Both the HRnet and HRindex one-parameter models capture most of the variation with a single parameter, 98.4% for the HRnet model and 99.1% for the HRindex model. The residuals in the HRnet model, however, show a significant trend (Ramsey Regression Equation Specification Error test, P = 3.6 × 10−8) with the model overestimating in the mid range (HRnet = 40-80) and underestimating in the upper range (HRnet > 100) (Table 4). In contrast, residuals from the HRindex model show no trend (Ramsey Regression Equation Specification Error test, P = 0.534), and points distribute randomly around the fitted line for the full range of HRindex (Table 3 and Fig. 2F) confirming HRindex as the superior model.
The large number of studies included in the analysis permitted a subgroup analysis (Table 4). In view of the superiority of HRindex, the subgroup analysis was based on this model. The total sum of squares is 7272.4 (degrees of freedom (df) = 220). The base model with a single parameter accounts for 7181.8 (98.75%) leaving a residual of 90.6 (df = 219). Fitting separate lines for males, females, and both combined did not significantly improve the fit (ANOVA, P = 0.666). Similarly, there was no advantage of distinguishing between submaximal and maximal tests (P = 0.123) or between exercise types (treadmill, cycle, other) (P = 0.050). Accounting for use of β-blockers did not improve the model (P = 0.074). There was, however, a statistically significant improvement in the model accounting for pathology (abnormal, normal) (P = 0.009). Although statistically significant, the practical significance was minimal. The one-parameter model explains 98.75% of the variation in data, whereas using separate models for normal and abnormal pathology increases this by 0.04%-98.79%. For an HRindex of 2.5, the common model predicts a V˙O2 of 10.15 (0.08) METs, whereas the separate models predict 9.93 (0.11) METs for the pathology subgroup and 10.30 (0.09) METs for the normal subgroup.
Three potential methods of determining the HR-V˙O2 relationship (HRabsolute, HRnet, and HRindex) were assessed using a large data set incorporating a diversity of age, body weight, pathology, and drug effect for both sexes. Whereas both the HRnet and HRindex models explained most of the variation at 98.4% and 99.1%, respectively, there was a significant trend in the HRnet model residuals that was not observed in the HRindex model residuals, making the HRindex the preferred model. The fitted HRindex model is V˙O2 = kHRindex − (k − 1) with k = 6.10 ± 0.05, an equation that may be simply expressed as V˙O2 = 6HRindex − 5 with no major loss in accuracy.
Because of the ability to predict V˙O2 independent of testing method, the clinical utility of maximal HRindex should be considered. Determination of V˙O2max is necessary for risk stratification of severe symptomatic disease, e.g., chronic heart failure. Should heart transplantation be considered an appropriate therapeutic option for chronic heart failure patients, a V˙O2max of >14 mL·kg−1·min−1 (4 METs) usually allows for deferral of surgery (20). To ensure accurate assessment, measurement of gas exchange is necessary. Screening could be simplified by utilization of the HRindex. In this instance, a maximal HRindex of <1.5 (equivalent to 4 METs) could be used for risk stratification.
The HRnet and HRindex models have distinct physiological interpretations, which can be used to identify why HRnet fails is inferior to HRindex for the prediction of V˙O2. According to the HRnet model, after adjustment for weight, the slope of the HR-V˙O2 line of individuals is constant irrespective of fitness (Fig. 1). Therefore, in using HRnet, a defined increment of HR, e.g., 10 beats·min−1, will be associated with a similar increment of V˙O2 (0.85 METs) for both fit and unfit individuals. In contrast, the HRindex model indicates that a fit person (HRrest of 55 beats·min−1) will have a greater increment of V˙O2 (1.11 METs) than a less fit person (HRrest of 75 beats·min−1, 0.81 METs) for a similar HR increment of 10 beats·min−1.
The potential utility of the HRindex for large-scale community screening can be shown by a study of 13,344 people followed for an 8-yr period (4). This study demonstrated a relationship between V˙O2max and the risk of premature death. Men in the lowest quintile of fitness (<6.5 METs) had 3.44 times the risk of all-cause death compared with those in the highest quintile (a maximal fitness level of ≥10 METs). Identifying individuals in the high-risk category could be facilitated by use of the HRindex. On the basis of the reference equation (METs = 6HRindex − 5), the corresponding maximal HRindex for these high-risk individuals is approximately 2.0 (∼7 METs). This demonstrates that an inability to double HRrest may indicate a need for intervention with lifestyle change and/or further medical investigation.
