Sinusoidal high-intensity exercise does not elicit ventilatory limitation in chronic obstructive pulmonary disease

New Findings

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  What is the central question of this study?

  Is it possible for patients with chronic obstructive pulmonary disease to avoid ventilatory limitation during high-intensity exercise by using a fast-fluctuating sinusoidal exercise task?

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  What is the main finding and its importance?

  Sinusoidal exercise, with a cycle time of 60 s superimposed upon a mean work rate at critical power, resulted in minimal fluctuations in the exercise ventilation. Thus, high-intensity exercise, with excursions well above peak aerobic power, was sustained for up to 20 min in chronic obstructive pulmonary disease patients, and the end-exercise ventilation was less than peak. This exercise protocol may prove beneficial in rehabilitative exercise training programmes where large gains in skeletal muscle adaptation are the goal.

During exercise at critical power (CP) in chronic obstructive pulmonary disease (COPD) patients, ventilation approaches its maximum. As a result of the slow ventilatory dynamics in COPD, ventilatory limitation during supramaximal exercise might be escaped using rapid sinusoidal forcing. Nine COPD patients [age, 60.2 ± 6.9 years; forced expiratory volume in the first second (FEV₁), 42 ± 17% of predicted; and FEV₁/FVC, 39 ± 12%] underwent an incremental cycle ergometer test and then four constant work rate cycle ergometer tests; tolerable duration (t_lim) was recorded. Critical power was determined from constant work rate testing by linear regression of work rate versus 1/t_lim. Patients then completed fast (FS; 60 s period) and slow (SS; 360 s period) sinusoidally fluctuating exercise tests with mean work rate at CP and peak at 120% of peak incremental test work rate, and one additional test at CP; each for a 20 min target. The value of t_lim did not differ between CP (19.8 ± 0.6 min) and FS (19.0 ± 2.5 min), but was shorter in SS (13.2 ± 4.2 min; P < 0.05). The sinusoidal ventilatory amplitude was minimal (37.4 ± 34.9 ml min⁻¹ W⁻¹) during FS but much larger during SS (189.6 ± 120.4 ml min⁻¹ W⁻¹). The total ventilatory response in SS reached 110 ± 8.0% of the incremental test peak, suggesting ventilatory limitation. Slow components in ventilation during constant work rate and FS exercises were detected in most subjects and contributed appreciably to the total response asymptote. The SS exercise was associated with higher mid-exercise lactate concentrations (5.2 ± 1.7, 7.6 ± 1.7 and 4.5 ± 1.3 mmol l⁻¹ in FS, SS and CP). Large-amplitude, rapid sinusoidal fluctuation in work rate yields little fluctuation in ventilation despite reaching 120% of the incremental test peak work rate. This high-intensity exercise strategy might be suitable for programmes of rehabilitative exercise training in COPD.

Exercise intolerance is a major symptom and the main disabling factor in chronic obstructive pulmonary disease (COPD). Exercise intolerance in COPD is largely mediated by dynamic hyperinflation of the lungs and dysfunction of the muscles of ambulation (Berry, 2007; Barnes & Celli, 2009; Casaburi & ZuWallack, 2009). Pulmonary rehabilitation is considered to be standard of care for COPD patients (Celli & MacNee, 2004; Troosters et al. 2005; Berry, 2007; Barnes & Celli, 2009) because exercise tolerance improvements are generally superior to any other COPD therapy (Casaburi et al. 1991, 1997; Emtner et al. 2003; Troosters et al. 2005). However, the clinical responses to the exercise programmes that are the cornerstone of pulmonary rehabilitation programmes vary among subjects (Hsieh et al. 2007).

Duration, frequency, type and intensity are all components of exercise training, but intensity is recognized as the pivotal determinant in eliciting physiological benefits from pulmonary rehabilitation (Tanaka et al. 2001; Rochester, 2003). Rehabilitation regimens that include high-intensity endurance training yield superior physiological benefits compared with low-intensity programmes (Casaburi et al. 1997; Troosters et al. 2005; Nici et al. 2006; Hsieh et al. 2007; Casaburi & ZuWallack, 2009). These studies show that high-intensity endurance training in COPD is associated with an increase in peak oxygen uptake (; Casaburi et al. 1997), an increase in the lactate threshold (Casaburi et al. 1991), improvement in aerobic capacity of the exercising muscles (Maltais et al. 1996a), improvement in the ability to sustain a given work rate (Emtner et al. 2003), reduction in ventilatory requirements at a given work rate (Casaburi et al. 1991, 1997) and reduction in dynamic hyperinflation associated with increased submaximal exercise endurance (Porszasz et al. 2005). Unfortunately, a great majority of patients with severe COPD are often unable to tolerate high training intensities (Maltais et al. 1997), partly due to muscle dysfunction and weakness (Maltais et al. 1996b) and partly because of ventilatory limitation (Casaburi et al. 1997; Tanaka et al. 2001; Vogiatzis et al. 2002). Muscle weakness and fatigue in COPD is associated with a loss of muscle mass and type I muscle fibres (Maltais et al. 1996b; Jobin et al. 1998; Whittom et al. 1998). This further highlights the need for a training programme that targets muscle strength and endurance gains more effectively. It is therefore suggested that facilitating higher intensity exercise during rehabilitative training would promote a greater physiological adaptation, resulting in an increased exercise tolerance and reduced ventilatory stimulus.

