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

Figures & data

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.

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.

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).

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).

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.