The highest intensity and the shortest duration permitting attainment of maximal oxygen uptake during cycling: effects of different methods and aerobic fitness level

Abstract

The aims of this study were: (1) to verify the validity of previous proposed models to estimate the lowest exercise duration (T _LOW) and the highest intensity (I _HIGH) at which VO₂max is reached (2) to test the hypothesis that parameters involved in these models, and hence the validity of these models are affected by aerobic training status. Thirteen cyclists (EC), eleven runners (ER) and ten untrained (U) subjects performed several cycle-ergometer exercise tests to fatigue in order to determine and estimate T _LOW (ET _LOW) and I _HIGH (EI _HIGH). The relationship between the time to achieved VO₂max and time to exhaustion (T _lim) was used to estimate ET _LOW. EI _HIGH was estimated using the critical power model. I _HIGH was assumed as the highest intensity at which VO₂ was equal or higher than the average of VO₂max values minus one typical error. T _LOW was considered T _lim associated with I _HIGH. No differences were found in T _LOW between ER (170 ± 31 s) and U (209 ± 29 s), however, both showed higher values than EC (117 ± 29 s). I _HIGH was similar between U (269 ± 73 W) and ER (319 ± 50 W), and both were lower than EC (451 ± 33 W). EI _HIGH was similar and significantly correlated with I_HIGH only in U (r = 0.87) and ER (r = 0.62). ET _LOW and T _LOW were different only for U and not significantly correlated in all groups. These data suggest that the aerobic training status affects the validity of the proposed models for estimating I _HIGH.

Introduction

Exercise intensity domains have been defined based upon their distinct metabolic profiles (Gaesser and Poole 1996). The moderate intensity domain consists of work rates at or below the lactate threshold (LT). The heavy domain includes work rates above LT, but at or below critical power (CP). The severe intensity domain encompasses work rates above CP in which maximal oxygen uptake (VO₂max) can be elicited. In fact, in the severe domain VO₂ continues to increase over time until VO₂max is attained (Poole et al. 1988; Hill et al. 2002). Therefore, it is not possible for a subject to perform a constant work rate that provides a VO₂ equivalent to a particular percentage of the VO₂max. This means that VO₂max is not associated with a unique work rate, rather it is attained over a range of work rates. While the same value of VO₂ (i.e., VO₂max) is achieved regardless of exercise intensity within this domain, the time to achieve VO₂max (TAVO₂max) is inversely related to exercise intensity (Margaria et al. 1965; Hill et al. 2002).

Several studies have shown TAVO₂max is shorter at higher intensities for both cycling (Margaria et al. 1965; Hill et al. 2002) and running exercises (Hill et al. 1997; Billat et al. 2000). Thus, there should be a unique exercise intensity within the severe domain, at which VO₂max would be achieved momentarily at the point of fatigue or maintained for a few seconds. However, few studies have specifically sought to characterize VO₂ responses within this exercise domain with regard to the lowest exercise duration (T _LOW) or the highest intensity (I _HIGH) at which the VO₂max can still be reached. Recently, Hill et al. (2002) and Hill and Stevens (2005) have described in intensities within the severe intensity domain a linear relationship between TAVO₂max and its respective time to exhaustion (T _lim), in active individuals. In the work of Hill et al. (2002), using TAVO₂max expressed as a function of T _lim, it was possible to estimate T _LOW (ET _LOW) (the unique T _lim at which VO₂max is achieved at the point of fatigue, where, i.e., TAVO₂max = T _lim, see the upper panel in Fig. 1). The power associated with ET _LOW, was considered as an estimative of I _HIGH (EI _HIGH), by using the two-parameter hyperbolic power–T _lim relationship (see the lower panel in Fig. 1), so called of Critical Power model (CP model) (Morton 2006). However, the authors did not directly validate the estimates by testing participants at and above their EI _HIGH. Thus, the actual assessment of I _HIGH and T _LOW from the VO₂ responses during the several short constant-load exercises performed at different intensities (a gold standard value) still remains to be done.

