## Services on Demand

## Journal

## Article

## Indicators

- Cited by SciELO
- Access statistics

## Related links

- Cited by Google
- Similars in SciELO
- Similars in Google

## Share

## Arquivos Brasileiros de Cardiologia

##
*Print version* ISSN 0066-782X

### Arq. Bras. Cardiol. vol.94 no.6 São Paulo June 2010 Epub May 28, 2010

#### https://doi.org/10.1590/S0066-782X2010005000054

**Equations
for predicting aerobic power (VO _{2}) of young Brazilian adults**

**Paula Magrani ^{I,
II}; Fernando Augusto Monteiro Saboia Pompeu^{I, II}**

^{I}Universidade
Federal do Rio de Janeiro, Rio de Janeiro, RJ - Brazil^{
} ^{II}Hospital dos Servidores do Estado, Rio de Janeiro, RJ -
Brazil

**ABSTRACT**

**BACKGROUND:
** VO_{2} may be predicted with base on anthropometric and physiological
parameters for determined populations.

**OBJECTIVE:** To propose models for submaximal and maximal VO_{2}
prediction in young Brazilian adults.

**METHODS:** A total of 137 volunteers (92 men) underwent graded maximal
exercise test (GXT) in a cycle ergometer (Monark^{TM}, Br). Gas exchange
and respiratory measurements were performed in an open circuit (Aerosport^{TM}
TEEM 100, USA). In another group, 13 volunteers underwent GXT and a square wave
test (SWT) in order to evaluate the external validity of Neder et al's formula,
ACSM's formula, and of Åstrand-Ryhming nomogram. The study design chosen
was a cross-validation and the significance level was set at p __<__ 0.05.

**RESULTS:** For men during submaximal exercises, a mathematical model was
deduced with base on workload, body mass, and age, which explained 89% of the
VO_{2} variation, with SEE (standard error of the estimate) = 0.33 l^{.}min^{-1}.
For the maximum load in the male group, another model with the same variables
explained 71% of VO_{2} variation, with SEE = 0.40 l^{.}min^{-1}.
For women, 93% of VO_{2} variation could be explained, with SEE = 0.17
l^{.}min^{-1}, both in submaximal and maximal exercise, with
only one equation by use e of the same independent variables.

**CONCLUSION:** The models derived in the present study proved to be accurate
to predict submaximal and maximal VO_{2} in young Brazilian adults.

**Key words:**
Maximal voluntary ventilation; physical exertion; exercise; exercise test.

**Introduction**

Exercise tolerance
is an important predictor of cardiovascular, pulmonary, metabolic, and muscle
and joint health. The ability of muscles to take up oxygen during exercise is
also an index of physical fitness^{1}. In order to measure this parameter
(VO_{2}), a continuous graded maximal exercise test (GXT) is usually
performed in a treadmill or cycle ergometer^{2}. In Brazil, treadmills
are more frequently used; however many laboratories also use cycle ergometers,
which are more adequate in the case of orthopedic lesions and lead to few artifacts
on electrocardiogram and blood pressure measurement. Mechanical cycle ergometers
are also more advantageous because of their lower cost and weight, and for not
requiring electricity^{3}.

Aerobic capacity
(VO_{2}) is an important measurement in exercise test because of its
close correlation with cardiac output, according to Fick's principle, and its
application in indirect calorimetry^{1,4}. Indirect calorimetry is a
noninvasive method used for VO_{2} measurement by means of an ergospirometer^{5}.
Difficulty of access to and high costs of ergospirometric evaluation, however,
cause predictive methods to be more frequently used than ergospirometry in the
assessment of functional capacity^{6}. Consequently, several equations
have been proposed to estimate maximal and/or submaximal oxygen uptake based
on easy-to-measure morphological and functional variables such as: body mass;
age; gender; height; perceived exertion; walk time; run time; and load in watts^{1,7-15}.
These equations may be used to determine exercise intensity. However, these
methods have considerable errors (15-20%)^{1} which increase unpredictably
when applied to populations different from the one used to develop them. And,to
date, equations generally used in this country come from populations with anthropometric,
cardiopulmonary and biomechanical characteristics different from those of the
Brazilian population.

