Direct Determination of Aerobic P-ower

Direct Determination
of Aerobic P-ower
James A. Davis, PhD
California State University at Long Beach
easurement of aer?bic power or maximal
oxygen uptake (V02max) is one of the
oldest and most common measurements in
exercise physiology. This chapter outlines the historical development of the equipment used to make the
measurement, the exercise test modes and protocols,
and the criteria used to determine achievement of
V02max. The last section of the chapter deals with
reference values for V02max.
The parameters of aerobic function are aerobic
power or maximal oxygen uptake (V02max), work
efficiency, time constant for V02 kinetics, and the
lactate threshold (Whipp, Davis, Torres, & Wasserman, 1981). Maximal V02 is an important parameter because it represents the upper limit of aerobic
exercise tolerance. Endurance activities are performed
at some fraction of V02max. If V02max is low, then
the level of endurance performance is necessarily
Whole-body oxygen uptake can be determined from
cardiovascular measurements or from respiratory
measurements, using equations based on the Fick
principle. From cardiovascular measurements,
V02 = e.o. (Ca02 - CV02),
where CO. is cardiac output, Ca02 is content of O2
in arterial blood, and CV02 is content of O2 in mixed
venous blood. From respiratory measurements,
V02 = VA(FP2 - FP2)
where VAis alveolar ventilation, F,02 is the fraction
of O2 in inspired gas, and Fti02 is the fraction of O2 in
the mean alveolar gas; this equation is not rigorous
because it does not account for the normally small
differences between inspired and expired alveolar
volumes. Thus, the determinants ofV02 are the heart
(CO.), the mechanical properties of the lungs and
the chest wall (VA)'diffusion of O2from the alveolus
into the pulmonary capillary blood (FX02 and Ca02),
and the extraction of O2 from the capillary blood by
the muscle cell (CV02)' A person with a high V02max
necessarily has good function in each of these determinants. Conversely, a sedentary person has relatively
poor function for each determinant, which results in
a low V02max. If a person has pathology associated
with one of these determinants (e.g., coronary artery
disease that would limit the cardiac output during
exercise), then the V02max will be very low. Hence,
one of the important reasons for measuring V02
during graded exercise testing (eXT) is to establish
whether the V02max is normal.
Two issues are unresolved regarding the measurement of V02max. The first is the criteria used to
establish whether V02max has been achieved during
eXT. The most widely accepted criterion is that
the V02 plateaus during the later stages of the eXT
as the work rate continues to increase. Many subjects,
however, clearly reach their limit of tolerance during
eXT without demonstrating a plateau in V02. The
second unresolved issue is the recommendation that
if a subject does not demonstrate a plateau in V02,
then the term should be V02peak, not V02max. A
later section of this chapter more fully discusses both
of these unresolved issues.
First, it is necessary to present the measurements that
need to be made. The basic equation is as follows:
where VI is inspired ventilation, VE is expired ventilation, FP2 is the fraction of O2 in the inspired
gas, and FfP2 is the fraction of O2 in the mixed
expired gas. However, it is generally assumed that
inspired nitrogen (VlIN 2) equals expired nitrogen
(VEF~2)' Thus,
Vf~2= VE'eN2
. =
where FiN
= 1-
(F E
F E CO 2 ) (2)
Replacement of V[ with
( )
in equation 1 yields
Under normoxic (room air) conditions,
dry FP2
equals 0.2093 and dry FIN2 equals 0.7904. The ratio
of dry inspired O2 to dry inspired N2 is 0.265. Hence,
equation (4) can be simplified to
V02 = V E [FeN2 (0.265) - FE02]
the quantities
to measure for determination of V02 at the mouth are VE, FE02, and
By convention, V02 is expressed under standard
temperature and pressure dry (STPD) gas conditions.
Because VEis typically measured under atmospheric
temperature and pressure saturated (ATPS) gas conditions, it must be converted to STPD gas conditions.
The STPD correction factor can be calculated using
the following equation:
STPD correction factor =
273 oK
(PB -PH2o)
where K is degrees Kelvin, TAis the gas temperature
at the time of measurement,
PB is the barometric
pressure, and PH20 is the water vapor pressure of
saturated gas at TA.Values of PH20 at various values
ofT, can be found in many exercise physiology textbooks.
