Introduction
Maximum heart rate (HRmax), achieved when one's heart rate reaches the greatest number of beats per minute possible during exercise, has many applications. To facilitate oxygen demand and blood distribution requirements to the working tissues during maximal physical exertion, heart rate increases above resting values until reaching a plateau (i.e., HRmax). This natural cardiac response to exercise is largely mediated by autonomic innervation of the heart, wherein vagal withdrawal and sympathetic overdrive modulate contraction rate and intensity in response to work rate (27). HRmax generally decreases with age and is influenced by gender and fitness level (16,17,28). Although the most accurate method for determining HRmax requires maximal exercise testing, this is not often performed in practical settings and is often not justifiable. Instead, estimation of HRmax with the use of age prediction equations has become a common practice.
HRmax is often used to determine target heart rate zones at specific exercise intensities (1), as a variable within certain predictors of aerobic power (25), and as a criterion that a maximal effort was achieved during a graded exercise test (3). However, age-predicted HRmax formulas have been shown to provide wide ranges of individual error (24). Naturally, this can result in inaccurate exercise intensities, inflated estimates of aerobic power, and invalid criteria as a maximal effort determinate.
The majority of research pertaining to HRmax estimation has been performed in nonathletic men across a wide range of ages, with females being largely underrepresented (7). Of the limited research on this topic pertaining to women, general age-predicted HRmax formulas tend to significantly overestimate values in sedentary and college-age individuals (7,14). Furthermore, there is a paucity of data available that has evaluated the validity of HRmax prediction equations in young-adult female athletes. Specific research among this population is needed, especially considering that athletes typically have lower HRmax values compared with nonathletes (21). The purpose of this study was to determine the accuracy of 3 general and 2 female-specific age-predicted HRmax prediction equations in female collegiate athletes.
Methods
Experimental Approach to the Problem
HRmax values were measured in a group of female athletes (n = 30) by graded exercise testing and predicted with 5 age-predicted equations. Of the 5 prediction methods, the equations of Fox et al. (13), Astrand (2), and Tanaka et al. (24) are general models that are commonly used for estimating HRmax in nonathletic adults from the general population. The equations of Fairbarn et al. (12) and Gulati et al. (14) were developed to specifically be used for women. The accuracy of the 5 HRmax prediction equations were compared as independent variables with observed HRmax derived from graded exercise testing, which served as the dependent variable.
Subjects
Thirty female collegiate athletes (age = 21.5 ± 1.9 years, age range = 19–25 years, height = 164.7 ± 6.6 cm, weight = 61.3 ± 8.2 kg) from the National Association for Intercollegiate Athletics sports volunteered to participate in the study. The study was approved by the University's Institutional Review Board for Human Participants. Each participant provided written informed consent. The participants were recruited from the University's soccer (n = 15), tennis (n = 8), and cross-country (n = 7) teams. Each participant completed a health history questionnaire, which indicated that they were free from cardiopulmonary, metabolic, and orthopedic disorders. Data collection occurred during any weekday between 7:00 AM and 9:00 AM, as close as possible to awakening from sleep. Each participant was required to report to the laboratory following an overnight fast, although the consumption of water (12 oz) was allowed. They were told to avoid consuming stimulants (e.g., caffeine) or depressants (e.g., alcohol) and refrain from strenuous exercise for 24 hours before data collection. All of the participants verbally agreed to the testing conditions. The study took place during the off-season when no athletic competitions occurred.
Maximal Exercise Testing
Each participant completed a maximal graded exercise test on a treadmill (Trackmaster; Full Vision, Inc., Carrollton, TX, USA). The Bruce protocol was used, which involved a series of 3-minute stages with consecutive increases in speed and grade. Expired gas fractions were evaluated with a metabolic cart (ParvoMedics TrueOne 2400, Sandy, UT, USA). The test was terminated when the participant reached at least 2 of the criteria for maximal oxygen consumption (V[Combining Dot Above]O2max) as follows: a plateau in V[Combining Dot Above]O2 (±2 ml·kg−1·min−1) with increasing work rate, respiratory exchange ratio ≥1.10, ratings of perceived exertion of at least an 8 of 10, or volitional fatigue.