With the purpose
of improving oxygen uptake prediction in our population, we conducted two studies.
The objective of study 1 was to develop equations to predict VO_{2}
in GXT, at submaximal and/or maximal intensities, with external validity equal
to or higher than that of the equations developed by Storer et al^{15}.
Study 2 had the purpose of comparing the external validity of the equations
developed here with predictions obtained by ACSM^{8}, Neder et al^{14},
and Åstrand -Ryhming^{16}.

**Methods**

**Study 1 - Model
proposed for VO _{2} prediction**

The subjects of
this study were 137 apparently healthy non-smoker, non-athlete adult volunteers.
The subjects were classified according to their body mass and divided into two
groups, by randomized systematic sampling. Seventy seven men (24 ± 5
years, 76.6 ± 10.9 kg, 178.4 ± 6.8 cm, VO_{2max}= 3.68
± 0.74 l^{.}min^{-1}, *W _{max} =* 271 ±
57 watts and AnT = 1.63 ± 0.31) and thirty women (25 ± 6 years,
58.4 ± 6.9 kg, 162.7 ± 7.1 cm, VO

_{2max}= 2.29 ± 0.48 l

^{.}min

^{-1}and

*W*184 ± 39 watts and AnT = 1.13 ± 0.22) were drawn for the internal validity group (

_{max}=*VI*); fifteen men (27 ± 7 years, 75.6 ± 9.3 kg, 176.9 ± 6.7 cm, VO

_{2max}= 3.92 ± 0.70 l

^{.}min

^{-1},

*W*273 ± 44 watts and AnT = 1.67 ± 0.34) and fifteen women (25 ± 6 years, 59.3 ± 7.9 kg, 161.9 ± 8.1 cm, VO

_{max}=_{2max}= 2.22 ± 0.55 l

^{.}min

^{-1},

*W*182 ± 35 watts and AnT = 1.08 ± 0.23) comprised the external validity group (EV). Prior to undergoing the tests, the volunteers gave a written informed consent. The experimental study protocol was approved by our institutional Ethics Committee on Human Research. On the day before the test, the individuals were advised to refrain from engaging in strenuous physical activity (> 5 METs) and to keep a mixed diet. They were also advised to avoid caffeine and food in the three hours prior to the exercise.

_{max}=**Test protocol**

The continuous
graded maximal exercise (GXT) protocol^{17} was adopted, consisting
of an initial six-minute rest with the individual sitting on the cycle ergometer
(Monark^{TM}, Brazil), followed by a four-minute warm-up of pedaling
with no load, and by the progressive phase with increments by 10% in VO_{2max}
per minute^{18}. The maximum load was estimated by using anthropometric
parameters^{19}. The graded phase lasted between 8 and 12 minutes at
most, and the pedal cadence was not changed during the exercise (approximately
1.23 Hz). Tests not interrupted by fatigue within the established time were
disregarded.

The respiratory
and gas exchange variables were recorded every 20 seconds and measured by a
metabolic analyzer (Aerosport^{TM} TEEM 100, USA) with a pneumotachograph
(Hans Rudolph^{TM}, USA). Heart rate (HR) was measured by a cardiotachometer
(Polar^{TM} Vantage NV, Finland) every five seconds.

Equipment was calibrated
before each test was performed. All tests were performed in the same cycle ergometer
and the pedal cadence was controlled by means of an audiovisual metronome. The
ergospirometer was calibrated by means of a certified gas mixture (AGA^{TM},
Brazil) containing 17.01% oxygen, 5.00% carbon dioxide, and balanced with nitrogen.
Flow was calibrated by using a three-liter syringe (Hans Rudolph^{TM},
USA), and the cycle ergometer by using a 3-kg weight.

