Relationship Between Percentages of Heart Rate Reserve and Oxygen Uptake Reserve During Cycling and Running: A Validation Study : The Journal of Strength & Conditioning Research

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Relationship Between Percentages of Heart Rate Reserve and Oxygen Uptake Reserve During Cycling and Running: A Validation Study

Guimarães, Giovanna C.1; Farinatti, Paulo T.V.2,3,4; Midgley, Adrian W.5; Vasconcellos, Fabrício2,3; Vigário, Patrícia1; Cunha, Felipe A.1,2,3

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Journal of Strength and Conditioning Research 33(7):p 1954-1962, July 2019. | DOI: 10.1519/JSC.0000000000002079
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General recommendations for aerobic exercise prescription include manipulation of training frequency, intensity, duration, and mode of activity according to the age, fitness level, and clinical condition of the exercising individual (11,13). Intensity is arguably the most important of these variables because of its relative efficacy in altering cardiorespiratory fitness when manipulated (25). According to the American College of Sports Medicine (ACSM), the current “gold standard” method for prescribing aerobic exercise intensity is the application of the linear relationship between percentages of heart rate reserve (HRR) and oxygen uptake reserve (Vo2R) (2,13). Specifically, exercise intensities between 40 and 85% HRR or Vo2R are recommended to promote health in adults (2,13). From a practical perspective, the HRR can be used to monitor and adjust power output to achieve the target intensity, and the Vo2R can be used to determine the duration of exercise required to elicit target energy expenditure. Accurate determination of energy expenditure associated with exercise is particularly important when prescribing exercise to promote weight loss and maintenance (10). The Vo2R also can be used in the ACSM metabolic equations to derive the required power output and speed for cycling, running, and several other exercise modalities (2).

The ACSM recommendation for using %HRR and %Vo2R is based on the assumption that there is a 1:1 relationship between these 2 variables (21–23). Two important issues must be considered concerning this hypothetical 1:1 ratio and the use of the ACSM metabolic equations, however. First, the use of heart rate as an indicator of relative metabolic intensity is based on validation studies that used cardiopulmonary exercise tests (CPETs), characterized by relatively short duration maximal incremental exercise (9). Whether the change in heart rate is a valid marker of change in relative metabolic intensity during more prolonged constant power output exercise is uncertain. A question, therefore, arises regarding the extent to which results obtained by studies that described the hypothetical 1:1 relationship between the %HRR and %Vo2R during CPET, extrapolate to training bouts characterized by relatively long duration and constant power output. Another unanswered question is whether the power outputs and speeds defined by the ACSM metabolic equations produce target heart rate (%HRR), Vo2 (%Vo2R), and energy expenditure values during isocaloric exercise bouts. It is possible that these equations underestimate or overestimate the metabolic demand with important practical consequences for exercise prescription, especially within the context of weight control programs or experimental research, where exercise volume between different bouts needs to be matched. Furthermore, exercise modality influences the magnitude of cardiorespiratory responses at submaximal and maximal intensities (1,8,17); however, no study has investigated directly the extent to which different exercise modalities affect the %HRR-%Vo2R relationship.

The main aim of this study was to investigate the validity of the hypothetical 1:1 relationship between %HRR and %Vo2R during CPET and prolonged constant power output exercise bouts using 2 exercise modalities (cycling and running). The second aim was to investigate whether the power outputs and speeds defined by the ACSM metabolic equations for cycling and running reproduce the predicted heart rate, Vo2, and time to achieve the target energy expenditure during the exercise bouts, when assuming a 1:1 relationship between %HRR and %Vo2R.


Experimental Approach to the Problem

Figure 1 shows a fluxogram of the first and second parts of the study. Panel A includes procedures for investigating the hypothetical 1:1 relationship between %HRR and %Vo2R derived from cycling and running CPETs. Panel B includes procedures for establishing the validity of the %HRR-%Vo2R relationships throughout the isocaloric constant power output and constant speed cycling and running bouts, and the accuracy of the ACSM metabolic equations for determining power outputs and speeds associated with absolute values of Vo2 and associated energy expenditures.

Figure 1.:
Experimental design overview for the first (A) and second (B) parts of the study. Vo 2 = oxygen uptake; Vo 2R = oxygen uptake reserve.

