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O2 during exercise in humans: the peak vs. maximum issue
1Department of Physiology, St. George's Hospital Medical School, London SW17 ORE, United Kingdom; 2Division of Physiology, Department of Medicine, University of California, San Diego, La Jolla 92092-0623; and 3Division of Respiratory and Critical Care Physiology and Medicine, Harbor-UCLA Medical Center, Torrance, California 90509
Submitted 10 January 2003 ; accepted in final form 8 July 2003
| ABSTRACT |
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O2 max), a parameter characterizing the effective integration of the neural, cardiopulmonary, and metabolic systems, requires oxygen uptake (
O2) to attain a plateau. We were interested in whether a
O2 plateau was consistently manifest during maximal incremental ramp cycle ergometry and also in ascertaining the relationship between this peak
O2 (
O2 peak) and that determined from one, or several, maximal constant-load tests. Ventilatory and pulmonary gas-exchange variables were measured breath by breath with a turbine and mass spectrometer. On average,
O2 peak [3.51 ± 0.8 (SD) l/min] for the ramp test did not differ from that extrapolated from the linear phase of the response in 71 subjects. In 12 of these subjects, the
O2 peak was less than the extrapolated value by 0.1-0.4 l/min (i.e., a "plateau"), and in 19 subjects,
O2 peak was higher by 0.05-0.4 l/min. In the remaining 40 subjects, we could not discriminate a difference. The
O2 peak from the incremental test also did not differ from that of a single maximum constant-load test in 38 subjects or from the
O2 max in 6 subjects who undertook a range of progressively greater discontinuous constant-load tests. A plateau in the actual
O2 response is therefore not an obligatory consequence of incremental exercise. Because the peak value attained was not different from the plateau in the plot of
O2 vs. work rate (for the constant-load tests), the
O2 peak attained on a maximum-effort incremental test is likely to be a valid index of
O2 max, despite no evidence of a plateau in the data themselves. However, without additional tests, one cannot be certain. oxygen uptake; plateau; incremental ramp; cycle ergometry
O2 max), reflecting the upper limit of the body's aerobic functioning, is the most widely used parameter characterizing the effective integration of the central nervous, cardiopulmonary, and metabolic systems (e.g., Refs. 8, 14, 15, 26, 32, 39, 46). As such, it is used to characterize function in subjects ranging from elite athletes to patients with various pathophysiological conditions (22, 38, 41, 43-45), although in the latter group often a "system-limited" peak oxygen uptake (
O2 peak) value, rather than a
O2 max, is reported. Obtaining accurate and valid
O2 max values is of physiological importance when comparing individuals or groups, when following subjects longitudinally, or when different modes of exercise are used. Its quantification (typically by using a cycle ergometer or treadmill) requires oxygen uptake (
O2) to reach a value such that further increases in work rate result in no further (or trivially small) increases in
O2 (i.e., a "plateau" is attained). Such a
O2 plateau has been viewed as the best criterion for establishing
O2 max from as far back as 1923 (16): "the rate of oxygen consumption... increases as [running] speed increases... reaching a maximum... for speeds beyond 260 m/min. However much the speed be increased beyond that limit, no further increase in oxygen intake can occur."
However, the advent of continuous work rate tests, where the work rate is increased every 1 or 3 min (9, 19-21), largely replaced the progressive, constant-load format. Concern has been expressed whether the
O2 max attained from these tests was as high as those from the "traditional" discontinuous protocol (12). However, a number of groups found no difference in
O2 max between incremental (i.e., progressively increasing work rate every 3 min) and discontinuous (where discrete square waves of different work rates are separated by periods of rest) constant work rate treadmill tests (e.g., Refs. 19, 20). Available evidence (17, 30, 33) suggests that "end-exercise" plateaus in
O2 may only be evident in as little as
50% of the incremental treadmill tests.