The tests were
considered maximal when at least three of the following criteria were observed,
according to Howley et al^{4}: VO_{2} plateau (increase __<__
150ml^{.}min^{-}¹ or 2 ml^{.}kg^{-}¹^{.}min^{-}¹);
RER (respiratory exchange ratio) __>__ 1.15; HR_{max} __>__
90% of age-predicted HR (220 - age); perceived exertion rate __>__ 18.
Maximal volitional fatigue with inability to keep the pre-established rhythm.
VO_{2max} was determined as the highest value obtained during maximal
exertion. In the present study, the maximum load was defined as that observed
at VO_{2max}. The anaerobic threshold (AnT) was established by using
the V-slope method^{20}, by determining the inflexion point in the VO_{2}
x VO_{2} curve^{21}. The measurements mentioned were taken by
two independent observers and AnT was the mean of the two observations.

**Study 2 - External
validity of ACSM ^{8}, Neder et al^{14} and Åstrand-Ryhming^{16}
VO_{2} prediction models**

Thirteen adult volunteers participated in the second study; of these, eight were men (24 ± 3 years, 81.5 ± 13.6 kg, 181.9 ± 5.6 cm) and five were women (22 ± 3 years, 63.2 ± 11.7 kg, 163.9 ± 2.2 cm), all apparently healthy, non smokers and non-athletes.

**Test protocol**

Following the same
procedures for calibration and control used in study 1, the subjects underwent
GXT and square wave test^{1} (SWT) alternated within a period from one
to 14 days. SWT comprised two loads, the first one submaximal (*SWT _{sub}*)
and the second one maximal (

*SWT*. The individuals cycled for six minutes at the submaximal load, and the mean HR measured in the last two minutes was used to estimate VO

_{max})_{2max}by means of the Åstrand-Ryhming nomogram

^{16}. After a 10-minute rest with the individual sitting on the cycle ergometer and connected to the ergospirometer, the second load of 110% to 115% of the estimated load for VO

_{2max}was started. The last load was controlled during the exercise in order to lead to exhaustion at between two and three minutes.

**Statistical
analysis**

The statistical
analysis was carried out by using the Statistical Package for the Social Sciences^{TM}
(SPSS, USA) and Microsoft Excel^{TM} for Windows XP^{TM} (USA).
Descriptive statistics was used with mean ± standard deviation (SD).
For group VI, regression equations were derived for VO_{2} prediction
at several exercise intensities. The external validity of the derived equations
was tested in cross-validation by applying them to group EV. The values predicted
and measured were compared by using the paired t test. The external validity
of Storer et al's equation^{15} for men and women (03M and 03F, respectively)
proposed for the same GXT protocol were analyzed in group EV by using two-way
ANOVA and post-hoc Tukey-HSD test. With the maximum values obtained in group
VI, a specific regression equation was also derived to predict VO_{2max}
for the male group. The external validity of this equation was tested in group
EV, and the values predicted and measured were compared by using two-way ANOVA
and post-hoc Tukey-HSD test, together with the maximum predicted values for
the same group by using Storer et al's equation^{15}.

Bland and Altman's
limits of agreement^{22} were used between the measured and calculated
results. The prediction error was also observed by means of the technical error
of measurement (*s* = SD_{dif} ÷Ö2) and of the coefficient
of variation (CV).

Values measured
in GXT and SWT were compared by using two-way ANOVA; post-hoc Tukey-HSD test
with VO_{2max} estimated by Åstrand-Ryhming nomogram^{16}
by using the workload (06M-NW and 06F-NW); and the VO_{2} value measured
(06M-NV and 06F-NV). Åstrand-Ryhming^{16} normogram estimates
corrected for age by using the equations proposed by Siconolfi et al^{23}
(07M and 07F) were also compared to the values measured. VO_{2max} and
VO_{2} accuracy, as estimated by recent (05M and 05f) and old equations
(04M and 04F) proposed by ACSM^{8}, was checked. Neder et al ^{14}
model (08M and 08F) for the Brazilian population was compared only to the values
measured in SWT. The level of significance for all statistical tests was set
at * <* 0.05.