In young, healthy, active men, a short-duration (or intermittent) high-intensity interval training programme resulted in similar changes in the maximal activity of cytochrome c oxidase and its subunit II and IV protein content in the muscle (a correlate of aerobic function) when compared with a greater volume of long-duration, lower-intensity endurance training (Gibala et al. 2006). In that study, the total training volume was 90% less in the high-intensity interval training group, demonstrating that this training modality is more time efficient in inducing skeletal muscle adaptations and gains in exercise performance (Gibala et al. 2006; Burgomaster et al. 2008). In addition, as few as two sessions of short-duration high-intensity interval training have been shown to speed oxygen uptake kinetics to a similar degree to long-duration endurance training (McKay et al. 2009).

It is of note, therefore, that interval training in COPD has not likewise been shown to elicit a superior training response in comparison to high-intensity constant work rate (CWR) training (Zainuldin et al. 2011). This may be in part due to particular design features of these studies, incorporating, for example, a greater training volume (duration × work rate) in the group assigned to CWR training (Varga et al. 2007), or employing an exercise stimulus in the interval training that did not exceed the maximal work rate (W_max) achieved during incremental testing (Coppoolse et al. 1999; Vogiatzis et al. 2002). Therefore, an exercise protocol that could access work rates above W_max while ensuring that ventilation remained below the limiting value would be a good candidate for promoting superior training adaptations even in patients with very severe COPD (Tanaka et al. 2001).

In designing an exercise protocol to achieve these aims, we drew on our previous work in healthy subjects demonstrating that large swings in work rate elicited small oscillations in ventilatory amplitude when work rate fluctuations were imposed as a high-frequency sinusoidal function (Casaburi et al. 1977). We also drew on previous demonstrations that ventilatory kinetics in COPD patients are slow (Nery et al. 1982; Casaburi et al. 1997; Somfay et al. 2002), which suggested that the amplitude of ventilatory fluctuation would be dampened relative to the fluctuation in work rate. Patients with COPD approach or achieve ventilatory limitation during CWR exercise nearing the critical power (CP; Neder et al. 2000). We therefore hypothesized that a rapid sinusoidal fluctuation in work rate, with a peak of 120%W_max superimposed on CP, would be well tolerated without reaching ventilatory limitation, and would feature only minimal sinusoidal fluctuations in ventilation. We also reasoned that ventilatory limitation would be rapidly attained during a slower sinusoidal work rate fluctuation of the same amplitude. We therefore aimed to characterize the kinetic responses of minute ventilation () and other cardiopulmonary variables [oxygen uptake () and heart rate] to the sinusoidal work rate forcing in comparison to CWR exercise at CP.

Methods

Ethical approval

The John F. Wolf Human Subjects Committee of the Institutional Review Board at the Los Angeles Biomedical Research Institute at Harbor-UCLA Medical Center approved this study. This approval assured that the study was conformant with the Declaration of Helsinki. All subjects signed the approved informed consent document prior to taking part in any study-related procedures.

Study subjects

All together, 19 subjects consented to participate in this study. Ten patients were excluded for various reasons, as follows: three patients showed signs of active COPD exacerbation during the screening phase; one patient showed arterial desaturation deeper than 88% during incremental exercise; one had atrial fibrillation; one had joint pain that limited exercise capacity; and four did not achieve peak ventilation in their preliminary incremental test of at least 70% of their maximal voluntary ventilation (MVV), apparently due to peripheral muscle weakness.

The remaining five men and four women with Global Initiative for Chronic Obstructive Lung Disease (GOLD) II–IV COPD completed the study. All were able to reach at least 40 W in the initial incremental test, and in all of them the primary exercise-limiting symptom was shortness of breath.

Pulmonary function testing

Subjects underwent resting spirometry (Vmax 229; VIASYS SensorMedics, Yorba Linda, CA, USA) during each of the six visits. Patients took 400 mg of albuterol by inhalation 20 min before testing in order to provide a stable level of bronchodilatation. During the first study visit, lung volumes were measured using body plethysmography (AutoBox 6200-D, Vmax; SensorMedics). Pulmonary function testing fulfilled American Thoracic Society and European Respiratory Society guidelines (Miller et al. 2005). To calculate normal values, we used the National Health and Nutrition Examination Survey (NHANES)-III standards (Hankinson et al. 1999) for spirometry and European Coal and Steel Community standards for the lung volumes (Quanjer, 1983). The MVV was calculated as forced expiratory volume in the first second (FEV₁) × 40 (Hansen et al. 1984).

Exercise testing

Subjects performed an incremental exercise test on an electrically braked cycle ergometer (Ergoline 800; SensorMedics) at a target pedalling rate of 60 ± 3 r.p.m.; subjects breathed through a mouthpiece with nose-clip in place. Respired gas was analysed breath by breath (Vmax Spectra; SensorMedics), and heart rate was recorded from the electrocardiogram. On days 4–6, Borg dyspnoea and leg effort ratings were recorded every 2 min during exercise. In all tests, exercise continued until the subject was unable to maintain the pedalling rate above 50 r.p.m. despite verbal encouragement, or (in the constant work rate and sinusoidal tests) until the predefined exercise duration of 20 min was reached. Subjects completed the following eight exercises on six non-consecutive days.

