Selecting Constant Work Rates for Endurance Testing in COPD: The Role of the Power-Duration Relationship

Abstract

Constant work rate (CWR) exercise testing is highly responsive to therapeutic interventions and reveals physiological and functional benefits. No consensus exists, however, regarding optimal methods for selecting the pre-intervention work rate. We postulate that a CWR whose tolerated duration (t_lim) is 6 minutes (WR₆) may provide a useful interventional study baseline. WR₆ can be extracted from the power-duration relationship, but requires 4 CWR tests. We sought to develop prediction algorithms for easier WR₆ identification using backward stepwise linear regression, one in 69 COPD patients (FEV₁ 45 ± 15% pred) and another in 30 healthy subjects (HLTH), in whom cycle ergometer ramp incremental (RI) and CWR tests with t_lim of ∼6 minutes had been performed. Demographics, pulmonary function, and RI responses were used as predictors. We validated these algorithms against power-duration measurements in 27 COPD and 30 HLTH (critical power 43 ± 18W and 231 ± 43W; curvature constant 5.1 ± 2.7 kJ and 18.5 ± 3.1 kJ, respectively). This analysis revealed that, on average, only corrected peak work rate ( = WR_peak–1 min × WR_slope) in RI was required to predict WR₆ (COPD SEE = 5.0W; HLTH SEE = 5.6W; R² > 0.96; p < 0.001). In the validation set, predicted and actual WR₆ were strongly correlated (COPD R² = 0.937; HLTH 0.978; p < 0.001). However, in COPD, unlike in HLTH, there was a wide range of t_lim values at predicted WR₆: COPD 8.3 ± 4.1 min (range 3.6 to 22.2 min), and HLTH 5.5 ± 0.7 min (range 3.9 to 7.0 min). This analysis indicates that corrected WR_peak in an incremental test can yield an acceptable basis for calculating endurance testing work rate in HLTH, but not in COPD patients.

Keywords :

• Exercise
• gas exchange
• ventilation
• critical power

Introduction

Constant work rate (CWR) testing is highly responsive to therapeutic interventions and reveals both physiological and functional benefits. Consequently, exercise endurance is used (although perhaps underused) as a primary outcome measure in clinical research in chronic obstructive pulmonary disease (COPD) patients (1, 2). No consensus exists, however, regarding optimal methods for selecting the pre-intervention work rate for endurance testing.

Endurance exercise tests are commonly performed at a fixed percentage (70–80%) of peak work rate attained during a preceding incremental exercise test (WR_peak) (1, 3–5). This approach has a logical concern relating to the hyperbolic nature of the relationship between tolerated exercise duration (t_lim) in the very-heavy intensity domain and power output (P); this is determined by two seemingly independent parameters: the critical power (CP) and the curvature constant (W′) (6–9). Since both CP and W′ vary widely, e.g. CP ranges ∼60–85% of WR_peak and W′ ranges ∼5–30 kJ among individuals (10–12), selection of a fixed percentage of WR_peak for all subjects predictably leads to wide variations in t_lim (13).

The shape of the P-t_lim curve highlights an additional complexity: if pre-intervention CWR test durations vary among subjects (as commonly occurs at a given%WR_peak), then the expected magnitude of improvement will also vary, leading to non-normal distribution of t_lim change (3, 14). This dramatically complicates statistical comparisons and the interpretation of intervention -efficacy (2, 3, 9, 15, 29).

Arguments can be made for adoption of a fixed pre-intervention CWR endurance in interventional studies (9). As mentioned, fixing endurance test initial duration simplifies interpretation of t_lim change. Additionally, for work rates tolerated for more than ∼30 minutes, t_lim is likely determined by factors other than cardiopulmonary limits, such as substrate availability and motivation (8, 16). Work rates causing t_lim in less than ∼2 minutes are typically limited by pain and/or peripheral muscle fatigue (17), especially in COPD patients whose ventilatory and gas exchange kinetics are generally slow (10, 18).

