Bayesian Analysis of the HR–VO2 Relationship during Cycling and Running in Males and Females

Professional organizations advise prescribing intensity of aerobic exercise using heart rate reserve (%HRR) which is presumed to have a 1:1 relationship with either maximal oxygen uptake (%VO2max) or %VO2 reserve (%VO2R). Even though running and cycling are popular modes of training, these relationships have not been investigated in a group of males and females during both running and cycling. This study evaluated the %HRR-%VO2max and %HRR–%VO2R relationships in 41 college-aged males (n = 21) and females (n = 20) during treadmill running and cycling. Heart rate (HR) and VO2 data were collected at rest and during maximal exercise tests on a treadmill and cycle ergometer. The HR and VO2 data were analyzed using a Bayesian approach. Both the %HRR-%VO2max and %HRR–%VO2R relationships did not coincide with the line of identity in males and females in both treadmill running and cycling. %HRR was closer to %VO2max than to %VO2R. There were no significant differences in the intercepts of the %HRR–%VO2max and %HRR–%VO2R relationships between males and females during running or cycling, or between running and cycling in males or females. The credible intervals of the intercepts and slopes suggest interindividual variability in the HR–VO2 relationship that would yield significant error in the prescription of intensity of aerobic exercise for an individual.


Introduction
There are an increasing number of positive health outcomes linked to physical activity [1,2]. The current recommendation is that adults should accrue at least 150 min to 300 min of moderate intensity physical activity per week, 75 min to 150 min of vigorous aerobic exercise per week, or an equivalent combination of the two [1,3,4]. Because of the dose-response relationship between exercise and cardiorespiratory fitness (CRF), greater volumes of exercise are necessary to further improve or maintain CRF [5]. The concept of a threshold intensity of exercise necessary for the improvement of CRF has long been suggested [6] and remains an important principle of the exercise prescription [3,7]. Incremental changes in the intensity of aerobic exercise are reflected in the heart rate (HR) and oxygen consumption (VO 2 ) responses to exercise. Because the relationship between HR and VO 2 during incremental aerobic exercise is considered to be linear [8], the intensity of aerobic exercise is typically expressed relative to maximal heart rate (HRmax), HR reserve (HRR), VO 2 max, or VO 2 reserve (VO 2 R). The classification of intensity of aerobic exercise based on these methods is described by the American College of Sports Medicine (ACSM; [3,7]). The inherent problems with expressing intensity of aerobic exercise as a %HRmax or %VO 2 max have previously been described [9][10][11][12]. Briefly, there is an inequality between a given percentage of maximal HR and the equivalent percentage of VO 2 max due to disproportional non-zero values at rest. Using a percentage of reserve values to describe intensity of aerobic exercise corrects for non-zero resting values. The ACSM previously assumed that a given %HRR was equivalent to the same %VO 2 max [13,14]. Subsequent research has shown that the %HRR-%VO 2 max relationship does not coincide with the line of identity (x = y) and the %HRR-%VO 2 R relationship is indistinguishable from the line of identity in healthy [11] and obese [15] adults, elite cyclists [16], and during aerobic dance [17]. Other studies have reported that although the %HRR-%VO 2 R relationship did not coincide with the line of identity, there was a closer relationship between %HRR and %VO 2 R than between %HRR and %VO 2 max [18,19]. To the contrary, Gaskill et al. [20] reported that the slope and intercept for the relationship between %HRR and %VO 2 max were closer to the line of unity than the slope and intercept for the %HRR and %VO 2 R relationship. Although previous research is not in complete agreement about the HR-VO 2 relationship, the ACSM now recognizes an equivalency between %HRR and %VO 2 R [3,7,21]. The current ACSM guidelines [3,7] define the threshold for moderate and vigorous intensity aerobic exercise to improve CRF as 40-59% and 60-89% of HRR or VO 2 R, respectively.
The HR-VO 2 relationship can be influenced by the mode of exercise. Due to differences in the recruitment of muscle mass and movement patterns during exercise, one could reasonably expect to observe differences in the cardiovascular and metabolic responses to exercise between different modes of exercise, especially between weight-bearing (e.g., running) and non-weight-bearing (e.g., cycling) exercise. Findings from previous research suggest a form of exercise effect on the HRR and VO 2 R relationship [11,18,22,23]. Previous studies have evaluated the HR-VO 2 relationship during cycle ergometry [11,16] and treadmill running [9,15,18,22,24] in only males [9,16,22], only females [24] and both males and females [11,15,18,25].
The HR-VO 2 relationship may also be different between males and females. Although previous studies evaluating the relationship between HRR and VO 2 R included nearly equal numbers of male and female participants, the effects of sex on the HRR-VO 2 R relationship have either not been reported [18] or not presented in detail [11,15]. An earlier study [25] reported sex differences in the HR-VO 2 relationship expressed in absolute terms (HR bpm; VO 2 L/min).
To determine one's HRR and VO 2 R, resting HR and VO 2 must also be measured. Cunha et al. [26,27] described the influence of the exercise testing protocol and the manner in which resting HR and VO 2 are measured on the HRR-VO 2 R relationship. Previous studies have measured resting values in the seated, standing or supine positions for durations ranging between 5 and 30 min [9,11,15,16,18,22,26,27]. Another study assumed a resting VO 2 of 3.5 mL/kg/min [19]. VO 2 R is closer to HRR when a standardized protocol is used to measure resting energy expenditure [27].
Since there is a wide subject-to-subject variability in HR responses to incremental aerobic exercise [28,29], the HR-VO 2 relationship should be individually determined when prescribing intensity of aerobic exercise. Although running and cycling are popular modes of training and are the basis of some endurance events, to the best of our knowledge no recent studies have compared the HR and VO 2 relationship during running and cycling in the same male and female subjects when also using a standardized protocol to measure resting HR and VO 2 . Therefore, the purpose of this study was to evaluate the HR-VO 2 relationship in males and females during treadmill running and cycling when also measuring resting HR and VO 2 using standardized protocols.

