 Excel file was made and all data not from 

Study #30 for the 132 subjects of interest were deleted. A search of the original 1998 Excel file 

was done, and a print out of these data obtained (i.e., pp. 14-18, 36-40, 58-62, and 80-84). All 

entries in the 2001 file were double-checked against the 1998 print-out for the first 12 subjects, 

and for subjects 13, 45, 46, 58, 59, 66, 107, 131, 132, 150, 151, and 152. Finally, the values on 

the last page of data for all subjects was verified. In no case was any difference seen. 

Formulation of the file for the resting protocol (#2) was initiated by transferring data from 

summary CARB study electronic data files (in a similar, but not exact format for each subject) to 

the present electronic data file. Individual data values for all variables in each posture were 

double-checked against a print-out of the 1998 data for the first 12 subjects, and for every 10 

subjects thereafter. In no case was any difference seen. As a further cross-check, I then 

calculated entire group (N = 132) means for each posture in the present file, and compared these 

values to weighted tabular mean values in the original Final Report, and found no difference 

greater than 0.7%, i.e., within the range of rounding error. 

Formulation of the file for the play protocol (#3) entailed entering VE, HR, and breathing 

frequency data from handwritten data summary sheets. All values were double-checked 

immediately after entry for each time period (4 to 7) for each subject (N=92). In addition, I then 

calculated an entire group mean for each time period, and compared these values to weighted 

tabular mean values in the original Final Report. Again, I found very close agreement. Intensity 

 A-29 
 A-30 

values available for each time period for each subject were entered from handwritten data 

acquisition sheets into the electronic data base (File #3). As I entered them, I double-checked 

these values against that read from the data sheet, and that the adjacent HR and breathing 

frequency data were for the correct subject and time period. 

Procedures used for establishing the health history data base from handwritten responses to a 

questionnaire, together with how data was entered in each column, are described above. The data 

were typed directly into the electronic file (#4) for each subject from the handwritten responses 

on the questionnaire. The numerical values entered were double-checked for each question (#s 1, 

2, 3, 7, and 11) for each subject immediately after each subject’s data entry. 

Procedures used for predicting each subject’s VO2max from submaximal HR and VO2 data (the 

latter obtained from File #1), together with how data was entered in each column, are described 

above. The data for columns 1-4 were transferred directly from File #1 and a mean, with 

standard deviation, calculated for each column which matched those previously calculated in File 

#1. The individual submaximal HR and VO2 values entered into a STATVIEW simple 

regression analysis were each double-checked before each individual analysis was done. The 

resultant y intercept and b exponent values were written on a printout of the subjects’ 

submaximal HR and VO2 values, with each set double-checked as they were entered in the File 

#5 Excel spread sheet. In addition to recalculating all values for the first 10 subjects, any subject 

who had a predicted VO2max value < 33 or > 66 ml/min/kg was double-checked. In no case was 

an error found. Please note that 18 subjects only had 3 sets of submaximal values (i.e., all at three 

walking speeds). In all but 4 cases (subjects # 3, 29, 108, and 142), the spread of observed HR 

and VO2 values was sufficient (in my estimation) to obtain valid predicted VO2max values. Thus, 

I recommend deleting the predicted VO2max values for these four subjects. If this is done, the 

mean VO2max for the group is 47.63 ml/min/kg, a value that I consider highly likely in a group 

of healthy children and adolescents of probable slightly greater fitness than the average 

population. 

I believe that this final report letter contains additional information beyond the electronic data 

base that you wanted and clarifies the format and procedure that were used. If you have 

questions, however, please do not hesitate to give me a call or drop me a note by FAX. I look 

forward to hearing from you and working again with you in the future. 

Best regards, 

William C. Adams, Ph.D. 
Attachment A2 to Appendix A 

Data Set Manipulation. The data file needed significant manipulation to facilitate statistical 

analysis. Principally, the row and column structure of the file had to be altered to put them into 

proper alignment. Row headings were scattered within rows of the data set due to two different 

test protocols (cycle and treadmill) that required different parameter measurements. In addition, 

within-person measurements for the same parameter (e.g., total ventilation or VE) over multiple 

stages of the test (VE1, VE2, VE3, etc.) were carried across the dataset in multiple columns. It was 

desired to have the multiple measurements as a single vector for a given parameter. Therefore, 

the following changes were made to the data set: 

• 11 separate data sets were created in Excel by the 11 heading groupings within the raw 

data set (more than one study could be combined under previous headers) 

• A master list of parameters was created such that the 11 data sets could be combined 

under one heading having 102 unique designations. Specific changes made were: 

o Parameter heading for step 14 was removed since there were no parameters 

supplied for this step (e.g. VE14, VO2 14, etc.). 

o Common data were recoded into vectors having a common descriptor. Originally 

identical names were not used to describe the same parameter at different steps 

(e.g., the speed parameter for the cycle ergonometer used “spd” for steps under 10 

(e.g., spd1) and “sp” for steps >9 (e.g., sp13). It was assumed that “sp”=“spd”, 

and for grade, “gr”=“grd”). 

o Removed inconsistent coding. Spd12 on one instance was mislabeled as Spd11 in 

Study #1. This was corrected. 

o Cleaned up variable name conventions. Both “Age” and “LBM” parameters 

contained a space after the label characters. This space was removed. 