All running tests were performed on the same motorized treadmill ( Super ATL; Inbramed, Porto Alegre, RS, Brazil) and the cycling tests were performed on the same cycle ergometer (Cateye EC-1600; Cateye, Tokio, Japan). Ambient temperature and relative humidity throughout the study ranged from 292 to 295 K and 50–70%, respectively.


A total of 30 apparently healthy men volunteered for the study (mean [range]: age, 24 [18–34] years; height, 1.81 [1.63–1.98] m; body mass, 84 [59–116] kg; body mass index, 25 [20–30] kg·m2; percentage body fat, 18% [9–27%]; resting heart rate, 62 [44–84] b·min−1; and resting Vo2, 542.2 [326.8–971.2] ml·min−1). All subjects were involved in aerobic activities for at least the previous 3 months, 2–5 times per·week, and 20–60 min·bout−1. Among the 30 subjects involved in the first part of the study, only 10 volunteered to participate in the second part of the study that involved performing 2 constant power output exercise bouts. The study gained approval from the University of Rio de Janeiro State ethics committee (reference 3082/2011) and subjects were informed of the benefits and risks of the study before signing an institutionally approved informed consent document to participate in the study.


Resting Vo2 was determined in accordance with the recommendations of Compher et al. (4): abstention of physical exercise, alcohol, soft drinks, and caffeine in the 24 hours preceding the assessment, fasting at least 8 hours before the assessment, and minimum effort when traveling to the laboratory. In the laboratory, subjects laid in a calm environment in a supine position for an acclimation period of 10 minutes, after which the Vo2 was determined for 40 minutes. The mean Vo2 between minutes 35–40 was used to calculate the %Vo2R because this time period has previously been shown to elicit a Vo2 steady-state and high test-retest reliability (6). The resting Vo2 was always measured at the same time of the day, between 07:00 and 11:00 am.

The ramp-incremented maximal CPETs were performed as described elsewhere (5,7). The power output and speed increments were individualized to elicit each participant's limit of tolerance in 8–12 minutes. The criteria for test termination followed the recommendations of the ACSM (2). The test was considered to have elicited peak capacity when at least 3 of the following criteria were observed (15) (a) maximum voluntary exhaustion defined by attaining a 10 on the Borg CR-10 scale; (b) ≥90% predicted maximal heart rate (HRmax) (220 − age) or presence of a heart rate (HR) plateau (ΔHR between 2 consecutive power outputs or speeds ≤4 b·min−1); (c) presence of a Vo2 plateau (ΔVo2 between 2 consecutive power outputs or speeds <2.1 ml·kg−1·min−1); and (d) respiratory exchange ratio >1.10.

Based on the HRmax and maximal oxygen uptake (Vo2max) obtained in the running and cycling CPET and on the values of resting heart rate and resting Vo2, the values corresponding to 75% of the HRR and Vo2R were calculated to determine the intensity of the 2 constant power output exercise bouts. The energy expenditure was calculated individually from the net Vo2, which is the Vo2 induced by the exercise bout (i.e., net Vo2 = gross Vo2 − resting Vo2) (21). The net Vo2 values expressed in ml·kg−1·min−1 were converted to L·min−1 and then to kcal·min−1. The predicted time to achieve 400 kcals at 75% Vo2R for each exercise modality also was calculated. The cycling and running bouts were preceded by a 5-minutes warm-up at 30 W and 65–75 revs·min−1, and 5.5 km·h−1 and 1% grade, respectively.

The absolute Vo2 values obtained from the %Vo2R equation were used to calculate the associated running speeds and cycling power outputs by applying the ACSM metabolic equations: Vo2 running (ml⋅kg−1⋅min−1) = 0.2 (speed m⋅min−1) + 0.9 (speed m⋅min−1) (grade %) + 3.5 (ml⋅kg−1⋅min−1) and Vo2 cycling (ml⋅kg−1⋅min−1) = 3.5 ml·min−1·kg−1 + 12.24 × (power W) × (body mass kg−1) (2). The grade of the treadmill was set at 1%, and the speed converted to km·h−1. Expired gases were collected during the exercise bouts through the metabolic cart. Based on the values obtained for Vo2 and associated energy expenditure determined throughout the exercise bout, the subjects were encouraged to perform an additional amount of exercise beyond the time predicted to expend 400 kcals, until they reached an observed energy expenditure of 400 kcals. Because the exercise bouts were designed to be isocaloric, the total duration of the bouts was expected to vary between subjects with different fitness levels. To allow comparisons of the cardiorespiratory responses across time within exercise bouts, data for the whole exercise bout were split into energy expenditure quartiles of 100, 200, 300, and 400 kcals.