Materials and Methods
Participants completed a resting energy expenditure study to determine resting HR and VO 2 and two maximal graded exercise tests during two visits to the laboratory separated by 48 to 72 h. During the first visit, the resting energy expenditure study was conducted prior to performing a maximal graded exercise test on either a treadmill or an electronically braked cycle ergometer. On the second visit, the participant completed a maximal graded exercise test on the opposite mode of exercise testing that was performed during the first visit.

Participants
This study was reviewed and approved by the Institutional Review Board prior to the collection of any data. Forty-one (21 males; 20 females) apparently healthy adults, 18-39 years of age participated in this study. A pre-participation questionnaire was used to screen participants for known existing conditions or health issues that would limit exercise tolerance or increase the risk of untoward events during exercise. All participants provided informed written consent.
All participants met minimal physical activity recommendations for adults [1,3,4], namely, 150 to 300 min of moderate intensity physical activity per week, 75 to 150 min of vigorous aerobic exercise per week, or an equivalent combination of moderate and vigorous aerobic exercise. All participants included both running and cycling (either outdoor running and cycling or indoor running and cycling on a treadmill and a stationary bike or a combination thereof) as part of their exercise program. None of the participants were training for a specific competitive endurance event in either mode of exercise. Participants were instructed to: (a) drink plenty of fluids over the 24 h period prior to testing, (b) fast (except water) for the 8 h prior to testing, (c) refrain from the use of tobacco, alcohol, and caffeine for 4 h prior to testing, and (d) refrain from purposeful exercise during the day prior to testing.