The concept of maximal HRindex identifies that each individual has an "operating range" of HR from rest to maximum. For a middle-aged male with a V˙O2max of 10 METs, this corresponds to an HRindex of 2.5. By comparison, an elite endurance athlete is likely to achieve a fourfold increase in HRindex. Lance Armstrong (seven-time winner of the Tour de France) recorded a V˙O2max of 81.2 mL O2·kg−1·min−1 (23.2 METs) in September 2003 (10). Armstrong's maximal HR was 202 beats·min−1. Although the HRrest was not stated, the HRindex equation would predict this to be approximately 43 beats·min−1, a commonly observed HRrest in trained endurance athletes. The limitation of prediction based on HRnet is exposed at high levels of V˙O2: if Armstrong's HRrest and HRmax were used in the HRnet equation, the predicted V˙O2max would be 14.5 METs, a gross underprediction. This demonstrates the limitation of the HRnet equation when values of HRnet are >100 beats·min−1.
Although the linear relationship between V˙O2 and HR does not extend below HRflex, linearizing around the rest point, (HRindex, V˙O2rest) = (1,1), produced a superior model. To determine the significance of HRflex, an appreciation of the current use of HR to assess EE over extended periods (e.g., 24 h) is warranted. At low levels of EE (near resting/sedentary), the relationship between HR and V˙O2 becomes increasingly inaccurate because of the nonlinearity of HR-V˙O2 (7). In determining physical activity EE, time spent below HRflex is considered to be equal to the resting metabolic rate. The EE for time spent above the HRflex is calculated from individual HR-V˙O2 calibration curves (27). Unfortunately, there is no consensus as to the methodology that should be used to determine the HRflex. In addition, individual calibration of the HR-V˙O2 response is a time-consuming and costly process. Various studies have shown that the HRflex is frequently in the range of 8%-16% above HRrest, i.e., equivalent to an HRindex of 1.08-1.16 (18,21). Using the reference equation of METs = 6HRindex − 5, the corresponding MET levels for this HRflex range would therefore be 1.5-2.0 METs. For studies determining EE, HRindex therefore has the potential to 1) provide a surrogate for HRflex by using an HRindex of 1.15 (equivalent to approximately 2 METs) and 2) eliminate the need for HR-V˙O2 calibration.
The observed relationship between V˙O2 and HR involves two factors with independent prognostic power, namely, HRrest and maximal HRindex. Accurate calculation of HRindex is dependent on standardization of methodology for measuring HRrest. The prognostic importance of HRrest as a cardiovascular risk factor is well recognized, and the need for standardization of its measurement continues to be an issue (11). The current JNC 7 (2003) (Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure) recommendation advises a minimum of 5 min of rest in a seated position with a minimum counting period of 30 s (8). A review of the method of measurement in 56 studies (26) suggested the following requirements: 20 min of rest in a quiet visually balanced environment, with a temperature between 20°C and 24°C, in a seated position, with a 1-min recording of HR by physical palpation, repeated twice and averaged. In the analysis presented here, only 12 of the 60 studies documented how HRrest was obtained. Any variation in measured HRrest that occurred as a result of nonstandardized testing would contribute to the small observed variation in the data set (Fig. 2F). It is expected that standardization of the conditions under which HRrest is obtained would decrease the technical variation within the sample set and improve the robustness of the association even further. The potential errors of measurement of V˙O2 have been extensively reported and variations from 3% to 10% have been recorded in studies when validated against the criterion standard of the Douglas bag method (16,19).
A statistically robust relationship between HR and V˙O2 has been demonstrated when using HRindex. Both submaximal and maximal V˙O2 can be predicted using simple HR measurements. The relationship entails two components that have independent prognostic power, namely, HRrest and maximal HRindex. An inherent advantage of the HRindex method is that it is independent of mode of testing (cycle ergometry, treadmill testing, or free-range activity) and accounts for variables such as age, gender, body weight, fitness, and drug effect. The need for expensive equipment (and maintenance thereof) to measure V˙O2 directly is also avoided. The simplicity of HRindex and prediction of V˙O2 lends itself to clinical use, although there is a need for standardization of the measurement of HRrest. Continued development and validation of the basic equation of METs = 6HRindex − 5 will assist with screening to assess aerobic fitness and EE. The HRindex equation has been derived from 220 data points that are group averages; therefore, it is not possible to establish the prediction error of the model for an individual. Prediction errors for individuals can be determined from further studies.
No funding was received for this work.
The authors thank Prof. Edward Howley (Department of Kinesiology, Recreation, and Sport Studies, University of Tennessee, Knoxville, TN) for his critique of the draft of the article and the staff of the Gold Coast Hospital Library for their invaluable assistance in sourcing reference materials.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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NET HR; RESTING HR; OXYGEN UPTAKE; ENERGY EXPENDITURE; EXERCISE TESTING
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