Fig. 1

Estimation of the lowest exercise duration (ET _LOW) and the highest exercise intensity (EI _HIGH) at which VO₂max can be attained. In the upper panel, ET _LOW (80 s) was estimated by solving for the time for which T _lim was equal to TAVO₂max, represented as the point of intersection between the T _lim and TAVO₂max regression line (solid line) and the line of identity (dashed line). In the lower panel, EI _HIGH was estimated as the intensity associated with ET _LOW, by using the two-parameter hyperbolic power–time relationship (solid line). Triangle is the highest exercise intensity (I _HIGH = 435 W) and its respective duration (72 s) at which VO₂max was attained, when directly determined. Data from a representative participant. See text for details

The advantages of using such models are based on the usefulness of a test protocol (e.g., 2–4 constant-load tests to establish simultaneously the relationships between power–T _lim and TAVO₂max–T _lim) that provides an estimate of both, the lowest and the highest exercise intensity at which VO₂max can be reached, along with other parameters of CP model, as the measurements of aerobic and anaerobic capacity. It would therefore be useful if a valid and reliable means of establishing these exercise intensities are available in a single test protocol.

In this way, some important aspects might be highlighted with regard to these two models utilized by Hill et al. (2002) for estimating T _LOW and I _HIGH. It can be hypothesized that the linear relationship between TAVO₂max and T _lim would be dependent on both, the speed of the VO₂ response, and the relationship between relative exercise intensity (e.g., percentage of VO₂max) and its respective T _lim. As TAVO₂max is determined by VO₂ kinetics, the individuals with faster VO₂ kinetics would be expected to achieve VO₂max faster, and therefore, would have a lower TAVO₂max. Additionally, differences in T _lim at a given relative intensity might also to modify the linearity and slope of relationship between TAVO₂max and T _lim. Some studies have reported that aerobic training may accelerates VO₂ kinetics and increase T _lim during cycling exercise at the intensity associated with VO₂max (Caputo et al. 2003; Caputo and Denadai 2004; Messonnier et al. 2004). Thus, it is likely that aerobic training status may influence the relationship between TAVO₂max and T _lim, and hence the estimative of T _LOW.

Regarding the CP model, extrapolation of the relationship to high exercise intensities requires that an infinitely high power output can be sustained for a very short time. Clearly, this requirement is not met in nature, and the two-parameter CP model may break down when T _lim is too low (e.g., T _lim = ET _LOW, see the lower panel in Fig. 1) (Bosquet et al. 2006; Hopkins et al. 1989; Morton 1996). Bosquet et al. (2006) have shown that critical velocity (extension of power–T _lim to velocity–T _lim model) determined by two-parameter hyperbolic model overestimated the real performance of exercise lasting ∼136 s. In this way, as EI _HIGH is obtained from CP model by using ET _LOW, it is likely that the two-parameter CP model shows a limitation to estimate EI _HIGH when lower ET _LOW values are utilized. As stated above, the higher the aerobic fitness, the lower TAVO₂max, and consequently, the lower ET _LOW. In this scenario, it can be hypothesized that aerobic fitness level can differently affect the validity of these two models for estimating T _LOW and I _HIGH.

Therefore, the main purpose of the present study was to verify the validity of the linear relationship between TAVO₂max and T _lim to estimate T _LOW and of the CP model to estimate I _HIGH, by direct determining I _HIGH and T _LOW. The second aim was to test the hypothesis that both, TAVO₂max and T _lim relationship and CP model might be affected by aerobic training status through a cross-sectional analysis. Since endurance runners exercising on cycle-ergometer show a moderate aerobic fitness (Caputo and Denadai 2004), they were studied as an intermediate aerobic fitness group between trained and untrained subjects.