Measurement of Resting and Exercise HR and VO 2
The measurement of resting HR and VO 2 and performance of the exercise tests occurred in the morning. Upon arrival to the lab, participants confirmed that they complied with the pre-test instructions. During the measurement of resting VO 2 and the two graded maximal exercise tests, ventilation, expired gases, and VO 2 were measured using a TrueOne 2400 metabolic measurement system (Parvo Medics, Sandy, UT, USA). Prior to each test, the oxygen and carbon dioxide analyzers were calibrated using medical grade gases of known concentrations and the flow meter of the metabolic measurement system was calibrated using a 3.0 L syringe at appropriate flow rates.
After measuring the height and body mass of the participant, he/she lied in the supine position on a padded table for 15 min, after which HR and VO 2 was measured for an additional 30 min. The measurement of resting HR and VO 2 occurred in a quiet, dim-lit room with a light blanket placed over the participant for comfort. A clear plastic dome-shaped "hood" was placed over the participant's head. The hood was sealed by tucking its' plastic sheet under the body or sealing the edges with towels. The hood allows for the exchange and measurement of oxygen and carbon dioxide during normal breathing without the use of a mouthpiece and nose clip. The metabolic measurement system allowed the adjustment of airflow through the system based on the carbon dioxide concentration in the hood. The metabolic measurement system was configured to calculate and display average values every minute. Resting HR was continually monitored using a radiotelemetry heart rate monitor (Polar Electro Kempele, Kempele, Finland). Resting HR and VO 2 were calculated as the average steady-state value during the test after discarding the first 5 min of data.
After completing the resting measurements, the participant completed a maximal graded exercise test to volitional fatigue on either a treadmill (TrackmasterTMX425, Full Vision, Inc., Newton, KS, USA) or an electronically braked cycle ergometer (Lode Medical Products, Groningen, The Netherlands). Participants completed the two exercise tests in a randomized order, so half of the participants performed the running test first and half of the participants performed the cycling test first. To facilitate the measurement of oxygen consumption during exercise, participants were fitted with a one-way breathing valve, mouthpiece, and nose clip. The one-way breathing valve was held in place by a head harness. During the exercise tests, the metabolic measurement system was configured to display and print 15 s' average breath-by-breath data. Rating of perceived exertion (RPE) was self-reported using the Borg 15-point scale [30].
In order to capture data across a full range of the HR and VO 2 values, we began each exercise test at a relatively low workload and advanced the intensity of exercise in small increments of workload. Each stage of the exercise test was 3 min in duration. During the treadmill exercise test, the first three stages progressed from walking at a self-selected normal walking pace, a brisk walking pace, and jogging at a self-selected jogging speed on a level grade. This was followed by jogging at the same speed at a 1.5% grade and subsequently increasing the grade by 1.5% every stage until volitional fatigue occurred, at which time the exercise test was terminated. During the cycling exercise test, participants began by pedaling at a self-selected comfortable cadence between 70-90 rpm at a workload of 50 W (males and females). Each subsequent stage included increments of 20 W (females) or 25 W (males) until volitional fatigue occurred, and the subject was unable to maintain a pedal cadence of at least 50 rpm. During both exercise tests, the administrator coached the participant in order to achieve a valid maximal effort during the test. Upon reaching the point of volitional fatigue the participant grasped the hand railings on the treadmill or simply stopped pedaling during the cycling test. If performing a running test, the treadmill speed and grade were decreased to a walking speed on level grade to allow a cool down for any desired amount of time. If performing a bike test, the workload was reduced to 25-50 W and the participant pedaled at their own cadence for any desired amount of time.
In both exercise tests, participant effort was considered maximal if physical signs suggestive of exhaustion were apparent and at least two of the following three criteria [7,[31][32][33][34] were met: (a) maximal respiratory exchange ratio (RER) ≥ 1.10, (b) a HRmax no more than 15 bpm below age predicted maximal HR, and (c) leveling off of VO 2 despite an increase in workload. VO 2 max during the treadmill test and VO 2 peak during the cycle test was defined as the highest average VO 2 value recorded over any 30-s time period near the end of the test, provided RER was greater than or equal to 1.10. Maximum HR was defined as the highest HR value recorded during the test.

