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Which Cutoffs for Secondary V˙O2max Criteria Are Robust to Diurnal Variations?


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Medicine & Science in Sports & Exercise: May 2019 - Volume 51 - Issue 5 - p 1006-1013
doi: 10.1249/MSS.0000000000001869
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The maximum volume of oxygen uptake per minute (V˙O2max, L·min−1) is considered the gold standard to measure cardiorespiratory fitness. Therefore, V˙O2max is used in intervention studies as a primary outcome to assess changes in physical fitness, in competitive sports to evaluate the effectiveness of training programs or in clinical settings for risk estimation of all-cause mortality (1). To maximize signal-to-noise ratio, it is crucial to measure V˙O2max with sufficient rigor, especially when baseline and follow-up values are being compared. If the “true” V˙O2max were not determined in both, baseline and follow-up tests, the intervention would account for changes in V˙O2max, which may actually result from an inaccurate measurement. Participants’ maximum possible effort is necessary to ensure that peak oxygen uptake (V˙O2peak) and true V˙O2max are achieved (2). The primary criterion to distinguish V˙O2max from V˙O2peak is the appearance of a V˙O2 plateau. However, a V˙O2 plateau may not be found in all participants, even if performing the exercise test at maximal effort (3–5). Furthermore, the criteria to define a V˙O2 plateau are controversial (6). Verification phases (i.e., additional supramaximal exercise tests performed immediately after a short regeneration phase subsequent to the cardiopulmonary exercise test [CEPT]) have been discussed as an additional method to determine true V˙O2max (2,7). However, verification tests are rather time-consuming, and their day-to-day reliability has not been investigated. Additionally, the procedure to perform these verification tests is not standardized (8) and many previous studies that promote the use of verification tests failed to report the required data to support the use of verification phases. In detail, it has been criticized that V˙O2 from the initial phase of exercise testing and V˙O2 from the verification phase were only compared on a group level (9) and it was not reported in which proportion of participants V˙O2max could actually be verified (10–14). In those participants that show no V˙O2 plateau and without a verified V˙O2max, secondary criteria are used to distinguish between V˙O2peak and V˙O2max (2,6,15). However, secondary criteria to define V˙O2max are rarely reported, despite their importance. Only 76% of studies published in Medicine and Science in Sports and Exercise from October 1993 to May 1994 (16) and 44% of studies published from October 2005 to May 2006 (6) reported criteria for V˙O2max. The most commonly secondary V˙O2max criteria are maximum RER (RERmax), maximum HR (HRmax), maximum RPE (RPEmax), and maximum concentration of blood lactate (BLmax) (6). Values used to confirm V˙O2max attainment include ≥1.00 (17) and ≥1.10 (18,19) to ≥1.15 (5,20) for RERmax, 85% (21) to 100% (22) of age-predicted HRmax (based on the formula 220 – age in years), ≥17 (18) to ≥19 (6) for RPEmax, and from ≥8 (16) to ≥10 mmol·L−1 (6) for BLmax. Interestingly, and as noted by Midgley et al. (6), participants reached these criteria in nearly all studies, leaving room for speculation as to whether exhaustion criteria were defined postanalysis. However, defining secondary V˙O2max criteria is a trade-off between mistakenly assuming that subjects have reached V˙O2max when they have not (i.e., low criteria, type I error) and declaring subjects to have not reached V˙O2max even though they have (i.e., high criteria, type II error). Therefore, this study analyzed data from two studies with endurance-trained athletes, pursuing the following aims:

Aim I was to define secondary V˙O2max criteria based on the results of the first study. Therefore, differences in V˙O2 were assessed at time points during the CEPT when different criteria were reached based on various cutoffs used in various studies. Based on the results, criteria were defined to reduce type I errors without increasing the risk of type II errors. Aim II was to test if the criteria defined in Aim I would be robust to diurnal variations and day-to-day variations.


Study design

In this work data from two different studies were analyzed. The first study was conducted between April 2014 and April 2015 ( Identifier: NCT02203539) and the second study between December 2016 and April 2018 in the laboratories of the Department of Sport, Exercise and Health at the University of Basel, Switzerland under consistent conditions (air humidity, 40%–55%; room temperature, 20°C–22°C) with the same equipment. Both studies were approved by the local ethics committee “Ethikkommission Nordwest- und Zentralschweiz” (EKNZ 2014-056 and EKNZ 2016-01572) and written informed consent was obtained from all participants before the start of studies. Study 1 primarily investigated the influence of different light exposures on cycling performance. All CEPT data analyzed in this work were performed without previous light exposure under normal room lighting conditions. The purpose of study 2 was to investigate the time of the day when athletes achieve their peak performance and the association of this time of the day with participants’ chronotype and training habits.