**Results**

Submaximal VO_{2}
values measured and Watt for group EV were 2.01 (±1.11) l^{.}min^{-1}
and 273 (±44) watts for men and 1.25 (±0.63) l^{.}min^{-1}
and 182 (±35) for women. The prediction equation for oxygen uptake derived
for the male group was:

**Equation 01M**

VO_{2}
= -0.131 + (0.01103 x Watt) + (0.007786 x Body Mass) - (0.00617 x Age)

*R ^{2}*
= 0.89 and

*SEE*= 0.33 l

^{.}min

^{-1}

For the female group:

**Equation 01F**

VO_{2}
= -0.461 + (0.01043 x Watt) + (0.007096 x Body Mass) + (0.01006 x Age)

*R ^{2}*
= 0.93 and

*SEE*= 0.17 l

^{.}min

^{-1}

Where: *R ^{2}*
= coefficient of determination;

*SEE*= standard error of the estimate.

The results of
the predictions through equations 01M, 01F, and 03F for submaximal values were
not significantly different from the values measured in group EV. A significant
difference between the submaximal values measured and predicted was detected
for equation 03M (p = 0.02). Likewise, at peak exercise, equations 01F and 03F
did not show significant differences between the values measured and predicted.
Equations 01M and 03M, in turn, showed significant differences when used for
VO_{2max} prediction (p = 0.001 and p = 0.04, respectively). The external
validity of equations 01M, 03M, 01F and 03F are shown in Figures
1 and 2. In order to determine the quality of equations
01M and 01F at other intensities, the values measured and predicted at three
submaximal loads were compared. No significant differences were found for equation
01M at 40% VO_{2max} (p = 0.40), 60%VO_{2max} (p = 0.72) and
80% VO_{2max} (p = 0.13); or for equation 01F at 40%VO_{2max}
(p = 0.06), 60% VO_{2max} (p = 0.15) and 80% VO_{2max} (p =
0.70). In order to improve VO_{2max} prediction for the male group,
another equation was derived to be applied at peak exercise:

**Equation 02M**

VO_{2max}
= 0.518 + (0.01016 x Watt_{max}) + (0.01482 x Body Mass) - (0.0292 x
Age)

*R ^{2}*
= 0.71 and

*SEE*= 0.40 l

^{.}min

^{-1}

No significant difference was found between the maximum values measured and predicted in group EV when equation 02M was used.

In the second study,
submaximal values of VO_{2} and of the load obtained in *SWT _{sub}*
were 1.55 (±0.46) l

^{.}min

^{-1}and 100 (±19) watts for men, and 0.93 (±0.35) l

^{.}min

^{-1}and 70 (±21) watts for women. Submaximal VO

_{2}values predicted by all models were not significantly different from the values measured (Table 1). The maximum oxygen uptake value (VO

_{2max}) obtained in GXT was 3.09 (±0.99) and 1.49 (±0.13) l

^{.}min

^{-1}for men and women, respectively. For the female group, there were no significant differences between VO

_{2max}values predicted and measured by GXT. For the male group, VO

_{2max}values measured by GXT were statistically different from the values predicted by 07M-NV (p = 0.04, CV = 35.31%,

*s*= 0.90 l.min

^{-1},

*r*= 0.46) and by 07M-NW (p = 0.03, CV= 39.3%,

^{2}*s*= 1.01 l.min

^{-1},

*r*= 0.25) when Siconolfi et al's correction

^{2}^{23}was applied to Åstrand-Ryhming nomogram

^{16}. VO

_{2max}and W

_{max}obtained in SWT

_{max}were 3.12 (±0.73) l

^{.}min

^{-1}and 215 (±46) watts for men, and 1.63 (±0.14) l

^{.}min

^{-1}and 139 (±22) watts for women. For the female group, no significant difference was found between VO

_{2max}values predicted and measured in SWT

_{max}. For the male group, in turn, VO

_{2max}values obtained in SWT

_{max}were statistically different from the values predicted by 07M-NV (p = 0.01) and by 07M-NW (p = 0.01), when the Siconolfi et al's correction

^{23}was applied to Åstrand-Ryhming nomogram

^{16}. The male group also showed VO

_{2max}values statistically different from those predicted by equation 08M (p = 0.02). Results from the analysis carried out by using VO

_{2max}predictive methods compared to values measured in SWT

_{max}are shown in Table 1.

