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Estimation ofO2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method

An Erratum to this article was published on 17 November 2004


The effects of ṫ̇raining and/or ageing upon maximal oxygen uptake (O2max) and heart rate values at rest (HRrest) and maximal exercise (HRmax), respectively, suggest a relationship betweenO2max and the HRmax-to-HRrest ratio which may be of use for indirect testing ofO2max. 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-specificO2max (ml·min−1·kg−1) and HRmax·HRrest −1 is ~15. In the study we experimentally examined this relationship and evaluated its potential for prediction ofO2max.O2max 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 HRmax·HRrest −1 and mass-specificO2max was 15.3 (0.7) ml·min−1·kg−1. Using this value,O2max 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 HRmax 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 HRmax-to-HRrest ratio may provide a tool for estimation ofO2max in well-trained men. The applicability of the test principle in relation to other groups will have to await direct validation.O2max can be estimated indirectly from the measured HRmax-to-HRrest 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 forO2max estimation based on resting measurements alone.

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Fig. 1a, b
Fig. 2a, b


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We are grateful to Dr. L. Bruce Gladden for constructive help in the preparation of the manuscript.

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Correspondence to Niels Uth.

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An erratum to this article can be found at



Derivation of an equation for a relationship betweenO2max and the ratio between HRmax and HRrest

According to the Fick principle,O2max may be expressed as the product of cardiac output () and the arterio-venous O2 difference (CaO2Cv̄O2).

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

Thus, since is the product of HR and stroke volume (SV),O2max can be expressed as:

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

When applied to restO2max can be expressed as:

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

implying that:

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

During maximal exercise the Fick equation reads:

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

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

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


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

This implies thatO2max may be calculated as the product ofO2max and the ratios of maximal versus resting values of, respectively, HR, SV, and (CaO2Cv̄O2).

O2rest is dependent on and increases with the individual’s body mass. Åstrand and Rodahl (1986) suggest that, relative to body mass (BM), restingO2 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 restingO2max. Accordingly,O2rest (ml·min−1) may be expressed as 3.4 ml·min−1·kg−1 times BM in kg.

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

From a test perspective only the HRmax-to-HRrest ratio is readily obtainable. The other two ratios in the equation involve complicated measurements, in fact more complicated than the measurement ofO2 itself. Equation 8 suggests, however, that if the max-to-rest ratios of SV and (CaO2Cv̄O2) were approximately constant across individuals,O2max per kg BM may be estimated by experimentally determining the HRmax-to-HRrest 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 SVmax·SVrest −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 SVmax·SVrest −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 (CaO2Cv̄O2) to be 3.4 in men. We therefore replaced (CaO2Cv̄O2)max·(CaO2Cv̄O2)rest−1 in Eq. 8 with 3.4. Altogether, data from the literature suggest that Eq. 8 may be simplified to the approximation:

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

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Uth, N., Sørensen, H., Overgaard, K. et al. Estimation ofO2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method. Eur J Appl Physiol 91, 111–115 (2004).

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  • HRmax-to-HRrest ratio
  • Maximal heart rate
  • Maximal oxygen uptake
  • Resting heart rate