Methods

Subjects

Ten untrained males (U) (24.4 ± 3.3 year; 74.4 ± 11.8 kg; 175.3 ± 5.4 cm), thirteen endurance cyclists (EC) (25.6 ± 4.5 year; 67.9 ± 7.2 kg; 175.6 ± 5.1 cm), 11 endurance runners (ER) (27.2 ± 8.9 year; 64.6 ± 5.9 kg; 173.1 ± 5.6 cm) volunteered their written informed consent to participate in the study. The study was performed according to the Declaration of Helsinki and the protocol was approved by the São Paulo State University’s Ethics Committee. ER had been competing for 4.2 ± 2.3 year and EC for 9.7 ± 4.3 year. Mean training distances (km) a week were 105 ± 34 for ER and 403 ± 145 for EC. The current 5 km time trials for ER were 1,025 ± 76 s. The subjects were asked not to train hard during the last 2 days before each test and to report to the laboratory at least 3 h after the last meal. The individuals in U group might be involved in recreational activities (e.g., soccer, jogging, and tennis) but all have not been engaged in any form of aerobic training.

Experimental design

Subjects visited the laboratory for three stages of experimentation. (1) An incremental test to determine VO₂max and the intensity associated with the achievement of VO₂max (IVO₂max), (2) second stage involved three laboratory sessions to determine VO₂ kinetics (TAVO₂max), T _lim, CP model parameters, ET _LOW and EI _HIGH, with the subjects performing in random order constant work rate transitions from rest to one of three exercise intensities: 95, 100, 110% IVO₂max. (3) The third stage involved the determination of I _HIGH and T _LOW from two to four constant work rate tests to exhaustion. All tests were performed at the same time of day (±2 h) to minimize the effects of diurnal biological variation on the results (Carter et al. 2002). Subjects performed only one test on any given day and the tests were each separated by ≥48 h but completed within a period of 3–4 weeks.

Procedures

Materials

All exercise testing was conducted on a mechanically braked cycle ergometer (Monark 828E, Stockholm, Sweden). Pedal frequency was maintained at a constant 70 rpm for all cycle tests. Throughout the tests, the respiratory and pulmonary gas-exchange variables were measured using a breath-by-breath portable gas analyzer (Cosmed K4b², Rome, Italy). These analyzers have previously been validated over a wide range of exercise intensities (McLaughlin et al. 2001). Before each test, the O₂ and CO₂ analysis systems were calibrated using ambient air and a gas of known O₂ and CO₂ concentration according to the manufacturer’s instructions, while the K4b² turbine flowmeter was calibrated using a 3-l syringe (Cosmed K4b², Rome, Italy). Heart rate (HR) was also monitored throughout the tests (Polar, Kempele, Finland). Breath-by-breath VO₂ and HR data were reduced to 15 s stationary averages in the incremental test for VO₂max determination (Data Management Software, Cosmed, Rome, Italy).

Incremental tests

Subjects performed incremental exercise (3-min stages) to volitional exhaustion to determine VO₂max and IVO₂max. The untrained subjects began the test at 35 W, runners at 70 W and the cyclists at 140 W, with increases in power of 35 W at each stage. At the end of each stage without interrupting the protocol an earlobe capillary blood sample was collected. Each subject was encouraged to give a maximum effort. The VO₂max was defined as the highest 15 s VO₂ value reached during the incremental test. All subjects fulfilled at least two of the following three criteria for VO₂max: (1) respiratory exchange ratio (RER) greater than 1.1; (2) a blood lactate concentration greater than 8 mM; and (3) peak HR at least equal to 90% of the age-predicted maximal (Taylor et al. 1955). The IVO₂max was defined as the power output at which VO₂max occurred (Faina et al. 1997).

Constant power tests

The subjects subsequently performed a series of constant work rate transitions at the three exercise intensities (95, 100, 110% IVO₂max) on separate days. The exercise protocol began with a 10 min warm-up at 50% IVO₂max followed by 5 min rest, after which the subjects were instructed to perform the required intensity until they were unable to maintain the fixed intensity. At the start of cycling exercise, the subjects pedaled against zero resistance, until a pedal cadence of 70 rpm was reached, at that point, the pre-selected work rate was imposed and timing began. The test was terminated when the subject could not maintain a cadence of >67 rpm despite of verbal encouragement. T _lim was measured to the nearest second. The transition from rest to exercise took <5 s. During the constant work rate tests the peak of VO₂ (VO₂peak) was defined as the highest 15 s average value.

