Background: Prescription of an appropriate exercise training intensity is critical to optimise the outcomes of pulmonary rehabilitation; however, prescribing cycle ergometry training is challenging if peak work is unknown. Recently two studies reported regression equations which allow estimation of peak cycle work rate from the 6-minute walk distance (6MWD) in chronic obstructive pulmonary disease (COPD). Objectives: To compare estimates of peak work and target training work rate (60% peak) obtained from these equations. Methods: Sixty-four (38 male) subjects, mean ± SD age 70 ± 8 years and FEV1 49 ± 18% predicted with COPD performed the 6-minute walk test according to a standardised protocol. Estimates of peak work were obtained using the published equations and agreement was examined using Bland and Altman plots. Results: Mean 6MWD was 376 ± 86 m compared to 464 ± 110 m and 501 ± 83 m in samples used to derive the equations. There was substantial variation in estimates of peak work between equations (range 1–75 Watts difference) with a coefficient of variation of 35%. Differences were greater in men than in women (p < 0.001). The Luxton equation predicted higher peak work than the Hill equation in younger subjects and at work rates over 50 Watts. Estimated training work rate differed by more than 20 Watts in 18 subjects (28%). Conclusions: This comparison of reference equations for predicting peak cycle work rate from 6MWD indicates substantial variation between methods that differs systematically across the range of work rates. Further research is required to validate the equations and assess their utility for exercise prescription in pulmonary rehabilitation.

Aerobic exercise training is a crucial component of pulmonary rehabilitation for patients with chronic obstructive pulmonary disease (COPD) and requires careful attention to prescription of an appropriate training load. Current recommendations suggest that an intensity of at least 60% of peak work (Wpeak) is required to produce a physiological training effect [1]. However, the ability to accurately prescribe exercise intensity in the clinical setting is frequently constrained by the available assessment tools. Many programs do not have the resources for patients to undergo symptom-limited incremental cycle ergometry from which direct measurements of Wpeak can be obtained, relying instead on field walking tests such as the 6-minute walk test [2,3,4]. The ability to prescribe accurate and effective cycle training work rates from field walking tests would be of significant clinical and practical benefit.

Recently, two studies have investigated the relationship between a direct measurement of Wpeak and data obtained from the 6-minute walk test in subjects with COPD [5,6]. Peak work could be estimated from equations using 6-minute walk distance (6MWD) and height [5], 6-minute walk-work (6MWW) [5] or 6MWW, age and gender [6]. 6MWW is defined as the product of 6MWD and body weight. This may be a better estimate of the energy expenditure required to perform the test than walking distance alone [7]. These equations explained 67, 60 and 80% of the variance in Wpeak, respectively. Both studies include populations that were broadly representative of patients with COPD undergoing pulmonary rehabilitation and recruited individuals with a range of 6MWDs (192–692 m in Hill et al. [5] and 385–695 m in Luxton et al. [6]). It is unclear whether the resulting estimates are similar and which equation should be used in clinical populations. The aim of this study was to compare the Wpeak estimates obtained from the 2 predictive equations in a clinical population of individuals with COPD undergoing pulmonary rehabilitation.

Adults with COPD were recruited from the pulmonary rehabilitation programs at 2 tertiary hospitals. All were subjects in a study investigating the measurement properties of the 6-minute walk test. The research protocol was approved by the Human Research Ethics Committee at each institution and written informed consent was obtained prior to testing.

Subjects were included if they had a diagnosis of COPD according to GOLD criteria [8] and were in a clinically stable state. Exclusion criteria were supplementary oxygen therapy, requiring a gait aid to complete the 6-minute walk test or significant comorbidities that would adversely affect walking ability (severe musculoskeletal, neurological or cardiovascular disorders).

The 6-minute walk test was performed at the commencement of the pulmonary rehabilitation program according to the American Thoracic Society guidelines on a 30-metre straight track [9]. Standardised instructions were given prior to the test and standardised encouragement was provided each minute. Pulse rate and oxygen saturation were monitored continuously throughout the test using a pulse oximeter. Two tests were performed separated by 30 min of rest and the best distance was recorded.

Estimates of peak work rate were obtained using the following equations:

Hill equation 1: Wpeak = (0.122 × 6MWD) + (72.683 × height) – 117.109 [5].

Hill equation 2: Wpeak = 17.393 + (1.442 × 6MWW [km·kg–1]) [5].

Luxton: Wpeak = 103.217 + (30.50 × gender) + (–1.613 × age) + (0.002 × 6MWW [m·kg–1]) [6].

In the above equiations, height is given in metres and gender is given a value of 1 for male and 0 for female.