The subsequent evolution of continuously incrementing ramp work rate tests (where work rate is rapidly incremented as a "smooth" function of time; Ref. 47) allows noninvasive estimation of four parameters of aerobic function from a single test:
O2 max, the estimated lactate threshold, mean response time for the kinetics of
O2, and an index of work efficiency. Comparisons of discrete increments and rapidly incrementing tests were made by Zhang et al. (48), who found no differences in the determination of these parameters of function (similar to Refs. 10, 47). However, it is still persistently suggested that a plateau in
O2 is a necessary consequence of the now-common incremental ramp test, and that a failure to attain a
O2 plateau may be due to "insufficient effort" from the subject and result in a
O2 peak that is not truly the individual's maximum (e.g., Ref. 40). Conversely, it has been suggested by others that plateaus of
O2 are rarely attained during such tests (e.g., Refs. 30, 36, 37) despite "good effort" from the subjects.
We were therefore interested in 1) whether a
O2 plateau was a consistent manifestation of rapid incremental ramp cycle ergometry (of slopes between 15 and 25 W/min) performed to the limit of tolerance in a large group of normal subjects and 2) the relationship between the
O2 peak from this test and that determined from a single maximal constant-load test and also that from a series of progressive maximal constant-load tests.
| METHODS |
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After familiarization with the laboratory and procedures the 71 subjects each initially performed an incremental ramp exercise test to the limit of tolerance on an electromagnetically braked cycle ergometer (Excalibur Sport, Lode, Groningen, The Netherlands). The incrementation rates were one of either 5 W/20 s, 5 W/15 s, or 5 W/12 s, corresponding to ramp slopes of 15, 20 or 25 W/min, respectively, depending on the subject, which were chosen to bring the subject to the limit of tolerance within
10-15 min. Fatigue was determined as the point at which the subject (under encouragement from the experimenters) could no longer sustain a pedaling cadence of at least 60 rpm (this "fatigue" criterion was used for all exercise tests).
In addition to the incremental ramp test, 38 of these subjects completed a single constant-load exercise test that was performed to the limit of tolerance at an average of
90% of the peak work rate attained during the ramp test and that lasted for durations between 4 and 10 min. This allowed us to compare the
O2 at the point of fatigue on a constant-load test with that obtained in the incremental ramp test in the same subjects.
Finally, six of the subjects completed five further constant-load tests to the limit of tolerance, in a randomized sequence, all in the "very heavy"-intensity domain (cf. Ref. 27). Three of these tests were completed at work rates different from that previously undertaken. The remaining two tests were performed at the same work rate as one of the previous tests; each subject, therefore, performed three tests at different work rates and three at the same work rate, with all tests bringing the subjects to the limit of tolerance. All the tests were preceded by (3-4 min) and followed by (6 min) 20-W cycling.
Equipment. The subjects breathed through a mouthpiece connected to a low-dead-space (90 ml), low-resistance (<1.5 cmH2O at 3 l/s) turbine volume transducer (Interface Associates, Irvine, CA) for the measurement of inspiratory and expiratory flows and volumes. Respired gas was continuously sampled (at 1 ml/s) from the mouthpiece and analyzed by mass spectrometry (model QP9000, Morgan Medical, Gillingham, UK) for the concentrations of oxygen, carbon dioxide, and nitrogen. Before each experiment, the mass spectrometer was calibrated using two precision-analyzed gas mixtures chosen to span the range of inspired and expired gas concentrations. Stability of the gas calibration was confirmed on a regular basis by analysis known gases every 10 min for a 2-h period, and the calibration was also verified at the end of each experiment. The time delay between the gas concentrations and volume signals was measured by passing a bolus of a known gas mixture through the system by using a low-dead-space solenoid valve (4). The electrical outputs of these devices were digitally converted every 20 ms and sampled by computer for the calculation of
O2, carbon dioxide production, and respiratory exchange ratio breath by breath with the use of the algorithms of Beaver et al. (3). Heart rate was measured from the R-R interval of the ECG (model Q-5000, Quinton Instruments) by using a six-lead arrangement. This was also digitized to the computer as described above. Arterial blood oxygen saturation was determined from the forefinger by pulse oximetry (model 3740, Biox, Ohmeda, CO).
Analyses. Editing of the
O2 responses was performed to exclude occasional errant breaths caused by swallowing, coughing, sighing, and so forth, which were considered not to be reflective of the underlying response; i.e., only values >3 SDs from the local mean were omitted (18).