.•....., ..- .•.•......
:-. '.1i1U·~i!.~~'J~':~~?"'::':
r ...
Hlstorlcel Development
of V02 Measurement
One of the first open-circuit equipment configurations used to measure V02 during exercise was the
Tissot spirometer-volumetric
gas analyzer system.
The Tissot spirometer measured expired ventilation.
An aliquot sample of the mixed expired gas was
drawn from the spirometer and analyzed by a volumetric gas analyzer (e.g., Haldane or Scholander) for
fractional concentrations
of O2 and CO2,
A slight variation
of the Tissot spirometervolumetric
gas analyzer system was the Douglas
gas analyzer system. In later years,
lightweight meteorological
balloons replaced the
heavy, bulky Douglas bags and a gas meter replaced
the Tissot spirometer for measurement of gas volume.
Over time, electronic gas analyzers replaced the volumetric gas analyzers. This system is called the meteorological balloon-electronic
gas analyzer system.',
The next development in equipment configuration
was the semiautomated
system (Wilmore &. Costill,
1974). In this system, the subject's expired air first went
into a mixing chamber and then into .agas meter. A
pump pulled approximately 500 ml of gas per minute
from the mixing chamber and sent it to a 2 L latex
bag; a second pump pulled the gas from the bag and
sent it to the electronic analyzers for determination
ofFE02 and FEC02• The system used three bags. While
the gas analyzers were sampling the contents of one
bag, a second bag was being filled with gas from the
mixing chamber and a third bag was being evacuated.
The bags were part of a spinner device that was manually rotated 120 each minute so that the evacuated
bag would move to a new position and be filled with
gas from the mixing chamber. The other bags would
likewise move to new positions. A problem with this
mixing-chamber system is that the measurement of
ventilation and the mixed expired gas fractions occur
at different times. Ventilation is measured without any
delay, but measurement of the mixed expired gases is
delayed. This delay has two components. One is the
transport delay between the subject's mouth and the
analyzers. The other delay is due to the response time
of the analyzers. Unless the mixed expired gas fractions
are not changing, the calculated V02 will be in error
for this system. The magnitude of the error depends
on the degree of temporal misalignment between the
measurements of ventilation and the mixed expired
gas fractions. Fortunately, at heavy exercise, the ventilation is usually large enough to cause the temporal
misalignment to be quite small, resulting in little error
in the calculated V02max value.
~-'>":' -
Bowing the semiautomated system was the
mated system developed by Beckman Instrunts (Wilmore, Davis, ~ Norton, 1976) called
'metabolic measuring <tart(MMC). This system
-sured ventilation with a turbine volume transer (Davis & Larnarra. 1984), had a mixing
ber, and measured the mixed expired gas
.ons with O2 and CO2 electronic gas analyzers.
e MMC did not have the latex bag arrangement
f the semiautomated system. The gas drawn from
e mixing chamber was sent directly to the O2 and
2gas analyzers. A small computer was an attrace feature of the MMC. The computersampled the
alog signals from the turbine volume transducer
d the electronic gas analyzers over a duration of
ically 1 min. The computer would then calculate
e standard variables of interest (e.g., V02, VC02,
d R, the respiratory exchange ratio) and output
em via a printer a few seconds after the end of the
mpling interval.
The MMC had many advantages over its predecesrs. It eliminated hand calculation of the variables
f interest and manual turning of the spinner device
er each sampling interval, and it provided nearly
. nline analysis of V02 and VC02. A limitation of
the MMC was that it made no attempt to align ventilation and the mixed expired gas fractions temporally. However, the second generation of the MMG
called the MMC Horizon, was programmed to time
align these signals so that the accuracy of the computed V02 and VC02 would be independent of the
ventilation magnitude (Jones, 1984).
The equipment configurations just described collected or sampled many breaths over some time interval, typically 1 min. The calculated V02 represented
the average V02 during the sampling interval. These
types of equipment configurations are sufficient for
the measurement of V02max. But other parameters
of aerobic function, most notably the time constant
for V02 kinetics, require a greater density of data.