• These 11 Excel data sets were combined in SAS to create a SAS data set 

(adams.sas7dbat). 

• In SAS, multiple measurements for a parameter (e.g., VE1, VE2, VE3, etc.) were combined 

under a single vector (e.g., VE) to create a second SAS data file: adams2.sas7dbat. A new 

variable was created to account for the multiple measurements for a given parameter 

termed ‘step’ (e.g., step=1 is for where VE and VO2 were first recorded; step=2 for the 

second measurement of VE, etc.). 

• This data set contained a total of 19 variables: 

o Step Step or stage measurement taken within an individual 

o Age Subjects age in years (yrs) 

o BM Body mass (kg) 

o Char A characteristic of an individual acting as a surrogate for fitness level 

• 1= Trained athlete 

• 2= Trained non-athlete 

• 3= Active individual 

• 4= Sedentary individual 

• 5= Obese 

o ET Cumulative test time at the end of each step (min) 

o Gend Gender: ♂ = -1; ♀ = 1 

 A-31 
o Grd Grade on treadmill (in percent) 

o HR Heart rate (bpm or beats min-1) 

o HT Height (cm) 

o LBM Lean body mass (kg) 

o Mach Machine used: Cycle Ergometer = 1; Treadmill = 2 

o VO2 VO2 (L min-1 BTPS) 

o Spd Speed of the Subject on Treadmill (m min-1) 

o stud Study number 

o Subj Subject number 

o TT Total test time (min) 

o VE VE (L min-1) 

o VO2m Observed or estimated VO2 maximum for the test (L min-1 STPD) 

o Wk Watts (power setting for the cycle ergometer) 

Maximum VO2 (VO2m) was reported for all of the studies but one. Study 30 contained estimates 

of VO2m for some of the data (individuals < 18.9 years old) however the study also contained 79 

individuals where VO2m was neither measured nor estimated. The method reported by Adams 

(see Appendix B) to estimate VO2m for the younger individuals was duplicated here for the 

missing data. Briefly, maximum heart rate (HRm) was estimated using an equation provided in 

Nieman (1999) (i.e., HRm=220-age). A simple linear regression analysis followed for each 

individual (of the form y=mx+b) where HR measurements were regressed on concomitant VO2. 

The slope (m) and intercept (b) estimates were then used to approximate VO2m from the HRm 

estimate and added to the final data set. 

Quality Assurance. Data values--mostly VE, VO2, and BM, since these were the principal 

analytical parameters-- were spot-checked by hand from the original Excel spreadsheet to both 

newly created SAS data sets. No errors were found in either of the SAS data sets. The number 

of individuals in the newly created data sets was each 956, equivalent to that reported by Dr. 

Adams upon transfer of the data set (in Appendix A) and the total number of measurements of 

VE and VO2 for individuals >18 years old was equivalent (n=5,681) to that reported by Johnson 

(2002). 

A simple plot of the body mass-normalized total ventilation versus the body mass-normalized 

oxygen consumption revealed that two individuals (i.e., stud=1 subj=25 step=8; stud=31 subj=9 

step=8) had exceptionally large oxygen consumption levels during one sample collection. These 

data were considered to be questionable, and upon inspection seemed to be the result of a 

misplaced decimal point (30.8 and 28.5 should be 3.08 and 2.85, respectively). 

Data were replaced in the SAS data sets to reflect this assumption rather than delete the 

datapoints altogether, even though there is no direct evidence that the decimal was misplaced. 

Due to the number of samples for a given parameter in the data set (>5,000), the impact of this 

change on the analyses presented here is negligible. The new dataset was saved as 

‘adams3.sas7dbat’ (from data set ‘adams.sas7dbat’) and ‘adams4.sas7dbat’(from data set 

‘adams2.sas7dbat’). 

