Combined heart rate and activity improve estimates
of oxygen consumption and carbon dioxide production rates
JON K. MOON AND NANCY F. BUTTE
United States Department of Agriculture/Agricultural Research Service, Children’s Nutrition
Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas 77030-2600
energy expenditure; human; respiration calorimetry; electronic
monitor; physical activity; 24-hour free-living measurement
that does not accurately describe the nonlinear relationships of V̇O2 to HR and PA.
Several models have been used to provide HR-based
predictions of V̇O2. Linear equations were used in the
first attempts to predict V̇O2 from HR (2). A model with
two linear segments that intersect at an inactive-active
(FLEX) HR threshold has proven the most popular (1,
4, 14). Several continuous nonlinear equations have
also been proposed, including cubic, sigmoid, and logistic functions (2, 13).
This report addresses two questions. Does a 24-h
calibration period of V̇O2 and carbon dioxide production
(V̇CO2) to HR and PA improve predictions of subsequent
24-h metabolic rates compared with previous efforts?
Do nonlinear and discontinuous functions provide better models of the V̇O2-to-HR and -PA relationships than
a linear function of HR?
Three approaches to modeling the relationships of
V̇O2 or V̇CO2 to HR and PA were evaluated. Method I
modeled the relationships with a linear equation and
five nonlinear equations based on HR alone. Method II
combined PA with HR as independent variables in six
nonlinear functions. Method III used a threshold level
of PA to assign HR to separate active and inactive
V̇O2-to-HR functions.
METHODS
NUMEROUS STUDIES have demonstrated the potential for
using heart rate (HR) and physical activity (PA) to
estimate free-living metabolic rates. Electronically recording HR and PA is cheaper and less intrusive than
calorimetric techniques. It also provides detailed information on daily activity patterns. However, several
limitations of HR and PA monitoring have prevented
their widespread use in clinical and nutritional studies.
Until recently, electronic monitors were often uncomfortable, lacked resolution, and had limited data-storage
capacity. Rapid advances in microcircuitry have made
electronic monitors smaller, cheaper, and more powerful. Commercial devices are available that continuously
record HR, PA, or both at resolutions of 1 min for
several days.
Individual errors in measurement of energy expenditure (EE) by HR or PA can be quite large, as much as
30% for estimates of 24-h EE (1, 4, 8, 14). Group mean
errors in the range of 65% by HR monitoring have been
higher than doubly labeled water, the current standard
for the measurement of free-living EE (11).
The relationships of oxygen consumption (V̇O2) rates
to HR and PA are very different among individuals. For
an individual, the relationships are complex and change
with age, body composition, and fitness. Errors arise
when the investigator chooses a mathematical function
1754
The study required 5 days of 24-h HR and PA recordings
within a 1-wk period. On days 1 and 5, the subjects were
confined to room calorimeters in the Metabolic Research Unit
of the Children’s Nutrition Research Center. Days 2–4 were
free living, including normal work or school with no restrictions on activity. Written informed consent was obtained
under a protocol approved by the Baylor College of Medicine
Review Board for Human Subject Research.
Subjects
Twenty Houston-area adults (19–40 yr) volunteered for the
study. Equal numbers of sedentary and active individuals
were selected to represent a range of fitness levels. Volunteers
were nonsmokers, had a body mass index , 26, and were not
taking prescription medication other than birth control. One
subject was a vegetarian.
Weight (491KL, Healthometer, Bridgeview, IL) and body
composition (HA-2, EM-Scan, Springfield, IL) (15) were measured on the morning the subjects left the calorimeter after
a 12-h fast. Peak V̇O2 (V̇O2 peak) was estimated in the calorimeter from HR and V̇O2 during moderate stationary cycle
exercise with the equation V̇O2 peak 5 V̇O2(220 2 age 2 b)/
(HR 2 b), where b 5 73 for the women and 63 for the men (10).
HR Recording
HRs were collected at 1-min intervals on each day of the
study. Electrodes (LRM306, Lead-lock, Sandpoint, ID) were
applied after the skin was cleaned with alcohol. On study
0161-7567/96 $5.00 Copyright r 1996 the American Physiological Society
Downloaded from http://jap.physiology.org/ by 10.220.33.4 on July 31, 2017
Moon, Jon K., and Nancy F. Butte. Combined heart rate
and activity improve estimates of oxygen consumption and
carbon dioxide production rates. J. Appl. Physiol. 81(4):
1754–1761, 1996.—Oxygen consumption (V̇O2) and carbon
dioxide production (V̇CO2) rates were measured by electronically recording heart rate (HR) and physical activity (PA).