Hence, an equipment configuration was designed
to provide online, breath-by-breath measurement
of ventilation and the gas concentrations (Beaver,
Wasserman, & Whipp, 1973). Now, more than
12 companies manufacture over 20 automated
systems. In a comprehensive review of automated
systems, Macfarlane (2001) provides a table show-.
ing the details of these systems. Of the 22 listed as
laboratory-based systems, 12 are breath-by-breath
systems, 7 are mixing-chamber systems, and 3 can
provide either breath-by-breath or mixing-chamber
The manufacturers of current automated systems
use a variety of technologies to measure V£,FE02, and
__ ...
FEC62:~Measurement of VE is made with a turbine
device, a pneumotachometer, Pitot tubes, or a hot
wire sensor. Technically, these four devices measure
flow. Volume is found by integrating the area under
the flow curve. A few manufacturers use a mass
spectrometer to measure both F-02
and F-C0
2, but
most of them use separate analyzers to measure the
fractional concentrations of each gas. Most manufacturers use infrared radiation absorption technology for the FeC02 measurement and a polargraphic
electrode, a paramagnetic analyzer, or a fuel cell for
the Fe02 measurement.
Several issues are specific to automated systems.
One is the temporal alignment of the ventilation and
gas concentration measurements. If misalignment is
present, especially in breath-by-breath systems, large
errors (as much as 30% at high breathing frequencies)
can occur in the calculation of V02 (Proctor & Beck,
1996). Some of the sensors for the VE measurement
and the Fe02 and FEC02 measurements generate
nonlinear outputs given linear inputs. Automated
systems typically solve these nonlinear hardware
problems with software corrections. Knowing the
temperature and humidity of gas collected in a
meteorological balloon is easy, but it is not so easy
to know this information during each minute of a
GXT for the flow and gas concentration sensors of
an automated system. Hughson, Northey, Xing, Dietrich, and Cochrane (1991) have shown that errors in
the gas temperature measurement, or the assumed
value of that measurement, can result in errors in
the computed V02, for example, a 3.6% error in V02
for a 2 C error in the temperature measurement or
the assumed value of that measurement. A number
of independent studies have been published dealing with the validity and reliability of automated
systems. A summary of these studies presented by
Macfarlane (2001) provides evidence that several
of these systems are both valid and reliable. Finally,
the cost of a typical automated system-$20,000 to
$25,000-is a significant issue. Given the complexities of these systems, some investigators purchase
maintenance contracts with their systems, which
further increase the cost.
Of the equipment configurations described, only
the automated systems and the meteorological balloon-electronic gas analyzer system are used routinely today. Fay, Londeree, LaFontaine, and Volek
(1989) used the latter system to measure V02max
in female distance runners. Expired gas was directed
through 3.175 em ID smooth rubber tubing, corrugated plastic tubing, and a three-way valve into
meteorological balloons. The gas was collected continuously in 30 s intervals after the subject indicated
tures of any system are desirable. First, the system
should not have any leaks. Second, the resistance
to inspit'ation-6r'~explration caused by the system - -,
should be less than 5 cm H20 pressure at any
ventilation. Third, the device used to measure gas
volume should provide measurements to within 3%
of the true value. Fourth, the device or devices used
to measure fractional gas concentrations should be
able to measure both O2 and CO2 to within 0.0003
of their true values.
that she could only run 90 s longer. An aliquot sample
was' taken from each meteorological balloon and
measured-for FE02 with a paramagnetic gas analyzer
and F CO2 with an infrared gas analyzer. Reference
gases for calibration of the electronic gas analyzers
were verified with the Scholander apparatus. Expired
gas volumes were measured with a gas meter. Oxygen
uptake was calculated using equation (5), presented
earlier in this chapter.
