The effects of ṫ̇raining and/or ageing upon maximal oxygen uptake (V̇O2max) and heart rate values at rest (HRrest) and maximal exercise (HRmax), respectively, suggest a relationship between V̇O2max and the HRmax-to-HRrest ratio which may be of use for indirect testing of V̇O2max. 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 V̇O2max (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 of V̇O2max. V̇O2max 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-specific V̇O2max was 15.3 (0.7) ml·min−1·kg−1. Using this value, V̇O2max 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 of V̇O2max in well-trained men. The applicability of the test principle in relation to other groups will have to await direct validation. V̇O2max 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 for V̇O2max estimation based on resting measurements alone.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
Andersen LB (1995) A maximal cycle exercise protocol to predict maximal oxygen uptake. Scand J Med Sci Sports 5:143–146
Åstrand P-O, Rodahl K (1986) Textbook of work physiology. McGraw-Hill, New York, pp 362, 368
Åstrand P-O, Ryhming I (1954) A nomogram for calculation of aerobic capacity (physical fitness) from pulse rate during submaximal work. J App Physiol 7:218–221
Bland MB, Altman DG (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1:307–310
Blomqvist CG, Saltin B (1983) Cardiovascular adaptations to physical training. Annu Rev Physiol 45:169–189
Chapman CB, Fisher NJ, Sproule BJ (1960) Behavior of stroke volume at rest and during exercise in human beings. J Clin Invest 38:1208–1213
Fox EL (1973) A simple, accurate technique for predicting maximal aerobic power. J Appl Physiol 35:914–916
Howley ET, Bassett DR, Welch HG (1995) Criteria for maximal oxygen uptake: review and commentary. Med Sci Sports Exerc 27:1292–1301
Katona PG, McLean M, Dighton DH, Guz A (1982) Sympathetic and parasympathetic cardiac control in athletes and nonathletes at rest. J Appl Physiol 52:1652–1657
Kline GM, Porcari JP, Hintermeister R, Freedson PS, Ward A, McCarron RF, Ross J, Rippe JM (1987) Estimation of V̇O2max from a one-mile track walk, gender, age, and body weight. Med Sci Sports Exerc 19:253–259
McCann DJ, Adams WC (2002) A theory for normalizing resting V̇O2max. Med Sci Sports Exerc 34:1382–1390
Nottin S, Vinet A, Stecken F, Nguyen LD, Ounissi F, Lecoq AM, Obert P (2002) Central and peripheral cardiovascular adaptations during a maximal cycle exercise in boys and men. Med Sci Sports Exerc 34:56–63
Tanaka H, Monahan KD, Seals DR (2001) Age-predicted maximal heart rate revisited. J Am Coll Cardiol 37:153–156
We are grateful to Dr. L. Bruce Gladden for constructive help in the preparation of the manuscript.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00421-004-1268-1
Derivation of an equation for a relationship between V̇O2max and the ratio between HRmax and HRrest
According to the Fick principle, V̇O2max may be expressed as the product of cardiac output (Q̇) and the arterio-venous O2 difference (CaO2−Cv̄O2).
Thus, since Q̇ is the product of HR and stroke volume (SV), V̇O2max can be expressed as:
When applied to rest V̇O2max can be expressed as:
During maximal exercise the Fick equation reads:
This implies that V̇O2max may be calculated as the product of V̇O2max and the ratios of maximal versus resting values of, respectively, HR, SV, and (CaO2−Cv̄O2).
V̇O2rest 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 V̇O2max. Accordingly, V̇O2rest (ml·min−1) may be expressed as 3.4 ml·min−1·kg−1 times BM in kg.
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 of V̇O2 itself. Equation 8 suggests, however, that if the max-to-rest ratios of SV and (CaO2−Cv̄O2) were approximately constant across individuals, V̇O2max 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 (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:
About this article
Cite this article
Uth, N., Sørensen, H., Overgaard, K. et al. Estimation of V̇O2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method. Eur J Appl Physiol 91, 111–115 (2004). https://doi.org/10.1007/s00421-003-0988-y
- HRmax-to-HRrest ratio
- Maximal heart rate
- Maximal oxygen uptake
- Resting heart rate