A work rate yielding t_lim in ∼4–8 minutes, on the other hand, provides information on the key physiologic processes contributing to exercise intolerance during the activities of daily living, e.g., dynamics and capacities for aerobic (19–22) and anaerobic energy provision, and ventilatory and circulatory system characteristics (23–26). Indeed, cardiopulmonary exercise testing guidelines suggest CWR tests should be “at least 6 minutes” (1, 9, 27). Consequently, identification of a CWR that achieves intolerance in 6 minutes (WR₆) may provide a sound basis for endurance testing. Additionally, a WR₆ test would be of comparable duration to other commonly used clinical tests such as the 6-minute walk (27, 28) and the endurance shuttle walk (30).

While WR₆ can be derived directly from the power-duration (P-t_lim) relationship, traditional approaches to determine P-t_lim typically require 4 CWR exercise tests (7, 8, 17), severely hampering clinical application. We therefore sought to determine whether WR₆ can be predicted from incremental exercise responses and clinical characteristics, thereby bypassing complex P-t_lim determination. We aimed to develop a prediction algorithm for WR₆ in two groups with widely differing exercise capabilities and spirometric characteristics: COPD patients and healthy subjects (HLTH). We based this analysis on a database of paired incremental and CWR tests, selecting subjects with a CWR t_lim of ∼6 minutes. We then sought to validate this algorithm using a database of HLTH and COPD subjects in whom P-t_lim had been established from multiple CWR tests from which WR₆ could be interpolated. Finally, we calculated the t_lim distribution at the predicted WR₆ in both groups to assess the algorithm's utility for work rate selection in endurance testing.

Methods

Ethical approval

The Institutional Review Board of the Los Angeles Biomedical Research Institute approved the COPD studies and the Research Ethics Committee of the University of Leeds approved studies of HLTH subjects. Studies were performed in compliance with the Declaration of Helsinki. Written informed consent was obtained from all volunteers prior to participation.

Study subjects

Data from 156 people were utilized: 96 COPD patients and 60 HLTH males. Participant characteristics are presented in Table 1. HLTH subjects were screened with a health history, physical activity readiness questionnaire, and resting 12-lead electrocardiogram. HLTH subjects were involved in regular recreational activities or amateur competitive sport. No COPD patient was participating in a formal exercise program.

Table 1.  Participant characteristics and exercise responses

		COPD		HLTH
		Prediction	Validation	Prediction	Validation	Main effect
n (f/m)		69 (14/55)	27 (15/12)	30 (0/30)	30 (0/30)
Age	yrs	65.2 ± 9.0	61.8 ± 7.7	22.1 ± 3.4	23.0 ± 3.5	p < 0.001
Height	cm	172 ± 9	169 ± 8	180 ± 6	179 ± 7	p < 0.001
Body mass	kg	76.2 ± 14.6	80.8 ± 14.0	78.9 ± 11.8	76.7 ± 10.1	N.S
BMI	kg/m^2	25.8 ± 4.0	28.4 ± 5.2	24.4 ± 3.0	24.0 ± 2.2	p < 0.001
FEV1	L	1.3 ± 0.5	1.2 ± 0.5	–	–	–
FEV1	% predicted	44 ± 13	47 ± 17	–	–	–
FEV1/FVC	%	44 ± 12	42 ± 14	–	–	–
RV/TLC	%	57 ± 10	53 ± 11	–	–	–
WRslope	W/min	9.2 ± 3.0	7.2 ± 2.5†	20.0 ± 2.9	20.8 ± 3.2	p < 0.001
WRpeak	W	76 ± 29	68 ± 25	330 ± 36	328 ± 45	p < 0.001
VO2peak	L/min	1.15 ± 0.35	1.18 ± 0.34	4.04 ± 0.45	3.92 ± 0.63	p < 0.001
VO2peak	mL/kg/min	15.2 ± 4.3	14.7 ± 3.6	52.0 ± 7.5	51.3 ± 6.9	p < 0.001
HRR	beats/min	24 ± 16	30 ± 16†	12 ± 10	9 ± 6	p < 0.001
LT	L/min	0.80 ± 0.23^1	0.77 ± 0.24	1.94 ± 0.26	1.95 ± 0.36	p < 0.001
LT	% VO2peak	68 ± 16^1	65 ± 12	48 ± 6	50 ± 5	p < 0.001
VEpeak	L/min	43 ± 12	44 ± 16	167 ± 19	163 ± 21	p < 0.001
MVV	L/min	53 ± 18	49 ± 18	–	–	–
VEpeak/MVV	%	84 ± 19	93 ± 24	–	–	–
CP	W	–	43 ± 18	–	231 ± 43	p < 0.001
CP	% corrected WRpeak	–	70 ± 14	–	75 ± 4	p = 0.135
W´	kJ	–	5.1 ± 2.7	–	18.5 ± 3.1	p < 0.001