Heart rate was monitored continuously during the test with an electronic heart rate monitor (Polar Electro Oy, Kempele, Finland). The heart rate monitor was moistened and fitted to each participant's chest at the level of the xiphoid process. When V[Combining Dot Above]O2max was reached, the highest HR value was recorded as observed HRmax. Predicted HRmax was determined with the following equations of Fox et al. (13), Astrand (2), Tanaka et al. (24), Fairbarn et al. (12), and Gulati et al. (14):
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Statistical Analyses
All data were analyzed with a software package (SPSS version 22.0, Somers, NY, USA) and spreadsheet (Microsoft Excel 2010 Microsoft Corp., Redmond, WA, USA). Mean values and standard deviations were determined for the observed and predicted HRmax values, which were compared with repeated-measures analysis of variance, followed up with paired T-tests to determine where differences existed. A Bonferroni's adjusted p value was applied to reduce the chances of obtaining a type I error when multiple pairwise tests were performed, which resulted in an adjusted alpha level for significance of p < 0.01. Cohen's d statistic was calculated as the effect size of the differences in observed and predicted HRmax values (8), and Hopkin's scale of magnitude was used where an effect size of 0–0.2 was considered trivial, 0.2–0.6 was small, 0.6–1.2 was moderate, 1.2–2.0 was large, >2.0 was very large (15). The standard error of the estimate (SEE), total error (TE), and constant error (CE) were calculated for each of the predicted versus observed HRmax values. The method of Bland-Altman was used to identify the 95% limits of agreement between the observed and predicted HRmax values (5). Significance for the trend between the mean and differences of each predicted versus actual HRmax was determined as alpha <0.05.
Results
Observed and predicted HRmax values are shown in Table 1. There was no significant difference between observed mean HRmax and that of the Fairbarn and Gulati equations. All of the other equations significantly (p < 0.01) overestimated mean HRmax values. The Cohen's d statistic indicated small effect sizes for Fairbarn and Gulati, large effect sizes for Tanaka, and very large effect sizes for Fox and Astrand. The SEE was similar among the prediction equations (between 5.0 and 5.4 b·min−1), but the TE was smallest for Fairbarn and Gulati (5.3 b·min−1 for each) and largest for Fox and Astrand (13.9 and 13.3 b·min−1, respectively). The CE was smallest for Gulati (1.2 b·min−1) and Fairbarn (1.6 b·min−1) and largest for Fox (12.6 b·min−1) and Astrand (12.2 b·min−1). Table 2 represents the number of participants that each age-predicted HRmax equation provided overestimated values.
Table 1: Comparison of actual and predicted maximal heart rate (n = 30).*
Table 2: Number of subjects for which each equation provided overpredicted HRmax (n = 30).
Bland-Altman Plots are shown in Figures 1–5. The limits of agreement (±1.96 SD of the CE) were comparable for all of the prediction equations (values ranging between 9.9 and 10.5 b·min−1). Additionally, the trend between the mean and difference of the HRmax values were significantly strong and negative for all prediction equations (r values varying from −0.74 to −0.90).
Figure 1: Bland-Altman plot comparing observed HRmax and the age-predicted HRmax values of Fox (n = 30). The middle solid line represents the constant error. The 2 outside dashed lines indicate the 95% confidence interval of the difference and their mean values. The dashed-dotted regression line represents the trend between the difference of the methods and their mean.
Figure 2: Bland-Altman plot comparing observed HRmax and the age-predicted HRmax values of Astrand (n = 30). The middle solid line represents the constant error. The 2 outside dashed lines indicate the 95% confidence interval of the difference and their mean values. The dashed-dotted regression line represents the trend between the difference of the methods and their mean.