 A-32 
 A-33 

Data Transformation. Figure A2-1 shows the relationship between total ventilation and oxygen 

consumption rates. In general, the relationship is non-linear and exhibits greater variability 

among individuals at higher oxygen consumption rates (i.e., the data are heteroscadistic), similar 

to findings of other researchers (e.g., Baba et al. 2002). Normalization of VE and VO2 by body 

mass is commonly done to account for a portion of the variability inherent between the two 

physiological measures (Figure A2-2). 

Figure A2-1. Relationship between total ventilation Figure A2-2. Relationship between body 

rate (VE) and oxygen consumption rate (VO2) mass normalized total ventilation rate 

during exercise. (VE/BM) to oxygen consumption rate 

 (VO2/BM) during exercise. 

 Due to the non-linear relationship between VE and VO2, a number of the parameters were 

transformed by taking the natural logarithm (Ln) of the variable. These include: 

• Ln(VE) natural log of VE

• Ln(VO2) natural log of VO2

• Ln(VE/BM) natural log of body mass normalized VE

• Ln(VO2/BM) natural log of body mass normalized VO2

• VQ ventilatory equivalent or VE / VO2

• Ln(age) natural log of age 

A logarithmic transformation directly applied to the parameters allows for a significant reduction 

in the dispersion (Figure A2-3 compared to Figure A2-1), and when used in combination with 

body mass normalization, yields a mostly linear relationship having a more balanced dispersion 

across the range of oxygen consumption rates (Figure A2-4), that is, it better demonstrates a 

degree of homoscadisticity. It should be noted that this linearity and balanced dispersion was 

also demonstrated among different age groups investigated in the body of the report. 
Figure A2-3. Relationship between the natural Figure A2-4. Relationship between the 

logarithm of total ventilation rate Ln(VE) and natural logarithm of body mass 

oxygen consumption rate Ln(VO2) during normalized total ventilation rate 

exercise. Ln(VE/BM) and oxygen consumption rate 

 Ln(VO2/BM) during exercise. 

 A-34 
Attachment A3 to Appendix A 

Selected ventilation algorithms were evaluated using the APEX model by adjusting the 

ventilation.txt file (see U.S. EPA, 2005). 20,000 persons were simulated for one day using the 

algorithms described in the main body text and parameters in Tables 2 and 3. Model output was 

nearly 800,000 event-based ventilation rates, typically around 40 events per individual simulated. 

Figure A3-1 presents the mid to upper range percentiles based on these 800,000 events to 

encompass the possible maximum ventilation rates generated by each simulation. Algorithms 

evaluated included the following: 

MLR: multiple linear regression algorithm using equation 3 and parameters from Table A-3. 

MER: mixed-effects regression model using equation 4 and parameters from Table A-3. 

MLR+MER: regression coefficients from MLR coupled with variance components estimated 

from the MER model. 

Johnson: Johnson (2002) regression model using equation 2 and parameters from Table A-2. 

SMER: a simplified mixed effects regression model using equation 2 and parameters derived for 

all age groups from the Adams data set as follows: 

b0

Ln(VO2/BM) Residuals

b1 eb ew

Females 4.1017 1.1904 0.1408 0.1186 

Males 3.9332 1.1638 0.1445 0.1277 

Results are very similar for each of the algorithms, not surprisingly since they were for the most 

part derived from the same data set. At any given percentile, ventilation rates increase rapidly 

with age for those less than 20 years old, stabilize from ages 20 to about 60, then gradually 

decline with further increases in age. Increased variability at ages greater than 75 is also evident, 

a function of both the limited amount of data available for the development of the algorithm and 

the limited number of persons simulated at these ages from the population of 20,000. At each of 

the percentiles, the Johnson (2002) algorithm generated lower ventilation estimates for persons 

under age 5, a function of the method of the algorithm derivation, whereas the intercept was 

modified based on published literature VE/VO2 relationships while the residuals were assumed 

the same as those greater than 18 years of age. When considering a simple mixed effects 

regression (SMER) algorithm, flattening out of the percentiles occurs across the ages, mostly due 

to elevation of ventilation rates of young children that resulted from ignoring age as an 

independent variable in development of the regression parameters. 

Figure A3-2 presents the full range of percentiles for the event-based ventilation rates generated 

from the APEX model using the mixed effects regression (MER) model and the Johnson (2002) 

model. Results are very similar, however at young ages (<5 years old), the Johnson (2002) 

model estimates lower ventilation rates at both the lower and upper percentiles. The percent 

difference between the two model estimates is large, ranging from about 40-120% lower (Figure 

A3-3). The lower percentiles (min, p1, p5) for all ages >5 are moderately different, the Johnson 

(2002) ventilation estimates are less than the MER by about 20-40% for ages 10-45, then 10-

 A-35 
 A-36 

20% greater than the MER estimates for ages above 45. The MER algorithm estimates higher 

ventilation rates for persons above age 60 by about 20% considering the upper percentiles (p95, 

p99, max), with greater differences at age 90 and older (20-60%). 
Figure A3-1. Comparison of selected percentiles of estimated event-based ventilation rates from 20,000 person AP

using different ventilation algorithms. 