Determination of CP

Individual values for power–T _lim from the constant work rate tests were fit to the hyperbolic model, using iterative nonlinear regression procedures on Microcal Origin 6.0 (Northampton, MA, USA):

$$ T_{{{\text{Lim}}}} = {\text{AWC}} \cdot ({\text{power}} - {\text{CP}})^{{ - 1}} . $$

(1)

Values were derived for two parameters: CP, which is the power asymptote of the relationship, and AWC, which is the area bounded by CP, the x-axis, and any point on the power–time curve, and which represents the anaerobic work capacity (Barker et al. 2006). Regressions were also performed using the mathematically equivalent linear power–T ⁻¹_lim and work–T _lim relationships. The parameters estimates (CP and AWC) were not significantly different between the mathematical models. Thus, for each participant, the parameter estimate generated using the hyperbolic model was used as the criterion measure (EC, SEE = 5.3 ± 5.7 and R ² = 0.98 ± 0.03; ER, SEE = 4.6 ± 3.1 and R ² = 0.97 ± 0.02; U, SEE = 6.0 ± 4.2 and R ² = 0.98 ± 0.02).

VO₂ kinetics

For each exercise transition, breath by breath VO₂ responses were fit to the following equation using iterative nonlinear regression procedures on Microcal Origin 6.0 (Fig. 2):

$$ V{\text{O}}_{2} (t) = V{\text{O}}_{{2{\text{b}}}} + A{\text{ }}{\left( {1 - {\text{e}}^{{ - (t/\tau )}} } \right)} $$

(2)

where VO₂ (t) is oxygen uptake at time t, VO_2b is the pre-exercise VO₂; A is the asymptotic amplitude, and τ is the time constant of VO₂ kinetics (defined as the time required to attain 63% of the A). Occasional errant breath values were deleted from the data set if they fell more than four standard deviations outside the mean 30-s periods (Ozyener et al. 2001). The VO₂ was assumed to have essentially reached its maximal value when the value of (1 − e^−(t/τ)) from Eq. 2 was 0.99, (i.e., when t = 4.6 × τ) and it was assumed that the VO₂ was projecting to VO₂max. Therefore, for each test, TAVO₂max, was defined as 4.6 × τ. Time maintained at VO₂max (TMVO₂max), was determined by subtraction of the TAVO₂max from T _lim. We have showed that confidence intervals for τ estimation, which is based on oxygen uptake amplitude and the standard deviation of breath-by-breath fluctuations (Lamarra et al. 1987) were between ±2 and 5 s for one transition eliciting VO₂max in groups with different aerobic fitness levels (Caputo and Denadai 2004).

Fig. 2

Modeling of breath-by-breath VO₂ response to severe exercise (from top to bottom) at 95, 100 and 110% IVO₂max, respectively, for a representative subject, including the corresponding residual plots. Dashed line represents VO₂max obtained during incremental test. The curves were fitted by a mono-exponential function

Estimation of ET _LOW and EI _HIGH

Linear regression techniques using Microcal Origin 6.0 were employed to describe individually the relationship between the TAVO₂max and T _lim. With TAVO₂max expressed as a function of T _lim, it was possible to solve for the unique T _lim, at which VO₂max might hypothetically be achieved momentarily at the exhaustion (ET _LOW), i.e., when TAVO₂max = T _lim. EI _HIGH was calculated using Eq. 1, utilizing ET _LOW instead of T _lim (Fig. 1).