Abbreviations – COPD: chronic obstructive pulmonary disease; HLTH: healthy subjects; n: number; f/m: female/male; BMI: body mass index; FEV₁: forced expiratory volume in 1 s; FVC: forced vital capacity; RV: residual volume; TLC: total lung capacity; WR_slope: work rate slope in ramp incremental; WR_peak: peak work rate in the ramp incremental; VO_2peak: peak oxygen uptake; HRR: heart rate reserve in the ramp incremental; LT: estimated lactate threshold; V_Epeak: peak expired ventilation in the ramp incremental test; MVV: maximum voluntary ventilation calculated from FEV₁·40; CP: critical power; W´: curvature constant. Main effect refers to COPD vs HLTH. ^† p < 0.05 vs COPD prediction group. ¹n = 53, due to difficulty in discerning confident LT in 16 patients.

Pulmonary function testing

Each COPD subject underwent resting spirometry (Vmax 229, VIASYS SensorMedics, Yorba Linda, California); 200–400 μg of albuterol was inhaled at least 10 min before testing. Maximum voluntary ventilation (MVV) was calculated as FEV₁ × 40 (where FEV₁ is forced expiratory volume in 1 s during maximal exhalation). Lung volumes were measured by plethysmography (AutoBox 6200D, SensorMedics). Testing fulfilled ATS/ERS guidelines (31–33).

Exercise protocols

Exercise tests used electromagnetically braked cycle ergometers (HLTH: Excalibur Sport, Lode BV, NL; COPD: Ergoline800, SensorMedics). Participants undertook ramp-incremental testing, consisting of ∼1–3-minute seated rest, ∼3–4-minute low work rate exercise (unloaded for COPD, 20W for HLTH), a linear work rate increase to intolerance, and 2–5 minutes of recovery. Incrementation rate (WR_slope) was selected with the aim of achieving the limit of tolerance in ∼8–12 minutes and was 15–25 W/min for HLTH, and 5W/min (FEV₁ < 1.0 L) or 10 W/min (FEV₁ > 1.0 L) for COPD. Verbal encouragement was provided.

Participants also completed one or more CWR tests; subjects sat at rest (∼1 minute) and then completed ∼4 minutes of low intensity cycling (unloaded for COPD, 20W for HLTH), after which work rate was abruptly increased and the subject verbally encouraged to -continue to the limit of tolerance.

These tests were drawn from a database of 370 paired tests in which COPD and HLTH subjects had performed incremental tests followed by CWR tests. Testing was performed in the course of a variety of clinical trials or experimental series involving interventions (including exercise training and, in COPD patients, anabolic steroids). Both pre- and post-intervention data were included, but any individual was only included once, and the exercise tests were drawn from the same time point in any one study. We identified for analysis in this investigation 69 COPD and 30 HLTH participants in which t_lim was ∼6 minutes (range: 5–7 minutes).

Additionally, 30 HLTH and 27 COPD participants completed a semi-randomized series of at least 4 CWR tests to tolerance, each at a different work rate, to characterize the P-t_lim relationship and determine CP and W′. The t_lim of CWR tests aimed to span ∼3–15 minutes. For HLTH, tests were on separate days with at least 48 hours between tests. For COPD a maximum of two tests were completed on each day with at least 2 hours of recovery separating tests; prior exercise does not affect CP, and the >2 hour recovery allows near-complete W′ restitution (34, 35). Within each visit, the lower of the two work rates was completed first.