Mean daily V̇O2 and V̇CO2 measurements by HR and PA were
validated in adults (n 5 10 women and 10 men) with room
calorimeters. Thirteen linear and nonlinear functions of HR
alone and HR combined with PA were tested as models of 24-h
V̇O2 and V̇CO2. Mean sleep V̇O2 and V̇CO2 were similar to basal
metabolic rates and were accurately estimated from HR alone
[respective mean errors were 20.2 6 0.8 (SD) and 20.4 6
0.6%]. The range of prediction errors for 24-h V̇O2 and V̇CO2
was smallest for a model that used PA to assign HR for each
minute to separate active and inactive curves (V̇O2, 23.3 6
3.5%; V̇CO2, 24.6 6 3%). There were no significant correlations between V̇O2 or V̇CO2 errors and subject age, weight, fat
mass, ratio of daily to basal energy expenditure rate, or
fitness. V̇O2, V̇CO2, and energy expenditure recorded for 3
free-living days were 5.6 6 0.9 ml · min21 · kg21, 4.7 6 0.8 ml ·
min21 · kg21, and 7.8 6 1.6 kJ/min, respectively. Combined HR
and PA measured 24-h V̇O2 and V̇CO2 with a precision similar
to alternative methods.
1755
HEART RATE AND ACTIVITY
days 1 and 5 (in the calorimeter), HR was recorded by telemetry
as the total number of cardiac cycles each minute (DS-3000,
Fukuda Denshi, Tokyo, Japan). The transmitter was clipped
on the belt or waistband. On free-living days (days 2–4), HR
was recorded with a battery-powered transmitter worn on the
chest and a wristwatch storage unit (Vantage XL, Polar
Electro, Kempele, Finland).
Activity Recording
PA was recorded at 16-s intervals as counts from a vibration sensor (Act I, Mini-mitter, Sun River, OR). The sensor
was securely taped on the outside of the dominant leg
approximately halfway between the hip and knee (5).
Calorimeter Procedures
Free-Living Procedure
Free-living HR and PA were recorded for 24 h on days 2–4.
Days 2 and 3 were identified as ‘‘weekdays’’ when the subject
went to work or otherwise engaged in activities that generally
represented their schedule for 4 or more days each week. Day
4 was designated ‘‘weekend.’’ Recordings were interrupted
only for bathing or showers. The PA monitor was removed
during swimming, but the HR recording was maintained with
the storage unit sealed in a plastic bag and placed in the
swimsuit. Data from the HR and PA monitors were copied to a
computer each morning.
Prediction Models of V̇O2 and V̇CO2 from HR and PA
Activity data were collapsed from 16-s to 1-min intervals.
Twenty-four-hour records of HR, PA, V̇O2, and V̇CO2 were
Method I: HR Regression
The first series of models evaluated the accuracy of one
linear and five nonlinear functions based on HR alone (Eqs.
1–6). a, b, c, and d are coefficients. In Eq. 6, e represents the
natural logarithm base, not a coefficient. Three data sets were
prepared from day 1: 24 h, awake, and sleep. V̇O2 and V̇CO2
were fitted by regression to HR for each data set. With six
functions and three data sets, a total of 18 regressions were
performed for each subject
Linear
V̇O2 or V̇CO2 5 a 1 b · HR
(1)
HR2 V̇O2 or V̇CO2 5 a 1 b · HR2
(2)
HR3 V̇O2 or V̇CO2 5 a 1 b · HR3
(3)
V̇O2 or V̇CO2 5 a 1 b · HR c
(4)
Logistic
V̇O2 or V̇CO2 5 a 1 b/[1 1 (HR/c) d ]
(5)
Sigmoid
V̇O2 or V̇CO2 5 a 1 b/[1 1 c · e (HR/d )]
(6)
Power
Method II: HR and Activity
Day 1 data again were separated into 24-h awake and sleep
periods. PA data from both days were low-pass filtered to
match the dynamics of V̇O2 and V̇CO2 by calculating an
adjusted PA (PA*) with Eq. 7. The coefficients a and b in Eq. 7
were determined by iteration to maximize the linear correlation of PA to V̇O2 and V̇CO2. Two sets of values for a and b were
calculated separately to fit awake and sleep V̇O2 and V̇CO2 and
were constrained to be .0 and ,1. The symbol PA*21 in Eq. 7
represents the value of PA* calculated for the previous
minute
PA* 5 a · PA*21 1 (1 2 a) · PA for PA $ PA*21
PA* 5 b · PA*21 1 (1 2 b) · PA for PA , PA*21
(7)
Awake V̇O2 and V̇CO2 were combined with HR and PA in
multiple regression functions (Eqs. 8–13). f, g, and h are coefficients. Mean regression statistics were assembled for each
equation across all subjects. The best fit equations were used
to estimate V̇O2 and V̇CO2 on day 5. For minutes where
PA* data were missing, a similar equation from method I
based on HR alone was used
V̇O2 or V̇CO2 5 a 1 b/[1 1 (HR/c)d ] 1 h/[1 1 (PA*/f ) g]
(8)
