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Critical Power can be Estimated From Nonexhaustive Tests Based on Rating of Perceived Exertion Responses

Nakamura, Fábio Y1; Okuno, Nilo M1; Perandini, Luiz AB1; S. Caldeira, Lúcio F1; Simões, Herbert G2; Cardoso, Jefferson R1; Bishop, David J3

Journal of Strength and Conditioning Research: May 2008 - Volume 22 - Issue 3 - p 937-943
doi: 10.1519/JSC.0b013e31816a41fa
Original Research

The purpose of this study was to evaluate a novel procedure, based on the perceived exertion threshold (PET) concept, involving non-exhaustive tests (PET14-17) to estimate critical power (CP), as well as to examine the reproducibility of these indices. Twenty young men performed 2 trials (Trial 1 and Trial 2) of 4 exhaustive predictive tests to estimate CP, PET, and PET14-17. The slope coefficients of the regression lines corresponding to the ratings of perceived exertion (RPE) versus time relationship (y axis) obtained during the predictive tests were plotted against the power outputs (x axis) to estimate PET. PET was calculated as the intersection point of the regression line in the power axis. The 14-17 RPE range of each predictive test was modeled using the same mathematical procedures used to estimate PET14-17. CP was derived from the power-time hyperbolic equation. Analysis of variance revealed no significant differences among CP (189-194 W), PET (190-191 W) and PET14-17, (191-195 W). The correlations between CP and PET (r = 0.87), CP and PET14-17 (r = 0.89), and PET and PET14-17 (r = 0.88) were all strong. Additionally, the bias ± limits of agreement when plotting CP and PET was -2.16 ± 31.60 W, and -5.70 ± 31.21 W when comparing CP and PET14-17. Relatively high reproducibility levels of CP (ICC = 0.96), PET (ICC = 0.85) and PET14-17 (ICC = 0.83) were recorded in the test-retest fashion. It can be concluded that the PET14-17 can be utilized with relatively high accuracy and reproducibility to estimate CP without causing exhaustion in the subjects.

1Universidade Estadual de Londrina, Paraná, Brazil; 2Universidade Católica de Brasília, Distrito Federal, Brazil; 3Facoltà di Scienze Motorie, Università di Verona, Verona, Italy

Address correspondence to Fábio Yuzo Nakamura,

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The critical power (CP) index has been extensively used in endurance capacity assessment of athletes (6,7,11,31), as well as healthy nonathletes and diseased populations (24,26). It is based on nonlinear modeling of the power-duration relationship derived from constant power output exhaustive trials (predictive tests). Thus, it is considered a noninvasive and relatively simple method, and has been shown to provide a valid estimate of the maximal lactate and oxygen consumption steady state (14,15,27,28). In addition, the power-duration hyperbolic curve fitting has been proved to be useful in predicting middle (4) and long distance (11,30,31) cycling and running performances.

The critical power modeling allows for the estimation of a second parameter (anaerobic work capacity, AWC) which represents a finite amount of work that can be performed above CP, regardless of the rate at which it is performed. The AWC reflects the energy store comprised of phosphagen pool, and a source related to anaerobic glycolysis, with consequent cellular acid-basic disturbances (13,21).

The time to exhaustion in severe exercise trials (i.e., above CP) is a function of AWC and CP, in the following hyperbolic form (13):

According to Hill and colleagues (14,15), the time to achieve VO2max during the predictive tests can also be expressed as a hyperbolic function of power. The power asymptote was not different from CP, and they were highly correlated (r = 0.95-0.97). Considering that the time to achieve VO2max is shorter than the time to exhaustion, the method proposed by Hill and colleagues (14,15) can be considered nonexhaustive. In other words, the subjects may stop cycling before the discomfort associated with severe metabolic acidosis becomes difficult to bear. Consistent with this is the lower estimated AWC until the VO2max attainment. It is an important feature for practical purposes, since the exhaustive nature of the tests is one of the most limiting factors in traditional CP and AWC determination, especially among diseased individuals (18).