Statistical Analysis
We analyzed all data using a Bayesian approach. The initial analysis of the data included a comparison of demographic data (age, height, body mass, BMI), resting HR and VO 2 data, maximal exercise HR (HRmax), RER, and VO 2 max or VO 2 peak data, and HRR and VO 2 R data. In some cases, we only considered sex differences (i.e., age, height, body mass, BMI, resting HR and VO 2 ) and in other cases (HRmax, maximal RER, VO 2 max or VO 2 peak, HRR, and VO 2 R) we examined differences between males and females during treadmill exercise and during cycling exercise as well as differences between treadmill exercise and cycling exercise in males and in females. In all cases, mean parameters were given the same prior, and variances were given the same prior. We allowed the variance in each setting to be different (i.e., there was no constraint to impose equal variances in any of the cases). Priors for the means and variances were as follows: µ case~N ormal (50, 10,000) The primary analysis of data in this study was a comparison of the intercepts and slopes of the HR-VO 2 relationships during exercise. For each subject all 15-s interval HR and VO 2 data were used in two models: (1) when HR and VO 2 data were expressed as a percentage of reserve values, and (2) when HR data was expressed as a percentage of reserve values and VO 2 data was expressed as a percentage of maximal values. Each of these two models were evaluated in the responses of men and women during treadmill running and cycle ergometry. Thus, there were eight analyses performed (2 models, 2 genders, 2 modes of exercise). Each of these analyses were accomplished using a Bayesian hierarchal model to appropriately account for multiple measurements for each individual. In our framework, each subject's linear response is considered to be a deviation from an overall population linear response. Although we actually estimate the intercept and slope parameters for each individual, it is these population parameters for intercept and slope that are of primary interest. We used fairly noninformative priors for the population parameters. All posterior inference was performed on the posterior distributions of the population parameters. For each of the eight relationships we described above, we had the following set up relative to the HR measurement. (In the text that follows, the normal distribution is noted as N (mean, variance), and the gamma distribution is noted as Gamma (shape, rate; i.e., the mean of the gamma is shape/rate.) HR i~N ormal (µ i , σ 2 ) µ i = b0 id + b1 id * VO 2i The intercepts (b0 id ) and slopes (b1 id ) are estimated for each individual (as identified by the id). The prior distributions for the parameters in each case for each individual were as follows: b0 id~N ormal (µ b0 , σ 2 intercepts ) b1 id~N ormal (µ b1 , σ 2 slopes ) The prior distributions for the population parameters were fairly noninformative and were: µ b0~N ormal (0, 1000) µ b1~N ormal (1, 10) The prior distributions for the variance components were as follows: σ 2~G amma (1.1, 0.01) σ 2 intercepts~G amma (1.1, 0.01) σ 2 slopes~G amma (1.1, 1) Thus, we appropriately accounted for all sources of variation, including random error, and error due to the individual intercepts and slopes.
Code was run in R [35] using JAGS (Just Another Gibbs Sampler) [36]. Since complicated Bayesian models rely on Markov chain Monte Carlo (MCMC) methods it is important to consider convergence diagnostics of the MCMC samples. Each chain of the models was run using 1000 burn in iterations and 11,000 total iterations. We used 20 chains and thinned our output by 20 for each run, yielding a total of 10,000 saved iterations for each estimated parameter. The Rhat statistic was computed for each posterior chain [37] and in each case was less than 1.002. The Raftery-Lewis statistic [38] was computed for each chain and never exceeded 1.05. Effective sample sizes all exceeded 8600. All posterior convergence diagnostics were computed using the R package, coda [39]. All inferences were made using posterior distributions of the population parameters.
In the analysis of age, height, weight, BMI, resting HR and VO 2 , maximal HR, RER and VO 2 , and HRR and VO 2 R, differences between males and females or differences between treadmill exercise and cycling exercise were considered significant if zero (0) fell outside of the 95% credible interval (CI) and the posterior probability of the difference being greater than zero was greater than or equal to 95%.
In the analysis of HR and VO 2 relationship, VO 2 was considered the independent variable and HR was considered the dependent variable. We were interested in determining if the intercept and slope of the line of best fit through the data of each of the HR-VO 2 relationships were different from zero (0) and one (1), respectively. Means, standard deviations, and posterior probability intervals, or CI, were generated for the slope and intercept of each of the eight models. The intercept was considered significantly different from zero (0) if zero was outside the 95% CI. The slope was considered significantly different from one (1) if one was outside the 95% CI.
We also compared the intercepts and slopes of each HR-VO 2 relationship in males and females between the two modes of exercise, as well as within each mode of exercise. The intercept and slope of each HR-VO 2 relationship in females was considered significantly different than that of males if the posterior probability exceeded 95%.
We estimated the mode and 95% credible intervals for %HRR values at 45%, 55%, 65%, 75% and 85% of VO 2 max and VO 2 R values. We considered the %HRR point estimate to be significantly different from the same %VO 2 max or %VO 2 R value if the estimated %VO 2 max or %VO 2 R value fell outside of the CI of the %HRR. Table 1 includes some of the personal characteristics of the participants in the study. Table 2 includes results from the REE and maximal exercise test results. Resting HR was significantly higher in females. Resting VO 2 was significantly higher in males. Males achieved a significantly higher maximal RER than females during treadmill running but not cycling. There were no sex differences in maximal HR or HRR during treadmill running or cycling. Males achieved significantly higher VO 2 max (or VO 2 peak) and VO 2 R values than females during both treadmill running and cycling. There were no significant differences in maximal HR, VO 2 max (or VO 2 peak), HRR, and VO 2 R between treadmill running and cycling in either males or females.   Table 3 includes the intercepts and slopes for the regression lines for the %HRR-%VO 2 max and %HRR-%VO 2 R relationships for males and females during treadmill running and cycling. The intercepts and slopes of the %HRR-%VO 2 max and %HRR-%VO 2 R relationships during running and cycling in both males and females were all significantly greater than an intercept of zero (zero lies outside the CI) and less than a slope of 1 (1 lies outside the CI), respectively.

