Three domains of exercise intensity have been defined based upon their distinct metabolic profiles (2,11,13). At the onset of exercise in the moderate intensity domain, which encompasses work rates at or below the lactate threshold, V̇O2 demonstrates rapid kinetics, rising with a gain of ∼10 mL O2·min−1·W−1 to achieve a steady state within 3 min in healthy young individuals (14). During exercise in the heavy domain, which includes work rates above the lactate threshold, a slow component of the V̇O2 kinetics is superimposed upon the rapid response, resulting in a delayed submaximal steady state. By definition, during fatiguing exercise at yet higher work rates, i.e., in the severe domain, the V̇O2 increases to a maximal value (1,2,9,10,11).
Few studies have sought specifically to characterize pulmonary gas exchange responses within the severe domain. Responses to severe intensity exercise appear to be more complicated than responses to moderate and heavy exercise. Margaria et al. (6) and Whipp (12) have stated that V̇O2max is achieved faster at higher intensities (for cycle ergometer [1,5] and treadmill [3] exercise) and, by definition, these intensities would fall within the severe domain.
Poole et al. (9,10) hypothesized that the heavy and severe exercise domains were demarcated by critical power (Pcritical). Pcritical is the asymptote of the relationship between power and time to fatigue (Tfatigue) (7,8). Direct support for this hypothesis was provided when Poole et al. (9,10) showed that, during exercise at Pcritical, V̇O2 reached a steady state at ∼75% of V̇O2max. In contrast, during exhaustive exercise at power outputs that averaged about 16–23 W (8–11%) above Pcritical, V̇O2 reached V̇O2max. More support for this hypothesis was provided by Hill and Ferguson (3) and Hill and Smith (5), who calculated the asymptote of the hyperbolic relationship between power and time to V̇O2max (TV̇O2max). This asymptote, which they called P′critical, represents the threshold intensity above which V̇O2max can, in theory, be elicited. They found that P′critical was identical to Pcritical.
The severe intensity domain is characterized by the attainment of V̇O2max. Given the finite speed of the V̇O2 response, there should be an upper bound to this domain and, therefore, there should be a fourth, higher intensity domain. At the upper bound of the severe intensity domain, V̇O2max would be achieved momentarily at the point of fatigue. At higher intensities, exercise duration would be too short to permit attainment of V̇O2max. To date, descriptions of exercise intensity domains have not provided for this fourth domain and have not provided a point of demarcation for intensities above which V̇O2max cannot be attained (1,2,9,10,12,14).
The purpose of the present study was to evaluate methods for estimating both the upper and lower bounds of the severe intensity domain. The first hypothesis was that Pcritical represents the lower bound of the severe intensity domain. Specifically, it was proposed that Pcritical and P′critical would not be statistically different and that V̇O2max would in fact be elicited during exercise at an intensity slightly above Pcritical but not at Pcritical. The second hypothesis was that there would be a linear relationship between TV̇O2max and Tfatigue, and that this relationship could be used to estimate the unique intensity above which the tolerable duration of exercise would be too short to allow V̇O2max to be elicited. This intensity would represent the upper bound of the severe intensity domain.
MATERIALS AND METHODS
Participants.
Nine men and two women provided voluntary written informed consent to participate in the study, which previously had been approved by the university Institutional Review Board for the Protection of Human Subjects. The men were of mean (± SD) age, 25 ± 6 yr, height, 186 ± 7 cm, and mass 82.4 ± 6.0 kg. The women were aged 18 and 21 yr, with heights of 155 and 169 cm, and masses of 57.2 and 59.9 kg, respectively. All participants were involved in recreational activities, and three men were involved in off-season training for basketball.
Overview.
