Estimation of V̇O_2max from the ratio between HR_max and HR_rest – the Heart Rate Ratio Method

Abstract

The effects of ṫ̇raining and/or ageing upon maximal oxygen uptake (V̇O_2max) and heart rate values at rest (HR_rest) and maximal exercise (HR_max), respectively, suggest a relationship between V̇O_2max and the HR_max-to-HR_rest ratio which may be of use for indirect testing of V̇O_2max. Fick principle calculations supplemented by literature data on maximum-to-rest ratios for stroke volume and the arterio-venous O₂ difference suggest that the conversion factor between mass-specific V̇O_2max (ml·min⁻¹·kg⁻¹) and HR_max·HR_rest ⁻¹ is ~15. In the study we experimentally examined this relationship and evaluated its potential for prediction of V̇O_2max. V̇O_2max was measured in 46 well-trained men (age 21–51 years) during a treadmill protocol. A subgroup (n=10) demonstrated that the proportionality factor between HR_max·HR_rest ⁻¹ and mass-specific V̇O_2max was 15.3 (0.7) ml·min⁻¹·kg⁻¹. Using this value, V̇O_2max in the remaining 36 individuals could be estimated with an SEE of 0.21 l·min⁻¹ or 2.7 ml·min⁻¹·kg⁻¹ (~4.5%). This compares favourably with other common indirect tests. When replacing measured HR_max with an age-predicted one, SEE was 0.37 l·min⁻¹ and 4.7 ml·min⁻¹·kg⁻¹ (~7.8%), which is still comparable with other indirect tests. We conclude that the HR_max-to-HR_rest ratio may provide a tool for estimation of V̇O_2max in well-trained men. The applicability of the test principle in relation to other groups will have to await direct validation. V̇O_2max can be estimated indirectly from the measured HR_max-to-HR_rest ratio with an accuracy that compares favourably with that of other common indirect tests. The results also suggest that the test may be of use for V̇O_2max estimation based on resting measurements alone.

Introduction

The maximal rate of oxygen uptake uptake (V̇O_2max) is an important determinant of cardiorespiratory fitness and aerobic performance (Howley et al. 1995). Direct measurements of oxygen uptake (V̇O₂) during maximal work provide the most accurate value for this parameter, and measurements are reproducible with a coefficient of variation of about 2–4% (Howley et al. 1995). Direct measurements of V̇O_2max are, however, technically demanding and require access to expensive laboratory equipment and skilled personnel. As a consequence, alternative procedures have been developed in which V̇O_2max is estimated from physiological responses during submaximal exercise (e.g. Åstrand and Ryhming 1954; Fox 1973) or from physiological responses in combination with performance measures (e.g. Kline et al. 1987).

Training status is a major determinant of V̇O_2max. It is well documented that V̇O_2max increases with training and that inactivity or cessation of training reduces V̇O_2max (e.g. Blomqvist and Saltin 1983). Training, likewise, has been shown to lower resting heart rate (HR_rest) (Blomqvist and Saltin 1983) whereas detraining is associated with increased HR_rest (Katona et al. 1982). This suggests that one would expect a negative relationship between V̇O_2max and HR_rest. Whether such a relationship is close enough to merit interest in indirect estimation of V̇O_2max is uncertain.

Ageing is associated with decrements in both V̇O_2max and HR_max (Tanaka et al. 2001). The effect of ageing would therefore suggest a positive relationship between V̇O_2max and HR_max. If we combine the mentioned influences of training, or ageing, upon the V̇O_2max and HR response, it appears likely that a positive relationship exists between V̇O_2max and the ratio between HR_max and HR_rest (HR_max·HR_rest ^–1). Calculations based upon the Fick principle and incorporating literature data for maximum-to-rest ratios for HR, stroke volume and arterio-venous O₂ difference, respectively (see Appendix), suggest that mass-specific V̇O_2max may be estimated by multiplying HR_max·HR_rest ^–1 by a factor of about 15.0. The purpose of the present study was therefore (1) to examine whether this theoretical proportionality factor could be confirmed by experimental data, and (2) to evaluate in a group of well-trained men the limits of agreement (LOA) (Bland and Altman 1986) for prediction of V̇O_2max using the experimentally established proportionality factor.