Deviations from linearity in the
O2 response to the incremental ramp exercise were assessed by using a linear regression through the linear portion of the response (using standard least squares fitting procedures; Origin, Microcal). That is, the first 4 min and the last 3 min of the
O2 response to the ramp phase of the test were excluded from the fitting field (to eliminate the influence of the
O2 kinetics early in the response and possible deviations from linearity, e.g., a plateau, from the later part of the response). Deviation from linearity during the last 3 min of exercise was determined by the difference between the extrapolated linear fit and the actual response at the point of fatigue. The residual between the "best-fit" projection and the actual response was plotted both to better visualize any differences and to obtain a numerical value representing the range of responses. This was produced by averaging the last 30 s of the residual, which alleviated the effects of breath-to-breath noise on the determination of a deviation from linearity.
An ANOVA was used to establish any difference between the
O2 peak values from the incremental ramp and maximal constant-load exercise tests. The test-retest variability of
O2 peak was calculated for the six subjects who performed all seven maximal exercise tests. The differences between each of the paired combinations from all seven maximal tests were established; i.e., any pair may be considered to reflect values obtained between two particular tests. A probability density function was then calculated from these values and fit with a Gaussian function. Significance was established at the P < 0.05 level. The dispersion about the mean is expressed as ± SD, unless otherwise stated.
| RESULTS |
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O2 peak determined from the average of the last 30 s of the incremental test in the 71 subjects averaged 3.51 ± 0.8 (SD) l/min. This value did not differ significantly from that extrapolated from linear regression of the response (i.e., from 4 min after the ramp onset to 3 min from the end); the mean difference was only 0.017 ± 0.15 l/min. In 12 of the 71 subjects, however, the
O2 peak was less than the extrapolated value by 0.1-0.4 l/min (i.e., a plateaulike response; Fig. 1). This method, naturally, does not differentiate between a deceleration of the
O2 response and a true plateau, i.e., no increase in
O2 with increasing work rate. Figure 1 illustrates a typical response from this group of 12 subjects.
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In 19 of the subjects, the
O2 peak was actually higher than the extrapolated linear fit by 0.05-0.4 l/min (Fig. 1). In the remaining 40 subjects we could not discriminate a difference between the linear extrapolated fit and the response (Fig. 1).
The differences between the extrapolated fit and the actual response were normalized (by using the actual maximum attained as 100%) and are plotted on a modified Bland-Altman display (6) in Fig. 2. The mean "error" (that is, the difference between the value attained and the extrapolation at the time of exhaustion) was functionally indistinguishable from 0 (average 0.3%). However, the 95% prediction bands suggested that the expected bounds of function varied, in the both positive and negative direction (an "acceleration" or a plateau), between -9.5 and +10%. For a subject with a
O2 peak of 3.5 l/min, the expected (mean)
O2 response increases linearly up to the limit of tolerance but manifests a range of responses during the later stages of the exercise (95% confidence) that vary from a deceleration of
O2 by -330 ml/min to an acceleration of +350 ml/min during the last minutes of exercise (Fig. 2). There was no correlation between
O2 max (or age) and the degree of nonlinearity in the later stages of the
O2 response (as shown in Fig. 2); i.e., subjects with a low
O2 max had no greater tendency to exhibit a plateau than those subjects with a high
O2 max.
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Constant-load tests. The mean
O2 peak from the constant-load tests was 3.64 ± 0.7 l/min (n = 38). This was not significantly different (P < 0.01) from that determined from the incremental ramp test in the same subjects (3.64 ± 0.7 l/min; Fig. 3), suggesting a "true," task-specific
O2 max. The 95% confidence bands illustrate the extremely close relationship obtained from the regression, with 95% of the measurements from the ramp and constant-load tests (at the average
O2 peak) lying within ±40 ml/min of each other.
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An example from one of the six subjects who performed repetitions of the constant-load tests is given in Fig. 4. The
O2 peak values attained from these tests (mean = 4.51 ± 0.4 l/min) and the
O2 peak from the incremental ramp test (4.50 ± 0.3 l/min) did not differ (ANOVA) in these six subjects. The
O2 max was independent of both the constant-load work rate (in this very heavy-intensity domain) and the input function (ramp vs. constant-load). The test-retest variability of
O2 max was determined in these six subjects and was found to conform well to a Gaussian probability function with a standard deviation of 228 ml/min and a peak center functionally at zero (Fig. 5). The
O2 peak value obtained from the incremental ramp exercise, therefore, was not significantly different from that obtained by using the traditional criterion of constant-load testing, despite there being no plateau in 83% (59 of 71) of the subjects.