 A-37 max VE from events of 20,000 person APEX simulation 020406080 100 120 140 160 0 10 20 30 40 50 60 70 80 90 100 age (years) VE (L/min) MLR+MER-max MER-max Johnson-max MLR-max SMER-max p99 VE from events of 20,000 person APEX simulation 0102030405060 0 10 20 30 40 50 60 70 80 

age (years) VE (L/min) MLR

MERJohMLRSME

p95 VE from events of 20,000 person APEX simulation

05

1015202530354045

0 10 20 30 40 50 60 70 80 90 100

age (years)

V

E (L/min)

MLR+MER-p95MER-p95Johnson-p95MLR-p95SMER-p95

p50 VE from events of 20,000 person APEX simulation

02468

10121416

0 10 20 30 40 50 60 70 80 

age (years)

V

E (L/min)

MLRMERJohMLRSME
Figure A3-2. Comparison of estimated event-based ventilation rate percentiles from 20,000 person APEX model si

effects regression (MER-left) and Johnson (2002) (right) ventilation algorithms. 

 A-38 Mixed Model Estimates of VE from for 796,714 events from 20,000 person APEX simulation Lower Percentiles

05

10152025

0 10 20 30 40 50 60 70 80 90 100

age (years)

VE (L/min)

MER-p50MER-meanMER-p5MER-p1MER-min

Johnson Model Estimates of VE from for 799,355 events 

Lower Percentiles

05

10152025

0 10 20 30 40 50 60 

age (years)

VE (L/min)

Mixed Model Estimates of VE from for 796,714 events from 20,000 person APEX simulation

Upper Percentiles

0

20406080

100120140

0 10 20 30 40 50 60 70 80 90 100

age (years)

VE (L/min)

MER-p50MER-meanMER-p95MER-p99MER-max

Johnson Model Estimates of VE from for 799,355 events f

Upper Percentiles

0

20406080

100120140

0 10 20 30 40 50 60 

age (years)

VE (L/min)
 A-39 Figure A3-3. Percent difference of estimated event-based ventilation rate percentiles from 20,000 person APEX mo

mixed effects regression (MER-left) and Johnson (2002) (right) ventilation algorithms. 

-140-120-100

-80-60-40-20

0

20406080

0 10 20 30 40 50 60 70 80 90 10

Age (years)

% difference (Johnson-MER)/(Johnson+MER)*200 max p99 p95 p50 p5p1

min
APPENDIX D 

RESPONSE PREPARED BY S. GRAHAM (U.S. EPA) 

TO PEER-REVIEW COMMENTS ON APPENDIX A 
TABLE OF CONTENTS 

1. Purpose ........................................................................................................................... D-4 

2. APEX Model Description .............................................................................................. D-4 

3. Ventilation Algorithm Evaluation .................................................................................. D-5 

4. Comparison of APEX Estimates with Brochu et al. (2006a, b) ..................................... D-6 

5. Results of Comparison of APEX Estimates with Brochu et al. (2006a, b) .................. D-6 

6. Concluisons of Brochu et al. (2006a, b) Comparison .................................................. D-11 

7. Comparison of APEX Estimates with Arcus-Arth and Blaisdell (2007) ..................... D-12 

8. Results of Compariso of APEX Estimates with Arcus-Arth and Brochu et al. 

(2006a, b) ..................................................................................................................... D-13 

9. Issues ............................................................................................................................. D-13 

10. Conclusions of Arcus-Arth and Blaisdell (2007) Comparison .................................... D-13 

11. References to Appendix D ........................................................................................... D-15 

D-2 
LIST OF FIGURES 

D-1. Body mass comparison ................................................................................................... D-7 

D-2. Mean resting energy expenditure comparison ................................................................ D-8 

D-3. Comparison of body mass normalized mean basal energy expenditure (BEE-kg). ....... D-8 

D-4. Comparison of mean total daily energy expenditure (EE) .............................................. D-9 

D-5. Comparison of mean physical activity level (PAL) ...................................................... D-10 

D-6. Comparison of mean daily ventilation rate (VE) ........................................................... D-10 

D-7. Comparison of body mass normalized mean daily ventilation rate (VE-kg) ................ D-11 

D-8. Comparison of body mass normalized mean ventilation rates (VE-kg) correcting 

Brochu et al. (2006a) results with child appropriate VQ estimates .............................. D-12 

D-9. Comparison of mean daily ventilation rate (VE) in children ........................................ D-14 

D-10. Comparison of body mass normalized mean ventilation rates (VE-kg) in children ...... D-14 

D-3 
1. Purpose 

This appendix addresses comments provided by external peer reviewers on Appendix A 

of this document. In particular, clarification of how U.S. EPA’s Air Pollutants Exposure 

(APEX) model can be used to estimate ventilation rates is provided, and model ventilation 

estimates are compared with recently published estimates of ventilation rate. 