Except as noted below, each of the 11 participants performed a total of 9 exhaustive cycle ergometer tests, all on the same electronically braked cycle ergometer (Mijnhart 800S, Bunnik, The Netherlands), and all under similar conditions in a temperature-controlled laboratory (20–22°C). During each exercise test, and during the warm-up that preceded it, expired gases were collected and analyzed using a MedGraphics (St. Paul, MN) CardiO2 metabolic cart. The cart was calibrated before and after each test according to the manufacturer’s instructions by using precision-analyzed gases, which spanned the expected O2 and CO2 concentration ranges, and a 3-L syringe. Testing sessions were separated by at least 24 h and were scheduled at approximately the same time of day for each participant. On testing days, participants did not exercise before arriving at the laboratory, and they were directed to be well rested for the testing sessions, not to smoke, not to drink beverages containing alcohol, caffeine, or carbonation before tests, and to eat only lightly in the hours before testing. Adherence was verified before each test.
Incremental tests.
The initial power in the incremental test was individually selected for each participant by one of the investigators, based upon the physical characteristics of the participant. The goal was to select an intensity that would permit completion of five to seven 2-min stages before fatigue. Increments for the stages were 20 W for women and 25 W for men. V̇O2max was determined as the highest 30-s average determined from rolling averages of 15-s means. Pmax was defined as the highest power that was sustained for a full minute.
Constant power tests.
All participants performed fatiguing constant power tests at 100% of their individual Pmax (practice trial, results not used in any statistical analyses), 110%, 135%, 95%, and 100% of Pmax, in that order. Each test was preceded by a 6-min warm-up at a work rate selected to elicit a heart rate of between 120 and 140 beats·min−1, and a 5-min recovery. Participants received verbal encouragement throughout the tests. Tfatigue was measured to the nearest second and V̇O2max for that test was determined as the highest 30-s average determined from rolling averages of 15-s samples. The participants were not given information about the work rate or their elapsed time for any test until after all data collection had been completed.
Determination of Pcritical.
Individual values for power and Tfatigue from the constant power tests were fit to the hyperbolic model, using iterative nonlinear regression procedures on SAS (Raleigh, NC). Values were derived for two parameters: Pcritical, which is the power asymptote of the relationship, and AWC, which is the area bounded by Pcritical, the x-axis, and any point on the power–time curve, and which represents the anaerobic work capacity. Regressions were also performed using the mathematically equivalent linear power–Tfatigue−1 and work–Tfatigue relationships. For each participant, results from the practice trial were excluded and regressions were performed using all possible combinations of three or four powers. Experience in this laboratory is that different combinations of predicting trials usually produce estimates within about 5 W of each other. Identification of the set of three or four data points for which the data best fit the mathematical model is designed to increase precision of the estimate (4). For each participant, the parameter estimate generated using the hyperbolic model with this data set was used as the criterion measure of Pcritical.
Determination of P′critical.
The first step in determining P′critical was to calculate TV̇O2max for each test. For each participant, for each test, breath-by-breath V̇O2 responses were fit to the following equation using iterative nonlinear regression procedures on SAS: where V̇O2(T) is the value for V̇O2 at time = T, and V̇O2inital is the preexercise V̇O2. Values were derived for two parameters: V̇O2projected, which reflects the asymptote value to which the V̇O2 is projecting, and Tmean response, a measure of the rate of V̇O2 response. The V̇O2 has essentially reached its maximal value when the value of (1 − e(−T/Tmean response)) from Equation 2 is 0.99, i.e., when T = (4.6 · Tmean response), and it is assumed that the V̇O2 is projecting to V̇O2max. Therefore, for each test, TV̇O2max was defined as 4.6 · Tmean response. Time spent at V̇O2max was determined by subtraction of the TV̇O2max from Tfatigue.
The power and TV̇O2max were fit to a hyperbolic model (4,6), and estimates of A and P′critical were derived as described above for AWC and Pcritical · P′critical is the threshold intensity at or below which V̇O2max cannot be attained, and A represents the anaerobic contribution utilized before V̇O2max being achieved.
Tests at Pcritical and Pcritical + 10 W.