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| DISCUSSION |
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O2 was consistently manifest in the plot of
O2 as a function of work rate for a series of maximum-effort constant-load exercise bouts (or compared with that achieved during an incremental ramp test), this was not necessarily the case for the actual
O2 response to an incremental test. A plateaulike response was, in fact, only evident in 17% of our 71 subjects on the incremental test.
For the progression of constant-work rate tests, we have merely reconfirmed the concept of the maximum
O2 as formally proposed by Taylor et al. (38), Mitchell et al. (22), and Åstrand and Saltin (1) (see Ref. 2 for review). The origins of this concept may be traced back at least to Hill and Lupton (16), who stated that, with respect to increases in treadmill speed, a speed would be attained such that "however much the speed increased beyond that limit, no further increases in oxygen uptake can occur."
Progressive ramp-type tests are now much more common as a form of exercise testing (30, 41, 45) because they allow a large body of physiological information to be obtained in a single laboratory session, including parameters of aerobic function such as the estimated lactate threshold; the
O2 gain (i.e., change in
O2/change in work rate; 
O2/
WR), reflective of the work efficiency; and even its mean response time (13, 47). However, because such a ramp is typically continued to the limit of subject tolerance, a "maximally achieved" O2 uptake or "peak"
O2 is also standardly determined. This is commonly taken to be equivalent to the
O2 max in subjects who give good effort. However, results from numerous laboratories show a
O2 profile from such a test that does not evidence a plateau despite apparent good effort (e.g., Refs. 30, 36, 37). It must be recognized, however, that a plateauing of the actual
O2 response on a single test was not a necessary requirement of the original multiconstant-load tests; the only requirement was that the maximally attained value not get higher when a higher work rate was imposed. In other words, during a single high-intensity constant-load test, the
O2 was expected to continuously increase throughout exercise until a peak was achieved. At this point, the limit of tolerance was typically attained, and the
O2 response was not required to plateau. The plateau arose once a second constant-load test was performed (perhaps on a separate day) at a higher work rate than before that resulted in the same
O2 peak; i.e., the plateau requirement is based in the plot of the final values and not, necessarily, in the response that brings the
O2 to that final value. The highest value attained on the ramp test may therefore be likened more to the highest value achieved on one of the constant work rate tests that provides the
O2 max. The plateau demands of a ramp test may therefore differ from those of the original formulation of the
O2 max tests. This proved to be the case in our studies; plateaus were rare during the ramp format. It might be argued that the subjects were not "pushed" to the limit of tolerance in the incremental test and as such did not continue to those work rates that would evoke a
O2 plateau [as suggested by Wagner (40)]. However, we made every effort to ensure that all the subjects gave their maximum effort, not simply those who exhibited a plateaulike response. Also, there was no correlation between those subjects who did express a
O2 plateauing during the incremental test and their maximal aerobic capacity or "state of training." The suggestion that trained, or physically active, subjects are more likely to manifest a
O2 plateau during incremental exercise (40) is not borne out by the results of the present study.
The maximally attained
O2 value, however, was also established in a square-wave format in 38 subjects: There was no significant difference between these maximal values and those attained on the ramp. We believe it unlikely that the subjects would give precisely the same "submaximum" effort in the two quite different exercise tests. However, more compelling evidence for this notion is provided by the results of the subgroup of six subjects, each of whom performed six high-intensity square-wave tests for comparison (e.g., Fig. 4). Again, there was no systematic difference between the maximal values attained in the incremental test and those of the square waves. It has been commonly noted (e.g., Refs. 2, 11, 12, 17, 19, 23, 24, 28, 48) that
O2 max, defined as reaching a plateau of
O2 at high work rate, is by no means consistently attained. And, indeed, we also found such a plateau to be relatively rare during a ramp test (expressed in only 17% of our subjects). However, to establish
O2 max, plateaus are, by definition, necessary in the plot of
O2 as a function of work rate obtained from different tests (i.e., comparisons either of different constant-load tests or of incremental and constant-load tests). This was consistently achieved in each of our 38 subjects.