Recently, we have outlined a method of CP estimation using rating of perceived exertion (RPE) responses (22,23). During 3-4 exhaustive tests, the individuals were instructed to report their RPE according to the 15-point Borg scale (3) each 15 m (deep water running) or each 30 s (cycling on an ergometer). The linear regression slope coefficients of the rate of rising RPE over time at each test (y axis) and the intensity indicator (velocity or power output, x axis) presented a strong linear relationship. The x-intercept (perceived exertion threshold, PET) was considered the theoretical intensity corresponding to the maximal RPE steady state, because the slope coefficient would be equal to zero. PET was neither different from CP, nor from an indicator of maximal oxygen consumption steady state, and was highly correlated with these parameters (22,23). Despite the usefulness of PET in predicting CP, it still involves exhaustive exercise tests.

Therefore, the first aim of this study was to evaluate a novel procedure (PET14-17) involving nonexhaustive efforts to estimate CP, based on submaximal RPE responses during constant work rate tests, avoiding the inherent discomforts associated with maximal duration severe efforts. The second aim was to examine the reproducibility of PET, PET14-17, and CP in a test-retest fashion.

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Experimental Approach to the Problem

In this study, the subjects were required to visit the laboratory on 10 occasions. The exercise sessions were comprised of 2 practice trials followed by 2 series (Trial 1 and Trial 2) of 4 severe constant-load work bouts until exhaustion. The mean power outputs corresponding to CP, PET, and PET14-17 were estimated from the 4 bouts conducted in both trials and then statistically compared and intercorrelated. Additionally, reproducibility of each parameter was calculated based on a test-retest design.

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A total of 20 young and healthy male subjects took part in this investigation (age, 22.9 ± 3.5 years; weight, 77.2 ± 11.0 kg; height, 176.5 ± 5.6 cm). They provided written informed consent to participate, and the study received approval by the Ethics Committee of Universidade Estadual de Londrina. All participants were recreationally active and fully familiar with laboratory exercise testing procedures.

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A Monark cycle ergometer (Model 814E, Vansbro, Sweden) with frictional flywheel resistance was utilized in all tests. The seat height was adjusted according to the individual's lower limb length, so that legs were at near full extension during each pedal revolution. Toe clips held subjects' feet fixed in the pedals.

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On alternate days, the subjects performed two severe exercise intensities on the ergometer until voluntary exhaustion. All practice sessions were preceded by a 5-minute loadless warm-up period, followed by a rest period of equal duration. The aim of these practice trials was to familiarize the subjects with the type of effort that they would perform during the predictive tests for critical power model parameters, as well as PET and PET14-17 estimation. In general, the practice trials caused exhaustion in 1-15 minutes. These trials were also used to guide the choice of cycling power outputs for the subsequent phases of the study. These results were not used in any analyses.

During the familiarization trials, subjects were introduced to the use of a 15-point Borg scale (3). The instructions given to the subjects included information about “anchoring” of the scale at the extreme values (6, a very light activity near resting metabolic rate; 20, the greatest effort sensation already experienced) and the correspondence of the intermediary values of scale to verbal attributes related to graded RPE levels.

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Predictive Tests

Four all-out exhaustive tests were used for the CP, PET, and PET14-17 estimations. At the end of the first sequence of 4 tests (Trial 1), the subjects performed the same predictive tests in a random order on subsequent days (Trial 2), in order to evaluate the reproducibility of the parameters. All tests were preceded by a 5-minute loadless warm-up, followed by a rest period of equal duration. In general, participants reached exhaustion within 1-15 minutes during the tests. Subjects were asked to avoid participation in vigorous physical activities in the 24-hour period before each test. They were instructed to remain in a fasting state in the 3-hour period previous to the tests, and to not ingest beverages containing alcohol in the previous 24 hours. All trials were performed at approximately the same time of day. All procedures were conducted within a 4-week period.

The cadence was fixed at ∼78 rpm. The exhaustion point was set by the incapacity of subjects to keep the target velocity for a period greater than 5 seconds despite strong verbal encouragement. Time to exhaustion was recorded to the nearest second. The participants were not informed about the power output against which they were requested to cycle, nor the expected duration of each predictive test. To fit the individual results to the critical power model, Equation 1 was solved by nonlinear regression. During the predictive tests the subjects were asked to report the RPE, corresponding to a number on the Borg scale fixed in front of them, whenever they felt that the exertion sensation was increased. The first reported value was free and could be chosen as soon as the subject felt able to accurately point to the RPE levels.

The increase of RPE as a function of time until the attainment of the maximal level (19 to 20) presented an approximately linear relationship in all subjects (Figure 1). The slope coefficients of the regression lines were proportional to the power output performed during the predictive trials.

