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.

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)