Figure 3: Bland-Altman plot comparing observed HRmax and the age-predicted HRmax values of Tanaka (n = 30). The middle solid line represents the constant error. The 2 outside dashed lines indicate the 95% confidence interval of the difference and their mean values. The dashed-dotted regression line represents the trend between the difference of the methods and their mean.
Figure 4: Bland-Altman plot comparing observed HRmax and the age-predicted HRmax values of Fairbarn (n = 30). The middle solid line represents the constant error. The 2 outside dashed lines indicate the 95% confidence interval of the difference and their mean values. The dashed-dotted regression line represents the trend between the difference of the methods and their mean.
Figure 5: Bland-Altman plot comparing observed HRmax and the age-predicted HRmax values of Gulati (n = 30). The middle solid line represents the constant error. The 2 outside dashed lines indicate the 95% confidence interval of the difference and their mean values. The dashed-dotted regression line represents the trend between the difference of the methods and their mean.
Discussion
The purpose of this study was to determine the accuracy of several age-based HRmax prediction equations in female collegiate athletes. The findings indicated that substantial intermethod discrepancy exists when using age-predicted HRmax equations among a heterogeneous group of young collegiate female athletes. Of the equations included in the study, the Fairbarn and Gulati methods provided the closest estimates of mean observed HRmax, with the lowest CE and TE values. The other equations provided significantly overestimated HRmax values, on average, compared with the criterion. For example, the Fox and Astrand methods overpredicted mean HRmax by more than 12 b·min−1, and each provided the highest CE and TE values. All of the equations provided large limits of agreement, with 95% confidence intervals (i.e., ±1.96 SD) ranging approximately 10 b·min−1 above and below their respective mean error. In addition, the trend between the mean and difference of predicted versus actual HRmax values was significant and negative for all equations. This finding indicates that the age-predicted equations provided a greater overestimation of HRmax, as the observed values decreased across the group.
The results of this study suggest that Fairbarn and Gulati methods are most appropriate for predicting the average HRmax in a group of college-age female athletes. However, because of the wide limits of agreement and tendency to overpredict especially among participants with lower observed HRmax, the equations for predicting individual HRmax within this population should be used with caution.
The Fox equation (220 − age) is the most popular method for estimating HRmax. However, the validity of the equation has been questioned primarily because it was observationally derived from reviewed research related to physical activity and heart disease and not from original data using regression modeling (22). The equation, along with the other general models of Astrand and Tanaka, has provided overpredicted values, on average, in women (7,14,23). It is because of this that a few studies have resulted in modified prediction methods that are specific to women, but the research has occurred primarily in nonathletic participants (12,14).
Fairbarn et al. (12) developed several age-predicted HRmax equations based on data from 231 men and women that were equally divided in 20-year increments between 20 and 80 years of age. The authors reported that the female-specific equation best predicted HRmax in women between the ages of 20 and 40 years (12). More recently, Gulati et al. (14) sought to characterize the cardiovascular response to maximal exercise testing in 5,437 asymptomatic, low-risk, middle-age women. A single equation was derived from the study that best predicted HRmax across the large cohort of women (14). The Fairbarn and Gulati equations were cross-validated in the current sample of athletic collegiate female participants. The 2 equations were not significantly different compared with the observed HRmax. However, a common feature of all the equations, including the female-derived models, was the tendency to provide overpredicted values in the participants with lower observed HRmax. This is most likely due to athletes typically displaying lower HRmax values compared with the general population (21).
The HRmax for female athletes reported in the literature varies. Other studies involving maximal exercise testing in young-adult female athletes demonstrated mean HRmax values that are comparable with (9,11,20,26,29), lower than (4,6), or higher than (18) the average values found in the current investigation. The discrepancy is possibly related to differences in athletic background of participants and exercise testing modalities. Therefore, the results of this study may not be able to be extrapolated to all female athletes of various competitive sports. However, because of the inconsistent observed HRmax across studies, inaccurate estimates of age-predicted HRmax equations in collegiate female athletes are perhaps common.