Figure 1

Figure 1

The relationship between RPE increase rates (y axis) and exercise intensities (power output, x axis) presented a strong linearity in all investigated subjects. Individually, the PET intensity was defined as the intersection point of the regression line in the power axis (Figure 2). In theory, it represents the maximum intensity at which the RPE increase rate would be equal to zero (“steady state”).

Figure 2

Figure 2

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Nonexhaustive Procedure

In order to test the possibility of using submaximal RPE measures to estimate CP, the intermediary portion of the linear regression relating RPE and time was analyzed. The 14-17 RPE range of each predictive test was fitted to a linear function to the slope coefficient determination. The mathematical procedure illustrated in Figure 2 of extrapolation of the linear relationship between the RPE increase rate and power output to the x axis was applied to the estimation of PET14-17. It can be considered a nonexhaustive version of the original PET.

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Statistical Analyses

The results were expressed as mean ± standard deviation. Least square linear and nonlinear regressions were used to fit the data in order to estimate CP, PET, and PET14-17. Analysis of variance (ANOVA) with repeated measures was used to compare CP, PET, and PET14-17 estimates obtained in Trial 1 and Trial 2. All data were assessed for sphericity using the Mauchly test, and whenever the test was violated, we performed the necessary technical corrections through the Greenhouse-Geisser test. Whenever the F test was significant, the analysis was complemented by means of a Bonferroni multiple comparison test. Pearson product moment correlations were used to quantify the relationships between CP, PET, and PET14-17 estimates. Bias and limits of agreement were calculated by plotting the difference between the estimates against their means (Bland-Altman analysis), as well as for the reproducibility analysis of these parameters (2). The reproducibility was also accessed by the calculation of the intraclass correlation coefficient (ICC). The level of statistical significance was set at p ≤ 0.05. All data analyses were performed using the Statistical Package for Social Sciences (SPSS), version 13.0 for Windows.

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The mean power outputs and the respective durations of the tests to estimate the CP, PET, and PET14-17 parameters during Trial 1 and Trial 2 are presented in Table 1.

Table 1

Table 1

Critical power modeling presented a high goodness of fit to the performance data derived from Trial 1 and Trial 2; the coefficient of determination (R2) approached 1 in both trials (Trial 1 = 0.961 ± 0.033; Trial 2 = 0.980 ± 0.020). During Trials 1 and 2, the R2 values corresponding to the linear regression between RPE and time for overall predictive tests of PET averaged 0.973 ± 0.030 and 0.980 ± 0.025, respectively. The same estimates for PET14-17 were 0.981 ± 0.024 and 0.985 ± 0.014. Finally, the linear regression slope coefficients of the rate of rising RPE over time (y axis) and the intensity indicator (power output, x axis) presented a strong linear relationship for both PET (Trial 1 = 0.950 ± 0.040; Trial 2 = 0.945 ± 0.063) and PET14-17 (Trial 1 = 0.928 ± 0.060; Trial 2 = 0.928 ± 0.117) estimation.

The mean values of CP, PET, and PET14-17 during Trials 1 and 2 are presented in Table 2. Repeated measures ANOVA revealed no differences among the estimates (P = 0.641).

Table 2

Table 2

The group's estimated AWC was 22,896 ± 5161 J during Trial 1, and 21,366 ± 5802 J during Trial 2. The estimates were not significantly different (P = 0.18).

The correlations between CP and PET (r = 0.87), CP and PET14-17 (r = 0.89) (Figure 3, upper panels), and PET and PET14-17 (r = 0.88) were all strong. Figure 3 (lower panels) also shows the results of a Bland-Altman analysis when comparing PET and PET14-17 with CP. The mean difference (bias) ± limits of agreement (LoA 95% CI) of CP and PET was -2.16 ± 31.60 W. The plot ratios of measures give 0.81 and 1.17 as the lower and upper limits (95% CI) of the differences between CP and PET. This suggests that for about 95% of cases, the individual differences between estimates range from 0.81 to 1.17 times the average value ((CP + PET)/2).