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  Day 1, an incremental exercise test to assess W_max and peak cardiac, gas exchange and ventilatory variables.

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  Days 2 and 3, four CWR exercise tests to derive the power–duration curve and estimate CP. Two tests were performed on each day, with at least 2 h separating the tests; the lower of the two work rates was always applied first on each of these days (Malaguti et al. 2006).

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  Day 4, a CWR exercise test at CP.

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  Days 5 and 6, fast (sinusoidal period, 60 s) and slow (sinusoidal period, 6 min) sinusoidal work rate tests presented in randomized order.

Incremental exercise test After 3 min of rest and 3 min of unloaded cycling, work rate was increased at 5 W min⁻¹ (FEV₁≤ 1 litre) or 10 W min⁻¹ (FEV₁ > 1 litre) and was continued to the limit of tolerance. The highest work rate that was maintained for at least 30 s was taken as W_max.

Determination of critical power Four CWR exercise tests were performed to determine the power–duration relationship and estimate CP (Neder et al. 2000). In each test, after 3 min of rest and 3 min of unloaded cycling, the selected work rate was abruptly instituted. Work rate was set at 100%W_max for the first test. In the second test, work rate was selected to be between 110 and 120%W_max, with the expectation that participants would be able to continue for no less than 2 min. In the third test, work rate was 80%W_max, and for the fourth test, work rate was selected with the intention of eliciting an endurance time(t_lim) of 6–7 min based on interpolation of the responses from the previous three tests. Work rates and the corresponding endurance times for the four CWR tests were plotted to establish the power–duration curve (Fig. 1, upper panel). Critical power was determined as the y-intercept of the regression line of power versus the inverse of endurance time (Fig. 1, lower panel), and the nearest 5 W step was taken as CP (5 W is the limit of resolution of the cycle ergometer used). The slope of this linear regression line, the curvature constant (W′), is the total work that can be performed above critical power (Moritani et al. 1981; Poole et al. 1988; Miura et al. 2000).

Figure 1

Determination of critical power based on the power–duration curve derived from four constant work rate tests in nine subjects with chronic obstructive pulmonary disease (COPD)
Upper panel shows power–duration curves interpolated from the regression line of power versus inverse of endurance time (1/time (in seconds); lower panel). Lower panel shows individual regression lines of power versus 1/time for all subjects (mean CP, 40.3 ± 17.9 W; curvature constant (W′), 5.36 ± 2.4 kJ; and r²= 0.957 ± 0.034).

Constant work rate exercise at critical power A constant work rate exercise was performed at the determined CP; this work rate was abruptly instituted after an initial 3 min of rest and 3 min of unloaded cycling. If the subject stopped prior to 15 min, work rate was reduced by 10% (or 5 W, whichever was larger) and the test was repeated after at least 2 h of recovery. If the test continued to the target 20 min duration, but minute ventilation did not reach 80% of MVV, work rate was increased by 10% or by 5 W (whichever was greater) and the exercise was repeated after at least 2 h of recovery. In further tests, this ‘corrected’ CP was used as the mean for the sinusoidal work rate exercise bouts.

Sinusoidal work rate exercise For these tests, a sinusoidal fluctuation in work rate was superimposed on the verified CP. The peak of the sine was set to 120%W_max. Tests with sinusoidal periods of 60 s (fast sine; FS) and 360 s (slow sine; SS) were performed in random order on separate days. Patients sat at rest on the cycle ergometer for 3 min, followed by 3 min of unloaded cycling, after which the sinusoidal exercise was initiated, starting at its nadir (assuring a smooth work rate transition at onset; see right panels of Fig. 2). The modulating sine wave work rate forcing was generated by a computer program (IGOR Pro version 5.0; WaveMetrics, Inc., Lake Oswego, OR, USA) and applied to the analog input of the cycle ergometer through digital-to-analog conversion (16 bit D/A converter, NI USB 6210 A/D; National Instruments, Austin, TX, USA). Work rate was measured synchronously with the measured gas exchange by supplying the cycle ergometer work rate output to one of the analog input channels of the Vmax system.

Figure 2

Typical oxygen uptake ( ) and minute ventilation ( ) responses to constant work rate exercise at critical power (35 W; left panels), fast sine wave exercise (middle panels) and slow sine wave exercise (right panels; fluctuating between 0 and 70 W), with mean work rate equal to the critical power in a typical subject with severe COPD
‘Horizontal arrow’ denotes peak work rate in the incremental test. The grey horizontal lines denote peak (upper panels) and peak (lower panels) from the incremental exercise test.

Modelling the response kinetics

Breath-by-breath gas exchange measurements during the CWR and both sine wave exercises were edited for obvious outliers (Whipp & Rossiter, 2005) and, after interpolating 1 s, 3 s averages were used for further analyses. A non-linear curve-fitting algorithm (Marquart–Levenberg) was used to determine the response kinetics (SigmaPlot 10.0 non-linear curve-fitting function; Systat Software Inc., Chicago, IL, USA). Responses following the work rate increase were modelled starting from the phase II exponential after omitting the initial response (phase I, ∼20 s). The kinetics of the and responses were analysed using a model that included an exponential function [eqn (1)]. Where the subsequent slow component (in phase III) was present, it was approximated by a second exponential [see eqns (3)–(5) below]. The sine wave exercise responses were fitted with the same exponential function superimposed with a sinusoidal component [eqns (2) and (4)].