Pulmonary gas exchanges were determined using a Vo2000 analyzer (Medical GraphicsTM, Saint Louis, MO, USA) and a silicone face mask (Hans Rudolph, Kansas, MO, USA). The gas exchange variables were 30-seconds stationary time-averaged, which provided a good compromise between removing noise in the data while maintaining the underlying trend (16). Before testing, the gas analyzers were calibrated according to the manufacturer's instructions, using a certified standard mixture of oxygen (17.01%) and carbon dioxide (5.00%), balanced with nitrogen (AGA, Rio de Janeiro, RJ, Brazil). The flows and volumes of the pneumotachograph were calibrated with a syringe graduated for a 3-L capacity (Hans Rudolph, Kansas, MO, USA). Heart rate was measured continuously using a cardiotachometer (RS800cx; Polar, Kempele, Finland) and beat-by-beat data were 30-seconds stationary time-averaged.

Statistical Analyses

All statistical analyses were performed using Statistica 10 software (StatSoft, Tulsa, OK, USA). Sample data are described using the mean ± SD. Statistical significance was accepted as p ≤ 0.05. Cohen's d effect sizes for mean differences were calculated and defined as small (0.20), moderate (0.50), and large (0.80) (3). In the first part of the study, a linear regression model was determined for each participant to compare the relationships between %HRR vs. %Vo2R. The heart rate and Vo2 values obtained at rest and during the CPETs were used as references to calculate %HRR and %Vo2R according to the following equations: (a) %HRR = (HRsubmax − HR at rest)/(HRmax − HR at rest) × 100 and (b) %Vo2R = (Vo2submax − Vo2 at rest)/(Vo2max − Vo2 at rest) × 100. In these equations, HRmax refers to the maximal heart rate reached in the CPET; the HRsubmax refers to the heart rate obtained throughout the CPET at 30-second intervals; Vo2max refers to the maximal Vo2 reached in the CPET; and Vo2submax refers to the Vo2 obtained throughout the test at 30-second intervals. The %Vo2R was used as an independent variable in the regression model and the predicted percentages of HRR associated with 40, 50, 60, 70, 80, and 90% of the Vo2R were determined. The mean ± SD intercepts and slopes were determined for each linear regression model and Pearson correlation for each relationship was calculated. The Student t test for paired samples was also used to test whether the intercepts and slopes of the regression models were significantly different from 0 and 1, respectively (7,22,23), and to test possible differences between the regression lines, as described in detail elsewhere (24). In addition, a 2-way ANOVA for repeated measures with exercise modality and intensity as factors was used for between and within group comparisons. The Tukey post hoc test was applied to determine pairwise differences when significant F ratios were obtained.

In the second part of the study, the differences between the predicted and observed heart rate and Vo2 were analyzed using a 2-way ANOVA for repeated measures. Where effects for exercise modality and time were statistically significant, Tukey post hoc pairwise comparisons were performed. Mean differences between the predicted and observed times to achieve 400 kcals at 75% Vo2R were investigated using one-sample t tests, using the difference scores and a test value of zero. The distribution of these differences was graphically displayed using Bland–Altman plots, which include the associated 95% limits of agreement.


Table 1 shows the mean ± SD values for cardiorespiratory variables and time to exhaustion obtained in the CPET. Mean HRmax and Vo2max were significantly higher during treadmill running compared with cycling, whereas maximal values for minute ventilation (second part of study only) and respiratory exchange ratio were significantly higher during cycling. Mean time to exhaustion was similar between exercise modalities.

