COUNTERPOINT: Theoretical and Empirical Basis for Equating Heart Rate Reserve with V̇o₂ Reserve

In 1957, Karvonen et al. (1) introduced a systematic approach for prescribing exercise intensity as a percentage of the difference between resting and maximum heart rate (HR), known as the heart rate reserve (HRR) method. This methodology was rapidly adopted by the field of exercise science. Although Karvonen et al. (1) did not measure oxygen consumption (V̇o₂) in their study, it was generally assumed that %HRR values provided equivalent exercise intensities as the same values of %V̇o₂max. Accordingly, the American College of Sports Medicine (ACSM) stated these variables were equivalent in a 1990 position stand (2), despite the fact that Davis and Convertino (3) had previously demonstrated that %HRR is equivalent to a percentage of the difference between resting and maximum V̇o₂, which they termed % net V̇o₂max and is today referred to as %V̇o₂ reserve (V̇o₂R).

In 1998, the ACSM modified their recommendations in a position stand stating, “the ACSM is now relating HRR to V̇o₂R rather than to a percentage of V̇o₂max. Using V̇o₂R improves the accuracy of the relationship, particularly at the lower end of the intensity scale. It is incorrect to relate HRR to a level of V̇o₂ that starts at zero rather than a resting level. This change makes [the ACSM's position stand] more scientifically accurate” (4). Among the research studies cited in support of this statement, Panton et al. (5) found that percentages of HRR were significantly lower than percentages of V̇o₂max across a range of exercise intensities in older adults, and Swain and Leutholtz (6) reported that %HRR values were significantly lower than %V̇o₂max values in younger adults but were statistically similar to %V̇o₂R values. The latter study determined regressions of %HRR versus %V̇o₂R and %HRR versus %V̇o₂max and found that the mean regression with %V̇o₂R was coincident with the line of identity, i.e., the slope was 1 and the y intercept was 0, while the regression with %V̇o₂max differed significantly from this relation. Moreover, the discrepancy of the regression with %V̇o₂max from the line of identity increased with decreasing aerobic capacity, or cardiorespiratory fitness (CRF) (6). In other words, when a person is at rest, the person is by definition at 0% of HRR but is at some percentage of V̇o₂max above 0. The %V̇o₂max value at rest is inversely proportional to one's V̇o₂max. That is, given a resting V̇o₂ of approximately 3.5 mL^.min^−1.kg⁻¹, individuals with V̇o₂max values of 17.5, 35, or 70 mL^.min^−1.kg⁻¹ (i.e., 5, 10, or 20 metabolic equivalents [MET]) must be at 20%, 10%, and 5% of V̇o₂max when resting, respectively. Given that individuals with a low V̇o₂max have a 20% difference between %HRR and %V̇o₂max when resting, exercise levels at low intensities will have substantial differences between %HRR and %V̇o₂max, whereas %HRR and %V̇o₂R values will be theoretically equal. This theory was confirmed by the Swain and Leutholtz (6) study. The use of %HRR and %V̇o₂R was again recommended by the ACSM in its 2011 position stand (7).

Several studies have compared the linear regression of %HRR versus %V̇o₂R, and most of these also performed regressions of %HRR versus %V̇o₂max. As described below, most of these studies confirm that %HRR and %V̇o₂R provide equivalent or nearly equivalent values, while there is a clear discrepancy between %HRR and %V̇o₂max values.

We identified 18 studies that determined regressions of %HRR versus %V̇o₂R. Fourteen of these studies, including Swain and Leutholtz in 1997 (6), used %V̇o₂R as the independent variable (x axis) and %HRR as the dependent variable (y axis) for physiological reasons, i.e., percentage of heart rate employed corresponds to the intensity of exercise, expressed as the relative oxygen requirement. Four of the 18 studies (8–11) reversed the axes, making %HRR the independent variable. Although it is possible to mathematically transpose the resulting regression equation, doing so will not yield the equation that would be obtained by plotting the data with %V̇o₂R as the independent variable. This transposition would only yield the proper equation if every data point fell exactly on the line; with increasing scatter in the data, the resulting equation becomes dramatically different from the equation obtained by replotting the data. Thus, these 4 studies were not included in our final analysis. One additional study examined the HR and V̇o₂ responses of cardiac transplant recipients (12). The hearts of transplant patients have been sympathetically denervated and demonstrate a markedly attenuated HR response to exercise. The mean values of resting and maximum HR were not provided in the study, making it difficult to gauge the potential value of the study's HR-V̇o₂ analysis, and this report was not considered further.