Inclusion criteria for both studies were physical and mental health, ages 18 to 35 yr, no shift work in the last 3 months and no travel across time zones in the 4 wk before the study, and high cardiorespiratory fitness. Only participants with a V˙O2max ≥ 95th percentile of ACSM references values (i.e., ≥56 mL·kg−1·min−1 for males and ≥50 mL·kg−1·min−1 for females) (23) were included in this analysis. For study 1, a further criterion was male sex. The main sports performed by participants in the first study were cycling (n = 27), triathlon (n = 8), other endurance sports (e.g., running, rowing, kayak) (n = 11), team sports (e.g., football, hockey, volleyball) (n = 14) and other sports (e.g., tennis, squash (n = 10). The main sports performed by participants in the second study were cycling (n = 8) and other endurance sports (e.g., running, rowing) (n = 5). Participants were advised to restrain from alcohol, caffeine, and vigorous exercise through the entire studies and advised to avoid malnutrition and dehydration.

Participant characteristics testing

In both studies, a physician physically examined participants, a 12-channel resting electrocardiograph was acquired, medical history was assessed, and body height was measured.

Cardiopulmonary exercise testing

In both studies, cardiopulmonary exercise testing until exhaustion was performed using a bicycle ergometer (Sport Excalibur; Lode Medical Technology, Groningen, The Netherlands). Participants were free to choose pedaling cadence as long as it remained over 60 rpm. Participants were allowed to cycle with their own pedals and shoes. Before each test body mass and body fat content were measured with four segment bioelectrical impedance analyses (Inbody 720; Biospace, Seoul, South Korea). In both studies workload linearly increased with 25 W·min−1 (20 W·min−1 for females in study 2) until exhaustion. In both studies, through the entire CPET gas exchange was measured breath by breath (MetaMax 3B; Cortex Biophysik GmbH, Leipzig, Germany). For analysis data were averaged in 10-s intervals. V˙O2max was determined as the highest 30 consecutive seconds of V˙O2. Maximum workload (Pmax) was defined as the highest value during exercise with a minimum of 60 rpm. RERmax was determined as the highest value during exercise. HR was monitored with a 12-channel electrocardiography (Custo med GmbH, Ottobrunn, Germany) to comply with ethical regulations. For data analyses, HR was additionally measured with a Polar T-34 HR belt (Polar Electro Europe AG, Zug, Switzerland). According to the 6-20 Borg scale (24), RPE was assessed at rest, after warm-up, and every 3 min until exhaustion. Capillary blood lactate concentration (analyzed by SuperGL Ambulance; Hitado Diagnostic Systems, Moehnesee, Germany) was measured at rest, immediately after exhaustion, 1, 3, and 5 min after exhaustion. The highest measured value was labeled as BLmax.

In study 1, the only CPET performed was scheduled around 4:00 pm (median time, 4:17 pm). In study 2, six CPET were performed at: 7:00 am, 10:00 am, 1:00 pm, 4:00 pm, 7:00 pm, and 9:00 pm in randomized order to investigate the diurnal variation in the criteria defined in study 1. Additionally, a seventh test was performed at the same time the sixth test was performed to investigate the day-to-day variability in the criteria. In study 2, a verification test was performed immediately after the CPET. After a regeneration period of 10 min in duration, workload was increased stepwise to 50% of Pmax for 2 min and then to 70% of Pmax for 1 min. Subsequently, workload was increased to 105% of Pmax until exhaustion (25). V˙O2max verification was accepted if the verification- V˙O2 was ±3% of the V˙O2max from the initial phase of the exercise test (25). This protocol has been used in a previous study where it led to a successful verification in all participants (25). However, this protocol showed an insufficient Gwet’s agreement coefficient for the diurnal variation indicating a rather low reliability (data not shown). Therefore, the verification data was not considered in this manuscript. A V˙O2 plateau was defined as an increase of V˙O2 < 125 mL·min−1 between the last and the second to last minute of the CEPT. This definition was based on the assumption that V˙O2 increases approximately 10 mL·min−1 in the submaximal intensity domain per increase of each watt (26). Therefore, the cutoff value amounts to half of the expected V˙O2 increase between neighboring 1-min sampling intervals (~250 mL·min−1), as recommended by Marsh (27).