V̇O2 or V̇CO2 5 a 1 b/[1 1 (HR/c)d ] · h/[1 1 (PA*/f ) g]
(9)
V̇O2 or V̇CO2 5 a 1 b · HR3 1 c · PA*0.5
(10)
V̇O2 or V̇CO2 5 a 1 b · HR2.5 1 c · PA*0.5 ln PA*
(11)
V̇O2 or V̇CO2 5 a 1 b · HR2.5 1 c · PA*
(12)
V̇O2 or V̇CO2 5 a 1 b · HR2.5 1 c · PA*0.5
(13)
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Measurements of V̇O2 and V̇CO2 over 24 h were performed
on days 1 and 5 in 31-m3 room calorimeters (9). A treadmill
(905E, Precor, Bothell, WA), cycle ergometer (Corval 400,
Lode, Groningen, The Netherlands), 10-cm step platform, and
metronome were added to the calorimeter equipment. Calorimeter temperature was set at 24°C, relative humidity was
30–50%, and the carbon dioxide concentration was controlled
to 0.45% by regulating the inflow.
Calorimeter tests began at 0800. Meals were served at
0830, 1200, and 1700, and a snack was served at 1800. The
meals provided 12.1 kJ for the men and 9.2 kJ for the women
as 49% carbohydrate, 32% fat, and 19% protein. The subjects
were allowed only water after 1900.
Day 1 calibration of HR and PA to metabolic rate included
two sessions of compulsory activities. The morning session,
which began at 0900, consisted of 30 min of supine rest, 20
min of seated rest, 5 min of seated timed respiration, 15 min
of standing, and two levels of cycle exercise for 15 min at
workloads intended to produce 50 and 75% of the estimated
peak HR. The afternoon activities were 15-min periods of
seated writing, walking around the room, and three levels of
treadmill exercise at 1 m/s and 50 and 75% of peak HR,
beginning at 1300. A 15-min step test was added to the
afternoon exercise routine beginning with subject 4. Exercise
was halted if V̇O2 exceeded 80% of V̇O2 peak or if the HR
exceeded 180 beats/min for .2 min. The compulsory activities
totaled ,4 h. For the rest of the day, the subjects were allowed
free choice of activities. The subjects were not allowed to nap
but chose the time they went to sleep at night. They were
awakened by 0710 and remained supine for 40 min to
estimate basal metabolic rates (BMRs).
On day 5, the subjects chose the type of exercise (cycle,
treadmill, aerobics, etc.) and duration (at least 20 min). A
minimum workload or speed was assigned to approximate
moderately heavy exercise. The subjects were allowed to
exceed the assigned minimums.
examined for proper alignment. Short periods (5 min or less)
of HR and PA data that were missing or contained obvious
artifacts were replaced with a prior value. Longer periods of
corrupted data caused by loss of recording or electrical
interference were removed from analysis. Sleep and awake
periods were determined by inspection of HR and PA records
for a rapid decline in HR followed by .1 h of minimal HR and
PA close to zero.
1756
HEART RATE AND ACTIVITY
Method III: Awake Separated Into Active
and Inactive Periods
The 24-h records of day 1 V̇O2 and V̇CO2 were separated into
awake and sleep segments by inspection of HR and PA as in
Method I: HR Regression and Method II: HR and Activity.
Awake periods were further separated into active (standing
and exercise) and inactive segments (awake exclusive of
standing, exercise, and 1- or 1.5-h postexercise ergometer and
treadmill, respectively). HR3 regressions were fitted to inactive
V̇O2 and V̇CO2. Linear regression of HR on active V̇O2 and V̇CO2
used mean data from standing, walking, the step test, and
exercise on both the bicycle and treadmill (Fig. 1B)
V̇O2 5 a 1 b · HR3
Inactive: PA , PA (22, 21, 0) or HR , HR
V̇O2 5 c 1 d · HR
(14)
Active: PA $ PA (22, 21, 0) and HR . HR
Statistical Analysis
Data are summarized as means 6 SD. Differences between
group means for men and women (by weight, body composi-
RESULTS
The men were older (32 6 5 vs. 28 6 8 yr) and heavier
(74 6 7 vs. 59 6 7 kg) and had a higher estimated
V̇O2 peak (43 6 10 vs. 37 6 8 ml · kg21 · min21 ) but a similar fat mass (14 6 5 vs. 15 6 2 kg) compared with the
women. All 20 subjects completed the calorimeter portion (days 1 and 5) of the study. Mean record durations
for HR, PA and V̇O2 on day 1 were 1,440 6 0, 1,400 6
167, and 1,440 6 0 min, respectively. Missing PA data
for one subject on day 1 occurred during sleep and did
not affect the analysis. Excluding this subject, the
average PA record was 1,437 6 7 min. PA data from day
5 for two subjects could not be analyzed.