The results of this analysis also allow us to assess the magnitude of change in the measured maximally attained
O2 necessary to discriminate the effect of an intervention on the value. As shown in Fig. 5 the test-retest variability for our subjects was normally distributed with a mean that was functionally zero (36 ml/min) but with 95% confidence limits of
400 ml/min; i.e., when referenced to the mean maximum of
4,500 ml/min this would require an
10% change for group significance.
Maximum exercise tolerance results, presumably, from the depletion or accumulation of metabolites that both interfere with efficient chemomechanical energy transduction and stimulate afferents that result in an intolerably high sense of effort. The latter is likely to be the case for the kind of intolerance elicited in this study, although the molecular mechanisms that contribute to this limitation remain poorly understood. Oxygen flux from the atmosphere to its site of utilization in the mitochondrion plays a prominent role in minimizing the rate at which this limitation occurs. Although it has been argued that transfer inefficiencies at any site in the conduction chain (34, 35, 39, 40) would lead to a reduction in both exercise tolerance and the
O2 max achieved, the heart itself is commonly considered to subserve a predominant function (33). However, although our study does not address the mechanism determining
O2 max, our results do suggest that normal healthy subjects become unable to continue to exercise at a point at which these stressors reach common intolerable levels, despite different rates of development during tests of different formats, at least as suggested by the maximally attained
O2. Those subjects who do achieve a
O2 plateau before this would necessarily require an acceleration of the rate of the fatigue induction to levels that they would subsequently find intolerable. Why this occurs in some subjects and not others is presently unclear.
It has been argued (24, 26) that, because a muscle mass recruitment reserve exists at exhaustion, the brain is likely to be the principal organ involved in determining when exercise will terminate (e.g., the "central governor theory"; Ref. 26). Although, as noted above, the present results do not directly address this mechanism it is salient to note that 38 subjects in this study volitionally terminated incremental and constant-load exercise at different work rates but that each achieved a consistent
O2 max. Also, the results from the six subjects who performed multiple tests at different work rates support the statement of Hill and Lupton (16) that "the actual oxygen intake, however, reaches a maximum beyond which no effort can drive it." In other words, exercise tolerance does not seem to be mediated (in the present study) by the maximum force production per se of the muscles of interest. Rather the fatigue induced by the particular muscle recruitment (i.e., yielding a maximum exercise response under those conditions) is proposed to play the limiting role. Other examples of this are available in the literature; for example, incremental tests with different slopes yield similar maximal values for
O2, but the values are achieved at different peak power outputs, which are a function of the incremental slope (10).
In
25% of our subjects there was a clearly discernible increase in the
O2/
WR slope at work rates approaching the maximum on the ramp test. This is presumably the result of either the development of a prominent "slow component" of the
O2 kinetics manifest in the leg muscles (e.g., Refs. 29, 31) or mechanical inefficiencies such as additional unmeasured upper body work (5, 7, 42). Even in these subjects, however, the maximally attained
O2 was not different from that achieved on the constant work rate tests, suggesting either that the same mechanism(s) was operative on both tests or that differences in exercising muscle mass are likely to be minimal.
We therefore conclude that a plateau in the actual
O2 response is not an obligatory consequence of incremental exercise testing. However, because the peak value attained was not different from the plateau obtained in the plot of
O2 vs. work rate (for the constant-load tests), these data suggest that the
O2 peak attained on a maximum-effort incremental test in subjects exercising to the limit of tolerance is likely to be a valid index of
O2 max, despite no evidence of an actual
O2 plateau. Without evidence from additional tests (e.g., constant load), however, one cannot be certain.
| DISCLOSURES |
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| FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
| REFERENCES |
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O2 slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue. J Appl Physiol 85: 2118-2124, 1998.
O2 during heavy exercise. J Appl Physiol 62: 199-207, 1987.
O2 max criteria: discontinuous versus continuous protocols. Med Sci Sports Exerc 29: 273-278, 1997.
O2 max. Exerc Sport Sci Rev 28: 10-14, 2000.
O2 a respiratory adaptation to anaerobiosis? Adv Exp Med Biol 393: 187-194, 1995.
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