**Discussion**

Despite the large
number of VO_{2} prediction equations, very few of them are not specific
for a determinate population. The high correlation and moderate standard error
of the estimate found in the present study showed that VO_{2} can be
predicted with satisfactory accuracy by using body mass, age, and workload as
independent variables.

Quality control
of measurements by means of calibration procedures and operation of equipment
by experienced technicians^{24} is fundamental for respiratory and gas
exchange parameters to be accurately reproduced. In tests where these procedures
are adopted, there is low variation in measurements repeated a short time apart^{24,25}.
The ergospirometer used in this study was validated by another group^{26}.
The quality of measurements taken by our equipment, in turn, was determined
by means of the intraclass correlation coefficient for test and retest measurements
of the respiratory and gas exchanges, which were 0.91 for EV; 0.95 for VO_{2}
and 0.93 for VO_{2}. These results were obtained at loads between 15
and 340 watts in the cycle ergometer. The difference in the accuracy of the
measurements obtained with equipments more sophisticated than the one we used
(3.8%^{27} *versus* 5.5%) may lead to a small error in the application
of our equations, but this error could not be determined.

The results obtained
by cross-validation of equations 01M and 01F (study 1) showed an accurate VO_{2}
prediction. When equations 01M and 03M were used to predict VO_{2max},
a significant difference was observed between values measured and predicted.
Unlike the results found for the male group, equations 01F and 03F were accurate
for VO_{2max} prediction in the female group. This result can be explained
by the fact that men are more aggressive during peak exercise, which leads to
an increased aerobic component and activation of fast muscle fibers, consequently
increasing power production and changing the linear VO_{2/watt} ratio^{28}.
In order to improve VO_{2max} prediction for the male group, equation
02M was proposed, which proved to be superior to equation 03M.

Malek et al^{29}
analyzed the external validity of Storer et al's equations^{15} for
VO_{2max} prediction in aerobically trained individuals, and showed
that these had the lower standard error of the estimate (SEE) among the equations
they analyzed. The SEE found by Malek et al^{29} was 0.32 and 0.27 l^{.}min^{-1}
for men and women, respectively, whereas in the original study, Storer et al^{15}
found SEE of 0.20 and 0.13 l^{.}min^{-1} for men and women,
respectively. In the present study, the SEE found for these equations were 0.41
and 0.15 l^{.}min^{-1}, for men and women, respectively. These
values were close to those found for equations 01F and 02M derived here.

The results obtained
in study 2 demonstrated accuracy in the prediction of VO_{2} values
by equations 01M, 01F and 02M. Equations 01M and 01F proved to be as good as
ACSM's^{8} and Neder et al^{14} (04M, 04F, 05M, 05F, 08M and
08F) for the prediction of submaximal values (Table
1). In an attempt to analyze the applicability of equations 01M, 01F and
02M in different protocols, two maximal tests were performed, one graded (GTX)
and another by using square wave (SWT_{max}). In both protocols, equations
01M, 01F and 02M predicted VO_{2max} accurately. Equation 02M, however,
was superior for it showed a lower coefficient of variation and total error
(TE= - 0.10 l^{.}min^{-1}), in comparison to equation 01M (TE=
0.39 L^{.}min^{-1}). Maximum values obtained in GXT and in SWT_{max}
were only different from the values predicted by Åstrand-Ryhming nomogram^{16}
when using the workload (NW) and VO_{2} (NV), when corrected by equation
07M. Siconolfi et al^{23} derived equations (07M and 07F) that modify
VO_{2max} values obtained by the original method of Åstrand-Ryhming
nomogram^{16}. We noticed that equation 07M worsens the original prediction
made by Åstrand-Ryhming method^{16}, producing a total error of
1.03 l^{.}min^{-1}. The high workload increments in 1-minute-duration
stages and the plateau criterion of 250 ml.min^{-1} and RER __>__
1.00 at peak exercise may have caused VO_{2max}to be underestimated
in Siconolfi et al's study^{23}. There was also a significant difference
between the VO_{2max} values measured and predicted when equation 08M
was applied^{14}. This method, which was developed for the Brazilian
population, did not prove accurate in predicting the VO_{2max} of active
subjects in SWT.

