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HR Index-A Simple Method for the Prediction of Oxygen Uptake


Medicine & Science in Sports & Exercise: October 2011 - Volume 43 - Issue 10 - p 2005-2012
doi: 10.1249/MSS.0b013e318217276e
SPECIAL COMMUNICATIONS: Methodological Advances

Purpose: Energy expenditure measured in METs is widely used in cardiovascular medicine, exercise physiology, and nutrition assessment. However, measurement of METs requires complex equipment to determine oxygen uptake. A simple method to predict oxygen uptake on the basis of HR measurements without requirement for gas analysis, movement-recording devices, or exercise equipment (treadmills, cycle ergometers) would enable a simple prediction of energy expenditure. The purpose of this study was to determine whether HR can be used to accurately predict oxygen uptake.

Methods: Published studies that reported a measured resting HR (HRrest), a measured activity HR (HRabsolute), and a measured oxygen uptake (mL O2·kg−1·min−1) associated with the HRabsolute were identified. A total of 220 data sets were extracted from 60 published exercise studies (total subject cohort = 11,257) involving a diverse range of age, pathophysiology, and the presence/absence of β-blocker therapy. Net HR (HRnet = HRabsolute − HRrest) and HR index (HRindex = HRabsolute/HRrest) were calculated from the HR data. A regression analysis of oxygen uptake (expressed as METs) was performed against HRabsolute, HRnet, and HRindex.

Results: Statistical models for the relationship between METs and the different HR parameters (HRabsolute, HRnet, and HRindex) were developed. A comparison between regression analyses for the models and the actual data extracted from the published studies demonstrated that the best fit model was the regression equation describing the relationship between HRindex and METs. Subgroup analyses of clinical state (normal, pathology), testing device (cycle ergometer, treadmill), test protocol (maximal, submaximal), gender, and the effect of β-blockade were all consistent with combined data analysis, demonstrating the robustness of the equation.

Conclusions: HRindex can be used to predict energy expenditure with the equation METs = 6HRindex − 5.

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1Department of Rehabilitation, Robina Hospital, Queensland, AUSTRALIA; 2University of Wisconsin School of Medicine and Public Health, Milwaukee, WI; 3Aurora Cardiovascular Services, Aurora Sinai/Aurora St. Luke's Medical Center, Milwaukee, WI; and 4Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Queensland, AUSTRALIA

Address for correspondence: John Richard Wicks, M.D., P.O. Box 7833 GCMC Bundall 4217 Australia; Email:

Submitted for publication December 2010.

Accepted for publication February 2011.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal's Web site (

Measurement of oxygen uptake (V˙O2) is an integral part of cardiopulmonary assessment and of estimating energy expenditure (EE) over extended periods of time. Because physical measurement requires the use of expensive complex gas analysis equipment, this estimation of EE is frequently based on V˙O2 prediction. With exercise testing, V˙O2 is frequently predicted from speed and incline of a treadmill or from watts with cycle ergometry and is often expressed in METs (13). Prediction formulae from reference texts and the American College of Sports Medicine's publications are commonly used, although these publications advise against the use of these formulae (derived from steady-state measurement) for the prediction of non-steady-state maximal activity (1,9,12,17). Inaccuracies are further compounded by the use of handrail support with treadmill testing. This practice is a more likely occurrence in those with severe functional impairment such as congestive heart failure (CHF) and can reduce V˙O2 by as much as 15%-20% (3).

Use of doubly labeled water is the gold standard for determining EE; however, this technique is costly and time-consuming. Therefore, use of HR as a predictive tool has been extensively investigated on the basis of the linear relationship between HR and V˙O2. At low levels of activity, the linear relationship between HR and V˙O2 breaks down. This is problematic because when estimating 24-h EE, a considerable amount of time is spent at low levels of physical activity (<2 METs), particularly in sedentary populations (27). The HR defining loss of linearity is the flex HR (HRflex) (7,24). This is called the average of the highest resting HR (HRrest) and the lowest activity HR (HRabsolute), with activities below HRflex considered to approximate 1 MET (24).

Currently, HR-the simplest physiological variable-has no established place for the prediction of EE. This limitation is based on the commonly accepted factors that influence the HR-V˙O2 relationship, namely, fitness, drug effect (particularly β-blockade), age, gender, and environmental factors (2,22). In attempting to limit the effect of these variables, net HR (HRnet), equal to absolute HR minus rest HR (HRabsolute − HRrest), has been used (2,5,15,23,28). Andrews (2) showed that this approach negated the effect of age, gender, and fitness in the subjects who were studied. A third HR variable, HR index (HRindex), equal to absolute HR divided by rest HR (HRabsolute/HRrest), has been used in one study to determine its relationship to V˙O2max (25). In another study, HRindex was used in conjunction with movement recorders and showed a remarkable consistency in predicted EE during seven continuous days of occupational and weekend activity (14). However, in this case, HRindex was not used for the prediction of V˙O2.

This study used existing data to evaluate the HR-V˙O2 relationship using the three variables, namely, HRabsolute, HRnet, and HRindex, and to assess the application of these variables in both exercise testing and prediction of EE. The potential relationship of HRabsolute, HRnet, and HRindex with V˙O2 was considered using a hypothetical model of a 50-yr-old sedentary male. This model was chosen because it is representative of a typical individual who may be at risk of developing cardiovascular disease. A predicted V˙O2max of 35 mL O2·kg−1·min−1 (10 METs) was assumed from equations developed by Bruce et al. (6). An age-predicted HRmax of 170 beats·min−1 was based on the widely used formula of 220 − age, and an HRrest of 68 beats·min−1 was considered appropriate. On the basis of the linear response of HR to V˙O2, models for HRabsolute, HRnet, and HRindex were constructed from rest (1 MET) to maximum (10 METs) (Table 1).