(1)

(2)

where y is the responding function, y₀ is the fitted value for the transition from phase I to phase II, t is time, τ is time constant, ϕ is phase shift of the response in relation to the forcing sinusoid; T is the sinusoidal period (i.e. 60 or 360 s), and A₁ and A₂ are the amplitudes of the exponential and sinusoidal components, respectively.

In those subjects where there was a distinct upslope during phase III (slow component), the model included a second exponential term with a time delay (T_D) designating the start of the slow component. Constant work rate responses were fitted with eqn (3) and fast sinusoidal exercise responses with eqn (4) to incorporate a slow component occurring after the time delay.

(3)

(4)

(5)

The Heaviside step function [H(t); eqn (5)] in eqns (3) and (4) assures that individual components of the composite function have zero values for times before the onset of each component (Ma et al. 2010); and A₃ is the slow component amplitude.

Given that there was a large variation in the CP work rate among patients, the amplitudes of the and responses were standardized for work rate to facilitate comparison between conditions. Total response asymptote was calculated as the sum of y₀, and ( and are the values of the respective amplitudes at the end of exercise). The total response asymptote was then standardized by the CP, and the amplitude of the sine response (A₂) was standardized by the mean-to-peak sine wave work rate amplitude.

Blood lactate determination

The blood lactate concentration was measured (Lactate Scout, Minneapolis, MN, USA) from blood samples taken from a fingertip before, at mid-exercise (10 min into the exercise period) and 2 min after the end of exercise.

Statistical analysis

The results are presented as means ± SD. All multiple comparisons were analysed by one-way ANOVA with Holm–Sidak multiple range comparisons and, if normality failed, a non-parametric Kruskal–Wallis ANOVA on ranks with Tukey's post hoc multiple range test was performed. For the paired comparisons, when normality criteria were met Student's paired t test was used and when normality failed the Mann–Whitney U test was performed. All statistical analyses were performed in SigmaStat 3.5 (Systat Software Inc.), and significance was accepted if P < 0.05.

Results

Patient characteristics and pulmonary function

Responses of nine COPD patients (FEV₁, 42 ± 17% of predicted) (five male) are analysed in this study. General characteristics and pulmonary function results are shown in Table 1. There was no significant difference in FEV₁ values among the six visits (ANOVA, P= 0.77); therefore, we used FEV₁ from visit 1 for calculating MVV.

Table 1. General characteristics, resting pulmonary function and peak exercise characteristics

Variables	(n= 9)
Age (years)	60.2 ± 6.9
Male/female (n)	5/4
Height (cm)	170.2 ± 7.9
Weight (kg)	80.1 ± 9.1
Body mass index (kg m^−2)	27.8 ± 3.5
FEV1 (litres) [% predicted]	1.18 ± 0.52 [42 ± 17]
FVC (litres) [% predicted]	3.03 ± 0.87 [85 ± 17]
FEV1/FVC	0.39 ± 0.12
MVV (l min^−1)	47.3 ± 20.8
RV (litres) [% predicted]	3.96 ± 1.71 [179 ± 67]
TLC (litres) [% predicted]	7.17 ± 2.10 [117 ± 21]
Peak work rate (W)	64 ± 24
(l min^−1)	1.20 ± 0.35
(l min^−1)	44.2 ± 21.0
/MVV (%)	93 ± 15

• Abbreviations: FVC, forced volume vital capacity; FEV₁, forced expiratory volume in the first second; MVV, maximal voluntary ventilation (MVV = 40 × FEV₁); RV, residual volume; TLC, total lung capacity; , peak minute ventilation; and , peak oxygen uptake.

Incremental exercise test

The peak work rate ranged from 40 to 115 W (mean, 64 ± 24 W), and was 59.5 ± 15% of predicted (Jones et al. 1985). Peak minute ventilation was 93 ± 15% of MVV (range, 75–116%; Table 1). Given that not all subjects were ventilatory limited, by definition of reaching ≥ 85% of MVV (American Thoracic Society; American College of Chest Physicians, 2003), we chose to evaluate the ventilatory demand in each of the exercise tests relative to the peak attained in the incremental test, i.e. (Table 1).

Characteristics of the power–duration curve

The upper panel of Fig. 1 illustrates the power–duration curves for each subject. The CP averaged 42.2 ± 16.0 W (range, 25–70 W), which was not statistically different from the value determined during the original regressions (40.3 ± 17.9 W; range, 18–73 W; Fig. 1, bottom panel), representing 66.4 ± 12.7% of W_max (range, 50–90%); the curvature constant averaged 5.4 ± 2.4 kJ (range, 3.0–10.9 kJ).