McArdle, Karch, and Pechar (1973) analyzed the
test-retest reliability data for the V02max measurement by the meteorological balloon-electronic gas
analyzer system. They performed duplicate cycle
ergometer GXTson 15 college-age males. The mean
±SDV02max values for the first and second tests were
4.157 ± 0.445 and 4.146 ± 0.480 L· min-I, respectively. The standard error of estimate was low (0.094
L· min-I), and the correlation coefficient was high
(.959). Hence, the meteorological balloon-electronic
gas analyzer system can provide excellent test-retest
Whether one uses a meteorological balloonelectronic gas analyzer system or an automated
system to measure V02max, several general fea-
Exercise Test Modes
The most popular modes for graded exercise testing
are the cycle ergometer and the motor-driven treadmill. Both modes can be controlled manually or by
computer. For cycle ergometers, the braking mechanism is done either by friction or electronically. The
electronic cycle ergo meters are more expensive and
more difficult to calibrate. Maximal V02 values in
typical people are approximately 10% higher when
measured during treadmill running compared with
cycle ergometry (see figure 2.1) (Davis & Kasch,
Cycle ergometer V02 max (L • rnirr")
Figure 2.1
Maximal V02 measured during treadmill running compared with cycle ergometry.
Data from Davis and Kasch. 1975.
D.iLecLD.eierruio.atioD-ULAe.mbkk>wer 13
Exercise Test Protocols
The most widely used exercise testing protocols are
continuous and graded. The study of Buchfuhrer et al.
(1983) is worthy ofreview before specific GXTprotocols are discussed. Buchfuhrer et al. examined the
possibility that the V02max measurement was protocoldependent. They found that "fast" protocols (i.e.,
those with large work rate increments per minute)
and" slow" protocols (i.e., those with small work rate
increments per minute) caused underestimations of
the true V02max value, which was found using "intermediate speed" protocols. Buchfuhrer et al. (1983)
suggested that the fast protocols caused subjects to
terminate the GXTearly because they had insufficient
muscle strength to accommodate the large work rate
increases during the final stages of the test. Two reasons probably explain why Buchfuhrer et al. (1983)
found low V02max values for the slow protocols.
First, these protocols, which lasted an average of 18
min for cycle ergometry and 26 min for treadmill
exercise, would likely result in a significant increase
in core temperature. This increase, in turn, would
result in a redistribution of the cardiac output so that
less blood (and, therefore, less O2) would be going
to the exercising musculature and more blood would
be going to the cutaneous circulation in an effort to
dissipate heat. Lessblood flow (and therefore less O2
delivery) to the working muscles at maximal work
rates would explain the lower V02max values found
for the slow protocols. A second plausible explanation for this finding is subject motivation. The slow
protocols are particularly exhausting, requiring high
motivation on the part of the subject to deal with the
high levels of lactate and heat associated with heavy,
prolonged exercise. Buchfuhrer et al. (1983) found
the highest V02max values with GXTprotocols that
lasted 8 to 12 min.
Using the results of Buchfuhrer et al. (1983), GXT
protocols should be designed in such a way to cause
the test to end somewhere between 8 and 12 min.
An example will demonstrate how the increment
size can be found. Consider a subject with a predictedV02maxof3,OOO ml min' for a cycle ergorneterGXT.According to Wasserman and Whipp (1975),
the relationship between V02 in ml mirr ' and work
rate (WR) in watts (W) for cycle ergometry is given
by the following linear regression equation:
10 ml-mirr' . WR + 500 ml-mirr"
Solving for the work rate that would result in a predicted V02 of3,000 ml- mirr ' yields 250 W. The predicted increment size per minute that would produce
a test duration of 8 min is 31 W (250 Wj8 min). For
a test duration of 12 min, the predicted increment
size per minute would be 21 W (250 Wj12 min).
A prudent choice of the increment size per minute
would be 25 W, which would be predicted to produce
a test duration of approximately 10 min.
The most widely used cycle ergometer GXT protocols have a warm-up period of approximately 4
min. The work rate during the warm-up period is
typically unloaded cycling or a light work rate such
as 15 W. Immediately after 4 min of warm-up, the
work rate is incremented by x W each minute until
the subject reaches his or her limit of tolerance; x
is the increment size that is predicted to produce
a test duration somewhere between 8 and 12 min
from the time when the work rate increments begin.
These cycle ergometer protocols can be used to test
the entire spectrum of subjects, from elite athletes
to patients with cardiopulmonary disease. Only the
increment size needs to be adjusted. Regarding the
pedal frequency during cycle ergometry GXT, Hermansen and Saltin (1969) found that 60 rpm gave
higher V02max values than did 50, 70, or 80 rpm.
Hence, the pedal frequency for cycle ergometry GXT
should be 60 rpm.