There was no significant change in the subjects’
weight (P 5 0.2) from day 1 to day 5. Subjects slept less
(436 6 78 min; 30.3%) on day 1 than on day 5 (489 6 66
min; 33.9%; paired difference P 5 0.02). Other differences between day 1 and day 5 measurements are
summarized in Table 1. Mean ratios of 24-h V̇O2 to basal
V̇O2 were 1.68 6 0.15 (range 1.33–1.96) on day 1 and
1.69 6 0.17 (range 1.36–1.95) on day 5.
Data were analyzed for 55 of the 60 free-living days
planned for the study. At least two free-living records
were obtained for each subject. Daily free-living records
of HR and PA in each 24-h period averaged 1,337 6 192
(93%) and 1,389 6 140 min (96%), respectively. Most
often, the subjects experienced interrupted HR recording during sleep on the first night. Further instructions
to the subject reduced data loss on subsequent nights.
Data lost during sleep had little effect on subsequent
analyses. Total awake and sleep records averaged
950 6 104 and 448 6 129 min, respectively.
Metabolic Rate Measurements
Fig. 1. Oxygen consumption (V̇O2) rate-to-heart rate (HR) relationship in a room calorimeter. A: 1-min values while subject was awake
and asleep over 24-h. Curve is a least squares fit of equation V̇O2 5
a 1 b · HR3, where a and b are coefficients, to 24-h data (method I, Eq.
3 in text). B: separate curve fits to active (linear) and inactive (HR3 )
portions of awake V̇O2-to-HR relationship (method III in text).
Method I. 24-h R 2 values for the nonlinear equations
(Eqs. 2–6, R2 5 0.86–0.91) were better than those for
Eq. 1 (R 2 5 0.77). There were no significant differences
in 24-h awake or sleep R 2 values among any regressions
involving nonlinear equations. HR3 (Eq. 3) had the
highest values for the F-statistic so that it was probably
the most computationally efficient model of the data
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V̇O2 and V̇CO2 for each minute of days 2–5 were estimated
from inactive HR unless both PA and HR exceeded fixed
thresholds (Eq. 14 for V̇O2). In Eq. 14, PA and HR denote the
threshold levels for that individual. The PA threshold was
calculated on day 1 as the median PA from either walking or
the slowest treadmill exercise (whichever was lower). The HR
threshold was the intersection of the inactive and active
equations for V̇O2. To be classified as active, each minute
required a HR above the threshold and PA had to exceed the
threshold during the current minute or either of the 2
previous min [PA (22, 21, 0) in Eq. 14].
tion, V̇O2 peak, and age) were evaluated for significance by
one-way analysis of variance. Differences within individuals
between test days (HR and sleep time) were evaluated by
paired t-test. The various V̇O2 and V̇CO2 prediction errors were
compared by multiple regression that included weight, body
composition, 24-h EE/BMR, V̇O2 peak, and age as independent
variables. Significance was assessed on the regression residuals. For all tests, the null hypothesis was rejected at P # 0.05.
PA* was calculated by numeric iteration with a conjugate
search at a precision of 0.01 and tolerance of 5% (Excel 4.0,
Microsoft, Redmond, WA). Nonlinear regression of V̇O2 and
V̇CO2 on HR (Eqs. 2–6) was performed by singular-value
decomposition (TableCurve 2D, Jandel Scientific, San Rafael,
CA). Multiple nonlinear regression of HR and PA (Eqs. 8 and
13) used Gaussian elimination with a convergence precision
of 6 and a linear significance of 0.1% (TableCurve 3D, Jandel).
Regression equations were evaluated primarily by a modified
F-statistic (calculated by TableCurve) that provided better
discrimination than R 2 because it imposed a cost on increasing model complexity (order).