Response to constant and sinusoidal exercise at the critical power

The and kinetic responses during CWR, as well as fast and slow sine exercise from a representative participant are shown in Fig. 2. The figure illustrates that exercise including rapid sinusoidal excursions up to 120%W_max was well tolerated by the patient, eliciting and responses that were almost indistinguishable from those during CWR exercise at CP and which remained below MVV and (respectively) throughout the 20 min task. This contrasts with the slow sinusoidal test, where physiological response dynamics were sufficiently fast relative to the work rate fluctuation frequency such that the subject was rapidly brought to task failure as his responses approached MVV and . The thick continuous lines overlying the data points in the upper and lower panels of Fig. 2 represent the model fits. In this case, both the CWR and fast sinusoidal tests featured a slow component; however, the fast sinusoidal test also featured a small, superimposed, sinusoidal component in both the and responses. In the slow sinusoidal exercise, the sinusoidal function was superimposed on a mono-exponential model, because the duration of exercise and large fluctuations consequent to the slow sine work rate obscured any slow component in the response, if present. The thin continuous lines represent the applied work rates.

The mean parameter estimates for the group are given in Table 2. The reached 93 ± 15, 96 ± 11 and 110 ± 8% of in the incremental test during CWR, FS and SS tests, respectively. Likewise, attained 103 ± 22, 98 ± 7 and 111 ± 6% of in the incremental test during CWR, fast and slow sine tests. Importantly, neither nor end-exercise model estimates differed significantly between FS and CWR protocols, but were significantly greater in the SS protocol (P < 0.05; Fig. 2 and Table 2).

Table 2. Comparison of physiological responses in the constant work rate, fast and slow sinusoidal exercise tests

Variable	Fast sine exercise	Slow sine exercise	CWR at critical power	P value
				Fast versus slow	Fast versus CWR	Slow versus CWR
Endurance time (tlim; min)	19.0 ± 2.5	13.2 ± 4.2	19.8 ± 0.6	<0.05*	n.s.	<0.05
time constant (τ1; s)	95 ± 41	–—	79 ± 26	–—	0.171†	–—
time constant (τ1; s)	122 ± 39	–—	92 ± 36	–—	0.063†	–—
Standardized sine amplitude (ml min^−1 W^−1)	0.8 ± 0.8	5.9 ± 1.9	–—	<0.001‡	–—	–—
Standardized sine amplitude (ml min^−1 W^−1)	37.4 ± 34.9	189.6 ± 120.4	–—	<0.001‡	–—	–—
Standardized total response asymptote (ml min^−1 W^−1)	28.9 ± 6.9	32.4 ± 6.2	30.0 ± 8.6	0.256*
Standardized total response asymptote (ml min^−1 W^−1)	1004 ± 256	1164 ± 314	951 ± 193	0.213§
Slow component response amplitude (% total, )	6.4 ± 3.4	–—	9.2 ± 4.2	–—	0.367†	–—
/ (%)	96 ± 11	110 ± 8	93 ± 15	0.02¶	0.584¶	0.004¶
/MVV (%)	88 ± 14	102 ± 15	85 ± 17	0.093*
Heart rate peak (beats min^−1)	131.4 ± 19.8	125.9 ± 12.8	125.2 ± 14.8	0.298§
Heart rate reserve (beats min^−1)	34.8 ± 19.4	40.3 ± 13.1	41.0 ± 13.3	0.298§
Blood lactate (at 10 min during exercise; mmol l^−1)	5.2 ± 1.7	7.6 ± 1.7	4.5 ± 1.3	0.025¶	0.473¶	0.006¶
	(n= 6)	(n= 5)	(n= 6)

• Abbreviations: CWR, constant work rate; MVV, maximal voluntary ventilation (MVV = 40 × FEV₁); , minute ventilation; , peak minute ventilation in the incremental test; and , oxygen consumption. Heart rate reserve was calculated as (208 – 0.7 × age; Tanaka et al. 2001. The P values are indicated as follows: *Kruskal–Wallis ANOVA with Tukey's post hoc multiple comparison (where appropriate); †Student's paired t test; ‡Mann–Whitney U test; §one-way ANOVA; and ¶one-way ANOVA with post hoc Holm–Sidak pairwise comparison.

The mean and responses during FS wave exercise were similar to those of CWR exercise with the same work rate. A further indication that exercise was well tolerated in both tests was that the test durations did not differ between the CWR the FS wave tests; 19.8 ± 0.6 and 19.0 ± 2.5 min, respectively. During FS and CWR tests, end-exercise was 96 ± 11 and 93 ± 15% of seen in the incremental test, respectively, with only three of nine subjects exceeding . In contrast, intolerance was attained during the first (n= 1), second (n= 5) or third sine wave (n= 4) in the slow sine wave exercise with average duration of 13.2 ± 4.2 min, and all subjects exceeded the reached in the incremental test (average end-exercise in SS test, 110 ± 8%).

Response kinetics of and

The standardized and sine amplitudes were significantly smaller in the fast than in the slow sine wave exercise (Fig. 2 and Table 2). There was no statistically significant difference in the standardized total and response amplitude between the fast sine and the CWR tests.

The time constants of the primary component for both and were slow, and the response of was found to be slower; however, the difference between the CWR and FS values was not statistically different (Table 2).