Further, we compared the secondary V˙O2max criteria, that is, the time points at which V˙O2 was analyzed, for RER (≥1.05, ≥1.10, ≥1.15) and HR (≥90%, ≥95%, and ≥100% of age-predicted HR). The formula for age-predicted HR 220 minus age (28) was adapted to 210 minus age in years to consider the lower muscle mass involved in a cycle ergometer test which results in a lower maximum HR in comparison to treadmill tests (29,30). Further, the values reached by the participants for RPEmax and BLmax were compared with the values stated in various guidelines.

Statistical analysis

In a first step, descriptive statistics were used to compare the number of participants reaching certain exhaustion criteria and the respective V˙O2 reached at that point in time. Based on these results, cutoff values were defined for secondary exhaustion criteria that were least likely to produce type II errors. The cutoff was defined as 2.5% of participants not reaching a criterion, based on the 95% confidence interval. Furthermore, we compared the four secondary exhaustion criteria (RERmax, HRmax, RPEmax, and BLmax) between participants showing a V˙O2 plateau and those showing no V˙O2 plateau to ensure that the recommendations for the cutoff values were not biased by type I errors. For the second aim, we ascertained the number of tests in study 2 where certain exhaustion criteria were not met. To analyze the day-to-day variation, intraclass correlations were calculated for performance parameters and the four secondary exhaustion criteria values between the sixth and the seventh test from study 2. Intraclass correlation coefficient values were interpreted as follows: <0.5: poor, 0.5–0.75: moderate, 0.75–0.90: good, >0.90: excellent (31). Intraclass correlation does not account for the fact that the coefficient is dependent on the standard deviation, which is irrelevant for the intraindividual reliability. Therefore, we further calculated the standard error of measurement (SEM) (32). Normality was assessed using normal quantile-quantile plots of the residuals and variance homogeneity was assessed using Tukey-Anscombe plots. Descriptive data are presented as mean and standard deviation or median and interquartile range. For our analyses, we used IBM SPSS Statistics for Windows, version 24 (IBM Corp., Armonk, NY) and R version 3.3.1 for graphics (R Foundation for Statistical Computing, Vienna, Austria). The data analyzed in this study were used from a previous study on which the sample size was calculated for. Therefore, we did not perform a sample size calculation for this study (33).


Participant flow and characteristics

Seventy males from study 1 and eight males and five females from study 2 were analyzed. Participant characteristics from medical examination and CEPT are presented in Table 1. There were no relevant differences between male participants from study 1 and study 2.

Definition of cutoff values for secondary exhaustion criteria

Table 2 shows the number and percentage of participants from study 1 reaching the different exhaustion criteria defined in the literature. The table shows the V˙O2 uptake at the time point, when the different exhaustion criteria were met and the relative proportion of each value from the measured V˙O2max. RERmax ≥1.1, HRmax ≥90% of age-predicted maximum HR (APHR), RPEmax ≥19 and BLmax ≥8 mmol·L−1 were reached by all participants suggesting that these values are unlikely to cause type II errors. Thus, exhaustion criteria in the literature with lower values then these may produce type I errors. The 95% of APHR and BLmax ≥10 mmol·L−1 values were not reached in only one participant. Therefore, these values fall within the defined 2.5% error range.

A V˙O2 plateau appeared in 40 of the 70 (57%) participants in study 1. There were no relevant or significant differences in any secondary exhaustion criteria between participants showing a V˙O2 plateau (RERmax 1.19 ± 0.04; HRmax 192 ± 8 bpm; RPEmax 19.9 ± 0.3; BLmax 14.8 ± 2.1 mmol·L−1) and participants showing no V˙O2 plateau (RERmax 1.18 ± 0.04; HRmax 193 ± 10 bpm; RPEmax = 19.9 ± 0.3; BLmax 14.4 ± 2.7 mmol·L−1). However, participants showing a V˙O2 plateau had a significantly higher V˙O2max (64.2 ± 4.9 mL·kg−1·min−1) and power output (417 ± 40 W) than the group without V˙O2 plateau (61.6 ± 5.4 mL·kg−1·min−1 and 396 ± 35 W). The mean differences were 2.6 mL·kg−1·min−1 (95% CI, 0.1–5.1; P = 0.042) and 22 W (95% CI, 3–40: P = 0.022). The coefficient of variation across all trials for V˙O2max (L·min−1) was 3.4%. Figure 1 shows the V˙O2–work relationship of three participants and the V˙O2 values at the points in time the respective criteria were achieved.

V˙O2–work relationship profiles from three participants and the V˙O2 at the time points certain secondary V˙O2max criteria were reached. HR 100%, 100% of APHR; HR 95% of APHR.
Participant characteristics.
Values for V˙O2 at the time point when exhaustion is reached based on different cutoffs.