Analysis of limits
of agreement showed a trend to overestimate VO_{2max} when the Åstrand-Ryhming
nomogram^{16} was used in the female group (Table
1). Zwiren et al^{30} analyzed the external validity of Åstrand-Ryhming
nomogram^{16} in women aged between 30 and 39 years with VO_{2max}
of 2.4 (± 0.45) l^{.}min^{-1} and concluded that the
Åstrand-Ryhming method^{16} overestimated VO_{2max} by
20%. When Åstrand-Ryhming nomogram^{16} was used to infer this
parameter in the male group, the values predicted were not significantly different
from those measured. On the other hand, Table
1 shows that 06M-NW and 06M-NV had higher coefficients of variation, typical
measure error, and lower correlation in comparison to the male equations 01M
and 02M. Davies et al^{31} studied a male group aged 22 (± 2)
years with higher VO_{2max} (50.7 ml.kg^{-1}.min^{-1})
and found a confidence interval (CI = 95%) of -0.96 (±0.47) l.min^{-1}
(HR = 120<140 bpm) and -0.64 (±0.39) l.min^{-1} (HR = 140<180),
as predicted by the workload, by using Åstrand-Ryhming nomogram. For Davies
et al^{31}, this method has a CV of 15% for estimates using VO_{2}
and of 21% using the load.

Recent studies
showed that the relationship between oxygen uptake and workload is linear up
to the intensity of 50% to 60%VO_{2max}. After this point, the function
becomes exponential^{32}. We analyzed this relationship by using the
single-phase or two-phase linear model. In the latter, it is understood that
there is a linear function up to the transition point, from which VO_{2}
starts to increase in exponential function. For the male group, the linear model
showed *R ^{2}* = 0.88, SEE = 0.34 and mean square errors (

*MSE)*= 0.12. When the two-phase model was used, the values obtained were adjustment of R

*= 0.80, SEE = 0.34 and MSE = 0.11. These results were quite similar and suggest that the two-phase model was not superior.*

^{2}In conclusion,
the models derived in the present study proved to be accurate in predicting
submaximum and maximum VO_{2} in young Brazilian adults. Based on study
1, equation 01M did not prove to be valid at maximal intensities. The other
equations (01F and 02M) may be used with satisfactory external validity at peak
exercise. VO_{2max} prediction significantly improved for the male group
when equation 02M was used. The equations derived by Storer et al^{15}
did not show a higher accuracy in predicting VO_{2max}. In study 2,
the equations derived were valid both for submaximal and maximal intensities.
The equation proposed by Siconolfi et al^{23} (07M) to correct Åstrand-Ryhming
method^{16}, and Neder et al's equations^{14} for men did not
show a satisfactory result for the local population. We also concluded that
the equations derived in this study showed satisfactory external validity in
protocols with or without steady state.

**Limitations**

Factors such as
variation in the mechanical efficiency at a given workload, medication or alcohol
intake, heat, hypobaric environments and individuals with diseases or body mass
and age different from those of the subjects of this study may increase prediction
error. Thus, this study does not present a form of replacing, with the same
accuracy, direct VO_{2} measurement. Other equations for other age ranges
and different patient groups should be further derived.

**Acknowledgements**

To *Associação
dos Amigos do Centro de Estudos e Aperfeiçoamento do Hospital dos Servidores
do Estado do Rio de Janeiro*, for its significant contribution to the realization
of this study, and to *Fundação de Amparo à Pesquisa
do Estado do Rio de Janeiro* - FAPERJ. We also thank our colleagues Lucenildo
Cerqueira and Fernando Nogueira for their invaluable technical help.