A slow component was clearly discerned during CWR at the critical power and during the fast sinusoidal exercise in seven of nine patients. The showed similar behaviour of the slow component in seven patients during fast sine wave exercise and in six patients during CWR exercise. In the fast sine wave and CWR exercise, the slow component amplitude represented 5.6 ± 2.3 and 6.2 ± 3.2% of the total , while the slow component represented 6.4 ± 3.3 and 9.2 ± 4.2% of the total ventilatory response, respectively. The difference between the two tests was not statistically significant.

Heart rate, symptom rating and blood lactate responses

Peak heart rate in the incremental test averaged 128.7 ± 19.0 beats min⁻¹, with a heart rate reserve of 37.5 ± 17.8 beats min⁻¹. As shown in Table 2, peak heart rate (and heart rate reserves) in the three subsequent tests were similar, with the peak heart rate being slightly, but not significantly, higher in the SS protocol. There were no significant differences in isotime dyspnoea ratings averaged for the CWR, FS and SS tests (3.7 ± 2.4, 3.6 ± 2.5 and 5.1 ± 3.4, respectively). For leg effort, the ratings averaged 4.0 ± 2.3, 4.6 ± 2.5 and 5.4 ± 2.9, respectively. The Borg ratings for both leg effort and dyspnoea were slightly greater in SS compared with the other conditions, although this did not reach statistical significance.

Blood sampling from the fingertip was successful in eight, eight and five subjects in the fast sine, slow sine and CWR tests, respectively. There was no significant change from mid-exercise to postexercise in the lactate concentrations in any of the three exercise tests. There was, however, a significantly greater mid-exercise lactate concentration in the slow sine exercise compared with the other two exercise modalities (Table 2).

Discussion

We have shown in this study that a fast sinusoidal work rate fluctuation, including excursions up to 120%W_max superimposed upon the critical power, does not elicit exercise limitation in patients with severe COPD, which enables high-intensity exercise to be sustained for extended periods of time (seven of nine subjects achieved the 20 min target). Furthermore, the kinetic analysis revealed that the mean and responses were similar between the fast sinusoidal work rate and the CWR protocols in these COPD patients. This was supported by detection of only a small and sustained ventilatory fluctuation during the fast sinusoidal exercise. The slow sinusoidal work rate fluctuation (with the same amplitude), however, elicited a much larger ventilatory response and brought the subjects to an earlier exercise limitation. We think that these are significant and novel findings in this study.

To our knowledge, this is the first study to demonstrate that exercise including intermittent excursions to 120%W_max can be tolerated for at least 20 min in patients with severe COPD without reaching ventilatory limitation. Despite the continuing rise in the ventilatory response (i.e. slow component) due to the repeated excursions into the severe intensity domain, ventilation did not reach a limit that curtailed exercise endurance. This is also consistent with the perception of breathlessness reported during the FS protocol, which was no greater than that during CWR exercise at the mean of the fluctuating work rate. Previous studies have applied higher than 100% peak work rate only during the second phase of a pulmonary rehabilitation programme (Vogiatzis et al. 2011). We have shown that it is physiologically feasible to introduce work rates intermittently reaching higher than peak work rate even at the start of a rehabilitation programme. This would be even more important because the training intensity seems to be pivotal to the effectiveness of achieving physiological training effects (Casaburi et al. 1997; Maltais et al. 1997; Tanaka et al. 2001; Troosters et al. 2005; Zainuldin et al. 2011).

We chose to study COPD patients with evidence of ventilatory limitation to exercise because their locomotor muscles are likely to have reserve capacity even at the highest work rates tolerated; four of 19 screened patients failed to meet criteria for ventilatory limitation. We showed that higher work rates could be tolerated transiently in this subject group. We suspect that subjects who display less ventilatory limitation would have lower muscle ‘reserve’ and would therefore be more challenged by the transiently high work rates in this sinusoidal protocol. This needs to be explored in future studies.

The superimposition of a rapidly fluctuating sinusoidal work rate task upon an individual's CP made sustained intermittent supramaximal exercise possible in ventilatory limited COPD patients because the work rate fluctuation was rapid in comparison to the long ventilatory time constants in these patients. For this reason, the response during fast sinusoidal exercise followed the work rate stimulus poorly, demonstrating only small-amplitude fluctuations. With these results, we have demonstrated that it is physiologically feasible to combine high-intensity exercise with tolerability and avoid ventilatory limitation that was not felt to be possible even in most recent reviews (Tanaka et al. 2001; Troosters et al. 2010). Recently, it has been shown that a combination of hyperoxia with interval training is beneficial in patients with the most severe COPD, but not in patients with coronary artery disease (Helgerud et al. 2010), although in that study the exercise intervals were long (4 min) and the applied work rate was only about 80–90% of .