Results
There were no significant differences in the intercepts of the %HRR-%VO 2 max and %HRR-%VO 2 R relationships between males and females (probability of a sex difference < 95%) during running and cycling, or between running and cycling in either males or females (probability of a mode difference < 95%). During running, the slopes of the %HRR-%VO 2 max and %HRR-%VO 2 R relationships were significantly greater in females than in males (probability of a sex difference > 95%). Values are intercepts and slopes ± SD (Credible interval). * = Significant sex difference in slopes within the mode of exercise (probability that the slope for females is greater than the slope for males is >95%).
During cycling, there were no significant differences in the slopes of the %HRR-%VO 2 max and %HRR-%VO 2 R relationships between males and females (probability of a sex difference < 95%). There were no significant differences in the slopes of the %HRR-%VO 2 max and %HRR-%VO 2 R relationships between treadmill running and cycling in either males or females (probability of a mode difference < 95%). Table 4 includes the modal %HRR value and credible interval at a range of moderate-to vigorous-intensity %VO 2 max and %VO 2 R values (45%, 55%, 65%, 75%, 85%) recommended by the ACSM [3,7] to improve CRF. The %HRR significantly overestimated %VO 2 R at all intensities less than 85% of VO 2 R during treadmill running and cycling for both males and females. The %HRR overestimated %VO 2 R more so at lower intensities of exercise than at higher intensities of exercise. The %HRR significantly overestimated %VO 2 max only at intensities of exercise representing 45% and 55% of VO 2 max during treadmill running and cycling for males. In females, %HRR significantly overestimated %VO 2 max only at intensities of exercise representing 45% and 55% of VO 2 max during treadmill running and 45%, 55% and 65% of VO 2 max during cycling.

Discussion
This study is unique in that we used Bayesian statistics to evaluate the HR-VO 2 relationship in a group of males and females during two modes of exercise, treadmill running and stationary bike cycling.