Determination of T _LOW and I _HIGH

Subsequently, to determine directly I _HIGH and T _LOW, the subjects performed 2–4 further constant work rate tests to exhaustion. The work rate of the first test corresponded to EI _HIGH. If during the first constant work rate test VO₂max could be reach or maintained, further subsequent constant work rate tests at a 5% higher work rate were performed on separate days until VO₂max could not be reached. If during the first constant work rate test VO₂max could not be reach or maintained, further constant work rate tests were conducted with subsequently reduced work rate (5%). The I _HIGH was defined for each subject as the highest power output at which the highest 15-s VO₂ average determined from rolling averages of 5-s samples was equal or higher than VO₂max (averaging the highest VO₂ values from incremental and constant work rate tests) minus one typical error of measurement (TEM) (Fig. 3). TEM for VO₂max was calculated as the SD of the change score in the highest VO₂ values obtained during incremental and constant work rate tests divided by √2 (Hopkins 2000). T _LOW was T _lim performed at I _HIGH. Additionally, in order to test the validity of CP model for predicting a given exercise intensity or duration, predictions of I _HIGH and T _LOW were also calculated using CP model from the actual T _LOW and I _HIGH [i.e., predicted I _HIGH = AWC × T ⁻¹_LOW  + CP or predicted T _LOW = AWC × (I _HIGH − CP)⁻¹].

Fig. 3

Determination of I _HIGH and T _LOW for the same subject represented in Fig. 1. Individual data points are 5-s average values. VO₂max − TEM is VO₂max average from incremental and constant work rate tests minus one typical error of measurement (TEM). T _LOW is the time to fatigue. Note that only in the upper panel (137% IVO₂max) the highest 15-s VO₂ value (open circle) was equal or higher than VO₂max − TEM, satisfying the criterion for I _HIGH determination

Statistics

Data are presented as mean ± SD. Normality of the distribution was checked by the Shapiro–Wilk’s test. The effects of both aerobic training status (all variables) and exercise intensity (T _lim and TAVO₂max) were tested using one-way ANOVA, with Scheffé (training status) and Tukey (exercise intensity) post-hoc tests where appropriate. Student’s paired t test and Pearson correlation coefficients were used to test the validity of the models for estimating I _HIGH and T _LOW. In addition, the typical error of estimate (TEE) was calculated (Hopkins, 2000). Significance was set at P ≤ 0.05.

Results

Incremental tests

The mean values for VO₂max determined in the incremental test for ER were lower than EC and higher than U (Table 1). There were no significantly differences (P = 0.31) for IVO₂max between U (231 ± 45 W) and ER (257 ± 40 W), but both were lower (P < 0.001) than EC (348 ± 30 W).

Table 1 The highest VO₂ values (ml kg^{− 1} min^{− 1}) obtained in the different tests for untrained (U), runners (ER) and cyclists (EC)

Responses to the constant power tests

T _lim and TAVO₂max obtained during constant work rate tests at 95, 100 and 110% IVO₂max are presented in Fig. 4. T _lim values at 95% IVO₂max for EC were similar (P > 0.20) to ER and U. However, U showed lower (P = 0.04) values compared to ER. There were no differences for T _lim at 100 and 110% IVO₂max between the groups. For ER and U groups, TAVO₂max at 95, 100, 110% IVO₂max were not different (P > 0.09), but higher compared to EC (P < 0.03). With regard to exercise intensity, TAVO₂max were longer in the lower power tests in U (P < 0.05). However, in EC and ER TAVO₂max were different only between 95 and 110% IVO₂max (P < 0.02).

Fig. 4

Graphic representation of the relationship between T _lim and TAVO₂max. ET _LOW was determined by solving for the time for which T _lim = TAVO₂max, represented here as the point of intersection of the T _lim and TAVO₂max regression lines with the line of identify. The dotted line is the line of identify; solid line represents the regression equation for each group. Filled triangle represents U, filled circle represents ER, filled square represents EC. The regression equation is represented on legend for each group. Data are mean ± SD. *Significant difference for T _lim between U and ER

CP parameters

The mean value for CP was not different (P = 0.08) between U (182 ± 52 W) and ER (222 ± 34 W), but higher (P < 0.001) for EC (299 ± 30 W). The mean value for AWC was not different (P > 0.07) between the three groups (U = 17.4 ± 3.4 kJ; ER = 14.9 ± 2.8 kJ; EC = 19.7 ± 6.7 kJ).