Mathematical modelling of the response dynamics predicts that rapid sine wave forcing would be accompanied by a small-amplitude . This response was greatly increased during a slow frequency sine wave forcing, resulting in early termination of exercise. The Appendix presents a mathematical model that predicts the response of a first-order system to the onset of a work rate input composed of a step increase with a superimposed sinusoidal component. If the first-order system has a time constant of 1.75 min (approximating the average ventilatory time constant seen in COPD subjects; Table 2), the equations in the Appendix predict that the ratio of response amplitudes to a 6 and a 1 min fluctuation will be 5.28. This is in close agreement with the observed ratio of sinusoidal ventilatory amplitudes of 5.07 (Table 2). We can consider factors that would dictate the ‘optimal’ frequency of the work rate fluctuation; these include maximizing the stimulus to muscular training adaptation (likely to be enhanced by maximizing the period), while minimizing encroachment on a limiting by minimizing the oscillatory amplitude (by minimizing the period). To estimate the optimal period for each individual, one would therefore require prior knowledge of the kinetics of , and the tolerable fluctuation amplitude, which would be related to the difference between the at CP and the peak tolerable . The prediction of an ‘optimal length’ for the sine wave cycle time is further confounded by the obligatory presence of the slow component in this work rate domain. Using the model presented in the Appendix, assuming that a amplitude of 5% of the CP will be tolerable and considering the two COPD patients studied with the shortest and longest time constants, the range of ‘optimal’ sinusoidal periods would be between 1 and 2.5 min.

We consider sinusoidal fluctuation of work rate to have several advantages over standard interval exercise protocols, where work rate transitions are implemented in a square wave fashion (abrupt increases and decreases in work rate). Sinusoidal forcing provides smooth increases in work rate that allow the patient sufficient time to respond to the increased pedal-force demands. The sinusoidal paradigm avoids sudden large, although transient, pedal-force increases necessary to reach greater than peak work rate, which are encountered in this high-intensity exercise. These sudden changes in the required pedal force usually result in anticipatory changes in pedalling frequency that are likely to add noise to the ventilatory response. For this very reason, we elected to start the sine wave at its trough to avoid the sudden change in work rate that would result if the work rate abruptly started at the subject's critical power. The benefit of smooth work rate transition might help in protocols involving subjects with peripheral muscle weakness, who cannot accommodate sudden substantial increases in pedal force. Furthermore, the amplitude of response to a sufficiently fast sinusoid is predictably smaller than that to square wave changes of identical amplitude. Finally, it might be argued that sinusoidal fluctuation of work rate requires computerized control of the cycle ergometer. However, a crucial component of the approach we describe is that work rate fluctuates rapidly relative to the time constant of the response. The only practical way to implement either a rapidly fluctuating square wave or sinusoidal work rate pattern is by computer control; most modern laboratory cycle ergometers enable computer control of work rate.

While we have demonstrated that patients with severe COPD may tolerate high-intensity exercise delivered in a fast-fluctuating sine wave fashion, the exclusion of patients with severe cardiovascular co-morbidities from the study might also prevent us from generalization. Hsieh et al. (2007) reported that GOLD III COPD patients with a higher incidence of cardiovascular disease (61 versus 31%) were those who could not tolerate high-intensity training and were therefore those at particular risk from inactivity-related declines in functional capacity. It therefore remains to be determined whether COPD patients with cardiovascular co-morbidities can tolerate fast sine wave exercise forcing. Additionally, in this study we included GOLD II–IV patients, who utilized a high percentage of their ventilatory reserve. These findings, therefore, may not be generalizable to milder disease states, where ventilatory limitation might be less prominent. It is also predictable that patients with milder disease, who tend to have faster and kinetics (probably because they are more active and have less muscle deconditioning), might have a larger response amplitude to sinusoidal exercise and therefore be less tolerant to this work rate waveform. In these patients, an even more rapid sinusoidal work rate fluctuation might be introduced in order to damp their ventilatory response sufficiently (see discussion above and the Appendix).

As regards cardiac tolerance of the sinusoidal waveform, we note that peak heart rate did not differ between the slow sine and the constant work rate tests (Table 2); therefore, the wide fluctuation in muscle tension apparently did not engender additional cardiac stress. This suggests that subjects who are, from a cardiac perspective, candidates for traditional high-intensity endurance training are also candidates for sine wave training. Furthermore, the high heart rate reserves observed in these tests (averaging about 40 beats min⁻¹) suggest that, in these ventilatory limited patients, high heart rates are probably not an important cardiovascular risk.

A significant slow component was observed in seven of nine subjects in both the and the responses. These represented 6–10% of the total oxygen uptake and ventilatory response that, even with the contribution from this additional component, still did not reach the respective peak values observed in the incremental test. The presence of the slow component might reflect important underlying metabolic processes related to increases in the intramuscular energy demand during exercise above the lactate threshold (Rossiter et al. 2002). Although there was a discernible slow component in the majority of subjects, we detected no statistically significant increase in blood lactate from mid-exercise to postexercise in either of the exercise modalities, suggesting that a lactate steady state had been achieved. Notably, in all but one subject, the highest lactate concentrations were observed after slow sine wave exercise.

This is partly in agreement with the results of Astrand et al. (1960), who showed that the serum lactate is remarkably lower after intermittent exercise with a duty cycle of 1:2 if the exercise period is short (10 s exercise with 20 s recovery in between), even if the total work done was the same over the same 30 min of exercise. The lactate concentration during fast sine was somewhat, but not significantly, higher than during CWR exercise at CP. This might reflect a slightly higher metabolic stimulus during fast sine wave exercise, although this was not associated with higher slow component amplitude in or in . We speculate that the work rate period of 30 s below the critical power does not give sufficient ‘relaxation time’ for the muscle metabolism to result in enhanced lactate clearance. Irrespective of these considerations, we can speculate that intermittently higher muscle tension requirements might trigger metabolic stimulation in these patients. This more intensive training stimulus during a training period and therefore efficient metabolic stimulation might result in greater physiological benefits in rehabilitative exercise programmes. However, these speculations will require experimental validation. This will include assessment of exercise responses before and after training and also direct determination of muscle adaptations, e.g. from muscle biopsies.