Table 1.:
Mean ± SD maximal physiological responses and time to exhaustion for the running and cycling cardiopulmonary exercise tests.*†

Relationship Between Percentages of Heart Rate Reserve and Oxygen Uptake Reserve

The mean ± SD intercepts and slopes for the individual linear regression models, derived from cycling and running CPETs, are shown in Table 2. Figure 2 shows the linear regression lines representing the association between the %Vo2R and %HRR during cycling and running CPETs. Significant mean differences were observed between intercepts (t = −6.59; p < 0.001) and slopes (t = −6.10; p < 0.001) obtained for %HRR vs. %Vo2R relationships. Moreover, mean intercepts and slopes in both exercise modalities were significantly different from 0 (p < 0.001) and 1 (p < 0.001), respectively (Table 2).

Table 2.:
Mean ± SD values for the Y intercept, slope, coefficient of determination (r 2), and standard error of estimate (SEE) from individual linear regression models representing the relationships between heart rate reserve and oxygen uptake reserve obtained in the cycling and running cardiopulmonary exercise tests.
Figure 2.:
Regression line of heart rate reserve (%HRR) and oxygen uptake reserve (%Vo 2R) observed during the cycling and running cardiopulmonary exercise tests for the total sample of men (N = 30). The regression equation is the average of 30 individual regressions.

Table 3 shows the values of %Vo2R corresponding to deciles of %HRR during cycling and running CPETs. There were significant main effects for exercise modality (F = 75.64; p < 0.001) and intensity (F = 9,706.80; p < 0.001), and a modality × intensity interaction (F = 51.33; p < 0.001). The mean %Vo2R was significantly lower than that predicted by the 1:1 relationship up to 60% HRR for cycling (p < 0.001) and throughout the whole range of observed speeds for running (p < 0.001). At all exercise intensities, the %Vo2R was significantly higher in cycling compared with running (p < 0.001) and the %HRR was closer to the %Vo2R during cycling compared with running.

Table 3.:
Mean ± SD percentages of oxygen uptake reserve (%Vo 2R) associated with different percentages of heart rate reserve (%HRR) determined during the cycling and running cardiopulmonary exercise tests (CPETs).

Figure 3 shows the relationships between the %HRR and %Vo2R at 100 kcal intervals during the continuous exercise bouts at 75% Vo2R. A 1:1 relationship between the %HRR and %Vo2R was not observed for either exercise modality, with an average difference of 6.5% and 7.0% between the 2 variables for cycling and running bouts, respectively (p = 0.007–p < 0.001). Furthermore, the %HRR and %Vo2R increased significantly over time (F = 2,104.0, p < 0.001), the rate of which was influenced by exercise modality (F = 2,659.0, p < 0.001).

Figure 3.:
Mean ± SD percentage of heart rate reserve (%HRR) and oxygen uptake reserve (%Vo 2R) at 100 kcal intervals during the continuous cycling and running bouts at 75% Vo 2R. *Significantly different from the value assessed at 100 kcal (p < 0.01). p values indicate significant differences between the %HRR and %Vo 2R.

Predicted and Observed Values During Submaximal Exercise Bouts

Table 4 shows the mean ± SD predicted and observed heart rate and Vo2 for cycling and running bouts. There were significant differences between the predicted and observed heart rates (F = 82.4, p < 0.001) and Vo2 (F = 35.5, p < 0.001). The heart rate was significantly higher than predicted from the second energy expenditure quartile (cycling: mean difference = 5 b·min−1, p < 0.001 and running: mean difference = 8 b·min−1, p < 0.001), with the difference progressively increasing until reaching a maximum in the fourth quartile (cycling: mean difference = 12 b·min−1, p < 0.001 and running: mean difference = 18 b·min−1, p < 0.001). By contrast, observed Vo2 was lower than predicted during all energy expenditure quartiles for cycling, with the largest differences in the first quartile (mean difference = 359 ml·min−1; p < 0.001) and progressively decreasing until the fourth quartile (mean difference = 211 ml·min−1; p = 0.005). Unlike cycling, observed Vo2 during running was lower than predicted only in the first quartile (mean difference = 234 ml·min−1; p = 0.001).