Validity of the proposed models

The mean values for actual, estimated and predicted I _HIGH and T _LOW are reported in Table 2. There were no differences for I _HIGH (W) between U and ER (P = 0.18), but both were lower (P < 0.001) compared to EC. When I_HIGH was expressed as percentage of IVO₂max there were no differences between EC and ER (P = 0.29), but U was lower compared to EC (P = 0.02). T _LOW were lower (P < 0.001) in EC, but similar between U and ER (P = 0.18). EI _HIGH was similar (P > 0.17) and significantly correlated with I _HIGH only in U (r = 0.87, P = 0.01) and ER (r = 0.61, P = 0.04). The CP model also overestimated the predicted I _HIGH only for EC (P = 0.04). We found significant correlations between the bias (EI _HIGH − I _HIGH) and ET _LOW for all groups (U = −0.85, P = 0.02; ER = −0.83, P = 0.002; EC = −0.59, P = 0.03) (Fig. 5). For each group, the mean correlation between TAVO₂max and T _lim were of 0.84 ± 0.2, 0.85 ± 0.2 and 0.85 ± 0.2 for U, ER and EC, respectively. See Fig. 4 for a graphical representation of these relationships for each group. EI _HIGH and T _LOW were different only for U (P = 0.03), however, they were not significantly correlated for all groups.

Table 2 Actual, estimated and predicted values for the lowest exercise time (T _LOW) and the highest absolute and relative intensity (I _HIGH) at which the VO₂max is reached for untrained (U), runners (ER) and cyclists (EC)

Fig. 5

Relationships between ET _LOW and the difference between EI _HIGH and I _HIGH (bias) for U (a), for ER (b), and for EC (c). Solid line represents the regression equation

The typical error of estimative (TEE) suggests a low validity of the models to estimate ET _LOW for U (15.6%) and ER (13.8%) but not for EC (7.2%). Higher values of TEE for ET _LOW suggested a very low validity of the TAVO₂max and T _lim relationship (15.3, 21.5 and 30.1% for U, ER and EC, respectively). The mean variability of the highest VO₂ obtained in incremental and constant work rate tests (95, 100, 110% IVO₂max) were not different between U [4.2 (0.5 − 8.4)%], ER [4.3 (1.6 − 6.8)%] and EC [3.4 (1.4 − 6.6)%], but there was a high variability within each group.

Discussion

The main finding of this investigation was that the aerobic training status affects the validity of both TAVO₂max and T _lim relationship and CP model for estimating I _HIGH (W), as the validity becoming progressively lower in individuals with higher aerobic fitness. However, the relationship between the TAVO₂max and T _lim was not valid to estimate ET _LOW, irrespective of aerobic training status.

Effects of training status

The severe-intensity domain is characterized by the attainment of VO₂max. Several studies have stated that VO₂max is achieved faster at higher intensities (Margaria et al. 1965; Billat et al. 2000; Hill et al. 2002; Hill and Stevens 2005). Indeed, there was a decrease of TAVO₂max, at higher intensities for U group. However, for ER and EC there was an intensity effect only between the two extremes, 95 and 110% IVO₂max. It is important to note that at 95% IVO₂max the VO₂ rises slowly towards its maximal value by the occurrence of slow component (Gaesser and Poole 1996; Billat et al. 2000; Ozyener et al. 2001). Despite of mathematical modeling employed in this study do not characterize the different phases of VO₂ kinetics (fast and slow phases), several studies analyzing separately both overall response (MRT) and each phase of VO₂ kinetics showed that the slower overall VO₂ responses were associated with the higher slow components amplitudes (Burnley et al. 2000; MacDonald et al. 1997). Hence, the slower overall VO₂ response at 95% IVO₂max might be responsible for the differences found on TAVO₂max between 95 and 110% IVO₂max. Moreover, the slow component seems to be reduced by aerobic training (Casaburi et al. 1987; Russell et al. 2002; Ocel et al. 2003), which might also provide an explanation for the difference found between 95 and 100% IVO₂max that was only apparent for U. Thus, our data confirms that in the severe-intensity domain, TAVO₂max is reduced at higher intensities irrespective of the specificity of training. Additionally, it seems that these differences are attenuated by an increase in aerobic fitness level.