Methods

Subjects

Forty-six healthy well-trained, non-smoking men volunteered to participate in the study. The mean (SD) values for age, height, body mass (BM) and V̇O_2max were 29.6 (7.7) years, 182 (6.1) cm, 76.3 (6.5) kg, 4.66 (0.49) l·min⁻¹ and 60.9 (5.5) ml·min⁻¹·kg⁻¹, respectively. They trained on average 8.7 (2.9) h per week. All subjects provided written informed consent in accordance with the guidelines of the local Ethics Committee. The experiments complied with the standards of the local Ethics Committee.

Study design

The subjects were randomly assigned to either of two groups. One group (n=10) validated the proportionality factor between the mass-specific V̇O_2max and the HR_max-to-HR_rest ratio (theoretical value ~15). The other group (n=36) was used to establish LOA between V̇O_2max estimates based upon the HR_max-to-HR_rest ratio and the above factor, versus direct measurements of V̇O_2max.

Experimental protocol

Height was measured to the nearest 0.5 cm and BM determined to the nearest 0.1 kg. Exercise experiments were performed on a motor-driven treadmill (Technogym Runrace, Gambettola, Italy). The subjects warmed up for 10 min at a speed and grade selected to impose a heart rate of ~140 beats·min⁻¹. The typical initial running speed was 13 km·h⁻¹. Speed (first part of the test) and/or inclination (later part) were subsequently increased stepwise every minute by 1 km·h⁻¹ or 2% slope, respectively, to exhaustion. The duration of the test ranged 5–10 min. Pulmonary gas exchange and heart rate were monitored continuously during the test. High-intensity and/or high-volume training was avoided for 48 h prior to testing. Resting heart rate was measured over a 5-min period by the subject in the morning the day after the test (supine, while in bed). HR_rest (beats·min⁻¹ with one decimal) was defined as the lowest value of any 1-min average during the 5-min sampling period. HR_max was defined as the highest 5-s average during the treadmill test.

Techniques

Pulmonary gas exchange was measured with an automated metabolic cart system (AMIS 2001, Innovision, Odense, Denmark). Ventilatory flow rate was measured on the inspiratory side with a differential pressure sensor (Pneumotachograph - Lilly type, Innovision A/S, Odense, Denmark.). V̇O_2max was defined as the highest V̇O₂ measured during any 30-s period. Heart rate was measured with a Polar Electro heart rate monitor (Kempele, Finland). A test was approved as being maximal when at least three of the following four criteria were met: (1) a plateau in V̇O₂ despite increased running speed or inclination (increase <150 ml·min⁻¹), (2) R-value ≥1.15, (3) ventilatory equivalent for oxygen >30, and (4) terminal HR within 10 beats·min⁻¹ of age-predicted HR_max. The HR_max was predicted from age using the formula of Tanaka et al. (2001): HR_max (age-predicted)=208–0.7·age in years.

Statistics

Analysis of variance (ANOVA) was performed to analyse differences between group means. Pearson’s coefficient of correlation (r) was used to describe the relationship between V̇O_2max as well as the mass-specific V̇O_2max and selected physiological variables. Bland-Altman plots (1986) were employed to establish the LOA between measured and estimated V̇O_2max. Operationally, LOA define the range within which 95% of the individual differences between measured and estimated V̇O_2max will lie. After calculating the standard error of estimate (SEE) for the differences between measured and estimated V̇O_2max, a 95% confidence interval (±1.96 SEE) is determined around the mean difference. As part of the analysis, differences between measured and estimated V̇O_2max were plotted against their average and tested for homoscedasticity. Statistical significance was set at P<0.05 for all analyses.

Results

The experimentally determined proportionality factor between mass-specific V̇O_2max and HR_max·HR_rest ^–1 was 15.26 (0.72) ml·min⁻¹·kg⁻¹ which is not significantly different from the theoretical value of ~15 ml·min⁻¹·kg⁻¹. Highly statistically significant correlations were found between measured V̇O_2max and the estimated counterparts using the Heart Rate Ratio Method. Correlation coefficients for V̇O_2max in ml·min⁻¹ averaged 0.91 (P<0.001; see Fig. 1a) and for mass-specific V̇O_2max 0.87 (P<0.001; see Fig. 1b). The average difference between measured and estimated V̇O_2max was not significantly different from zero (0.024 l·min⁻¹, P=0.83 and 0.28 ml·min⁻¹ kg⁻¹, P=0.83). The LOA for individual estimates of V̇O_2max averaged 0.41 l·min⁻¹ or 5.3 ml·min⁻¹·kg⁻¹, corresponding to about 8.7% (see Fig. 2a, b). The magnitude of the differences between measured and estimated V̇O_2max was not dependent on the actual level of V̇O_2max, confirming the homoscedastic nature of the data. Replacement of measured HR_max with its age-predicted match in the V̇O_2max calculation resulted in larger differences between measured and estimated V̇O_2max. LOA increased to ±0.72 l·min⁻¹, or 9.2 ml·min⁻¹·kg⁻¹, which corresponds to about 15% (see Fig. 2b). Moreover, statistically significant correlations were also found between BM·HR_max·HR_rest ⁻¹and V̇O_2max (r=0.92; P<0.001) and between HR_max·HR_rest ⁻¹and mass-specific V̇O_2max (r=0.86; P<0.001).