1757
HEART RATE AND ACTIVITY
Table 1. Mean V̇O2 , V̇CO2 , and HR for 24 h, awake, 30-min BMR and nighttime sleep
in a room calorimeter and free living
Calorimeter
Day 5
Day 2
Day 3
Day 4
Days 2–4
7.38 6 1.44
0.36 6 0.07
0.31 6 0.06
73 6 8.5
7.37 6 1.43
0.36 6 0.07
0.31 6 0.06
70 6 9.4*
7.7 6 2
0.38 6 0.1
0.32 6 0.08
76 6 9
8.1 6 1.4
0.4 6 0.07
0.33 6 0.06
73 6 8
7.1 6 1.4
0.35 6 0.07
0.29 6 0.06
75 6 10
7.8 6 1.6
0.38 6 0.08
0.32 6 0.07
75 6 9
9.14 6 1.85
0.44 6 0.09
0.38 6 0.08
82 6 9
898 6 53
9.2 6 1.83
0.45 6 0.09
0.39 6 0.08
78 6 10*
913 6 67
9.2 6 2.7
0.45 6 0.13
0.39 6 0.11
83 6 10
9 6 2.4
0.44 6 0.12
0.38 6 0.1
81 6 10
8.6 6 1.8
0.42 6 0.09
0.36 6 0.07
83 6 10
9 6 2.3
0.44 6 0.11
0.37 6 0.1
82 6 10
4.29 6 0.54
0.21 6 0.03
0.17 6 0.02
61 6 11
4.23 6 0.58
0.21 6 0.03
0.15 6 0.02
58 6 10*
4.23 6 0.65
0.21 6 0.03
0.17 6 0.03
57 6 9.4
436 6 78
4.21 6 0.6
0.21 6 0.03
0.17 6 0.02
55 6 10*
489 6 66*
4.3 6 0.6
0.21 6 0.03
0.17 6 0.03
59 6 9
4.4 6 0.6
0.22 6 0.03
0.17 6 0.03
57 6 9
4.3 6 0.6
0.21 6 0.03
0.17 6 0.02
59 6 10
4.3 6 0.6
0.21 6 0.03
0.17 6 0.02
58 6 9
Values are means 6 SD. V̇O2 , O2 consumption; V̇CO2 , CO2 production; HR, heart rate; BMR, basal metabolic rate; EE, energy expenditure.
Free-living EE, V̇O2 , and V̇CO2 were calculated from measured HR and physical activity by method III (see text). EE was calcualted from V̇O2
and V̇CO2 by nonprotein equation of de V Weir (3). * Significant difference between calorimeter days, P , 0.05.
(Fig. 1A). The sigmoid (Eq. 6) had the highest overall
R 2 of 0.91.
Predictions of V̇O2 and V̇CO2 from HR by Eq. 3 were
compared with measured V̇O2 and V̇CO2 on day 5. Mean
errors for sleep V̇O2 and V̇CO2 were 20.2 6 0.8 and
20.4 6 0.6%, respectively. Errors were higher awake
(Table 2) and over 24 h (25.5 6 5.6 and 27.5 6 6.7%,
respectively) for both V̇O2 and V̇CO2. The range of errors
between 24-h predictions and measurements of V̇O2
and V̇CO2 was 216.8 to 4.5 and 221 to 3.5%, respectively. Results from Eq. 6 (sigmoid) were similar. There
was no significant difference between Eq. 3 and Eq. 6
prediction residuals during the awake period for V̇O2
(P 5 0.37) or V̇CO2 (P 5 0.15; Fig. 2A). The nonlinear
sigmoid regression algorithm failed to converge to solutions for one subject on V̇O2 and for another on V̇CO2.
We concentrated further analysis on awake predictions for all three methods because sleep prediction
errors were sufficiently low in method I. For comparison to HR predictions, we calculated linear regressions
of day 1 V̇O2 during supine rest and BMR to day 1 sleep
and compared these with day 5 sleep. Mean prediction
errors were 1.0 6 8.1 and 28.8 6 5.1% for supine V̇O2
and V̇CO2 , respectively, and 2.3 6 6.5 and 0.4 6 6.7%
for BMR V̇O2 and V̇CO2, respectively. Of the four predictions, only the supine V̇CO2 prediction of sleep was
significantly different from that measured (P , 0.001).
Method II. HR and PA* were combined in regressions
against V̇O2 and V̇CO2 with Eqs. 8–13. Regressions were
calculated for awake periods because predictions of sleep
were satisfactory by method I. Equation 11 was judged
the best based on the F-statistic and R 2 (0.92).
V̇O2 and V̇CO2 calculated from Eq. 11 were compared
with measured V̇O2 and V̇CO2 on day 5 for 18 subjects.