**References**

1. Åstrand PO, Rodahl K, Dahl HA, Stromme SB. Textbook of work physiology. Champaign: Human Kinetics; 2003. p. 273-97. [ Links ]

2. Sanada K, Midorikawa T, Yasuda T, Kearns CF, Abe T. Development of nonexercise prediction models of maximal oxygen uptake in healthy Japanese young men. Eur J Appl Physiol. 2007; 99 (2): 143-8. [ Links ]

3. American College of Sports Medicine, Davis SE (editor). In: ACSM's health-related physical fitness assessment manual. 2nd ed. Philadelphia: Lippincott Williams & Wilkins; 2007. [ Links ]

4. Howley ET, Basset Jr DR, Welch HG. Criteria for maximal oxygen uptake: review and commentary. Med Sci Sports Exerc. 1995; 27 (9): 1292-301. [ Links ]

5. Marson F, Martins MA, Coletto FA, Campos AD, Basile-Filho A. Correlação entre o consumo de oxigênio obtido pelo método de Fick e pela calorimetria indireta no paciente grave. Arq Bras Cardiol. 2003; 82 (1): 72-6. [ Links ]

6. Rondon MUP, Forjaz CLM, Nunes N, Amaral SL, Barreto ACP, Negrão CE. Comparação entre a prescrição de intensidade de treinamento físico baseada na avaliação ergométrica convencional e na ergoespirométrica. Arq Bras Cardiol. 1998; 70 (3): 159-66. [ Links ]

7. Peterson MJ, Pieper CF, Morey MC. Accuracy of VO_{2max} prediction equations in older adults. Med Sci Sports Exerc. 2003; 35 (1): 145-9. [ Links ]

8. American College of Sports Medicine - Appendix D: Metabolic calculations. In: Guidelines for exercise testing and prescription. 6th ed. Philadelphia: Lippincott Williams & Wilkins; 2000. p. 300-12. [ Links ]

9. Bradshaw DI, George JD, Hyde A, LaMonte MJ, Vehrs PR, Hager RL, et al. An accurate VO_{2max} nonexercise regression model for 18-65-year-old adults. Res Q for Exerc Sport. 2005; 76 (4): 426-33. [ Links ]

10. Bruce RA, Kusumi F, Hosmer D. Maximal oxygen intake and nomographic assessment of functional aerobic impairment in cardiovascular disease. Am Heart J. 1973; 85 (4): 546-62. [ Links ]

11. Faulkner J, Parfitt G, Eston R. Prediction of maximal oxygen uptake from the ratings of perceived exertion and heart rate during a perceptually-regulated sub-maximal exercise test in active and sedentary participants. Eur J Appl Physiol. 2007; 101 (3): 397-407. [ Links ]

12. Foster C, Jackson M. Pollock L, Taylor MM, Hare J, Sennett SM, et al. Generalized equations for predicting functional capacity from treadmill performance. Am Heart J. 1984; 107 (6): 1229-34. [ Links ]

13. Malek MH, Housh TJ, Berger DE, Coburn JW, Beck TW. A new nonexercise-based VO_{2max} equation for aerobically trained females. Med Sci Sports Exerc. 2004; 36 (10): 1804-10. [ Links ]

14. Neder JA, Nery LE, Castelo A, Anderson S, Lerario MC, Sachs A, et al. Prediction of metabolic and cardiopulmonary responses to maximum cycle ergometry: a randomised study. Eur Respir J. 1999; 14 (6): 1304-13. [ Links ]

15. Storer TW, Davis JA, Caiozzo VJ. Accurate prediction of VO_{2max} in cycle ergometry. Med Sci Sports Exerc. 1990; 22 (5): 704-12. [ Links ]

16. Åstrand PO, Ryhming I. A nomogram for calculation of aerobic capacity from pulse rate during submaximal work. J Appl Physiol. 1954; 7 (2): 218-21. [ Links ]