The use of HRmax is prevalent in mainstream fitness and strength and conditioning settings for many reasons. Primarily, intensity for a given aerobic modality is often determined based on percentage of HRmax. An overestimated value could provide a targeted exercise intensity that is near maximal, which may result in overreaching and increased injury potential. For purposes of prescribing training heart rate ranges, errors of less than 8 b·min−1 are deemed acceptable (22). All of the equations that were analyzed in the study provided estimates of error that were larger than this recommendation (i.e., 95% confidence interval of the CE was approximately ±10 b·min−1).
Furthermore, HRmax is used within many popular methods to estimate V[Combining Dot Above]O2max (10,11,19,25). Inflated prediction values could result in large errors of estimated V[Combining Dot Above]O2max. Previous work has indicated that acceptable HRmax prediction errors of less than 3 b·min−1 are necessary for acceptable accuracy when estimating for V[Combining Dot Above]O2max (22). The large estimated error for the age prediction equations analyzed in this study suggests that these methods would not be appropriate for estimating V[Combining Dot Above]O2max in this population.
In addition, observed HR being within 10 b·min−1 of age-predicted HRmax is often used as a criterion for determining if a maximal effort was given on a graded exercise test (1,21). The Fox and Astrand equations are commonly used in exercise testing laboratories for this purpose. Of the 30 participants, the equations of Fox, Astrand, and Tanaka overpredicted HRmax by 10 b·min−1 or greater on 21, 21, and 9 occasions, respectively (Table 2). None of the estimates of Fairbarn and Gulati were beyond this margin (Table 2).
The lack of precision of the prediction equations is most likely related to the assumption that HRmax is correlated with age. Although this may be the case in large groups of heterogenous subjects, others have questioned the accuracy of age prediction equations in homogenous age groups (7). In the current sample, there was a wide range of observed HRmax (178–194 b·min−1) but a tight range for age (19–24 years for 29 participants, with 1 participant at 28 years). Retrospective zero-order correlation procedure was performed for HRmax and age, which demonstrated a coefficient that was near 0 (r = 0.01) in part because of the low variability in age in our sample. Therefore, age-based equations may not be appropriate for estimating HRmax in collegiate athletes. Instead, when graded exercise testing is not feasible, practitioners might consider exercise-based methods for deriving HRmax in a young-adult sample, such as 2 × 200 m sprint trials reported by Cleary et al. (7).
In any case, the development of appropriate prediction methods of HRmax among collegiate female athletes is needed. This will require additional research involving larger sample sizes and more types of athletes, as this study was limited to moderate sample size of only soccer, cross-country, and tennis athletes. Therefore, the findings may only be generalized to female athletes from these 3 sports. Until more research is completed, the female-specific equations of Fairbarn et al. (12) and Gulati et al. (14) may be appropriate for estimating the mean HRmax for a group of female collegiate athletes. However, similar to the general equations, they might provide overestimated values for an individual athlete.
Practical Applications
Personal trainers, strength and conditioning specialists, exercise physiologists, and fitness enthusiasts should be aware that the most accurate method for determining HRmax is with a maximal graded exercise test. Because that is often difficult to use within practical settings, HRmax is more commonly predicted with age-based equations. Most of the established models were validated in untrained men. Practitioners should be aware of this major limitation, as the merit of any prediction model for specific individuals depends on whether it was developed among participants with similar characteristics. The popular equations of Fox et al. (13), Astrand (2), and Tanaka et al. (24) significantly overestimated HRmax on average. The female-specific HRmax equations of Fairbarn et al. (12) and Gulati et al. (14) provided the most accurate mean values. However, all of the equations that were analyzed in the study provided large limits of agreement and showed tendencies to overpredict HRmax, especially among the participants with lower observed values. The novel findings of the study highlight the need for additional research designed to determine appropriate methods for predicting HRmax in female athletes.
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