Eight of the 11 participants were able to schedule exercise bouts at Pcritical and at Pcritical + 10 W. Tests were to exhaustion or were terminated at 25 min. The order of the tests was randomly assigned. Although Pcritical was calculated to the nearest 1 W, the work rate on the ergometer could be set only in multiples of 5 W. Therefore, the powers used in the tests were not exactly Pcritical and Pcritical + 10 W. The average difference was 2 ± 2 W. As in the shorter exhaustive tests, V̇O2 was measured, and the peak values were recorded.
Estimation of the upper bound of the severe intensity domain.
Linear regression techniques on SAS were used to describe the relationship between the TV̇O2max and Tfatigue. With TV̇O2max expressed as a function of Tfatigue, it was possible to solve for the unique Tfatigue, namely the upper bound of the severe intensity domain (Tupper bound), at which V̇O2max is achieved at the point of fatigue. The power associated with Tupper bound (i.e., Pupper bound) was calculated using Equation 1.
Statistical analyses.
Tfatigue and the parameters of the V̇O2 response profile derived from responses to the four different power outputs (95%, 100%, 110%, and 135% of Pmax) were compared using a one-way repeated measures analysis of variance (ANOVA) to test for differences and for evidence of a linear effect across intensities. The peak V̇O2 values obtained in the four constant power tests were compared with the V̇O2max obtained in the incremental test by using an ANOVA. When an ANOVA revealed significant differences, means were compared using Tukey post hoc tests.
To test the first hypothesis (that Pcritical would represent the lower boundary of the severe intensity domain), the criterion measures of Pcritical and P′critical were compared using a paired-means t-test, and the correlation between these two measures was calculated. In addition, the peak values for V̇O2 from the incremental test and from the tests at Pcritical and Pcritical + 10 W were compared using an ANOVA and Tukey post hoc tests.
To test the second hypothesis (that the upper boundary of the severe intensity domain could be identified), the strength of the individual relationships (i.e., the correlations) between TV̇O2max and Tfatigue were examined. These are the relationships that were used to estimate Tupper bound and Pupper bound.
V̇O2max values from the first and last (incremental) tests were compared using a paired-means t-test, and the correlation between these two measures was calculated. All results are reported as mean ± SD. Statistical significance was preset at an alpha ≤ 0.05 for all analyses.
RESULTS
The mean value for V̇O2max determined in the first incremental test (N = 11) was 3.13 ± 0.84 L·min−1 (39.5 ± 7.0 mL·kg−1·min−1). Pmax was 251 ± 56 W.
There was a hyperbolic relationship between Tfatigue and intensity for each participant (Figure 1). The mean value for Pcritical was 198 ± 44 W (79% of Pmax), and it was associated with a SEE of 1 ± 2 W and an R2 of 0.999 ± 0.002. The mean value for AWC was 19.5 ± 9.1 kJ. Mean values for Pcritical derived using the two linear models were both 198 W, as well. Tfatigue in the constant power tests are presented in Table 1.
FIGURE 1:
Data from a representative participant. Graphic representation of the relationships between power and fatigue (Tfatigue) and between power and time to V̇O2max (TV̇O2max). The severe intensity domain is bounded at its lower end by the two vertical power asymptotes, Pcritical and P′critical, which were not different for the participants in the present study. The upper boundary of the severe domain is represented by the point of intersection of the two curves. Above this power (or for exercise for which fatigue occurs in <Tupper bound), there is not enough time for the V̇O2 to reach V̇O2max.
Table 1:
Responses to the constant power tests.
The V̇O2 response was faster at higher intensities, and the results of the ANOVA revealed a highly significant linear effect, with Tfatigue, TV̇O2max, Tmean response, and the time that V̇O2max was sustained all being longer in the lower power tests. The values for V̇O2projected at the four exercise intensities were not different. Mean values are presented in Table 1. In addition, results of the ANOVA revealed that the peak values for V̇O2 in the constant power tests were at least as high as the criterion value for V̇O2max obtained in the incremental tests. Thus, it was possible to describe mathematically the relationship between TV̇O2max and exercise intensity using Equation 3. See Figure 1 for a graphic representation of this relationship. The mean value for P′critical was 196 ± 42 W (78% of Pmax), with a SEE of 4 ± 6 W and an R2 of 0.995 ± 0.010. The mean value for A was 11.6 ± 7.7 kJ. The mean values for P′critical obtained using the two linear models were 195 W and 197 W.