2. APEX Model Description 

U.S. EPA (2008a, b) provides more details on the approach to estimating ventilation rates 

using APEX. To summarize, the model is designed to estimate exposure to air pollutants and 

inhalation dose, accounting for the expected variability in both human behavior and physiology 

through consideration of important influential characteristics. One noteworthy feature of the 

model is its ability to estimate a time-series of exposure and dose for simulated individuals by 

correlating the time-series of microenvironmental concentration with the time series of 

activity-specific ventilation rates that could be as short as 1 minute in duration. 

Briefly, any number of individuals can be simulated in a model run to estimate exposure 

and exposure-related metrics (e.g., ventilation rate, body mass). Personal attributes of a 

simulated individual are first estimated (e.g., body mass, basal energy expenditure [BEE]) using 

either measurement data distributions (e.g., body mass distributions from CDC) or equations 

derived from measurement data and reported in the peer-reviewed literature (e.g., EE from 

Schoefield, 1985). Human time-location-activity diaries in U.S. EPA’s Consolidated Human 

Activity Database (CHAD) (McCurdy et al., 2000; U.S. EPA, 2002) are used to generate activity 

profiles for the simulated individuals for periods as short as one day upwards to a year. Each 

activity has a distribution of Metabolic Equivalents of work (METS) (e.g., point, lognormal, 

normal) that is sampled to estimate activity-specific METS for the individual performing the 

given activity. That combined with body mass dependent EE and a conversion for energy 

expenditure to oxygen consumption (e.g., H in Brochu et al., 2006a) result in activity-specific 

VO2 (typically in L-O2/min). These data are used as inputs to the regression equations reported 

in Appendix A (along with age, gender, and body mass) to estimate ventilation rate (VE, L/min). 

There are greater details in the approach such as those regarding adjusting the MET time-series 

to account for fatigue therefore regulating the duration of vigorous activities and excess 

D-4 
postexercise oxygen consumption whereby oxygen consumption is increased to repay oxygen 

debt that may have incurred from vigorous activities. See U.S. EPA (2008a, b) for more details. 

3. Ventilation Algorithm Evaluation 

Two recent publications were identified as potentially useful in the evaluation of the 

ventilation algorithm. Brochu et al. (2006a) presents data for ventilation rates, body mass, and 

energy expenditure for comparison, derived from data reported in studies that used the 

doubly-labeled water (DLW) method to estimate energy expenditure. Important reported subject 

characteristics include both genders, ages from 1 month to 96 years, and disaggregated by body 

mass (overweight/obese, normal body mass). For example, overweight individuals were defined 

as having body mass indexes (BMI) above the 97th percentiles for infants and toddlers <3 years, 

>85th percentile for children under 20, and BMI >25 for adults above 19 years old. Estimates of 

energy expended were combined with a fixed oxygen uptake factor (H = 0.21) and a fixed 

ventilatory equivalent (VQ = VE/VO2 = 27), while also accounting for stored daily energy cost 

for growth up to age 24, although this cost is generally only about 2% of total energy expended 

for ages above 1 year old. The DLW measurement generally extended from 7−21 days, resulting 

in time-averaged metrics that provide reasonable estimates for the mean (e.g., mean daily 

ventilation rate), but are not useful for estimating variability in an individuals ventilation rate (or 

other parameter) over shorter time periods. Reported data are averages for several age groupings 

(e.g., 1−<2, 2−<5, 5−<7, etc.) with derived percentiles assuming a normal distribution. 

Arcus-Arth and Blaisdell (2007) provide ventilation estimates for children <19 years of age 

using energy intake (EI, or calories consumed) and body mass data provided from the U.S. 

Department of Agriculture’s (USDA) Continuing Survey of Food Intake for Individuals (CSFII), 

adjusted for underreporting of food intakes (x 1.2 for children >8 years) and stored energy in 

infants alone (<1 years old). Two-day daily average EIs were combined with H (i.e., 0.22 for 

infants, 0.21 for non infants) and VQ (i.e., 33.5 for children 0−8, 30.6 for boys 9−18, 31.5 for 

girls 9−18 years old). Again, time-averaging of the data provide reasonable estimates of the 

mean, but offer no variability in ventilation estimates for time periods of shorter duration. 