Secondary exhaustion criteria: Diurnal variation

RERmax ≥1.15 was reached in all tests by nine participants. At one or more occasions (i.e., times of the day) four participants did not reach a value of RERmax ≥1.15. All participants reached the value of RERmax ≥1.10 at every time of the day except of one. BLmax ≥10 mmol·L−1 was not reached in all tests by four of five women and by two men in all tests.

Secondary exhaustion criteria: Day-to-day variability

There was a significant intraclass correlation for maximum power output (W) and V˙O2max (L·min−1) between the two CPET at the same time of the day (Table 3). These correlations indicate excellent reliability (31) and therefore low day-to-day variability in performance. RERmax and HRmax also showed significant correlations, indicating low day-to-day variability and robustness. Furthermore, the typical percentage error was lower than 3% for the respective value (Table 3). Twelve of 13 participants rated RPE at 20 on both tests and the remaining participant rated RPE at 19 and 20, respectively. Due to all values from the last test day being 20, no variation was present. Hence, an interclass correlation could not be calculated. BLmax showed no significant correlation between the two CPET at the same time of the day. There was no significant difference in lactate concentrations between the first and the last test, which indicates sufficient regeneration time between the tests. Furthermore, the percentage typical error was quite high in comparison to RERmax and HRmax. The coefficients of variation were 1.6% for Pmax, 2.6% for V˙O2max, 1.8% for RERmax, 1.4% for HRmax and 14.9% for BLmax, respectively.

Interclass correlation and standard error of measurement of performance and V˙O2max criteria regarding day-to-day variation (day 1, test 6; day 2, test 7 of study 2)—mean ± SD.


To determine V˙O2max in athletes rather high cutoff values for secondary V˙O2max criteria can be used without increasing the risk of type II errors. However, type I errors may still occur indicating that further methods, such as V˙O2 plateau or V˙O2 validation, may be required. Participant A in Figure 1 showed a V˙O2 plateau and therefore reached V˙O2max. However, if V˙O2max criteria were chosen too highly (i.e., RER ≥ 1.15, HRmax ≥100% of APHR) this participant would be misclassified as not reaching V˙O2max although he in fact did (i.e., type II error). Participant B showed a V˙O2 plateau and also reached the higher V˙O2max criteria. If this participant had stopped at a submaximal V˙O2 he would still have reached all criteria indicating possible type I errors for these criteria. Participant C, on the other hand, showed no V˙O2 plateau although he by far reached all criteria. For participant C it would still be unclear if the measured V˙O2peak is also the V˙O2max. A review by Midgley et al. (6) shows that many published studies have used relatively low exhaustion criteria (6). This strongly increases the chance to assume that subjects have reached V˙O2max when they actually have not. From a study with eight subjects, Poole et al. (15) recommended not to use any secondary exhaustion criteria due to the high risk of type I and type II errors. Based on the data from the present work RER ≥ 1.10, HRmax ≥95% of APHR and RPE ≥ 19 are highly likely not to produce type II errors. Therefore, participants are not misclassified for not reaching V˙O2max, they in fact did. If these values are used as the minimum for cutoff values in athletes, it may still occur that subjects are declared as not exhausted even though they are but with a smaller impact on V˙O2max than with lower cutoff values. Misclassification of exhaustion with lower secondary V˙O2max criteria may lead to the misinterpretation of study results or training progress. In our study population, for example, 75% of participants (i.e., the upper quartile) achieved only 93% or less of their actual V˙O2max when they reached RER ≥1.05 (Table 2). These participants would, therefore, be falsely classified as exhausted. If attainment of V˙O2max is achieved in a subsequent test, a performance increase of 7% is “measured” only due to higher exhaustion levels. Although, there is no ideal cutoff value to prevent all type I and type II errors this does not justify abandoning all secondary exhaustion criteria, because so far there is no acceptable alternative to be used in large-scale studies. Verification-phases are highly dependent of the participants’ motivation and V˙O2 plateaus do not appear in all participants (34–36). More importantly, large-scale studies generating reference values for V˙O2max need to use equivalent secondary exhaustion criteria to make the results comparable.