Figure 3

Figure 3

The gray area in Figure 3 (lower panels) represents the limits of agreement of the CP estimate, which were based on its repeatability using the Trial 1 and Trial 2 results. The thick arrow indicates an overlapping of 2 subjects' data. It can be noted that 14 out of 20 subjects of the sample, in the comparison between CP and PET, are within the variability range (95% CI) of their own CP, detected by the Bland-Altman reproducibility plotting (Table 3). Comparable results were observed in CP and PET14-17 analysis by Bland-Altman plotting. The bias ± LoA 95% CI was -5.70 ± 31.21 W. Thirteen out of 20 subjects were within the gray area, meaning that, for the most part, the sample had PET14-17 estimates inside the CP test-retest variance range. In addition, the plot ratios indicate that the lower and upper limits of agreement were 0.82 and 1.13, respectively. This suggests that for about 95% of cases, the individual differences between estimates range from 0.82 to 1.13 times the average value ((CP + PET14-17) / 2).

Table 3

Table 3

The ICC, the bias between Trial 1 and Trial 2, and the LoA 95% CI of CP, PET, and PET14-17, are presented in Table 3. The bias for all measures were relatively low (-5.02 to 4.07 W), whereas the LoA 95% CI presented narrower ranges for CP, compared to PET and PET14-17. The plot ratios of test-retest measures of CP (0.89 and 1.07), PET (0.83 and 1.21), and PET14-17 (0.78 and 1.29) were consistent with this trend. Nevertheless, all estimates presented relatively high reproducibility according to the ICC (0.83 to 0.96).

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The main purpose of the present study was to verify the possibility of using a nonexhaustive alternative method (PET14-17) for CP estimation based on submaximal RPE values reported individually during predictive tests. The results indicated no differences among CP (189-194 W), PET (190-191 W), and PET14-17 (191-195 W). In addition, they were highly correlated (r = 0.87-0.89) and presented relatively narrow limits of agreement when contrasted by the Bland-Altman plotting. Therefore, PET14-17 appears to provide an alternative, nonexhaustive method for CP estimation.

The mathematical methods for PET and PET14-17 calculations were similar to those proposed by Malek et al. (19) and Miller et al. (20) to determine the physical working capacity at the heart rate threshold (PWCHRT) and at the oxygen consumption threshold (PWCVO2). They are based on the determination of individual power outputs that can be maintained with no detectable rise in these cardiovascular variables, after the initial period (3 minutes) of fast phase adjustment kinetics (Phase 2 of VO2 kinetics), by means of extrapolation of the regression line between the slope of VO2 and heart rate rise as a function of time during 8-minute submaximal tests, and intensity (power output or velocity). In theory, both indices indicate the transition from moderate to heavy exercise intensity domain (9), since they were not significantly different from ventilatory threshold.

Previously, we have demonstrated that PET estimates determined in protocols involving fixed distances or periods of time laps to the RPE data recording were not different from the CP measures (22,23). The correlations between PET and CP in deep water running were around 0.85-0.88 (23), and in cycling, the value was 0.96 (22). In addition, PET was strongly correlated (r = 0.92) with an estimate of maximal oxygen consumption steady state based on the hyperbolic relationship between power output and the time to the achievement of VO2max during severe trials (14,15).

The anticipatory component attributed to the RPE was the basis to the purpose of PET14-17 measure. PET14-17 seems to be an attractive, nonexhaustive approach to assess the aerobic capacity based on the intermediary RPE responses. The main advantage of this approach is that it can be potentially applied to populations with maximal exercise intolerance, caused by some diseases or lack of physical fitness, avoiding unnecessary risks to the subjects. Even in apparently healthy and highly trained populations, nonexhaustive tests should be encouraged because they minimize subjective discomforts associated to the exhaustive efforts.

Previously, Capodaglio and Saibene (5) utilized the CR10 Borg scale (3) to assess the sustainable mechanical power output during daily activities in older people, using upper and lower-body exercises. The subjects cycled during 5-6 different constant-load work bouts until the moment that RPE reached the 4 (somewhat heavy) to 5 (heavy) transition, according to the scale. The total work done and time to achieve the 5 value presented a linear relationship. The slope coefficient of the regression line was recorded as an estimate of the everyday sustainable activity. On average, the sustainable power calculated for the lower limbs represented 55% of the maximal mechanical power.

For the PET14-17 calculation, we selected the 14-17 range from the 15-point Borg scale because the initial values of RPE during a constant-load exercise seemed to be inaccurate. This is due to delaying of the peripheral feedback signals that compose the central integration of perception. It is particularly true around the first minute of testing (33). Additionally, we have observed empirically that this RPE values range presents a high linearity. The results indicated that the slope coefficient values using the nonexhaustive procedure were probably similar to those observed for the entire straight line. In fact, PET14-17 and PET were very close.