Agreement between the 2 methods was assessed using Bland and Altman plots [10]. The relationship between subject mean and within-subject differences was examined using Kendall’s tau. Where a significant relationship was found, the data were log10 transformed. The within-subject coefficient of variation was calculated as aσw – 1, where aσw is the antilog10 of the within-subject standard deviation [11]. The analyses were repeated after: (1) excluding a subset of subjects (n = 9) who would not have met the inclusion criteria of Hill et al. [5] (FEV1 <15 or >70% predicted or oxygen desaturation <80% during the walk test), and (2) excluding those subjects (n = 30) with 6MWDs outside the range used to derive the Luxton equation [6] (6MWD <385 m). The effects of gender and age on the magnitude of the difference between equations were examined using independent samples t tests and Pearson’s product-moment correlation coefficient, respectively. The target training work rate of 60% Wpeak was calculated according to each equation. Data were analysed using SPSS version 17.0.

Characteristics of the 64 included subjects are shown in table 1. According to GOLD criteria [8], 3 subjects had mild disease, 29 had moderate disease, 22 had severe disease and 10 had very severe disease. The average FEV1 was 49% predicted, compared to 37 and 52% predicted respectively in the studies from which the prediction equations were derived [5,6]. The subjects were also slightly older (mean 70 years vs. 68 years [5] and 65 years [6]) and had a lower average 6MWD (370 m vs. 464 m [5] and 508 m [6]).

Table 1

Demographic characteristics of subjects (n = 64)

Demographic characteristics of subjects (n = 64)
Demographic characteristics of subjects (n = 64)

Agreement between the predicted peak cycle work of the subjects based on the Hill [5] and Luxton [6] equations is shown in figures 1a and b. A systematic relationship between the difference and mean values was evident across the range of values (Kendall’s τ = 0.66, p < 0.001), with the Luxton equation [6] predicting a lower Wpeak than either of the Hill equations [5] at mean values less than 50 Watts and higher Wpeak at mean values of greater than 50 Watts. The coefficient of variation, calculated using log10 transformed data, was 35%. A similar relationship was evident when 9 subjects who would not have met the inclusion criteria of Hill et al. [5] were excluded from the analysis (fig. 2a), with a coefficient of variation of 35%. The relationship also persisted when those subjects with 6MWDs less than 385 m (the minimum value in Luxton et al. [6]) were excluded (fig. 2b), with a coefficient of variation of 29%.

Fig. 1

Agreement between reference equations. a Luxton [6] and Hill (equation 1, walk distance) [5]. b Luxton [6] and Hill (equation 2, 6MWW) [5].

Fig. 1

Agreement between reference equations. a Luxton [6] and Hill (equation 1, walk distance) [5]. b Luxton [6] and Hill (equation 2, 6MWW) [5].

Close modal
Fig. 2

Agreement between reference equations in subgroups. a Subjects who met the inclusion criteria for Hill et al. [5] (n = 55). b Subjects with 6WMD in the range of Luxton et al. [6] (≥385 m, n = 34).

Fig. 2

Agreement between reference equations in subgroups. a Subjects who met the inclusion criteria for Hill et al. [5] (n = 55). b Subjects with 6WMD in the range of Luxton et al. [6] (≥385 m, n = 34).

Close modal

Differences between equations were greater in men (mean difference Luxton – Hill 27 Watts, 95% CI 21–34 Watts) than in women (–8 Watts, –14 to –1 Watts; p < 0.001 compared to men). The coefficient of variation for women was 25%, compared to 47% in men. Age was also associated with the difference between equations, with the Luxton equation [6] predicting higher Wpeak than the Hill equation [5] in younger subjects and lower Wpeak in older subjects (r = –0.54, p < 0.001; fig. 3). The estimated target training workload of 60% Wpeak varied by more than 10 Watts between methods in 34 subjects (50%) and by more than 20 Watts in 18 subjects (26%).

Fig. 3

Relationship between age and difference in estimates of peak work between equations.

Fig. 3

Relationship between age and difference in estimates of peak work between equations.

Close modal

This study shows that Wpeak estimated from the 6MWD varies considerably according to the chosen reference equation. Differences between methods were as large as 75 Watts and varied systematically according to the mean value of Wpeak. Coefficients of variation were large and the target training intensity of 60% Wpeak varied by more than 20 Watts in 26% of the subjects.