The first hypothesis involved comparison of Pcritical and P′critical. Results of a t-test revealed that Pcritical and P′critical were not statistically different (P = 0.29), and the values were highly correlated (r = 0.93, P < 0.01). A second way to determine whether Pcritical demarcated the heavy and severe intensity domains was to evaluate responses to prolonged exercise at Pcritical and at Pcritical + 10 W. All but one of the participants completed 25 min at Pcritical and all but two completed 25 min at Pcritical + 10 W, which was 4.7 ± 0.5% above Pcritical. Peak V̇O2 at Pcritical and Pcritical + 10 W were 2.90 ± 0.57 L·min−1 and 3.03 ± 0.60 L·min−1, respectively. For the eight participants who performed these tests, V̇O2max in the initial incremental tests was 3.17 ± 0.80 L·min−1. The ANOVA revealed a difference, and results of the post hoc tests revealed that the V̇O2 attained in the tests at Pcritical was significantly lower than the value for V̇O2max established in the incremental tests. In contrast, there was not a significant difference between the peak V̇O2 in the tests at Pcritical + 10 W and V̇O2max from the incremental tests. The difference between peak V̇O2 achieved in the tests at Pcritical and at Pcritical + 10 W did not reach statistical significance, and it is likely that this finding reflects that not all participants fatigued within 25 min at Pcritical + 10 W.
The second hypothesis was that there would be a linear relationship between Tmean response and Tfatigue, and that this relationship could be used to estimate the upper boundary of the severe intensity domain. For each participant, there was a strong relationship between the Tmean response and Tfatigue, with a mean correlation of 0.89 ± 0.08. See Figure 2 for a graphic representation of the relationship for a representative participant. For the group, the average relationship was Tmean response = 21 + (0.64 · Tfatigue), with both Tmean response and Tfatigue expressed in seconds. For each participant, the relationship was used to solve for the unique Tfatigue at which V̇O2max would be achieved just at the point of fatigue (i.e., Tfatigue = TV̇O2max = Tupper bound). For the group, the mean value for Tupper bound was 136 ± 17 s. The power associated with this Tupper bound (Pupper bound) was 342 ± 70 W.
FIGURE 2:
Data from a representative participant, whose responses are also portrayed in
Figure 1. T
upper bound was determined by solving for the time for which T
fatigue = T
V̇O2max, represented here as the point of intersection of the T
fatigue and T
V̇O2max lines.
There is often a concern in a study that involves repeated testing that a training effect may confound the results. At the end of the present study, participants completed a second incremental test, identical to the first. Because this second test was incorporated into the procedures after three participants had already completed all other requirements, only 8 of the 11 participants had a second incremental test. There was excellent reproducibility between results of the two tests, with the mean difference in V̇O2max being only 0.02 ± 0.22 L·min−1 (P = 0.85). The values were highly correlated (r = 0.97, P < 0.01).
DISCUSSION
Consistent with previous studies, the relationship between power output and Tfatigue fit closely to the hyperbolic model (Equation 2) (3–5,7–10). The SEEs associated with Pcritical were low and the R2 were high, indicating that the values for Pcritical were obtained with good precision. Accuracy of the Pcritical estimates was corroborated by the fact that similar values for Pcritical were obtained when the two linear versions of the power–Tfatigue relationship were used (3).
Margaria et al. (6) and Whipp (11) have asserted that V̇O2max is achieved faster at higher intensities. In the present study, Tmean response and TV̇O2max were smaller at the higher work rates, consistent with those assertions and with the results of several studies (1,3,5). The relationship between power and TV̇O2max fit closely to the three mathematically equivalent versions of the hyperbolic relationship (Equation 3). Considering the low SEE, the high R2, and the agreement among estimates generated by the three models, it was confirmed that there is a hyperbolic relationship between power and TV̇O2max (3,5).