Although it was not a major focus of this investigation, our findings have relevance to the debate regarding the mechanisms of the exercise hyperpnoea. Two recent studies, employing the elegant methodology of carefully metered epidural anaesthesia, suggest that lower limb sensory muscle afferents play an important role in the ventilatory response to exercise in healthy subjects (Amann et al. 2011) and COPD patients (Gagnon et al. 2012). The exceedingly small fluctuation of the ventilatory amplitude in the present study, despite large excursions in the work rate in FS, may be taken as evidence against involvement of muscle afferents in the ventilatory response (Casaburi, 2012). However, it is therefore possible that the rapid sinusoidal changes in work rate modify the integral of force production over time in such a manner that it reduces the influence on ventilation of the muscle chemoreflex in particular. It is also possible that additional (central) stimuli might be required to sensitize respiratory neurons to signalling from muscle afferents (Bruce & White, 2012). However, the slow kinetics of the ventilatory response in COPD patients complicate the ability to identify whether large fluctuations in mechano- and/or chemoreceptor stimulation to central respiratory drive in FS are, in fact, present. The debate continues.

Summary

In summary, this study demonstrated, for the first time, that high-intensity exercise featuring large-amplitude and rapid sinusoidal work rate fluctuation does not elicit ventilatory limitation in patients with severe COPD even if the sinusoidal peak work rates reach 120% of the peak work rate achieved in an incremental test. This modality of intermittent high-intensity exercise yields only small-amplitude fluctuations in the ventilatory responses. We have used physiological principles regarding the dynamic response of ventilation to variations in work rate to design an exercise strategy that allows the patient to achieve higher work rates than would be otherwise achievable and that can be sustained for longer periods of time in a training programme. Our data demonstrate that this approach is feasible. We suggest that a sinusoidally fluctuating work rate may be suitable for exercise training protocols, allowing high work rates to be tolerated without encroaching ventilatory limitation in patients with severe COPD. Whether such a training protocol yields a superior training response as compared with constant work rate training will require experimental verification. If it does, this training strategy might well find a place as a component of pulmonary rehabilitation and enhance this already effective therapy.

Appendices

Appendix: mathematical modelling of sinusoidal response amplitudes

The desired work rate input is the sum of a sinusoidal component (initiating at the nadir of the fluctuation) of the form:

(where t is time (in minutes), A is the amplitude of the sinusoid (in watts) and ω is the sinusoidal frequency (in radians per minute) and a step change in work rate of M watts. This sum can be represented by the following equation: , where H(t) is the Heaviside step function:

A convenient way to analyse the response of a first order linear system to this input is to take the Laplace transform of the input and apply to the identity: , where Y(s) and G(s) are the Laplace transforms of the output function and the transfer function, respectively.

The Laplace transform of the input u(t) is:

The transfer function for a first order system is: , where K is the system gain (the slope of the steady-state relationship between the system response and the work rate input) and τ is the system time constant (in minutes). Therefore, the output function takes the form:

Inverting the Laplace transform yields the time-domain result:

The terms in the first parentheses represent the transient response, and the terms in the second parentheses represent the response to the sinusoidal input after the transient response is complete. The sinusoidal terms can be further simplified by a trigonometric identity to yield:

The key term in this equation that governs the amplitude of the output oscillation is: . For given values of A, K and τ, A_out will vary as shown in Fig. A1 with frequency, ω. This plot shows that the normalized amplitude approaches 0 as ω approaches infinity.

Figure A1

Dependence of simulated normalized output amplitude (the response amplitude divided by the product of A and K) as a function of input frequency (ω)
Open circles represent the output amplitudes with input periods of 1 and 6 min, respectively.

It is useful to calculate the input forcing frequency, ω, that would yield an output amplitude, A_out, that is a given fraction, 0 < f < 1, of the input amplitude modulated by the gain, AK:

From this, it follows that the input forcing frequency that elicits a specified fraction (f) of AK can be calculated as follows:

Figure A2 shows the calculated ventilatory response time courses for a 6 and a 1 min sinusoidal period for system parameters used in this study. Note the similarity between these responses and those seen in Fig. 2.

Figure A2

Simulated normalized ventilatory response using average values for COPD subjects in this study
The response is to a step work rate change (0.67 × peak work rate), with a superimposed sinusoidal fluctuation of an amplitude of 0.53 × peak work rate to reach 1.2 × peak work rate at the peak of the sine, where peak work rate is the highest work rate in the incremental test. The ventilatory control system is assumed to have a first order response with a time constant of 1.75 min. Left panel; 6 min period work rate forcing; and right panel, 1 min period work rate forcing.

Acknowledgements

This work was funded by the Rehabilitation Clinical Trials Center and the Pulmonary Education and Research Foundation.