Furthermore, data for both genders are combined and reported by age, with gender differences 

reported only for aggregated age groups (males and females, 9−18 years old). Additional 

gender-specific age groupings are reported for comparison with other literature values, however 

D-5 
are limited in number to be of great use here. An APEX model simulation was performed to 

generate estimates of relevant parameters for comparison with some of the estimates reported in 

these two publications. 

4. Comparison of APEX Estimates with Brochu et al. (2006a, b) 

A 14-day simulation was performed (i.e., the median of 7−21 days for the DLW data) for 

comparison with the time averaged Brochu et al. (2006a) data. Twenty-five thousand persons 

were simulated by APEX to generate a reasonable number of persons within each year of age 

and other potential categorical variables (e.g., 100−200, although some age groups have only 

1−5 persons). It is important when comparing the two types of data to have them as similar as 

possible, particularly since age and body mass are important influential variables. Body mass 

and height estimates were used to calculate BMIs for use in identifying normal versus 

overweight individuals as was done for the Brochu et al. (2006a) data. Percentiles for BMI of 

children ages 2−20 were obtained from CDC (2000). Children <2 years old were classified as 

overweight based on whether or not they exceeded the 97th percentile for 2-year olds of the same 

gender (there were no data reported by CDC for ages less than 2 years), while children aged 

3−20 years were classified as overweight if they exceeded the 85th percentile. Adults were 

classified as overweight if their BMI > 25.0. A total of 9,613 normal-weight individuals were 

simulated by APEX and used for the following analysis. Multi-day parameter estimates (e.g., 

ventilation rates, physical activity level, or PAL) were time averaged across the 14-day 

simulation period, yielding a mean daily value for each person to best represent the DLW time 

averaging done in Brochu et al. (2006a). 

5. Results of Comparison of APEX Estimates with Brochu et al. (2008a, b) 

Figure D-1 compares the mean body mass (BM, kg) estimates of APEX simulated 

individuals by one year age intervals with the mean body mass reported in Table 2, page 684 of 

Brochu et al. (2006a) for several age groupings of normal-weight individuals. There are no 

apparent differences in the population reported by Brochu et al. (2006a) and the APEX simulated 

population regarding body mass. 

D-6 
0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 10

Age (years)

Mean Body Mass (kg) 

0

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-1. Body mass comparison. 

Figure D-2 compares the mean basal energy expenditure (BEE, Kcal/day) estimates of 

APEX simulated individuals by one year age intervals with the mean daily BEE reported in 

Table Web-3, page 3 of Brochu et al. (2006b) for several age groupings of normal-weight 

individuals. Little differences exist in the population reported by Brochu et al. (2006b) and the 

APEX simulated population regarding BEE. 

Figure D-3 compares the mean body mass normalized basal energy expenditure (BEE-kg, 

Kcal/day-kg) estimates of APEX simulated individuals by one year intervals and those reported 

in Table Web-3m, page 3 of Brochu et al. (2006b) for several age groupings of normal-weight 

individuals. Little difference exists in the population reported by Brochu et al. (2006b) and the 

APEX simulated population regarding BEE-kg. 

Figure D-4 compares the mean daily energy expenditure (EE, Kcal/day) estimates of 

APEX simulated individuals by one year age intervals and those reported in Table Web-3, page 3 

of Brochu et al. (2006b) for several age groupings of normal-weight individuals. Little 

difference exists in the population reported by Brochu et al. (2006b) and the APEX simulated 

population regarding EE for ages less than 15, APEX estimates of EE are higher by about 10% 

for both genders at greater ages. 

D-7 
0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Mean Basal Energy Expenditure (Kcal/day) 

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-2. Mean resting energy expenditure comparison. 

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Body Mass Normalized Basal Energy Expenditure (Kcal/kg-day)

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-3. Comparison of body mass normalized mean basal energy 

expenditure (BEE-kg). 

D-8 
0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Mean Daily Energy Expenditure (kcal/day)

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-4. Comparison of mean total daily energy expenditure (EE). 

Figure D-5 compares the mean physical activity levels (PAL, unitless) estimated by 

APEX simulated individuals by one year age intervals and those reported in Table Web-3, page 3 

of Brochu et al. (2006b) for several age groupings of normal-weight individuals. Little 

difference exists in the population reported by Brochu et al. (2006b) and the APEX simulated 

population regarding PAL for ages between 10 and 20. APEX estimates of PAL are higher for 

both genders at other ages when compared with similar age PAL estimates from Brochu et al. 