While the subjects were awake, the respective differences in mean V̇O2 and V̇CO2 averaged 24.4 6 6.6 and
26.0 6 6.5%, respectively (Table 2). The range of errors
was nearly as large as with method I: V̇O2, 213.4 to
10.6% and V̇CO2, 215.3 to 4.7%. Mean V̇O2 values
predicted from method II were 0.014 l/min greater than
those from method I (P 5 0.054).
Method III. Eighteen subjects averaged 897 6 53 min
awake on day 5, with 115 6 37 min classified as active
by the HR and PA thresholds described in Method III:
Awake Separated Into Active and Inactive Periods.
Prediction equations for active awake were obtained in
Table 2. Awake V̇O2 and V̇CO2 estimate errors relative to measurements in a room calorimeter
HR and Activity
(method II, Eq. 11)
HR (method I, Eq. 3)
Mean 6 SD
Range
HR Functions Assigned by Activity
(method III, Eq. 14)
V̇O2
V̇CO2
V̇O2
V̇CO2
V̇O2
V̇CO2
25.9 6 8.3
221.9 to 9.2
27.8 6 10.7
223.7 to 22.6
24.4 6 6.6
213.8 to 10.6
26.9 6 6.5
215.3 to 4.7
23.4 6 4.5
210.6 to 4.6
24.6 6 3.6
211.7 to 3.6
Values are in percent. See text of description of methods I, II, and III and Eqs. 3, 11, and 14.
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24 h
EE, kJ/min
V̇O2 , l/min
V̇CO2 , l/min
HR, beats/min
Awake
EE, kJ/min
V̇O2 , l/min
V̇CO2 , l/min
HR, beats/min
Duration, min
BMR
EE, kJ/min
V̇O2 , l/min
V̇CO2 , l/min
HR, beats/min
Sleep
EE, kJ/min
V̇O2 , l/min
V̇CO2 , l/min
HR, beats/min
Duration, min
Free Living
Day 1
1758
HEART RATE AND ACTIVITY
cant relationships between awake V̇O2 or V̇CO2 prediction errors and subject fitness (estimated V̇O2 peak), age,
weight (Fig. 2B), lean tissue mass, or 24-h EE/BMR
(from day 1 data). Twenty-four-hour measured V̇O2 and
V̇O2 predicted by method III are compared for one
subject in Fig. 4.
Free-living measurements. Sleep estimates of V̇O2
and V̇CO2 were obtained with HR3 (Eq. 3) developed in
method I, and predictions for the awake periods used
method III (Eq. 14). None of the differences between
days 2 and 3 (weekdays) and day 4 (weekend) were
significant. The mean 24-h V̇O2 and V̇CO2 values on all 3
free-living days were 0.01 6 0.06 and 0.008 6 0.06
l/min greater, respectively, than on day 1 in the calorimeter (Table 1).
DISCUSSION
Fig. 3. V̇O2 and HR responses to exercise measured in room calorimeter.
Fig. 4. Awake V̇O2 measured in a room calorimeter and V̇O2 predicted
from HR and physical activity (method III in text).
Fig. 2. A: difference between awake V̇O2 measured in a calorimeter to
V̇O2 predicted from HR3 (method I, Eq. 3 in text). B: HR combined
with physical activity (method III). Thick dashed lines, group mean
difference; thin dashed lines, ,95% prediction interval (6t0.975 · SD)
about mean.
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the calorimeter from walking, cycling, treadmill exercise, and the step test. Steady-state exercise averaged
11.0 6 1.9 min (Fig. 3).
Errors of estimated V̇O2 and V̇CO2 during awake
periods were 23.4 6 4.5 and 24.6 6 3.6%, respectively
(Table 2). During active periods, errors in estimated
V̇O2 and V̇CO2 were 22.2 6 8.1 and 22.3 6 8.4%,
respectively. One subject had substantially higher predicted V̇O2 and V̇CO2 (26 and 28%, respectively) during a
single exercise session. Means 6 SD for active periods
recalculated with this subject excluded were lower
(V̇O2, 23.9 6 4.1%; V̇CO2, 24.1 6 3.6%). Inactive mean
estimations contributed the most error (V̇O2, 24.3 6
5.5%; V̇CO2, 26.3 6 5.4%). We did not find any signifi-
Method III achieved improved precision in V̇O2 estimates by the classification of awake HR to active and
inactive functions by using PA. The active HR function
was calculated as a linear function with measurements
made during exercise (Eq. 14). Inactive periods were
estimated with a cubed function of HR during periods
with low PA levels. For much of the day, our subjects
confined themselves to relatively sedentary activities
characterized by a limited range of V̇O2 over a moderate
range of HR. Most individuals displayed a range of HR
with both higher and lower V̇O2 that was matched by
the two functions in the model (Fig. 1B).