The remaining 13 studies that obtained regressions on %HRR versus %V̇o₂R are summarized in the Table. Seven studies found that %HRR versus %V̇o₂R was not significantly different from the line of identity (3,6,13–17). Five of these 7 studies also calculated regressions of %HRR versus %V̇o₂max and found that the relationship was significantly different from the line of identity (6,13,14,16,17). Three of the remaining 6 studies found that neither %HRR versus %V̇o₂R nor %HRR versus %V̇o₂max were coincident with the line of identity, but in each of these studies, the line for %V̇o₂R was a significantly closer match than the line for %V̇o₂max (18–20). One study had paradoxical results in which, when using a Bruce treadmill protocol, both the %HRR versus %V̇o₂R and %HRR versus %V̇o₂max regressions were coincident with the line of identity, which should be physiologically and mathematically impossible (21). Finally, 2 studies found that neither the %HRR versus %V̇o₂R nor the %HRR versus %V̇o₂max regressions were on the line of identity, but the regression for %V̇o₂max was closer (22,23). In aggregate, 10 studies support the use of %HRR and %V̇o₂R over %HRR and %V̇o₂max, while 2 studies support the opposite. A closer examination of the opposing studies is warranted.

All but these 2 studies collected HR and V̇o₂ over the same length of time at the end of each stage of exercise (that duration varied between studies, but not within studies). However, Hui and Chan in 2006 (22) used the last 30 seconds of each 3-minute stage for HR and the last 60 seconds for V̇o₂, while Ferri Marini et al. in 2021 (23) stated that the last 60 seconds of each 2-minute stage was used for V̇o₂ but did not state the duration for HR, implying that it was 15 seconds based on other statements in the methodology. HR and V̇o₂ continuously rise during 2- to 3-minute stages of incremental exercise. Therefore, measuring the HR during a shorter period than V̇o₂ at the end of the stage will result in relatively greater HR values. In most studies, when %HRR is plotted against %V̇o₂max (see the Figure), the resulting regression falls below the line of identity. If the HR values are inflated in each stage of exercise, this would tend to move the regression with %V̇o₂max upward, making it more like the line of identity. Moreover, since the %HRR versus %V̇o₂R regression normally falls on the line of identity, inflated HR values would move it above that line. These results are precisely what was found for the regressions in Hui and Chan, 2006 (22), and Ferri Marini et al., 2021 (23), the only 2 studies that found %V̇o₂max is more closely related than %V̇o₂R to %HRR.

Another consideration is whether resting data were included in the regressions. Swain and Leutholtz, 1997 (6), included resting values because they were part of the continuous data collection from rest to maximum exercise. Ferri Marini et al., 2021 (23), argued that including resting data will bias the intercept of the %HRR versus %V̇o₂R regression toward 0. This is certainly true. It is also true that not including the resting data ignores the theoretical basis for the %HRR versus %V̇o₂R relationship and thus biases the regression in a different manner. Ferri Marini et al. (23) did not include resting data in their analyses. Hui and Chan (22) did not state whether they included resting data. Of the 10 studies supporting the %HRR versus %V̇o₂R relationship, 4 included resting data (6,16–18), 4 did not (3,13,14,19), and the remaining 2 provided insufficient information to clarify this issue (15,20). Accordingly, we suspect this is a moot point.