Fig. 1a, b

a Scatter plot between estimated and measured maximal oxygen uptake (l·min⁻¹), b Scatter plot between estimated and measured mass-specific maximal oxygen uptake (ml·min⁻¹·kg⁻¹). The solid lines depicted are the least-squares derived best-fitting lines

Fig. 2a, b

Limits of agreement (Bland and Altman 1986) for measured versus estimated maximal oxygen uptake using the Heart Rate Ratio Method. a HR_max is experimentally established as opposed to the age-predicted value (Tanaka et al. 2001) used in b. Upper and lower limit of agreement are indicated with solid lines while the mean difference is indicated by a dashed line

Discussion

By elaborating upon the Fick principle we developed an equation that predicts a relationship between the HR_max-to-HR_rest ratio and mass-specific V̇O_2max. Experimental testing of ten well-trained men demonstrated that the proportionality factor applied in the conversion of HR_max·HR_rest ^–1 to V̇O_2max was 15.26 (0.72) ml·min⁻¹·kg⁻¹, a value which is not significantly different from the theoretically assumed value of 15.0 ml·min⁻¹·kg⁻¹. Subsequent testing of 36 trained men demonstrated that individual values for mass-specific V̇O_2max (range 49–73 ml·min⁻¹·kg⁻¹) could be obtained with a SEE of 2.72 ml·min⁻¹·kg⁻¹, or ~4.5%. This yields a 95% confidence interval (LOA) for individual estimates of mass-specific V̇O_2max of about 8.7%.

In order to evaluate the relative merit of the above method for estimation of V̇O_2max we have compared its SEE value with data from some other indirect tests. The Åstrand-Ryhming nomogram test from 1954, which was based upon cycle ergometer testing of 27 male and 31 female subjects, reported SEE values of 7–15%. Fox’s (1973) cycle ergometer study which comprised of 87 young men reported SEE to be 6–11%. Kline et al. (1987) tested middle-aged men (n=83) and women (n=86) using a walking test in combination with anthropometry and arrived at SEE ~10%. Andersen (1995) used a maximal exercise protocol to predict V̇O_2max and found SEE to be ~8%. In comparison with these tests the Heart Rate Ratio Method may offer superior accuracy, although attention should be paid to the possible significance of its being based upon a relatively homogenous study group (“well-trained men”).

It should be noticed that the regression lines of Fig. 1 cross the line of identity. The slopes of both regression lines are not significantly different from 1 (P<0.001). The point at which the regression line intersects the y-axis is significantly different from 0 in Fig. 1b (P=0.04) but not in Fig. 1a (P=0.25).

Age-predicted versus experimentally determined HR_max

Instead of experimentally determining HR_max as in the above version of the test, HR_max may also be predicted from the person’s age. Use of a theoretical HR_max value rather than an experimental one would facilitate the accomplishment of the test and potentially increase its applicability to groups of individuals where maximal effort may be unwarranted, such as patients or elderly individuals. The accuracy of the V̇O_2max estimation was significantly less when age-predicted HR_max values replaced the experimental ones in the formula (SEE 7.8% versus 4.5% of the average V̇O_2max). Thus, the convenience obtained from not having to expose the individual to maximal exercise had a price. It is of note, however, that even with age-predicted HR_max values SEE was still comparable with other indirect tests. It may therefore be of interest to further examine its applicability to individuals of different age and training levels.

Standardization of measurement conditions

It should be noted that the SV_max-to-SV_rest ratio is about 1.3 when measured in the supine position (as presumed in the calculation of the proportionality factor), whereas the corresponding value for the standing position would be 1.82 (Chapman et al. 1960). This emphasizes the importance of HR measurements being performed under strictly standardized conditions. Furthermore, it is important to underline that the proportionality factor between mass-specific V̇O_2max and the HR_max-to-HR_rest ratio may vary between groups of individuals since both mass-specific resting V̇O_2max and the max-to-rest ratios of SV and the arterio-venous O₂ difference(CaO₂−Cv̄O₂) can be influenced by factors such as age, gender and training level. Therefore valid proportionality factors should first be experimentally established before the principle of the Heart Rate Ratio Method is extended to groups other than well-trained men.