To our knowledge, this study is the first to determine directly the lowest exercise duration and the highest constant exercise intensity at which the VO₂max can still be reached during cycling. EC showed higher I _HIGH (451 W) and lower T _LOW (117 s) compared to ER (319 W and 170 s) and U (269 W and 209 s), and both I _HIGH and T _LOW were not different between ER and U (Table 2). However, differences were not found between EC (130%) and ER (124%) for relative I _HIGH (expressed as a percentage of IVO₂max). At other intensities (95, 100 and 110% IVO₂max), there was an effect of specific aerobic training on VO₂ kinetics (TAVO₂max), which also decreased T _LOW for a similar I _HIGH (IVO₂max%) between EC and ER. Furthermore, for ER the transfer of training effects seems to disappear during high-intensity exercise, as observed for TAVO₂max, I _HIGH and T _LOW. Thus, adjustments induced by specific aerobic training seem to be required to the best interplay between caption, delivery and O₂ utilization allowing VO₂max be attained quickly, in just ∼2 min of commencement of exercise. Resolution of the determinants of exercise tolerance and their relationships to the VO₂max is of great importance for high-intensity aerobic training elaboration, in order to further increase the aerobic energy release mainly in highly trained athletes, likely sparing anaerobic substrates and prolonging exercise tolerance (Laursen and Jenkins 2002). Future research could to test the applicability and effectiveness of I _HIGH and T _LOW for prescribing high-intensity aerobic training.

Validity of the proposed models

The main aim of our study was to assess the validity of the ET _LOW and EI _HIGH estimates from the linear relationship between TAVO₂max and T _lim and from the CP model, concerning the aerobic training status. T _LOW was higher than ET _LOW only for U and no significant correlations between each other were observed for all groups. A possible limitation could be the reproducibility of T _lim at high-intensity exercise, which might lead to the differences found between T _LOW and ET _LOW. However, some studies have reported that T _lim is highly repeatable, with a difference of no more than 5% between trials performed within severe-intensity domain (Bishop and Jenkins 1995; Carter et al. 2006). This value is less than the 25% difference we have found between T _LOW and ET _LOW for U.

For EC, I _HIGH was overestimated by EI _HIGH. For U and ER, I _HIGH was not different and significantly correlated with EI _HIGH. In spite of the good correlation showed by U, EI _HIGH could not be determined in three subjects due to: (1) large differences between TAVO₂max values that increased the slope of linear regression, therefore, the line of regression could not cross the line of identify, or it crossed at an unphysiologically possible value; and (2) the TAVO₂max value projected by monoexponential fit was higher than T _lim. The impossibility to estimate EI _HIGH in 30% of subjects for U group weakens the model proposed by Hill et al. (2002) specifically for this group. Taken together, these results suggest that aerobic training status affects the validity of the proposed models for estimating both ET _LOW and EI _HIGH, as the validity becoming lower with the increase of the aerobic fitness level.

Possible limitations of the relationship between TAVO₂max and T _lim

Analyzing the predictive model utilized to estimate ET _LOW we could notice a training effect on the slope of linear regression between TAVO₂max and T _lim that resulted in lower ET _LOW values compared to T _LOW for U (Fig. 4). As stated above, this probably occurred in this group of lower aerobic fitness due to the higher effect of slow component (Casaburi et al. 1987; Russell et al. 2002; Ocel et al. 2003) and/or a lower T _lim at 95% IVO₂max. Some differences between actual and estimated variables may also be derived from model assumptions that are not fully convincing.