The first hypothesis was that Pcritical would represent the lower bound of the severe intensity domain. By definition, P′critical is the threshold power output above which V̇O2max can be elicited and, thus, P′critical demarcates the heavy and severe intensity domains. Consistent with previous reports (3,5), in the present study, Pcritical was equal to P′critical. In addition, and also consistent with previous studies (9,10), V̇O2max was not elicited during exercise at Pcritical. Despite that exercise at Pcritical + 10 W was not continued to fatigue, a power output just 5% above Pcritical (83% of Pmax) yielded an end-exercise V̇O2 that was not different from V̇O2max. Therefore, the first hypothesis was supported.
Determination of the lower limit of the severe intensity domain is associated with some potential limitations. First, Pcritical can be derived using any of three mathematical models, each of which may give slightly different results. So, the choice of model can influence results. Second, to enhance the validity of the Pcritical estimate, we identified the data set for which the three models gave the most similar value. Although the method is designed to increase precision of the estimate (4), it does affect the criterion measure for Pcritical. Third, although the goal was to test participants “at Pcritical,” the average ergometer settings were 2 W above or below the calculated value. Given that not all participants completed 25 min at Pcritical or at Pcritical + 10 W, it is possible that the values were incorrectly estimated in some cases. Moreover, V̇O2peak may have been higher at Pcritical + 10 W had all participants continued to fatigue. Finally, day-to-day variability in performance and V̇O2 responses, coupled with the relatively small sample size, may have hindered the ability to accurately describe relationships or detect significant differences. These considerations may explain the results of the ANOVA comparing peak V̇O2 at Pcritical, at Pcritical + 10 W, and in the incremental test. The peak V̇O2 at Pcritical was significantly lower than the incremental test value, whereas the peak V̇O2 value at Pcritical + 10 W was not. We interpreted this that V̇O2max was achieved at Pcritical + 10 W but not at Pcritical. Yet, the 4.5% (0.13 L·min−1) difference between peak values at Pcritical and Pcritical + 10 W was not statistically significant. Despite these possible limitations, the first hypothesis seems to be supported by the equality of Pcritical and P′critical, and by the peak V̇O2 at, and slightly above, Pcritical compared with the V̇O2max from the incremental tests. It is concluded that Pcritical is the lower bound of the severe intensity domain.
The second hypothesis was that there was a linear relationship between TV̇O2max and Tfatigue, and that this relationship could be used to estimate the upper bound of the severe intensity domain. For every participant, there was a linear relationship between TV̇O2max and Tfatigue, with a mean correlation of 0.89 between the two variables. The mean value for Tupper bound, 136 ± 17 s, was associated with a power (i.e., Pupper bound) of 342 ± 70 W or 136% of Pmax. These results suggest that an upper bound to the severe intensity domain can be estimated based on responses to fatiguing exercise at intensities that are above Pcritical, and clustered around Pmax.
Determination of the upper bound of the severe intensity domain as done in the present study is associated with some potential limitations. First, the precision of the estimation of Tupper bound is dependent upon the precision of the determination of TV̇O2max. TV̇O2max was defined based on the kinetics of the V̇O2 response. One possible source of error was in the use of a mono-exponential model across a range of exercise intensities. For many tests, it is likely that there was a slow component to the V̇O2 response. However, inspection of the data suggested that the effect on the calculation of TV̇O2max was negligible. Because the present study sought simply to define TV̇O2max and not to elaborate the nature of the response, the use of this model seems appropriate. Nevertheless, since the estimate of Tmean response (Equation 2) is associated with an error term (i.e., a SEE), each value for TV̇O2max also has an associated error term. Second, the precision of the estimation of Tupper bound is also dependent upon the strength of the relationship between TV̇O2max and Tfatigue. The relationship was less than perfect, with a mean correlation of “only” 0.89 between the variables. Third, precision of the estimation of the power associated with Tupper bound (i.e., Pupper bound) is dependent both on the accuracy of estimation of Tupper bound and on the accuracy of the calculated relationship between Tfatigue and exercise intensity (Equation 1). However, this relationship was very tight, with a mean R2 of 0.999. Finally, although we derived values for Pupper bound, we did not directly validate the estimates by testing participants at and above their calculated Pupper bound to determine whether, in fact, V̇O2max was elicited at, but not above, Pupper bound. This identifies a valuable avenue for future research.