The Balke test (Balke & Ware, 1959) is a widely
used treadmill GXTprotocol. It is basically a treadmill
walking test; the speed is 3.3 mph (5.3 kph) until a
grade of 25% is reached. Thereafter, the grade is constant and the speed is increased 0.2 mph (0.32 kph)
each minute. The grade is 0% for the first minute. The
grade is raised to 2% at the end of the first minute
and increased 1% per minute thereafter until it
reaches 25%. For low-fit subjects, this protocol elicits valid V02max values. For fitter subjects, however,
the test duration is very long. Also, these subjects are
required to walk at grades above 20% during the last
few minutes of the test and, according to McArdle et
al. (1973), complain of severe local discomfort in the
lower back and calf muscles, which may limit their
ability to achieve maximal work rates. McArdle et al.
(1973) compared V02max values measured using
the Balke treadmill test to those measured using a
continuous running treadmill test in reasonably fit
male subjects. They found that the Balke test yielded
V02max values that were approximately 4% lower
than those obtained on the continuous running test.
The Balke test could be modified to have a faster
walking speed, which would likely result in increased
V02max values for fitter subjects.
Maksud and Coutts (1971) provide a typical running treadmill protocol. Ii begins with the subject
running at 6 mph (9.7 kph) on the level (0% grade)
continuous test and 67.3 min for
the discontinuous
test. Both the subjects and the
preferred the continuous
test to the
test because of the long test duration
of the discontinuous
Over the years, cardiologists
have designed a
number of clinical treadmill protocols to test patients
with heart disease. Two of these protocols are those
of Bruce (Bruce, Kusumi, &. Hosmer, 1973) and Ellestad (1986)-see
figures 2.2 and 2.3, respectively.
The Bruce protocol is the most widely used clinical
treadmill protocol.
for 2 min. Thereafter, the grade is increased by 2.5%
each 2 min; the speed is constant throughout
Each of the protocols just described is continuous.
Some GXT protocols are discontinuous. An example
is the treadmill test of Mitchell, Sproule, and Chapman (1958). The test begins with the subject walking
at 3 mph (4.8 kph) for 10 min at 10% grade. The
subject then rests for 10 min. Next, the subject runs
for 2.5 min at 6 mph (9.7 kph) up a 2.5% grade.
After another 10 min rest period, the subject runs for
2.5 min at 6 mph (9.7 kph) up a 5.0% grade. This
procedure (rest followed by a 2.5% grade increase)
continues until the subject reaches his or her limit
of tolerance.
The V02max obtained using a continuous protocol
is the same as that obtained using a discontinuous
protocol. McArdle et al. (1973) compared the continuous Maksud and Coutts treadmill protocol with
the discontinuous
Mitchell et al. (1973) treadmill
protocol in 15 college-aged males. The mean V02max
values for the continuous and discontinuous
protocols were similar, 4.109 and 4.145 Lvmirr ', respectively. What differed markedly was the test duration:
. for Achievement
The most widely accepted criterion for the achievement of V02max during GXT is a plateau in V02 as
the work rate continues to increase. Typically, however, less than 50% of subjects tested demonstrate a
plateau. Cumming and Borysyk (1972) administered
GXT to 65 men aged 40 to 65 years. Only 43% of
3.4 mph
Figure 2.2
Time (min)
Bruce treadmill protocol for patients with heart disease.
by permission,
from the American
Williams, and Wilkins), 20.
College of Sports Medicine,
1986, ACSM's guidelines for exercise testing and prescription, 3"' ed. (Lippincott,
1.7 mph
Time (min)
Figure 2.3
Ellestad treadmill protocol for patients with heart disease.
Adapted, by permission, from the American College of Spons Medicine, 1986, ACSM's guidelines for exercise testing and prescription,
Williams, and Wilkins), 20.
ed. (Lippincott,
these men met the plateau requirement.
et al. (1986) found that less than 40% of 301 adults
undergoing GXT demonstrated a plateau. Cumming
and Friesen (1967); Cunningham, Van Waterschoot,
Paterson, Lefcoe, and Sangal (1977); and Astrand
(1952) found that less than 50% of young boys who
underwent GXT demonstrated
a plateau. Indeed,
Noakes (1988) has pointed out that the original
investigators who developed the plateau criterion
failed to find a true plateau in V02 as the work rate
continued to increase.