Conclusion

In a group of ten well-trained men, the proportionality factor between mass-specific V̇O_2max and the HR_max-to-HR_rest ratio was found to be 15.26 ml·min⁻¹·kg⁻¹, which was in good agreement with the theoretical value. Furthermore, when using this proportionality factor in 36 well-trained men we found that the mass-specific V̇O_2max could be estimated from the experimentally determined HR_max-to-HR_rest ratio with an SEE of 4.5%, which appears to be superior to other common indirect tests. Moreover, when replacing the experimentally determined HR_max with an age-predicted one, the mass-specific V̇O_2max could be estimated by the Heart Rate Ratio Method with an SEE of 7.8%. The results indicate that the principle of this test may provide a simple and useful tool for V̇O_2max estimation.

Appendix

Derivation of an equation for a relationship between V̇O_2max and the ratio between HR_max and HR_rest

According to the Fick principle, V̇O_2max may be expressed as the product of cardiac output (Q̇) and the arterio-venous O₂ difference (CaO₂−Cv̄O₂).

$$ \dot{V}{\text{O}}_{{\text{2}}} = \dot{Q} \cdot {\left( {C_{{\text{a}}} {\text{O}}_{{\text{2}}} - C{\text{\={v}O}}_{{\text{2}}} } \right)} $$

(1)

Thus, since Q̇ is the product of HR and stroke volume (SV), V̇O_2max can be expressed as:

$$ \dot{V}{\text{O}}_{{\text{2}}} = {\text{HR}} \cdot {\text{SV}} \cdot {\left( {C_{{\text{a}}} {\text{O}}_{{\text{2}}} - C{\text{\={v}O}}_{{\text{2}}} } \right)} $$

(2)

When applied to rest V̇O_2max can be expressed as:

$$ \dot{V}{\text{O}}_{{{\text{2rest}}}} = {\text{HR}}_{{{\text{rest}}}} \cdot {\text{SV}}_{{{\text{rest}}}} \cdot {\left( {C{\text{aO}}_{{\text{2}}} - C{\text{\={v}O}}_{{\text{2}}} } \right)}_{{{\text{rest}}}} $$

(3)

implying that:

$$ \frac{{\dot{V}{\text{O}}_{{{\text{2rest}}}} }} {{{\text{HR}}_{{{\text{rest}}}} \cdot {\text{SV}}_{{{\text{rest}}}} \cdot {\left( {C{\text{aO}}_{{\text{2}}} - C{\text{\={v}O}}_{{\text{2}}} } \right)}_{{{\text{rest}}}} }} = 1 $$

(4)

During maximal exercise the Fick equation reads:

$$ \dot{V}{\text{O}}_{{{\text{2max}}}} {\text{ = HR}}_{{{\text{max}}}} \cdot {\text{SV}}_{{{\text{max}}}} \cdot {\left( {C{\text{aO}}_{{\text{2}}} - C{\text{\={v}O}}_{{\text{2}}} } \right)}_{{{\text{max}}}} $$

(5)

By multiplying the right side of Eq. 5 with 1 in the form of Eq. 4 it follows that:

$$ \dot{V}{\text{O}}_{{{\text{2max}}}} = \frac{{{\text{HR}}_{{{\text{max}}}} \cdot {\text{SV}}_{{{\text{max}}}} \cdot {\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{{\text{max}}}} }} {{{\text{HR}}_{{{\text{max}}}} \cdot {\text{SV}}_{{{\text{max}}}} \cdot {\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{{\text{rest}}}} }} \cdot \dot{V}{\text{O}}_{{{\text{2rest}}}} $$

(6)

or

$$ \dot{V}{\text{O}}_{{{\text{2max}}}} = {\left( {\frac{{{\text{HR}}_{{{\text{max}}}} }} {{{\text{HR}}_{{{\text{rest}}}} }}} \right)} \cdot {\left( {\frac{{{\text{SV}}_{{{\text{max}}}} }} {{{\text{SV}}_{{{\text{rest}}}} }}} \right)} \cdot {\left( {\frac{{{\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{\max }} }} {{{\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{{\text{rest}}}} }}} \right)} \cdot \dot{V}{\text{O}}_{{{\text{2rest}}}} $$

(7)

This implies that V̇O_2max may be calculated as the product of V̇O_2max and the ratios of maximal versus resting values of, respectively, HR, SV, and (CaO₂−Cv̄O₂).