Dauncey and James (2) were the first to evaluate HR
monitoring against 24-h measurements of V̇O2 in a
room calorimeter. They tested several models for the
V̇O2-HR relationship, including linear, logistic, and
power functions, and recommended that future efforts
explore nonlinear equations to describe V̇O2 to HR as
continuous functions. They also looked forward to the
development of room calorimeters capable of faster
measurements.
We found the 24-h calibration period to be valuable in
two respects. First, it correctly weighted the predominant sedentary periods in the regression algorithms.
Second, it allowed us to define sections of lower V̇O2 and
moderate HR that did not correspond to any compulsory
HEART RATE AND ACTIVITY
were similar to Eq. 3, whereas the range of errors
decreased.
Method III was developed from the FLEX technique
and the recommendations of Haskell et al. (5), who
demonstrated improved correlations with multiple linear regressions of exercise V̇O2 on combined HR and PA
compared with regression based on HR or PA alone. The
authors proposed that PA be used to assign 1-min HR
values to separate active and ‘‘nonactive’’ equations. We
employed separate functions to model active and inactive periods while the subjects were awake.
Because the model in method III was discontinuous,
we were concerned that abrupt and nonphysiological
changes in estimated V̇O2 might be produced when the
HR shifted from one function to the other. We controlled
shifts between the two functions by adding hysteresis
to the PA criteria. Two minutes of PA above the PA
threshold were required from among the current minute
and 2 preceding min to allow a shift from the inactive to
the active function. We also identified the threshold HR
as the intersection of the inactive and active functions.
This value was set as the minimum HR allowed for the
active function. Either HR or PA was required to be
below their assigned thresholds to shift from the active
function to inactive function.
The range of errors in predicting day 5 awake V̇O2 by
method III was from 210.6 to 4.6% (16% overall). Only
a few recent studies have compared HR techniques
with room calorimetry, and all used the FLEX method.
Reported overall error ranges were 20 and 35% for
adult studies (1, 14) and only 10% in children (4). In
addition, 24-h HR monitoring has been validated
against the doubly labeled water method, with error
ranges of 40% or more (9, 13, 7). Doubly labeled water
has performed well in comparisons with calorimetry. In
a published summary of several validation studies,
labeled-water tests in adults had a weighted mean
error , 1% and a mean SD of 7% (12).
In method III, an average of 251 6 196 min were
above the threshold HR but below the PA threshold and
were thus classified as inactive. Reclassifying all these
points as active, as would occur with a method employing HR alone, would have increased the awake mean
V̇O2 and V̇CO2 to produce estimation errors of 5.3 6 8.6
and 3.5 6 7.4%, respectively. One subject’s V̇O2 and
V̇CO2 were clearly overestimated by this simulated
adjustment (errors: V̇O2, 30%; V̇CO2, 24%). With this
subject removed, the mean estimation errors were still
elevated (V̇O2, 4 6 6.6%; V̇CO2, 2.4 6 5.9%). The
threshold HR was similar to mean 24-h HR for most
subjects and lower than during any exercise.
Errors in HR estimation of metabolic gas exchange
may arise from inadequate calibration data, poor modeling of the V̇O2 and V̇CO2 relationships to HR, and
uncompensated effects on HR, stroke volume, and
oxygen extraction. Day-to-day intraindividual variations in the V̇O2-HR characteristic may exceed 10% (7).
Over longer periods, the V̇O2-HR relationship is altered
by growth, aging, and changes in fitness or body
composition. Our results confirmed the importance of
calibrating V̇O2 to HR for each individual. Frequent
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activities or exercise. These V̇O2-HR combinations appeared throughout the day but were most prolonged
during recovery from exercise.
Large calorimeters can now be operated with response times of ,5 min (9) and have been used by
others for calibration of EE-HR relationships (8). We
scheduled 15 min for compulsory activities to allow
time for the calorimeter and subject to reach a steady
state. An average of 11.0 6 1.9 min of steady-state data
were analyzed from each 15-min interval (Fig. 3).