Three other criteria often used to defend the
achievement of V02max are (a) blood lactate concentration in the first 5 min of recovery >8 mrnol/L,
(b) respiratory exchange ratio at test termination
>1.00, and (c) heart rate at test termination
of age-predicted maximum (220 - age). The third
criterion is the least rigorous because of the wellknown large variation in maximal heart rate at any
given age.
It has been suggested that if a subject fails to demonstrate a plateau in V02 as the work rate continues
t.o increase, he or she then reached a V02peak, not a
teau criterion for achievement of V02max (Noakes,
1988), however, many investigators accept that the
subject has achieved V02max if he or she meets the
plateau criterion or two of the three secondary criteria.
For patients, especially those with heart disease, a
special term has been developed, namely, symptomlimited V02max_ This quantity is simply the highest
V02 measured before the patient had to stop exercising because of symptoms like severe angina.
Thoden (1991) has developed a novel solution to
identifying the "true" V02maxvalue_ He uses a protocol with athletes that has two phases (see figure 2.4)
preceded by a 5 min warm-up. The progressive phase
is a GXTthat is initiated at about 30% of the athlete's
predicted V02max value and progresses at about 10
to 15% of that value for each work rate increment.
The duration of each work rate increment is 2 min.
The typical duration of the progressive phase is 8 to
12 min. Following the progressive phase, the athlete
recovers at low exercise intensity until his or her heart
rate returns to about 100 beats -mirr ', which typically
takes 5 to 15 min. At this point, the verification phase
V02ffiax. Given the concerns.raised regarding the pla-
begins. This phase is a constant-load
(square-wave) .:~';~':.. __"..
testat a work rate one increment higher than that
achieved during the progression phase. The typical
duration is 3 to 5;min. An increase of <2% compared
with that obtained in the progressive phase indicates
that VOzmax has been achieved. If the highest V02
during the verification phase is ~2% above that
found during the progressive phase, then the verification test is repeated at the next work rate prescribed
by the protocol. This procedure continues until the
increase is <2%. The "true" VOzmax is taken as the
highest VOz found in either the progressive phase or
the verification phase. The V02 response to the progressive phase will be linear up to the maximum after
a short delay at the start of the phase. For the squarewave forcing function of the verification phase, the
V02 response will be exponential up to the maximum.
Thoden (1991) reports excellent test-retest reliability
for this protocol. For 15 subjects with VOzmax ranging from 46 to 76 ml- min-I. kg', no significant difference occurred from test to retest. The correlation
coefficient was .95 between the two tests.
Many factors are known to influence VOzmax. Bed
rest causes it to go down, whereas endurance exercise training increases it (Saltin et al., 1968). When
V02max is expressed in the units of L· min-I, large
people (those with increased height or weight)
typically have higher values than small people do.
Women typically have lower V02max values than
men do. Old adults generally have lower VOzmax
values than young adults do. These factors (i.e.,
extent of physical activity in leisure time, height,
weight, gender, and age) can be used to predict V02max with some degree of confidence. Jones,
Makrides, Hitchcock Chypchar, and McCartney
(1985) performed cycle ergometer GXTson 50 male
and 50 female subjects of various fitness levels who
ranged in age from 15 to 71 years. From the data collected, they developed the following multiple linear
regression equation:
600 -
Time (min)
Figure 2.4 An example of a cycleergometer protocol used by Thoden (1991) to determine "true" V0 max in athletes. The protocol is preceded by a 5 min warm-up (not shown). The protocol has three parts, namely, a progressive
phase, ~ recoveryperiod, and the verification phase, The protocol shown in this figure is specificto athletes with predicted V02max valuesbetween 2 and 4 L·min-I.
- .....-.---.-.--------.-
..-- __ .
V02max (L'mirr ') = 0.025 (Ht) - 0.023 (Age)0.542 (Gender) + 0.019 (Wt) + 0.15 (Lei) - (8)
2.32 Lrnirr '
where Ht is standing height in em, Age is in years, and
Wt is body weight in kg. For male subjects, the gender
code is O. For female subjects, the gender code is l.