RER ≥ 1.15 and HRmax ≥100% of APHR were not reached by several participants during several CEPT in study 1. From the 40 participants showing a V˙O2 plateau in study 1, nine did not reach ≥1.15 and six did not reach HRmax ≥100% of APHR. This supports the conclusion drawn, from the results of study 1, that these two values are likely to increase the chance of classifying an exhausted participant as not-exhausted. In contrast, RERmax ≥1.10 and HRmax ≥95% were reached by all participants showing a V˙O2 plateau in study 1. In study 2, these cutoffs were not reached in only 1 of 78 cases (13 participants × 6 tests each) supporting the recommendation of choosing this cutoff. Furthermore, RERmax and HRmax showed low day-to-day variability as indicated by the moderate reliability (31) based on the lower bound of the 95% confidence interval of the intraclass correlation (Table 3). The standard error of measurement and typical percentage error are low for both RERmax and HRmax at 1.7% and 1.6%, respectively. As mentioned intraclass correlations for RPE could not be calculated due to the ceiling effect of this parameter. This ceiling effects lead to the fact that variations can only appear in one direction and therefore increase test–retest reliability. Therefore, it may be discussed if RPE might better serve as an external criterion.

Based on a sample size of 861 participants Edvardsen et al. (37) recommend to use a cutoff value for BLmax of 9 mmol·L−1 for treadmill exercise testing. Based on our data from study 1, a cutoff value for BLmax seems to be applicable; however, data from study 2 investigating the reliability showed a poor and nonsignificant intraclass correlation of 0.380 (−0.191; 0.759) representing poor reliability (31) (Table 3). Additionally, BLmax showed a very high typical percentage error of 13.9%. BLmax was also highly variable between participants (Table 1). In study 1, lactate concentrations ranged from 8.2 to 21.0 mmol·L−1, making it hard to define generalizable cutoffs for this parameter. Furthermore, blood lactate concentrations showed high variance during the day. This is likely due to varying nutrition status. This variation in nutrition status may lead to lower reproducibility of lactate concentration. However, it is remarkable in this context that RERmax showed much better reliability, since RERmax values >1.0 are mainly determined by the respiratory compensation of metabolic acidosis, which is affected by the lactate production. Finally, females are less likely to reach the cutoff values for lactate concentration. This may not be due to less exhaustion but rather from fewer fast-twitch fibers (38) and lower activity of total lactate dehydrogenase (38) producing less lactate (39).

Strengths and limitations

The strength of this study is that all CEPT were performed under standardized conditions with the same equipment. All measurements in the first study were performed at the same internal time for each participant and supervised by the same investigator (R.K.). This work is, to the authors’ knowledge, the first investigating the robustness of secondary exhaustion criteria regarding diurnal and day-to-day variability.

A limitation of this study is the low sample size for female athletes and the low sample size in study 2 in general, which makes the results not generalizable for female athletes. Furthermore, cutoff values for RERmax may differ if much higher (≥50 W·min−1) or lower (<13 W·min−1) increases in workload are chosen than the 25 W·min−1 used herein, (40) and that cutoff values for HRmax may differ if exercise is performed on a treadmill instead of a bicycle ergometer (29,41). In addition, the formula used for the APHR (210 – age [years]) has not been used in previous studies and therefore reduces comparability with other studies. However, the rationale for choosing this formula was to account for the previously reported lower maximum HR in cycle ergometer tests compared with treadmill tests (29,30). Further, the day-to-day variability was assessed at different times of the day but it is unclear if the biological variability is dependent on the time of the day.


In trained athletes, high secondary exhaustion criteria cutoffs need to be chosen to reduce type I errors. Based on our analyses we recommend the following cutoffs: (1) RERmax ≥1.10; (2) HRmax ≥95% APHR (defined as 210 bpm, age in years); (3) RPEmax ≥19. Lower cutoff values are likely to produce type I errors. The defined cutoff values have shown to be robust to diurnal and day-to-day variations. The signal-to-noise ratio in intervention studies and in the evaluation of athlete training programs can only be increased if high secondary exhaustion criteria cutoff values are used. Many of the currently used secondary exhaustion criteria are too low and therefore produce type I errors. However, type I errors may still occur with our defined cutoffs indicating that further methods, such as V˙O2 plateau or V˙O2 validation, may be required.

The authors thank all athletes who made this study possible by their participation.

This study was not funded. None of the authors involved in the present study have any conflict of interest, financial, personal, or otherwise, which would influence this research, and the results do not constitute endorsement by the American College of Sports Medicine. The authors declare that the results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation.

Author contributions: R. K., M. N., and J. W. participated in the writing original draft of the article. D. I., T. H., C. K., S. F., C. C., A. S. T. participated in the review and editing of the article. R. K., M. N., C. C., and A. S. T. participated in the concept and design. R. K., T. H., C. K., and S. F. participated in the data acquisition. R. K., M. N., J. W., and D. I. participated in the data analysis and interpretation. D. I. participated in the statistical expertise.


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