HR-VO 2 Relationship
A key finding in this study was that neither the %HRR-%VO 2 max or %HRR-%VO 2 R relationships coincided with the line of identity (intercept = 0; slope = 1) in either males or females during cycling or treadmill exercise (Table 3). Although neither relationship coincided with the line of identity, the %HRR-%VO 2 max relationship was closer to the line of identity than the %HRR-%VO 2 R relationship ( Table 4). The results of this study concur with three previous studies that have reported similar results during treadmill [18] and cycling [20,40] exercise. On the contrary, other studies reported that the %HRR-%VO 2 R relationship was not distinguishable from the line of identity, but the %HRR-%VO 2 max relationship did not coincide from the line of identity during treadmill [15] and cycling [11,16] exercise. Swain et al. suggested that the differences in the HR-VO 2 relationship they reported during cycling [11] and treadmill [18] exercise in the same lab could be attributed to the mode of exercise. Nevertheless, the subjects in the two studies [11,18] were not the same. Previous studies have evaluated the HR-VO 2 relationship during treadmill [15,18,24] or cycling [11,16,20,40] exercise. To the best of our knowledge, this may be the first study that used the same group of subjects to evaluate the HR-VO 2 relationship during both treadmill and cycling exercise. Our data, and that of three previous studies [18,20,40] that report an inequality in the %HRR-%VO 2 max and %HRR-%VO 2 R relationships add support to the need to rethink the HR-VO 2 relationship and its implications for exercise prescription.
Several factors may contribute to the disagreements in the data reported between this and previous studies. Differences in how resting HR and VO 2 are measured may contribute to differences in the calculation of HRR and VO 2 R and therefore the %HRR-VO 2 R or %HRR-%VO 2 max relationship. In this study, we followed the recommendations for measuring resting energy expenditure, namely ensuring a minimum of 10-20 min rest before the assessment, followed by a 25-30 min measurement duration, discarding the first 5 min [26]. Resting HR and VO 2 have been measured during 5 min of seated rest [11], during the last 2 min of a 5 min seated rest period [18], and during the last 5 min of a 20 min seated rest period [16]. Following a 10 min rest period, resting values have been measured for 30 min in the supine position, discarding the first 20 min [15].
The measurement of HR and VO 2 during exercise may also affect the HR-VO 2 relationship. In this study, we programmed our metabolic measurement system to average data every 15 s. The number of data points for each subject varied with the duration of the exercise test. For the 41 subjects, we had 4184 HR-VO 2 data points (an average of approximately 51 data points for each exercise test for each subject). Other studies averaged HR and VO 2 data during the last 30 s [18] or during the last minute of each stage [11,15,16].
One cannot assume an equivalency of the HR-VO 2 relationship between individuals. Training status or cardiovascular fitness level may also affect the HR-VO 2 relationship during exercise. For example, Swain et al. [11,18] reported a fitness effect in the %HRR-%VO 2 max relationship in that the individual regression lines for less-fit participants had a greater intercept than for the high-fit participants. The implications of this is that an exercise prescription based on the assumed equivalency of the %HRR-%VO 2 max relationship would produce greater errors for low-fitness individuals. Lounana et al. [16] reported that the regression for the %HRR-%VO 2 max relationship did not coincide with the line of identity, but the regression for the %HRR-%VO 2 R was indistinguishable from the line of identity in elite male (average VO 2 max = 70.9 ∀ 1.2 mL/kg/min) road cyclists.

Sex Differences in the HR-VO 2 Relationship
Despite sex differences in resting HR and VO 2 , VO 2 max, and VO 2 R (Table 2), (a) there were no sex differences in the intercepts of the %HRR-VO 2 R or %HRR-%VO 2 max relationship during treadmill running or during cycling (Table 3); (b) there were no differences in the intercepts between running and cycling in males or in females (Table 3); (c) there were no sex differences in the slopes during cycling; and (d) the slopes were significantly greater in females than in males during treadmill running. Our data is in agreement with that of previous studies that reported no differences in the intercepts or slopes of the regression lines between males and females during cycling [11] and during treadmill [15] exercise. Another study did not report an analysis of the data by sex during treadmill running [18]. In addition to the other factors that affect the HR-VO 2 relationship, one cannot presume that the relationship is equivalent in males and females. Future research can include both male and female participants, analyze data for sex differences, and report differences in the HR-VO 2 relationship between males and females.