V̇O_2rest is dependent on and increases with the individual’s body mass. Åstrand and Rodahl (1986) suggest that, relative to body mass (BM), resting V̇O₂ equals about 3.5 ml·min⁻¹·kg⁻¹ (one MET), but slightly lower values were reported by McCann and Adams (2002) (3.3 for men and 3.1 for women, respectively). As a compromise we chose 3.4 ml·min⁻¹·kg⁻¹ to represent the mass-specific resting V̇O_2max. Accordingly, V̇O_2rest (ml·min⁻¹) may be expressed as 3.4 ml·min⁻¹·kg⁻¹ times BM in kg.

$$ \dot{V}{\text{O}}_{{{\text{2max}}}} = {\left( {\frac{{{\text{HR}}_{{{\text{max}}}} }} {{{\text{HR}}_{{{\text{rest}}}} }}} \right)} \cdot {\left( {\frac{{{\text{SV}}_{{{\text{max}}}} }} {{{\text{SV}}_{{{\text{rest}}}} }}} \right)} \cdot {\left( {\frac{{{\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{\max }} }} {{{\left( {C{\text{aO}}_{{\text{2}}} - C\bar{v}{\text{O}}_{{\text{2}}} } \right)}_{{{\text{rest}}}} }}} \right)} \cdot {\text{BM}} \cdot {\text{3}}{\text{.4 ml}} \cdot {\text{min}}^{{{\text{ - 1}}}} \cdot {\text{kg}}^{{{\text{ - 1}}}} $$

(8)

From a test perspective only the HR_max-to-HR_rest ratio is readily obtainable. The other two ratios in the equation involve complicated measurements, in fact more complicated than the measurement of V̇O₂ itself. Equation 8 suggests, however, that if the max-to-rest ratios of SV and (CaO₂−Cv̄O₂) were approximately constant across individuals, V̇O_2max per kg BM may be estimated by experimentally determining the HR_max-to-HR_rest ratio, and multiplying this ratio with these constants and 3.4 ml·min⁻¹·kg⁻¹. Nottin et al. (2002) and Chapman et al. (1960) reported the average SV_max·SV_rest ⁻¹ to be 1.28 and 1.29, respectively, in men, when measured in the supine position. Thus, according to the studies mentioned it appears that SV_max·SV_rest ⁻¹ may be replaced by a dimensionless value of approximately 1.3.

The arterio-venous oxygen difference increases from rest to maximal exercise. Chapman et al. (1960) found the average ratio between maximal and resting (CaO₂−Cv̄O₂) to be 3.4 in men. We therefore replaced (CaO₂−Cv̄O₂)_max·(CaO₂−Cv̄O₂)rest⁻¹ in Eq. 8 with 3.4. Altogether, data from the literature suggest that Eq. 8 may be simplified to the approximation:

$$ \begin{array}{*{20}l} {{\dot{V}{\text{O}}_{{2\max }} } \hfill} & {{ = {\left( {1.3 \cdot 3.4 \cdot {\text{ml}} \cdot \min ^{{ - 1}} \cdot {\text{kg}}^{{ - 1}} } \right)} \cdot {\text{BM}}{\left( {{\text{kg}}} \right)} \cdot \frac{{{\text{HR}}_{{{\text{max}}}} }} {{{\text{HR}}_{{{\text{rest}}}} }}} \hfill} \\ {{} \hfill} & {{ = 15.0{\text{ ml}} \cdot \min ^{{ - 1}} \cdot {\text{BM }}{\left( {{\text{kg}}} \right)} \cdot \frac{{{\text{HR}}_{{{\text{max}}}} }} {{{\text{HR}}_{{{\text{rest}}}} }},\;{\text{or}}} \hfill} \\ \end{array} $$

(9)

$$ {\text{Mass - specific }}\dot{V}{\text{O}}_{{2\max }} = {\left( {15.0\;{\text{ml}} \cdot {\text{min}}^{{{\text{ - 1}}}} \cdot {\text{kg}}^{{ - 1}} } \right)}\frac{{{\text{HR}}_{{\max }} }} {{{\text{HR}}_{{{\text{rest}}}} }} $$

(10)