Incremental test analyses

Pulmonary gas exchange and ventilation were measured breath-by-breath (MSX, nSpire Health Ltd or Vmax, Carefusion). Lactate threshold (LT) was estimated using the v-slope method, with corroborating gas exchange and ventilatory criteria (36, 37). Peak oxygen uptake (VO_2peak) and peak expired ventilation (V_Epeak) were the average over the last 30s of incremental testing. Differences in ramp slopes among subjects (that are extreme in this study because of the wide difference in aerobic capacity between COPD and HLTH groups) will predictably yield differences in WR_peak (higher ramp slopes yielding higher WR_peak). We, therefore, applied an empiric correction factor: corrected WR_peak = WR_peak–1 min × WR_slope (9, 38) in an attempt to adjust for this. This correction factor incorporates the assumption that the mean response time of VO₂ kinetics is roughly 1 min, but will be inaccurate to the degree that VO₂ kinetics differ among subjects. Nevertheless, this difference is likely smaller than the differences among the ramp slopes used.

WR₆ prediction by backward stepwise regression

The prediction group was composed of 69 COPD and 30 HLTH subjects with CWR t_lim of ∼6 minutes, and was used to generate prediction equations for WR₆ (WR_6-pred). Pearson correlation was performed on all variables to obtain univariate correlation coefficients with WR₆. Variables with the highest correlation coefficients and without co-linearity were used in multiple linear regression analysis with backward elimination, to determine the strongest predictor variables for WR₆. Regression equations for WR_6-pred were then produced independently for COPD and HLTH.

A non-overlapping validation group was composed of 27 COPD and 30 HLTH subjects in whom the power-duration relationship had been determined and was used to validate WR_6-pred values. For the validation group, CP and W′ were estimated from the intercept and slope, respectively, of the linear relationship between P and 1/t_lim using least squares regression. For each subject in the validation group the ‘true’ WR₆ (WR_6-true) was calculated from the individual CP and W’ and compared to WR_6-pred (from the multiple linear regression). Additionally, the t_lim at WR_6-pred was calculated from CP and W′ for each validation group subject.

Statistics

Data normalcy was assessed by Shapiro-Wilk test. Two-way ANOVA compared condition (COPD vs HLTH) and group (prediction vs validation). Student's t-tests analyzed differences between paired comparisons (e.g. WR_6-pred vs WR_6-true). Bland–Altman plots (39) were used to assess agreement between WR₆ prediction and measurement. Frequency-distribution analyses with 7 cells spanning the data range assessed accuracy, precision and skewness of distributions of WR_6-pred and t_lim at WR_6-pred. A 3 parameter Gaussian fit produced the frequency distribution curve. Statistical analyses were performed in SigmaPlot 12.3 (Systat Software Inc., Chicago, IL). Values are reported ±SD, unless noted; significance was accepted at p < 0.05.

Results

Table 1 presents COPD and HLTH subject characteristics. COPD patients were older and shorter than HLTH subjects, but body mass was similar. Accordingly, body mass index (BMI) was greater in COPD. Pulmonary function testing revealed obstruction in COPD patients with an FEV₁ of 1.29 ± 0.45 L (45 ± 15% predicted) and FEV₁/forced vital capacity (FVC) of 43 ± 13%. WR_peak and VO_2peak during the ramp-incremental test in COPD were only ∼25–30% of HLTH (74 ± 30 vs 329 ± 40 W; 1.16 ± 0.35 vs 3.98 ± 0.54 L/min; p < 0.001), but LT occurred at a greater percentage of VO_2peak in COPD (67 ± 15 vs 49 ± 5%; p < 0.001). In COPD V_Epeak in the ramp test was only 43±13 L/min, which averaged 86 ± 21% of MVV.

Figure 1 shows examples of the power-duration relationship in a representative COPD and HLTH participant, together with their CWR VO₂ and V_E responses; Table 1 shows group means. As expected, CP was lower in COPD than HLTH (43 ± 18 vs 231 ± 43 W; p < 0.001), but occurred at similar percentage of corrected WR_peak in both conditions (70 ± 14 vs 75 ± 4%; p = 0.135). W′ in COPD averaged only 28% of HLTH (5.1 ± 2.7 vs 18.5 ± 3.1 kJ; p < 0.001).