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It is generally accepted that, above HRflex, there is a linear relationship between HR and V˙O2 such that

If V˙O2 is expressed in METs, this equation is normalized for weight. Seeking a correlation across a population, it would be appropriate to linearize around the flex point (HRflex, V˙O2flex). Because HRflex is difficult to determine, we will extend the correlation and linearize equation 1 around the resting point, HRrest.

Here, V˙O2∼rest is a fitting constant approximating 1 MET, as opposed to a measured EE. It should be stressed that equation 2 is not intended for fitting EE below HRflex.

In considering the linear relationship between HR and V˙O2, there are two possible scenarios for the slope, b (Fig. 1).



Scenario 1: the slope is constant across the population with the HR-V˙O2 relationship consisting of multiple parallel lines independent of a range of factors such as fitness, cardiopulmonary pathology, and drug effect (β-blockade).

Scenario 2: the slope is not constant, being influenced by fitness, pathology, and drug effect, with the HR-V˙O2 relationship being a series of nonparallel lines.

If b is constant (scenario 1), equation 2 simplifies to

Alternatively, the slope b may be assumed to be inversely proportional to HRrest (scenario 2):

where k is a species-related constant, which is dependent on body size and has been extensively researched in allometric scaling of mammals (29). Substituting equation 4 into equation 2,

If V˙O2∼rest is equal to the true resting EE (per definition 1 MET), equations 3 and 5 simplify to

(with V˙O2absolute expressed as METs).

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Suitable studies were obtained through both MEDLINE and Internet (Google Scholar) searches. Eligibility criteria included 1) measurement of V˙O2 using conventional gas analysis equipment with V˙O2 being expressed as milliliters per kilogram per minute, 2) HR associated with the measured V˙O2 (either maximal or submaximal), and 3) measured HRrest. Only 12 of the 60 studies selected included a statement on the conditions under which the resting HR was obtained. The specific conditions stated were highly variable between the 12 studies, with a resting period from 2 to 90 min in either a seated or a supine position. V˙O2 measurements were converted to METs using the definition V˙O2/V˙O2rest, with V˙O2rest equal to 3.5 mL O2·kg−1·min−1. These variables allowed for the HR-METs relationship to be assessed using HRabsolute, HRnet, and HRindex. A basic requirement of all studies was that of an intact autonomic nervous system for HR regulation. Data from heart transplant patients did not fit the model and were therefore excluded from the analysis.

Details of the selected studies are listed in Table 2 (references for each study are available in Table 1 of the Supplemental Digital Content 1, Cardiovascular disease (coronary artery disease, cerebrovascular disease/stroke, peripheral vascular disease, and adult congenital heart disease) was documented in 13 studies. Chronic heart failure was considered a separate disease entity and was documented in 20 studies. Other conditions included were chronic obstructive pulmonary disease (two studies), primary pulmonary hypertension, spinal cord injury, diabetes mellitus, obesity, and aging and frailty (all one study each). Data relating to healthy subjects were present in 26 studies. Factors influencing HR that were present in these studies included β-blockade (24 studies), physical training (21 studies), pregnancy, smoking, hypoxia, altitude, anemia, erythropoietin treatment, prolonged bed rest, and a wide range of age (10-85 yr).



An upper limit of 14 METs (V˙O2 of 49 mL O2·kg−1·min−1) was chosen as being representative of a level that could be achieved by a middle-aged person in response to endurance training. The range of workload studied (1-14 METs) is therefore an appropriate range of V˙O2 likely to be encountered in a clinical setting.

V˙O2max (or V˙O2peak) data were available in 50 studies with submaximal data in 15 studies. Treadmill testing was used in 28 studies, cycle ergometry in 30 studies, and other methods (walking, arm cranking, occupational work, activities of daily living, and upper and lower limb exercises) in 6 studies. The majority of studies used metabolic gas analysis for determination of V˙O2.

Regression analysis was performed using the statistics software package R ( Residual trend analysis was performed using the Ramsey Regression Equation Specification Error test.

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Sixty studies with a total cohort of 11,257 subjects met the inclusion eligibility criteria. Characteristics of these studies are shown in Table 2. From the 60 studies, 220 data points with HRabsolute and derived HRnet and HRindex were extracted. Each data point is the reported mean value for the relevant subgroup in a study. The number of subjects contributing to a data point ranged from 5 to 1909, with a median of 22. In studies where data for the entire cohort were given in addition to that of subgroups, only the subgroup data were used so as to avoid duplication.

The relationship of the three HR variables (HRabsolute, HRnet, and HRindex) to V˙O2 for all data from all 60 studies is shown in Figure 2 and summarized in Table 3. As expected, the HRabsolute model is the least satisfactory, describing only 77% of the variation in data. For the HRnet and HRindex models, we first tested if the intercept, V˙O2∼rest, could be assumed to be equal to the resting metabolic rate or 1 MET. For both models, the one-parameter model with V˙O2∼rest ≈ V˙O2rest = 1 was superior to the two-parameter model with V˙O2∼rest ≠ V˙O2rest.





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.

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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).

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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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