Lei is leisure time spent per week in physical activity. The four grades of leisure activity are as follows:
grade 1 for <1 h per wk, grade 2 for 1 to 3 h per wk,
grade 3 for 3 to 6 h per wk, and grade 4 for >6 h per
wk. An example illustrates how this equation can be
used to predict V02max. Assume that a 44-year-old
male subject is 183 cm tall, that he weighs 70 kg,
and that he jogs 2.5 h per week (hence, his leisure
activity grade is 2). Plugging these numbers into the
above equation yields a predicted V02max of 2.87
L· mirr '. The multiple correlation coefficient for this
equation is .892 and the standard error of estimate
is 0.415 L· min'. This latter statistic can be used
to compute the upper and lower 95% confidence
limits of the predicted value. In the above example,
the predicted V02max value of 2.87 L· mirr ' would
have lower and upper 95% confidence limits of2.05
and 3.69 L· mirr ', respectively.
Recently, Davis, Storer, Caiazzo, and Pham (2002)
developed multiple linear regression equations that
allow computation of the lower reference limit
for V02max. The unique feature of these equations
is that they were developed using sedentary people.
Hence, if the measured V02max value of a subject
falls below the lower reference limit, it cannot be
argued that the low measured value was due to sedentary living. For each gender, three equations with
different predictor variables were developed. Shown
below are the prediction equations for men including
the squared multiple correlation coefficient (R2),the
standard error of estimate (SEE), and the one-sided
95% confidence interval (95% CI) for each equation.
The units for the predictor variables of age, height
(Ht), mass, and fat-free mass (FFM) are years, em,
kg, and kg, respectively.
VOimax (Lrnin")
= - 0.0282 (Age) + 0.0205 (Ht) +
0.3200 L'rnin";
R2= .580; SEE = 0.398 Lrnirr";
. and 95% CI = 0.660 Lrnin'
V02max (Lrnin+) = - 0.0296 (Age) +
0.0167 (Mass) + 2.6538 Lrnirr ';
R2= .640; SEE = 0.369 L'min'";
and 95% CI = 0.612 L'min-'
..J2ir.e.cLD.e.tenninatiQ[LQtAerQblc ...P..Q.w.eL-J.I
V02max (L'rnirr") = - 0.0262 (Age) +
0.0266 (FFM) + 2.1154 L'mirr";
R2= .657; SEE = 0.359 Lrnin":
and 95% CI = 0.595 Lrnirr"
The corresponding prediction equations for women
are shown below.
V02max (Lrnirr") = - 0.0171 (Age) +
0.0160 (Ht) - 0.2740 Lrnirr";
R2= .500; SEE = 0.286 L'rnirr";
and 95% CI = 0.474 Lrnin?
V02max (Lrnirr") = - 0.0199 (Age) +
0.0135 (Mass) + 1.6267 L'mirr";
R2=.557; SEE = 0.269 L'rnirr";
95% CI = 0.446 L'rnirr"
V02max (L'rnirr") = - 0.0183 (Age) +
0.0230 (FFM) + 1.3405 L'mirr";
R2 = .554; SEE = 0.270 Lmirr ':
95% CI = 0.448 Lrnirr"
These equations were developed on a relatively large
sample (115 men and 115women) that ranged in age
from 20 to 70 years. The sample 'included about 23
subjects in each age decade. The GXT. mode was the
cycle ergometer. Thus, the predicted V02max values
are specific to cycleergometer GXT. The equations can
be used to predict V02max for treadmill GXT simply
by multiplying the predicted value by 1.10 to raise
that value by 10%.
An example will illustrate how the lower reference
limit can be calculated. The predicted V02max for a
40-year-old male who is 175 cm tall is 2.780 L· rnirr '
using the equation for men with the predictor variables of age and height. The lower 95% confidence
limit (lower reference limit) is calculated as the predicted V02max minus the one-sided 95% confidence
interval (0.660 L· rnirr ']. Thus, the lower reference
limit for this subject is 2.120 L· mirr-' (2.780 - 0.660
L· mirr"}.
If the only aerobic functionparameter of interest is
V02max, then the meteorological balloon-electronic
gas analyzer system is the simplest an'd, most inexpensive of the systems currently used to make the
measurement. But if the user wants to measure all the