Figure 1. Physiological responses to exercise tests at 4 different constant work rates (CWR) in COPD and healthy subjects (HLTH). Upper panels: Power-duration relationships in COPD and HLTH (horizontal dashed line is the critical power asymptote). Middle panels: Oxygen uptake (VO₂) responses to 4 different CWR tests in COPD and HLTH (horizontal dashed line is VO_2max from the ramp-incremental test). Bottom panels: Responses of ventilation (V_E) to 4 different CWR tests in COPD and HLTH (horizontal dashed line is estimated maximum voluntary ventilation). Vertical dashed line in all panels represents start of the CWR bouts.

WR₆ prediction in COPD and HLTH

The results of backward stepwise regression to predict WR₆ are shown in Table 2. Variables considered in backward regression for COPD were age, BMI, sex, FEV₁ (% predicted), residual volume/total lung capacity, FEV₁/FVC, corrected WR_peak, heart rate reserve (HRR) and V_Epeak. Variables excluded due to co-linearity were height, body mass, FEV₁, VO_2peak, breathing reserve and LT. This analysis revealed that, in COPD, only corrected WR_peak was a significant predictor of WR₆. The resultant COPD WR₆ prediction equation was (R² = 0.958, SEE = 4.98 W, p < 0.001):

Table 2.  Comparison between the results of the prediction algorithm for a constant work rate that results in exercise intolerance in 6 minutes (WR_6-pred) and the true WR₆ interpolated from the known power-duration relationship (WR_6-true) in the validation cohort of COPD patients and healthy subjects

		Mean	SD	Median	Min	Max	Test of normalcy^1
COPD (n = 27)	WR6-pred = 0.846** (corrected WRpeak) + 2.3
WR6-true	W	57	23	51	23	114	–
WR6-pred	W	54	20	47	23	104	–
WR6-pred – WR6-true	W (%)	–3 (–4.0)	6 (11.2)	–4 (–6.6)	–14 (–21.0)	8 (28.6)	p = 0.647
tlim at WR6-pred ^2	min	8.3	4.1	7.1	3.6	22.2	p < 0.001
HLTH (n = 30)	WR6-pred = 0.939* (corrected WRpeak) – 1.5
WR6-true	W	284	42	275	211	355	–
WR6-pred	W	287	41	284	212	360	–
WR6-pred − WR6-true	W (%)	4 (1.3)	6 (2.2)	3 (0.9)	–13 (–3.7)	17 (5.2)	p = 0.703
tlim at WR6-pred	min	5.5	0.7	5.5	3.9	7.0	p = 0.414

¹Shapiro-Wilk test: tests the null hypothesis that the sample is from a normally distributed population. ²Three outlying values for t_lim at WR_6-pred (−127, −7 and 68 minutes) are excluded from the mean data presented here, for assessment of range and distribution (see results for further explanation).

Table 2 shows results of the similar regression in HLTH. Variables entered were age, BMI, corrected WR_peak, HRR and V_Epeak (pulmonary function variables were not available). Variables excluded due to co-linearity were height, body mass, VO_2peak, and LT. As in COPD, corrected WR_peak was the only linear regression variable required to predict WR₆ (R² = 0.972, SEE = 5.60 W, p < 0.001):

Validation of WR₆ predictive equations

WR_6-pred prediction equations in each condition were validated against WR_6-true derived from interpolation of P-t_lim relationships in 27 COPD and 30 HLTH (Table 1). WR_6-pred was very strongly correlated with the WR_6-true in both COPD (R² = 0.937, p < 0.001) and HLTH (R² = 0.978, p < 0.001) (Figures 2A, 3A). COPD regression slope was significantly less than 1 (slope = 0.868, p = 0.007). Intercepts were 4.3 ± 2.8 W and 13.4 ± 11.6 W (SE) in COPD and HLTH, respectively. Mean differences between WR_6-pred and WR_6-true were only –3 ± 6 W and 4 ± 6 W for COPD and HLTH, respectively (Table 2; Figures 2B, 3B). Nevertheless, Bland–Altman analysis in COPD showed strong negative bias for WR_6-pred, such that at higher work rates the prediction algorithm tended to underestimate WR_6-true (Figure 2B), whereas there was no bias in HLTH (Fig 3B). In both groups, work rate predictions were normally distributed around WR_6-true (Table 2, Figures 2C, 3C). Although mean differences between WR_6-pred and WR_6-true were similar in the two groups, the lower WR_peak in COPD meant that this difference represented a greater percentage error (4.0 ± 11.2 vs 1.3 ± 2.2% in COPD and HLTH respectively; Table 2; p < 0.05).