Table 4.:
Mean ± SD predicted and observed heart rate reserve (HRR) and oxygen uptake reserve (Vo 2R) for the 400 kcal isocaloric exercise bouts performed at 75% Vo 2R.*†

Figure 4 shows the distribution of the differences between the predicted and observed times to achieve energy expenditure of 400 kcal at 75% Vo2R during cycling and running bouts. The time to achieve the target energy expenditure in each condition was significantly greater than predicted (F = 356.2, p < 0.001), with the greatest differences observed for cycling compared with running.

Figure 4.:
Bland–Altman plots showing individual differences between the predicted and observed times to achieve energy expenditures of 400 kcals at 75% oxygen uptake reserve (Vo 2R) during cycling and running. The first and third horizontal dashed lines in each graph represent the 95% limits of agreement.


This study adds to current knowledge by investigating the %HRR-%Vo2R relationships during CPETs and isocaloric bouts of constant power output exercise with energy expenditures of 400 kcals and using 2 different exercise modalities (cycling and running). The main finding was that the hypothetical 1:1 relationship between the %HRR and %Vo2R was not observed in either the CPET or constant power output exercise for either exercise modality. Moreover, the ACSM equations for cycling and running overestimated the observed energy expenditure and, therefore, underestimated the time to achieve 400 kcals during exercise at 75% Vo2R. Because of the association between energy expenditure and Vo2, similar errors were evident for Vo2, especially for the exercise modality involving a lower muscle mass (i.e., cycling). However, the ACSM metabolic equations for cycling and running predicted heart rate during the exercise bouts with a relatively high degree of accuracy during the first energy expenditure quartile, but subsequently observed heart rates were underestimated.

Cunha et al. (7) questioned the hypothetical 1:1 relationship between %HRR and %Vo2R during running CPET. The %Vo2R was underestimated in relation to %HRR, whereas differences between the %HRR and %Vo2R were inversely proportional to exercise intensity. In other words, the difference between %HRR and %Vo2R decreased when the exercise intensity was near maximal, at least within the context of maximal incremental exercise testing. The findings of this study concur with those of Cunha et al. (7) because the %HRR was significantly higher than the %Vo2R until 60% HRR for cycling (p < 0.001) and throughout the whole range of intensities for running (p < 0.001) (Table 3 and Figure 2). In any case, it is notable that %HRR was closer to %Vo2R during cycling (mean ± SD intercept and slope: 0.08 ± 0.05 and 0.93 ± 0.06, respectively) than during running (mean ± SD intercept and slope: 0.22 ± 0.10 and 0.80 ± 0.11, respectively) CPET (Table 2). Interestingly, the effect of exercise modality on the slope of the %HRR-%Vo2R relationship also has been observed by Swain and Leutholtz (22), (23). The %HRR vs. %Vo2R relationship during cycling CPET was indistinguishable from the line of identity (mean ± SD intercept and slope: −0.1 ± 0.6 and 1.00 ± 0.01, respectively) (22), whereas in running it was slightly different from the line of identity (mean ± SD intercept and slope: 1.5 ± 0.6 and 1.03 ± 0.01, respectively) (23). Comparison between results of the aforementioned studies should be viewed with caution, however, given the different exercise protocols and populations used.

Cunha et al. (8) investigated whether there was a 1:1 relationship between the %HRR and %Vo2R at an exercise intensity corresponding to the gas exchange threshold in 16 apparently healthy men during cycling, walking, and running CPETs. The authors observed that mean values of %Vo2R at the gas exchange threshold were 7% and 11% lower than the corresponding %HRR for the cycling and running exercise modalities, respectively. The present findings concur with the hypothesis that the %HRR-%Vo2R relationship is influenced by the exercise modality used during the CPET, because the average difference between the %HRR and %Vo2R was greater during running than cycling CPET (Figure 2). Exercise modality did not affect the average difference between the %HRR and %Vo2R during the 400 kcal exercise bouts at 75% Vo2R (cycling: 6.5%; running: 7%; Figure 3); however, the greatest increases in heart rate (%HRR) and Vo2 (%Vo2R) over time were observed during running compared with cycling (Table 4 and Figure 3).