17. Wasserman K, Whipp BJ, Koyal SN, Beaver WL. Anaerobic threshold and respiratory gas exchange during exercise. J Appl Physiol. 1973; 35 (2): 236-43. [ Links ]

18. Buchfuhrer MJ, Hansen JE, Robinson DY, Sue DY, Wasserman K, Whipp BJ. Optimizing the exercise protocol for cardiopulmonary assessment. J Appl Physiol. 1983; 55 (5): 1558-64. [ Links ]

19. Nogueira FS, Pompeu FAMS. Modelos de predição da carga máxima no teste clínico de esforço cardiopulmonar. Arq Bras Cardiol. 2006; 87 (2): 137-45. [ Links ]

20. Beaver WL, Wasserman K, Whipp BJ. A new method for detecting the anaerobic threshold by gas exchange. J Appl Physiol. 1986; 60 (6): 2020-7. [ Links ]

21. Yazbek Jr P, Carvalho RT, Sabag LMS, Batistella LR. Ergoespirometria: teste de esforço cardiopulmonar, metodologia e interpretação. Arq Bras Cardiol. 1998; 71 (5): 719-24. [ Links ]

22. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986; 1: 307-10. [ Links ]

23. Siconolfi SF, Cullinane EM, Carleton RA, Thompson PD. Assessing VO_{2max} in epidemiologic studies: modification of the Åstrand-Ryhming test. Med Sci Sports Exerc. 1982; 14 (5): 335-8. [ Links ]

24. Guimarães JI, Stein R, Vilas-Boas F, Galvão F, Nobrega ACL, Castro RRT, et al. Normatização de técnicas e equipamentos para a realização de exames em ergometria e ergoespirometria. Arq Bras Cardiol. 2003; 80 (4): 458-64. [ Links ]

25. Granja Filho PCN, Pompeu FAMS, Ribeiro AP. A acurácia da determinação do VO_{2máx} e do limiar anaeróbio. Rev Bras Med Esporte. 2005; 11 (3): 167-71. [ Links ]

26. Novitsky S, Degal KR, Chatr-Aryamontri B, Gubakov D, Katch Vl. Validity of a new portable indirect calorimeter: the Aerosport TEEM 100. Eur J Appl Physiol. 1995; 70 (5): 462-7. [ Links ]

27. Hopkins WG, Schabort EJ, Hawley JA. Reliability of power in physical performance test. Sports Med. 2001; 31 (3): 211-34. [ Links ]

28. Pedersen PK, Sørensen, JB, Jensen K, Johansen L, Levin K. Muscle fiber type distribution and nonlinear VO_{2}-power output relationship in cycling. Med Sci Sports Exerc. 2002; 34 (4): 655-61. [ Links ]

29. Malek MH, Berger DE, Housh TJ, Coburn JW, Beck TW. Validity of VO_{2max} equations for aerobically trained males and females. Med Sci Sports Exerc. 2004; 36 (8): 1427-32. [ Links ]

30. Zwiren LD, Freedson PS, Ward A, Wilke S, Rippe JM. Estimation of VO_{2max}: a comparative analysis of five tests. Res Q Exerc Sports. 1991; 62 (1): 73-8. [ Links ]

31. Davies CTM. Limitations to the prediction of maximum oxygen intake from cardiac frequency measurements. J Appl Physiol. 1968; 24 (5): 700-6. [ Links ]

32. Zoladz JA, Szkutnik Z, Majerczak J, Duda K, Pedersen PK. Non-linear relationship between oxygen uptake and power output in the Astrand nomogram - old data revisited. J Physiol Pharmacol. 2007; 58 (2): 265-73. [ Links ]

**
Mailing address:
** Fernando A. M. S. Pompeu

Av. Carlos Chagas Filho, 540 - Ilha do Fundão

21941-599 - Rio de Janeiro, RJ - Brazil

E-mail: pompeu_fernando@hotmail.com

Manuscript received January 31, 2009; revised manuscript received August 24, 2009; accepted October 22, 2009.