Figure 2. Comparison between the predicted and measured values for the constant work rate that results in intolerance in 6 minutes (WR₆) in the validation cohort of COPD patients. A) Regression between predicted WR₆ (WR_6-pred) and the true WR₆ (WR_6-true) determined from interpolation of the P-t_lim relationship. Solid line is the linear regression and dashed line is the line of identity. B) Difference plot between WR_6-pred and WR_6-true. Note the small mean bias (–3.2 W; solid line), wide 95% confidence intervals (–14.7 to +8.4 W; short dash), and bias in the distribution (long dash). C) Frequency distribution for the difference between WR_6-pred and WR_6-true. The data are fit to a Gaussian distribution (solid line) and zero difference is indicated (vertical dash). D) Frequency distribution for the t_lim at the WR_6-pred. The data are fit to a Gaussian distribution (solid line) and the target 6 minutes is indicated (vertical dash).

Figure 3. Comparison between the predicted and measured values for the constant work rate that results in intolerance in 6 minutes (WR₆) in the validation cohort of healthy subjects (HLTH). A) Regression between predicted WR₆ (WR_6-pred) and the true WR₆ (WR_6-true) determined from interpolation of the P-t_lim relationship. Solid line is the linear regression and dashed line is the line of identity. B) Difference plot between WR_6-pred and WR_6-true. Note the small mean bias (3.5 W; solid line), wide 95% confidence intervals (–8.8 to +15.8 W; short dash), and bias in the distribution (long dash). C) Frequency distribution for the difference between WR_6-pred and WR_6-true. The data are fit to a Gaussian distribution (solid line) and zero difference is indicated (vertical dash). D) Frequency distribution for the t_lim at the WR_6-pred. The data are fit to a Gaussian distribution (solid line) and the target 6 minutes is indicated (vertical dash).

The ability of WR_6-pred to yield a 6 min t_lim was assessed using the individual P-t_lim relationships in the validation group (Table 2). Three of 27 patients COPD had extreme calculated t_lim values at WR_6-pred. Two of these outlier t_lim values were negative (–127 and –7 minutes, implying that the calculated WR₆ was lower than the CP), and the other outlier was large and positive (68 minutes, representing that the calculated WR₆ was only marginally above the actual CP). These three outliers were excluded for distribution analyses. Mean t_lim at WR_6-pred was significantly greater than 6 min in COPD (8.3 ± 4.1 min; p = 0.012), but less than 6 minutes in HLTH (5.5 ± 0.7 min; p < 0.001) (Table 2). Importantly, however, predicted t_lim at WR_6-pred was not normally distributed in COPD and ranged widely between 3.6 and 22.2 min (Table 2; Figure 2D), whereas for HLTH t_lim distribution was tightly and normally distributed about the mean (range 3.9 to 7.0 minutes; Table 2; Figure 3D).

To help conceptualize the reason for the wide variation of t_lim at the calculated WR₆ in COPD, but not in health, we modeled both P-t_lim curves using the mean CP and W′ values from the validation groups (Figure 4). We superimposed on these curves, the range of t_lim values that would be seen for a 5 W variation (the limit of resolution of some cycle ergometers) around the calculated WR₆. Because of the steepness of the rectangular hyperbola in COPD patients, a consequence of the low W′, t_lim variation is wide (between 4.4 and 9.3 minutes). In contrast, the larger W′ in the healthy subjects yields only a modest t_lim variation (between 5.5 and 6.6 minutes).