Severe intensity exercise is defined by its ability to elicit V̇O2max. If there is an upper bound to the severe exercise intensity domain, there must be a fourth, higher intensity domain, in which intensity is so high that fatigue occurs before V̇O2max can be elicited. Although it may appear intuitive that V̇O2max cannot be achieved at very high intensities, to date, only three exercise intensity domains have been identified, based upon distinct metabolic profiles (2,11,13). This notwithstanding, there has been evidence in the literature that some minimum amount of time is necessary to allow V̇O2max to be achieved. For example, although not mentioned in the paper, inspection of Figure 1 in reference 1 reveals that the peak V̇O2 achieved in the shortest tests (Tfatigue, ∼2 min) appears systematically lower than that for the longer tests (Tfatigue, >4 min). Although technical limitations (bag collection of expired gases) may have impaired the ability to measure V̇O2 accurately in the nonsteady state in that study, the results suggest that fatigue might have occurred before a true V̇O2max was achieved during exercise at the highest intensity (1). Similarly, in the present investigation, the mean peak V̇O2 during the tests at 135% of Pmax was only 94% of the value attained in the tests at 95% of Pmax. Therefore, it appears that, for some participants, fatigue might have occurred before a true V̇O2max was achieved during exercise at 135% of Pmax in the present study. These findings indicate that there is an upper bound to the severe intensity domain and suggest that exercise bouts for which Tfatigue is less than ∼2 min do not allow enough time for the V̇O2 to increase to a maximal value.
The severe intensity domain has been shown to encompass a large range of intensities, from ∼170 W to ∼300 W for cycle ergometry in one group of university students (3), from ∼200 W to ∼340 W in the present study, and from ∼240 m·min−1 to ∼300 m·min−1 for running in another group of university students (5). In the present study, the range was ∼200 W to ∼340 W (or even less than 340 W if, in fact, for some participants, fatigue occurred before a true V̇O2max was elicited during exercise at 135% Pmax). Such a range of work rates suggests that there is substantial latitude in selecting exercise intensities when the purpose is to elicit V̇O2max. An important implication of there being an upper bound to the severe intensity domain is that exercise durations cannot be too short, or else V̇O2max will not be elicited. The results of the present study indicate that the upper bound can be estimated based on the responses to fatiguing exercise at intensities above Pcritical.
In summary, the results of this study showed that Pcritical is the threshold power output above which V̇O2max can be achieved and, therefore, the results confirm that Pcritical defines the lower bound to the severe domain (3,5,9,10). With respect to the upper bound to the severe intensity domain, the results of the present study were used to predict mathematically the highest intensity at which V̇O2max can be elicited (Pupper bound). For participants in the present study, the shortest duration that would permit attainment of V̇O2max was just over 2 min, on average. Finally, if exercise intensities are to be defined based on their distinct metabolic profiles, there should be four domains. In ascending order: moderate intensity exercise is associated with a rapid mono-exponential increase in V̇O2 to a steady state; heavy exercise engenders a slow component to the V̇O2 response and is associated with a delayed submaximal steady state; (only) severe exercise is characterized by the attainment of V̇O2max; and extreme exercise is associated with the development of fatigue before V̇O2max can be achieved.
Address correspondence to: David W. Hill, Ph.D., Dept. of Kinesiology, P.O. Box 311337, University of North Texas, Denton, TX 76203-1337; E-mail dhill@unt.edu.
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