Noakes (25), analyzing the data of Baldwin et al. (1), suggested a possible role of the anticipatory mechanisms, which allow the organism to make calculations about the exercise end caused by protective fatigue sensations. Ratings of perceived exertion were reported in subjects who began a 70% of peak O2 uptake in either the carbohydrate-replete or carbohydrate-depleted state. It was reported as a linear relationship between the RPE and the duration in both conditions. The slope coefficient was noted to be greater in the carbohydrate-depleted state. In contrast, when duration is expressed as percentage of the total exercise time, the RPE responses overlap. These findings support the hypothesis that RPE is an information source mechanism that can be used by the brain to predict the time left to exhaustion.

Apparently, the above mentioned study negates our contention that PET represents the maximal RPE steady state, because the exercise clearly below CP (∼85-90% of peak O2 uptake (27,28)) induced continuous rises of perceptual responses until near maximal levels (∼18.1), according to the 15-point Borg scale. We have observed the same pattern during intermittent exercise (unpublished data) and the interpretation is similar to that provided by Noakes (25). Below the CP intensity, the RPE is probably affected by factors such as the muscular glycogen content, supplemented by thermoregulatory and cardiorespiratory inputs. Therefore, the real RPE steady state might be just a theoretical fact.

Above CP, the slope coefficients of RPE rising along the duration of severe trials are necessarily much greater than below CP. It is assumed that the major afferent signal causing this rise is the AWC utilization rate. Therefore, the equivalence of CP, PET, and PET14-17 could be expected. In future studies, the relationship between PET and PET14-17 and the long-term performance must be tested. In addition, its potential in exercise prescription for athletes and disabled individuals has to be demonstrated.

Previous studies (13) have reported relatively high values (0.90-0.96) for test-retest reproducibility of CP, using Pearson coefficient correlation. In the present study, we have reported comparable ICC value (0.96) for this index. In addition, as in Taylor and Batterham's study (32), our results were analyzed by Bland-Altman plotting, which revealed plot ratios of 0.89 to 1.07 times the average intrasubjects CP estimates. In absolute terms, our CP estimates presented LoA 95% CI ranging from -22.53 to 12.49 W. We consider this range relatively narrow, since the subjects studied by Taylor and Batterham (32) presented -15 to 17 W of LoA 95% CI in upper body exercise, associated with a mean CP of 95 W, while our subjects presented ∼190 W of lower limbs' CP, on average. The PET and PET14-17 estimates presented minor ICC levels (0.82 and 0.83), associated with larger LoA 95% CI. The plot ratios of PET (0.83 and 1.21) and PET14-17 (0.78 and 1.29) impose less repeatability of these measures, when compared with CP. Nevertheless, considering the “subjective” nature of these estimates, and the non-exhaustive nature of PET14-17, we believe that both indices can be utilized in practical settings with good reproducibility. However, caution should be taken regarding the experience of the subjects with laboratory exercise testing and RPE scale use. Our subjects had previous experience with these procedures.

The major limitation of the present study was the absence of a square wave test at PET or PET14-17 in order to verify the RPE responses associated with other physiological measures (lactate and VO2). This kind of trial could also be used to establish the tolerance time to exercise at these intensities. However, the results convincingly demonstrate the potential of these estimates to evaluate the aerobic capacity non-invasively, and not necessarily using exhaustive tests.

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Practical Applications

The present results confirmed the possibility of estimating CP based on RPE responses derived from predictive tests. The adequate mathematical modeling allows for a relatively reproducible measure of CP using the PET concept. Nevertheless, the most striking finding is related to the possibility of estimating this important endurance capacity index without causing exhaustion in the subjects, which is frequently accompanied by discomfort related to severe metabolic acidosis. Thus, we believe that PET14-17 is a promising index to physical fitness routines developed in fitness centers and in rehabilitation settings. If confirmed in diseased populations, the aerobic functional capability of disabled subjects could be accessed more safely. However, it is still conjectural because our study was limited to healthy, young subjects. In addition, some athletes with transitory exercise intolerance (e.g., overtraining) could be evaluated through a nonexhaustive procedure. It remains to be established if overreaching or overtraining might dissociate PET14-17 and CP because of disturbed perceptual responses caused by the accumulated fatigue. In this case, future studies have to be designed to test PET14-17, as well as PET, in other populations.

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    critical power; rating of perceived exertion; cycle ergometer

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