Figure 4. An illustration of the magnitude of error in predicting exercise duration (t_lim) for an assumed 5W error on WR₆ prediction in healthy subjects and COPD patients. Power-duration (P-t_lim) curve and WR₆ estimates are based on the means of the two groups (Table 1). A 5W error in WR₆ prediction in HLTH projects to a small variation in t_lim (5.5 to 6.6 minutes; dark grey shading), whereas the same error in COPD projects to a large variation in t_lim (4.4 to 9.3 minutes; light grey shading). The difficulty in estimating a common CWR duration for both groups is suggested to be markedly influenced by the very low curvature constant (W´) in COPD (5.1 ± 2.7 kJ) compared to HLTH (18.5 ± 3.1 kJ). The selection of a 5W error is based on the typical SEE for WR₆ estimation using the P-t_lim curve (range ∼1–7 W in this study). It is noted that, were the precision of WR₆ estimation to be lower in COPD, then the wide t_lim distribution would be exacerbated in patients compared to healthy subjects.

Discussion

This study's novel demonstration was the efficacy of WR₆ prediction based only on variables established in ramp-incremental exercise testing (R² = 0.937 and 0.978 in COPD and HLTH, respectively). Backward stepwise regression techniques determined that the only variable required for WR₆ prediction was corrected WR_peak from the ramp-incremental. Importantly, however, despite these extremely tight limits of WR₆ prediction, only in HLTH was the individual WR_6-pred normally distributed around a t_lim of ∼6 minutes. In COPD, WR_6-pred based solely on ramp-incremental data resulted in a skewed distribution of t_lim values from ∼3 min to >60 min.

The (in)efficacy of predicting t_lim from WR_peak

Despite the common practice of assigning endurance testing work rates solely as a percentage of WR_peak, the finding that corrected WR_peak alone explains ∼95% of the variance for WR₆ prediction should be highly unexpected, because of the widely variable relationship between CP and WR_peak. To our knowledge, the data presented here represent the largest collection of P-t_lim derivations in humans; they demonstrate that CP as a percentage of WR_peak has a wide range in both healthy subjects (53–80%) and in patients with moderate to severe COPD (33–90%) (13, 35). This finding alone should invalidate WR₆ assignment based solely on corrected WR_peak.

The reason for the unexpectedly strong relationship between corrected WR_peak and WR₆ lies in the shape of the P-t_lim curve (22). That is, tolerable durations of CWR exercise are far less sensitive to a given change in WR assignment at WR well above CP compared to WR near CP (Fig 4). Also, for precisely the same reason, the WR₆ prediction did not result in a narrow range of tolerable durations close to 6 min in COPD (unlike in HLTH): in COPD, interpolated t_lim at WR_6-pred ranged between 3 minutes and ‘infinity’. The relative error in WR₆ estimation from corrected WR_peak (–21 to +29%; Table 2) rendered the equation ineffective in consistently establishing tolerable duration among patients (Fig 2D). In less than 50% (13 of 27) of the COPD patients was the t_lim for WR_6-pred within the recommended 4–8 minute range. These data, therefore, identify a crucial flaw in basing the work rate for endurance testing on a fixed percentage of WR_peak in COPD.

The danger of selecting CWR for interventional studies in COPD based on WR_peak was suggested in data presented by O’Donnell et al. (3), where CWR tests at 75% of WR_peak yielded t_lim values considerably skewed towards long endurance times. Therefore, exercise endurance improvement from an intervention was also part of a skewed distribution, thereby complicating statistical comparisons of t_lim improvement. This skewedness in COPD was confirmed in the present data, and is predictable based on P-t_lim parameters. First, CP values in COPD are extremely low (43 W in COPD vs 236 W in HLTH). Standard cycle ergometers can deliver work rates within ∼5 W, which may be inadequate to accurately determine WR₆ when CP is low. Secondly, W′ is extremely low in COPD (5.1 kJ COPD vs 18.5 kJ HLTH). This reduces the ‘buffer’ for errors in WR₆ assignment, by steepening the rectangular hyperbola in COPD, and thus narrowing the work rate range that will result in 5–7 minute tolerable durations (Figures 1 and 4). Therefore, despite the high ability of corrected WR_peak predict WR₆ in COPD (R² = 0.958; Figure 2A), this approach results in substantially inaccurate t_lim normalization. This finding undermines endurance test work rate assignment in interventional studies based on percentages of WR_peak.