One of the most important findings of Swain and Leutholtz, 1997 (6), was the effect of CRF on the %HRR versus %V̇o₂max relationship. Theoretically, as described earlier, one expects that individuals with a low aerobic capacity will have a more marked discrepancy between %HRR and %V̇o₂max than individuals with greater levels of CRF, especially at low intensities of exercise. Six of the 13 studies in the Table evaluated whether CRF had such an effect. All 6 found that individuals with lower fitness had larger discrepancies. Swain and Leutholtz, 1997 (6), reported that subjects with V̇o₂max values less than 30 mL^.min^−1.kg⁻¹ had a %HRR versus %V̇o₂max regression that was further from the line of identity than subjects with greater than 50 mL^.min^−1.kg⁻¹. Brawner et al., 2002 (13), found that heart failure patients with a V̇o_2peak of 16.5 mL^.min^−1.kg⁻¹ were further from the line of identity than cardiac patients without heart failure who had a V̇o_2peak of 19.4 mL^.min^−1.kg⁻¹. Pinet et al., 2008 (20), found that regressions were increasingly further from the line of identity for more obese groups with V̇o_2peak values of 27.0, 25.9, and 22.4 mL^.min^−1.kg⁻¹. Swain et al., 1998 (18), Byrne and Hills, 2002 (14), and Dalleck and Kravitch, 2006 (16), found that the aerobic capacity of subjects was inversely related to the intercept of the %HRR versus %V̇o₂max regression, i.e., lower fit subjects had a greater discrepancy. The Figure illustrates the %HRR versus %V̇o₂max relationship in 3 groups with widely disparate V̇o₂max values. Interestingly, Ferri Marini et al. in 2021 (23), with data on more than 500 subjects that ranged from 15.2 to 54.9 mL^.min^−1.kg⁻¹ in V̇o₂max, did not investigate this critically important point. The theoretical basis of the %HRR versus %V̇o₂max relationship predicts larger discrepancies for lower fit individuals, especially at low exercise intensities, and this should have been tested if the authors wished to demonstrate the superiority of %HRR versus %V̇o₂max over the currently accepted 1:1 relationship of %HRR versus %V̇o₂R to prescribe and monitor aerobic exercise intensity.

At rest, %HRR and %V̇o₂R are 0 by definition, while %V̇o₂max ranges from about 5% to more than 20%, being lower for individuals with high aerobic fitness, higher for those with low aerobic fitness. These statements are mathematical facts. The discrepancy between %HRR and %V̇o₂max at rest extends into the low to moderate exercise intensity range, being quite large for patients and clients with low aerobic fitness. Most available studies have confirmed this discrepancy during exercise and reinforce the notion that %V̇o₂R provides equivalent or nearly equivalent intensities of exercise to %HRR.

Research on the HR-V̇o₂ relationship has traditionally been conducted using incremental exercise tests of either a continuous or discontinuous nature, with stage durations less than or equal to 5 minutes. To our knowledge, no one has systematically examined the relationship of HR and V̇o₂ during typical aerobic exercise sessions that last 20 to 60 minutes. As body temperature rises during exercise, HR and V̇o₂ will invariably increase in a phenomenon known as cardiovascular drift. One study had 8 male cyclists perform a 1-hour bout of steady-state exercise at 70% of maximum power output and found that V̇o₂ increased from 3.26 L^.min⁻¹ to 3.43 L^.min⁻¹ from the 10th to the 60th minute, whereas HR increased from 153 to 164 b·min⁻¹ over the same period (24). Although the study did not evaluate %HRR or %V̇o₂R, it illustrates the challenge scientists and practitioners face. To accurately evaluate the “equivalency” of %HRR to either %V̇o₂R or %V̇o₂max for the purpose of exercise prescription, studies involving multiple trials of 20 to 60 minutes in duration would need to be performed on large numbers of young, middle-aged, and older subjects, with and without chronic disease, using different population groups. This is not particularly feasible, nor is it necessary for developing exercise prescriptions.

In practice, it is generally recommended to prescribe exercise intensity via the HRR method (7), using the rating of perceived exertion as an adjunctive intensity modulator. For coronary patients with exertional signs or symptoms of myocardial ischemia, the peak exercise HR should be greater than or equal to 10 b·min⁻¹ below the ischemic electrocardiogram or angina threshold. Alternative methods also include a calculated exercise workload based on V̇o₂. When this methodology is employed, the intensity should correspond to that normally derived via HRR using the %V̇o₂R method. However, all practitioners should recognize that any prescribed exercise intensity—whether via %HR_max, %HRR, %V̇o₂R, or %V̇o₂max—is merely the first step. The patient or client should be observed during exercise and the intensity adjusted accordingly, using hemodynamic responses, clinical signs or symptoms, and the rating of perceived exertion. This approach has long been recommended as the “art” of exercise prescription.

If there really is a timely and emergent issue about exercise prescription that we need to “rethink,” perhaps it is how we get more people worldwide to become more physically active on a regular basis since the current COVID-19 pandemic has decreased physical activity by 33% and simultaneously increased sitting time by 28% (25).