Nassis and Geladas (17) compared the physiological strain during prolonged submaximal cycling and running for 90 minutes at 60% Vo2max in a thermoneutral environment (23.8 ± 0.3° C) in the same group of 11 healthy men (mean ± SD: [cycling and running Vo2max: 48.5 ± 1.8 and 52.1 ± 2.2 ml·kg−1·min−1, respectively]). The authors observed a main effect for exercise modality, where Vo2, heart rate, cardiac output, stroke volume, and rectal temperature were significantly greater during running compared with cycling (p < 0.01). The cardiac output declined only during cycling; however, presumably because of the greater drop in stroke volume, despite a higher degree of whole body dehydration and hyperthermia observed in running. This in turn may explain the plateau in Vo2 throughout the cycling bout compared with the progressive increase in Vo2 until minute 43 in the running bout (17). In others words, these findings suggest that active muscle mass played a role in the cardiovascular responses, which reinforce the notion that the relationships between %HRR and %Vo2R observed during CPETs are not valid in the context of aerobic training programs. In this sense, it is known that the increase in Vo2 during prolonged exercise with constant power output due to the slow component of Vo2 kinetics has been related to integrated mechanisms of kinetic control, including the activation of additional muscle groups, greater respiratory muscle activity, recruitment of type II muscle fibers, increases in muscle temperature, and higher blood lactate levels, among others (18). The progressive increase in Vo2 has been shown to be concomitant to a decrease in stroke volume and a compensatory increase in heart rate, with little variation in the cardiac output (19). Parallel to this is that the increase in body temperature and decreased hydration level may contribute to a decline in filling pressure and end-diastolic volume, promoting increased heart rate (12) and a further dissociation between %HRR and %Vo2R.

To the best of our knowledge, this is the first study to investigate the extent to which the ACSM metabolic equations for cycling and running reproduce the prescribed heart rate (%HRR), Vo2 (%Vo2R), and time to achieve a target energy expenditure during isocaloric exercise bouts. Our findings raise doubts about the appropriateness of prescribing isocaloric exercise bouts based on a 1:1 ratio between the %HRR and %Vo2R because the predicted Vo2 was significantly overestimated throughout the submaximal exercise protocols (Table 4 and Figure 3). In practical terms, the subjects had to perform additional exercise in relation to the predicted time to reach the target energy expenditure of 400 kcals for the 2 exercise modalities (Figure 4). However, the predicted and observed heart rate values were quite similar across the 2 exercise modalities during the first energy expenditure quartile, after which the predicted heart rate was underestimated, especially for running (Table 4 and Figure 3). In practical terms, prescribing exercise intensity based on the Vo2 and then estimating the relative heart rate assuming a 1:1 relationship would probably overestimate energy expenditure, especially for high intensity and long duration exercise bouts. This is important for exercise prescription because previous studies using healthy adults (14), heart failure patients (26), and obese adults (20) have monitored heart rate to adjust the power output corresponding to the preferred exercise intensity and ensure the training bouts were isocaloric. In other words, using heart rate to ensure the intended training volume is being performed is not valid.

Practical Applications

The hypothetical 1:1 relationship between %HRR and %Vo2R could not be reproduced because the %Vo2R was underestimated by %HRR. Concurrently, the relationships between the %HRR and %Vo2R from maximal incremental exercise testing may not accurately transpose to prolonged constant power output exercise, regardless of exercise modality. Moreover, the present findings warrant further investigation regarding the applicability of the ACSM metabolic equations to calculate the target power outputs and speeds based on the Vo2 obtained by calculating the target %Vo2R because the cycling and running equations overestimated the predicted energy expenditure resulting in an underestimation of the observed time to achieve 400 kcals. This information is of paramount importance for exercise prescription to determine the predicted time to achieve a given energy expenditure during isocaloric exercise bouts (min·bout−1), and power output and speed (watts and m·s−1) and target heart rate (b·min−1). Further research is required to establish the accuracy of the ACSM metabolic equations for different exercise intensities and volumes, and populations with different levels of cardiorespiratory fitness and clinical conditions.


This research was partially supported by grants from the Carlos Chagas Filho Foundation for the Research Support in Rio de Janeiro State and Brazilian Council for the Technological and Scientific Development.


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cardiopulmonary exercise testing; isocaloric exercise; kilocalories; training intensity

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