The reference equations for predicting Wpeak were derived from samples of subjects with COPD that appear broadly representative of the population and were similar to the characteristics of subjects in the present study. Both the studies that derived the equations and the current study were carried out in Australia [5,6]. However, the samples are relatively small (n = 22 and n = 50) and may not reflect the range of characteristics of people with COPD in the population. The largest differences in Wpeak estimates between methods were seen in subjects with characteristics at the extremes of the range. For instance, a difference of 75 Watts in estimated Wpeak was evident in the youngest subject (49 years) and a difference of 42 Watts in the heaviest subject (113 kg). Important differences between equations were also evident according to gender and age. Differences between estimates of Wpeak were smaller in women (fig. 1), resulting in a smaller coefficient of variation. The Luxton equation [6] predicted a greater Wpeak in younger subjects. This was the only equation to include age and gender [6], factors which may contribute to variation due to differences in muscle mass.

On average, functional exercise capacity in our sample was lower than that reported in the 2 previous studies. The better functional status of subjects in the previous studies may reflect the more onerous nature of those protocols, where all subjects were required to undertake a maximal symptom-limited cycle ergometry test and attend the laboratory on more than one testing occasion. Subjects in our study were recruited from a clinical population undergoing pulmonary rehabilitation and the study did not require any additional testing. Although we included a greater number of subjects with more impaired 6MWDs, all subjects achieved distances within the range of 6MWDs reported by Hill et al. [5]. In contrast, the lowest 6MWD in the study of Luxton et al. [6] was 385 m and 30 of our subjects (47%) had walking distances below this. The applicability of this equation to a clinical sample such as ours, characterised by greater functional limitation, is therefore uncertain.

Both the studies from which reference equations were derived excluded patients who used supplemental oxygen or required a gait aid to complete the walking test. We used the same exclusion criteria to ensure that the equations were applied to a sample with similar characteristics. Hill et al. [5] also excluded subjects with an FEV1 <15% predicted or greater than 70% predicted, whereas these subjects were not excluded by Luxton et al. [6]. However, the systematic variation between reference equations persisted if data from subjects meeting these criteria were removed from the analyses, suggesting that other sources of variation were responsible for the observed differences.

There are small but important methodological differences in the test procedures which may account for some of the unexplained variation between reference equations. Both studies used step protocols for the cycle ergometry test; however, one study used individually determined work rate increments of 5–20 Watts, with the majority of subjects using increments of 10–20 Watts [6] whereas the other used standardised increments of 10 Watts for all subjects [5]. It has previously been demonstrated that although the choice of workload increments does not affect peak oxygen uptake (VO2peak), larger increments achieve higher peak workloads [12,13]. Peak work was defined as the highest work rate achieved for a maximum of 30 s in one study [5], whereas Luxton and coworkers [6] required the final workload to be sustained for 15 s and assigned a percentage of the final increment depending on the proportion of the minute that was completed. These different strategies would have affected the Wpeak achieved. Although both studies used robust 6-minute walk test protocols with standardised instructions and encouragement, one used a straight track [5] whilst the other used a continuous oval track [6]. These different track layouts may have had a small but significant effect on recorded distances [14]. Subjects who desaturated to less than 80% during the walk test were excluded from analyses in one study [5] whereas in the other study no subjects desaturated below 80% [6]. In addition, subjects in one trial were required to wear a portable metabolic monitoring system and mask to measure exhaled gases [6]. Whether this impacts on walking distance is not clear. Finally, different selection rules for variables included in the regression equations were applied, which may have affected the final choice of predictors.

It is not possible to determine which prediction equation provided the most accurate assessment of Wpeak in our subjects as an incremental cycle ergometry test was not performed. Whilst this limits the conclusions that can be drawn, it is representative of usual clinical practice in many pulmonary rehabilitation programs where the resources to perform such tests are often not available [3,4]. This study suggests that further validation of the equations in large prospective cohorts is required before clinicians can confidently prescribe exercise training loads from estimates of Wpeak derived from the results of a 6-minute walk test. However, the equations do provide a general estimate of the initial training work rate for patients with similar demographic characteristics who are undergoing pulmonary rehabilitation. Until further validation studies are available, clinicians should consider using the equation derived from the sample with the characteristics that most closely match their clinical population. Estimated training work rates should be refined by experienced clinicians using careful patient monitoring, to determine the patient’s tolerance to the training load with adjustments made according to symptoms and physiological responses.

In conclusion, this comparison of recently published equations for predicting Wpeak from the 6-minute walk test indicates substantial variation between estimates that differs systematically across the range of work rates. The target intensity for exercise training varied by more than 20 Watts in 26% of subjects, a significant difference which may impact on the ability of patients to train at the prescribed work rate. Further study is required to refine the equations for use in clinical populations participating in pulmonary rehabilitation.

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