(2006a, b), most notably at ages above 64. 

Figure D-6 compares the mean daily ventilation rate (VE, m3

/day) estimates of APEX 

simulated individuals by one year age intervals with those reported in Table 2, page 684 of 

Brochu et al. (2006a) for several age groupings of normal-weight individuals. The results were 

mixed for several ages and both genders when comparing those reported by Brochu et al. (2006a) 

and the APEX simulated population. APEX estimations were higher for children (age <11) and 

the elderly (age >64), while Brochu et al. (2006a) estimates were generally higher for males age 

12−40 and females age 18−40. For the young children, this may be a function of the fixed VQ 

used by Brochu et al. (2006 a, b) (see below). 

D-9 
0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Mean Physical Activity Level I

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-5. Comparison of mean physical activity level (PAL). 

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Age (years)

Mean Daily Ventilation (m3/day) 

APEX Females

Brochu et al. (2006) Females

APEX Males

Brochu et al. (2006) Males

Figure D-6. Comparison of mean daily ventilation rate (VE). 

D-10 
Figure D-7 compares the body mass normalized mean daily ventilation rate (VE-kg, 

m3/day-kg) estimates of APEX simulated individuals by one year age intervals with those 

reported in Table 2, page 684 of Brochu et al. (2006a) for several age groupings of 

normal-weight individuals. The two largest differences appear for children of both genders less 

than age 10 (Brochu et al., [2006a] estimates are systematically lower than APEX estimates) and 

ages between 16−33 (APEX estimates are lower than Brochu et al., [2006a]). Body mass 

normalized ventilation rates also appear to be slightly higher using APEX for ages above 64, 

both genders. 

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 1

Age (years)

Body Mass Normalized Mean Daily Ventilation (m3/day-kg)M

00

APEX Females

Brochu et al. (2006) Females

APEX MAles

Brochu et al. (2006) Males

Figure D-7. Comparison of body mass normalized mean daily ventilation 

rate (VE-kg). 

6. Issues 

One principal issue identified as responsible for some of the noted differences in 

ventilation estimates is in the VQ used by Brochu et al. (2006a). A single value of 27 was used 

in estimating ventilation rates for both children and adults, however it is widely recognized that 

while a VQ of 27 may be a reasonable approximation for estimating mean ventilation rates of 

adults, it is not appropriate for use in estimating mean ventilation rates in children. With this in 

D-11 
mind, the Brochu et al. (2006a) ventilation estimates were modified here using the VQ estimates 

offered by Arcus-Arth and Blaisdell (2007). Figure D-8 illustrates the comparison of APEX 

body mass normalized mean daily ventilation rates with that of Brochu et al. (2006a) corrected 

ventilation estimates. The body mass normalized ventilation estimates for children are more 

similar to those generated by APEX when correcting the Brochu et al. (2006a) VQ parameter. 

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 1

Age (years)

Body Mass Normalized Mean Daily Ventilation (m3/day-kg)M

00

APEX Females

Brochu et al. (2006) Females - Modified VQ

APEX MAles

Brochu et al. (2006) Males - Modified VQ

Figure D-8. Comparison of body mass normalized mean ventilation rates 

(VE-kg) correcting Brochu et al. (2006a) results with child appropriate 

VQ estimates. 

7. Conclusions of Brochu et al. (2006a, b) Comparison 

Mean estimates for all of the physiological parameters generated by APEX including 

ventilation rates are reasonably correlated with independent measures from the Brochu et al. 

(2006a, b) estimates, particularly when correcting the Brochu et al. (2006a) ventilation estimates 

for children using a more appropriate estimate of VQ for children. 

D-12 
8. Comparison of APEX Estimates with Arcus-Arth and Blaisdell (2007) 

A 2-day model simulation was performed using APEX to generate ventilation estimates 

(total ventilation and body mass normalized) for children to compare with results of Arcus-Arth 

and Blaisdell (2007). Table II (page 102) of Arcus-Arth and Blaisdell (2007) provided daily 

ventilation estimates, while Table III (page 103) provided body mass normalized ventilation 

rates. APEX ventilation estimates were time-averaged to generate mean daily values, and since 

the data reported in Arcus-Arth and Blaisdell (2007) were not separated by gender (outside of 

broad age categories), the APEX estimates were also combined to provide a mean estimate for 

each year of age (0−18). Body mass was also not used as a categorical variable in Arcus-Arth 

and Blaisdell (2007), therefore all APEX simulated individuals were used, regardless of whether 

they could be classified as overweight or of normal weight. In addition, data were obtained from 

Tables 3 and 4 of Brochu et al. (2006a) for a few age categories and considering both estimates 

for normal and overweight individuals (there were no combined data available). The Brochu et 

al. (2006 a, b) results have been corrected for VQ as noted above using VQ estimates of 

Arcus-Arth and Blaisdell (2007). 