Mean 24-h V̇O2 on day 5 was 0.36 l/min or 1.7 times
the measured basal V̇O2 . Twenty-four-hour V̇O2 and
V̇CO2 in the calorimeter (days 1 and 5) averaged 5.4 and
3.9%, respectively, lower than the mean free-living V̇O2
and V̇CO2 (days 2–4). Mean indexes of physical activity
(PAI 5 24-h EE/BMR) in the calorimeter (1.68 6 0.15,
range 1.33–1.96) were similar to free-living days (1.736
0.31, range 1.3–2.7), although the free-living range was
greater. The free-living PAI for the men (1.78 6 0.26)
was not significantly higher than that for the women
(1.68 6 0.36; P 5 0.4). The PAI values for both sexes
were within the ranges reported by others (1, 8, 12).
Schulz and Schoeller (12) reported a higher PAI for a
large number of men (1.84 6 0.31) and women (1.7 6
0.23) and noted that these values were higher than the
recommended dietary allowances.
R 2 values of all HR functions to V̇O2 and V̇CO2 during
sleep were low (0.15–0.21). PA signals were minimal
because slight motions fell below the threshold of the
PA sensor. Yet, predictions of day 5 V̇O2 and V̇CO2 from
HR3 were quite good, with mean errors of 20.2 6 0.8
and 20.4 6 0.6%, respectively. V̇O2 during sleep was
also adequately predicted by regressions across subjects with V̇O2 measured during supine rest (mean error
1.0 6 8.1%) or basal conditions (2.3 6 6.5%). Mean V̇O2
throughout sleep was approximately the same as the
BMR. Prediction of V̇CO2 from supine rest was less
accurate because subjects had just eaten.
Free-living sleep duration (450 6 89 min) was similar to sleep duration in the calorimeter, although the
range of free-living sleep times was large: 0–607 min.
Periods of awake, sleep, and activity were easily identified from the HR and PA records without the need of a
diary or notes from the subject. We suggest that HR or
PA be recorded for 24 h even when sleep is predicted by
standardized equations, especially in subjects whose
sleep may be frequently interrupted or truncated or
who cannot be expected to provide a reliable record.
When HR alone was used to estimate V̇O2 and V̇CO2
(method I), the nonlinear equations provided significantly better fits to both 24-h and awake data. HR3 (Eq.
3) was the most efficient of the nonlinear functions as
measured by the F-statistic. Equation 6 (sigmoid) had
the highest mean R 2. We preferred the HR3 equation in
further computations because it was efficient and
simple.
Computation of combined nonlinear regressions of
PA and HR (method II) required much more effort than
any of the models used in method I. F-statistics were
also calculated for this method, and Eq. 10 was the
most efficient. Mean day 5 prediction errors for Eq. 10
1759
1760
HEART RATE AND ACTIVITY
altered their substrate intakes by choosing to eat
different portions of their meals.
Most equations to estimate EE from V̇O2 and V̇CO2
can be reduced to linear combinations of the two
parameters, with V̇O2 making a much larger contribution than V̇CO2. For example, in the nonprotein equation of de V Weir (3), the contribution of V̇O2 is 3.5 times
greater than that of V̇CO2. Measurement errors from
V̇O2 and V̇CO2 contribute to errors in EE in the same
proportion. Thus estimates of EE are unlikely to be
improved by measurement of V̇CO2 from HR. However, if V̇CO2 is of interest separately, it might be beneficial
to supplement the HR recording with a dietary record.
Conclusions
The precision of V̇O2 and V̇CO2 predictions was improved by combining PA monitoring with electronically
recorded HR. PA data were most effective when used to
assign HR to separate active and inactive V̇O2 and V̇CO2
prediction functions than when entered simultaneously
with HR in nonlinear equations. In the present group of
healthy adults, the HR and PA method produced results
similar to other techniques available for free-living
measurements (23.3 6 3.5 and 24.6 6 3% for 24-h V̇O2
and V̇CO2, respectively). Further efforts should be made
to resolve the underestimation of V̇O2 and V̇CO2.
The authors thank Anne Adolph and Maurice Puyau for assistance
in programming and data analysis. We are grateful to Dr. Gerald
Spurr for his critical review of the manuscript.
This work was supported by US Department of Agriculture
National Research Initiatives Grant 94-37200-1156 and Agricultural
Research Service Cooperative Agreement 58-69250-1-003.
The contents of this publication do not necessarily reflect the views
or policies of the US Department of Agriculture, nor does mention of
tradenames, commercial products, or organizations imply endorsement by the US Government.
Address for reprint requests: N. F. Butte, Baylor College of Medicine, 1100 Bates St., Houston, TX 77030-2600 (E-mail: nbutte@bcm.
tmc.edu).
Received 1 August 1995; accepted in final form 6 May 1996.
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,1°C between day 1 and day 5. The subjects were not
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HEART RATE AND ACTIVITY
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