Implications for Exercise Prescription
The ACSM currently suggests prescribing the intensity of aerobic exercise based on the %HRR-%VO 2 R relationship [3,7,21]. This is supported by previous studies that have reported equality in the %HRR-%VO 2 R [11,15,16] relationship. Assuming the regression line representing the %HRR-%VO 2 R relationship coincides with the line of identity (intercept = 0, slope = 1), a given %HRR would approximate the same %VO 2 R. Thus, using a %HRR value to prescribe the intensity of aerobic exercise would provide an accurate estimate of the metabolic cost of the exercise. Basing an exercise prescription on %VO 2 R (rather than %VO 2 max) more accurately reflects the net energy expenditure of the exercise, which is more useful in exercise programs that include a weight loss intention [18].
We report an inequality between the line of identity and the %HRR-%VO 2 R and the %HRR-%VO 2 max relationships. Our data is in agreement with data previously reported during cycling [20,40] and treadmill exercise [18]. Our data supports the need to rethink the HR-VO 2 relationship and its accepted use for prescribing intensity of exercise-especially for an individual. The HR-VO 2 relationship is influenced by ambient and body temperature, hydration, training status, emotional state and the day-to-day variations in resting HR and HR responses to exercise [40]. The wide CI reported in this study for the slopes and intercepts (Table 4) reflects the interindividual variability in the HR and VO 2 responses during exercise. Understanding the potential variability in the intercepts and slopes of the HR-VO 2 relationship, but assuming an equivalency between %HHR and %VO 2 max or %VO 2 R, can introduce error when prescribing intensity of exercise for an individual. The efficacy of prescribing intensity of steady-state, constant-load aerobic exercise, using the HR-VO 2 relationship established during incremental intensities of exercise, is also controversial [40].
The ACSM [3,7] suggests a threshold for moderate intensity aerobic exercise (40-59% of HRR or VO 2 R) and vigorous intensity aerobic exercise (60-89% of HRR or VO 2 R) to improve CRF. A review of previous studies supports the use of 45% of VO 2 R as a minimal effective training intensity to improve CRF [10]. In this study, 45% and 55% HRR did not accurately estimate the corresponding %VO 2 R or %VO 2 max during treadmill running or cycling (Table 4). At higher intensities, 65%, 75% and 85% of HRR accurately estimated the corresponding %VO 2 max (but not VO 2 R) during treadmill running and cycling in men and treadmill running in women. Thus, it appears that the %HRR-%VO 2 max relationship approaches equality as intensity of exercise increases. This may be due to a greater variability in the HR responses to exercise at lower intensities. Based on the data reported in this study (Table 4), %HRR does not accurately estimate %VO 2 R at intensities of exercise below 85% of VO 2 R in both males and females during treadmill running or cycling.

Study Limitations
This study has several limitations. The participants in this study included college coeds ranging in age between 18 and 39 years of age. All participants included running and cycling as part of their exercise program. The time spent in each mode of training was not likely equal for each participant and quite variable between participants. The results of this study may not apply to other age groups or to individuals with more experience in either running or cycling. The results of a recent study [41] indicated that endurance-trained trail runners achieved similar VO 2 max values but lower maximal HR values during a treadmill exercise test that progressed in increments of incline, compared with one that progressed in increments of speed. The reported results [41] may suggest that the responses to a treadmill test that increases in speed or incline may reflect the type of training typically performed by the participant. The HR-VO 2 relationships observed in this study may be influenced by the nature of the exercise test performed.

Conclusions
The %HRR-%VO 2 R and the %HRR-%VO 2 max relationships during treadmill running and cycling in men and women are significantly different from the line of identity, and %HRR is more closely associated with %VO 2 max than to %VO 2 R. The %HRR accurately estimates %VO 2 max at intensities above 55% of VO 2 max. The variability in the intercepts and slopes of the HR-VO 2 relationships between individuals can lead to error in prescribing intensity of exercise for an individual. The inequality between %HRR and either %VO 2 max or %VO 2 R during treadmill running and cycling in males and females adds to the debate on the use of these relationships to prescribe intensity of aerobic exercise. Informed Consent Statement: Informed consent was obtained from all subjects involved in this study.

Data Availability Statement:
The data presented in this study and the R and JAGS code are available upon request from the corresponding author. The data are not publicly available.

Conflicts of Interest:
The authors declare no conflict of interest.