9. Results of Comparison of APEX Estimates with Arcus-Arth and Brochu et al. 

 (2006a, b)

Figures D-9 and D-10 illustrate ventilation rate estimates from the APEX simulation, 

along with relevant data for children (ages 0−18) obtained from the two papers. Mean daily 

ventilation estimates (Figure D-9) are quite similar at each year of age, with slightly higher 

estimates by Arcus-Arth and Blaisdell (2007) at ages 9 and above, particularly when compared 

with APEX ventilation estimates. When ventilation rate is normalized by body mass 

(Figure D-10), the largest difference occurs at ages less than 4, whereas APEX estimates are 

higher than Arcus-Arth (2007), possibly influenced by differences in body mass between the two 

sample populations, particularly between ages 0 and 1.

10. Conclusions of Arcus-Arth and Blaisdell (2007) Comparison 

Ventilation estimates are remarkably similar for children for all three sources of data, 

particularly when considering the differences in the type of input data used and the varied 

approaches of APEX, Brochu et al. (2006 a, b), and Arcus-Arth and Blaisdell (2007). 

D-13 
0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18

Age (years)

Mean Daily Ventilation m3/day 

APEX Mean

Brochu et al. (2006) Normals Mean - Modified VQ

Arcus-Arth and Blaiedell (2007) Mean

Brochu et al. (2006) OW/OB Mean - Modified VQ

Figure D-9. Comparison of mean daily ventilation rate (VE) in children. 

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18

Age (years)

Body Mass Normalized Ventilation (m3/day-kg) 

APEX Mean

Brochu et al. (2006) Normals Mean - Modified VQ

Arcus-Arth and Blaiedell (2007) Mean

Brochu et al. (2006) OW/OB Mean - Modified VQ

Figure D-10. Comparison of body mass normalized mean ventilation 

rates (VE-kg) in children. 

D-14 
D-15 

11. References to Appendix D 

Arcus-Arth, A; Blaisdell, J. (2007). Statistical distributions of daily breathing rates for narrow age groups of infants 

and children. Risk Anal 27(1):97−110. 

Brochu, P; Ducre-Robitaille, J-F ; Brodeur, J. (2006a) Physiological daily inhalation rates for free-living individuals 

aged 1 month to 96 years, using data from doubly labeled water measurements: a proposal for air quality 

criteria, standard calculations and health risk assessment. Hum Ecol Risk Assess 12(4):675−701. 

Brochu, P; Ducre-Robitaille, J-F; Brodeur, J. (2006b) Supplemental Material for Physiological daily inhalation rates 

for free-living individuals aged 1 month to 96 years, using data from doubly labeled water measurements: a 

proposal for air quality criteria, standard calculations and health risk assessment. Hum Ecol Risk Assess 

12(4):1−12. 

CDC (Centers for Disease Control and Prevention). (2000). CDC Growth Charts: United States. BMI-for-age 

charts. National Center for Health Statistics, Hyattsville. Available online at 

http://www.cdc.gov/nchs/about/major/nhanes/growthcharts/datafiles.htm. 

McCurdy, T; Glen, G; Smith, L; et al. (2000) The National Exposure Research Laboratory’s consolidated human 

activity database. J Expo Anal Environ Epidemiol 10:566−578. 

Schofield, W.N. 1985. Predicting basal metabolic rate, new standards and review of previous work. Hum. Nutr. 

Clin. Nutr., 39C (suppl. 1): 5-41. 

U.S. EPA Environmental Protection Agency) (2002) Consolidated Human Activities Database. Office of Research 

and Development, National Exposure Research Laboratory, Washington, DC. Available online at 

http://www.epa.gov/chadnet1/. 

U.S. EPA (2008a). Total Risk Integrated Methodology (TRIM) - Air Pollutants Exposure Model Documentation 

(TRIM.Expo / APEX, Version 4) Volume I: User’s Guide. Office of Air Quality Planning and Standards, U.S. 

Environmental Protection Agency, Research Triangle Park, NC. June 2006. Available online at 

http://www.epa.gov/ttn/fera/human_apex.html. 

U.S. EPA (2008b). Total Risk Integrated Methodology (TRIM) - Air Pollutants Exposure Model Documentation 

(TRIM.Expo / APEX, Version 4) Volume II: Technical Support Document. Office of Air Quality Planning 

and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC. June 2006. Available 

online at http://www.epa.gov/ttn/fera/human_apex.html.