One can conceive of several methods to overcome this difficulty. The first is, naturally, to determine the P-t_lim relationship in each subject. However, this requires multiple laboratory visits. A modification of this approach halves the number of laboratory visits by conducting two tests per visit (35, 40). Post-intervention testing may be performed in a single visit by assuming that W′ is unchanged by the intervention (9). However, this assumption's accuracy is questionable and depends on the intervention. A third approach employs a single-visit's tests to determine P-t_lim parameters, but requires 3 min of sustained ‘all-out’ exercise eliciting VO_2max within ∼30 seconds. This approach has been studied in healthy subjects (19, 41), but may not be feasible in COPD patients or other clinical populations. A final strategy is to perform a CWR test based on a targeted fraction of the WR_peak and then, if the test duration falls outside a desired limit (e.g., 4–8 minutes), the measured t_lim is used to select an adjusted work rate at which to repeat the test.

Comparison of WR₆ prediction equations in health and disease

Regression equations in COPD and HLTH suggested that WR₆ could be predicted from ∼85% and ∼94% corrected WR_peak respectively (both equations have very small intercepts). Considering that average ramp–incremental test duration is ∼10 minutes, and the WR_slope correction applied (1 minute) is roughly equivalent to 10% of WR_peak, then the WR₆ prediction was functionally ∼75% and ∼85% of WR_peak in COPD and HLTH, respectively. This is notable because several COPD clinical trials utilized 75% of WR_peak to assign CWR tests (3). However, the present data demonstrates that in COPD individual variability in t_lim is unacceptably wide using this approach.

It is interesting that the predictive equations were similar, despite the radically different physiological exercise limitations in the two groups. Neder et al. (12) provided compelling evidence that attainment of very high V_E (in relation to MVV) dictates tolerance limitation in COPD, suggesting that V_E kinetics are integrally related to exercise intolerance in COPD. Similarly, Murgatroyd et al. (42) showed that the rate of VO_2max attainment [combining fundamental and slow kinetic VO₂ components (3)] is the key t_lim determinant in healthy subjects. The difference we observed in percentage of corrected WR_peak required for WR₆ prediction between conditions presumably reflects differences in V_E and VO₂ kinetics between COPD and HLTH subjects. In health, V_E kinetics are slower than VO₂ kinetics, e.g. (18). Additionally, COPD V_E kinetics are slower compared to healthy subjects (10, 18). Therefore, during ramp-incremental exercise V_E lags farther behind the work rate increment than does VO₂ in the healthy participants. This results in a larger difference in the relationships of V_Epeak to WR_peak in COPD, than between VO_2max and WR_peak in HLTH. These kinetic differences imply that WR₆ should occur at a lower percentage of WR_peak in COPD than in HLTH, consistent with present findings.

Limitations

The suggestion that establishing P-t_lim parameters provides a stronger foundation for endurance testing focused on determination of intervention efficacy depends on the P-t_lim curve precision compared to other methods (e.g. the algorithms derived herein). However, precision of t_lim estimates based on CP and W′ is not known in COPD. Direct comparison of the SEE of each individual's WR₆ estimation derived using the P-t_lim curve with the SEE of the group regression based on WR_peak in the present study suggests that the P-t_lim curve should provide a superior measure. However, repeated CWR tests in comparison to the P-t_lim curve will be required to establish the precision of WR₆ estimation by this method in COPD. In addition, the algorithms that we have derived for WR₆ prediction apply to the subject population studied: COPD men and women with predominantly moderate or severe obstruction and young healthy men with a fairly wide range of aerobic fitness. The algorithms may not apply to subject groups with differing characteristics.

Conclusions

This study demonstrates that although the CWR resulting in exercise intolerance in 6 minutes can be predicted from a suitably corrected peak work rate attained during a ramp-incremental test, in COPD patients the t_lim associated with this work rate was highly variable. The wide variability in P-t_lim parameter estimates among patients wholly undermines the ability for WR₆ estimation to normalize exercise endurance in COPD using this approach and is reflective of very low CP and W′ values in these patients.

Declaration of Interest Statement

The Pulmonary Education and Research Foundation and BBSRC, UK (BB/I00162X/1) provided partial support for this study. HV, SM, HR, CC, RC, and JP have no financial or personal disclosures related to this research. The authors alone are responsible for the content and writing of the paper.

Acknowledgments

RC holds the Grancell/Burns Chair in the Rehabilitative Sciences.