The first assumption is that TAVO₂max decreases linearly at higher intensities until it approaches T _lim. This is based upon the strength of the relationship between TAVO₂max and T _lim. Indeed, this relationship does not appear to be strong, with a mean correlation of 0.84 between the variables in our study. Furthermore, it is worth noting that TAVO₂max presented by both ER and U at 110% IVO₂max were already lower than T _LOW. This adds even more disadvantage in using mathematical modeling to indirectly determine T _LOW. In this way, the precision of ET _LOW was also dependent upon the precision of the determination of TAVO₂max. As TAVO₂max was defined based on VO₂ kinetics (i.e., 4.6 × τ), one possible source of error was the use of a mono-exponential model to fit VO₂ response during exercise at 95% IVO₂max, with the likely emergence of a slow component during the VO₂ response (Gaesser and Poole 1996; Ozyener et al. 2001). Because the present study sought simply to determine TAVO₂max (by overall VO₂ response) and not to characterize the nature of the response, the use of this model seems appropriate (Fig. 2). Nonetheless, since the estimate of τ is associated with an error term, each value of TAVO₂max also has an associated error term. Despite we have performed only one transition, the signal to noise ratio of data can be improved in higher VO₂ amplitudes (Lamarra et al. 1987), therefore, the higher VO₂ amplitude the smaller the confidence interval. In summary, some of these aspects can help to explain the lack of validity of the relationship between TAVO₂max and T _lim for estimating ET _LOW.

Possible limitations of the CP model

Some authors have indicated the limitation of the two-parameter CP model for estimating the intensity or T _lim at high-intensity exercises (Hopkins et al. 1989; Morton 1996; Bosquet et al. 2006). Recently, Bosquet et al. (2006) have shown that critical velocity determined by two-parameter hyperbolic model overestimated the real performance for the exercise duration of ∼136 s. In the same way, in the present study the CP model overestimated both the estimated I _HIGH (EI _HIGH) and predicted I _HIGH only for EC, presumably because the effect of reduced exercise duration on the estimates from CP model (Table 2; Fig. 6). For U and ER, the CP model estimated and predicted similar intensities for these variables. As expected, the similar value of ET _LOW (compared to T _LOW) in ER group, when inserted in the CP model, generated similar values between I _HIGH and EI _HIGH. Unexpectedly, the lower ET _LOW for U also generated similar values between I _HIGH and EI _HIGH, even with the CP model not overestimating the intensity predicted from T _LOW. This likely occurred due to a lower statistical power (type 2 error) as a result of small sample size and large coefficient of variation. Other aspect would be the factual limitation of the CP model for estimating the intensity for short exercise duration, as demonstrated by Bosquet et al. (2006) and in the present study by EC (Fig. 6). Despite this, the CP model did not overestimate EI _HIGH for U and ER, but we found high significant negative correlations between the bias (EI _HIGH − I _HIGH) and ET _LOW (Fig. 5), suggesting that the shorter the estimated time (ET _LOW), the more the CP model overestimated the intensity (EI _HIGH).

Fig. 6

Representation demonstrating the potential limitation of the two-parameter hyperbolic CP model for estimating the intensity for short exercise duration. Note I _HIGH lie outside of regressions lines as decreasing of exercise duration. The solid, the dashed, and the dashed dotted lines represent the regression equations from CP model (using only 95, 100, 110% IVO₂max as predictive trials) for EC, ER, and U, respectively. Open triangle represents U, open circle represents ER, open square represents EC. See text for details

Possible limitations of the criterion for I _HIGH determination

For the determination of I _HIGH we assumed that a subject had reached VO₂max when VO₂ was equal or higher than VO₂max (averaging the highest VO₂ values from incremental and constant work rate tests) minus one TEM. Several studies have shown VO₂max is reached at these intensities or similar duration in both running (Billat et al. 2000; Hill et al. 1997; Carter et al. 2006) and cycling (Hill et al. 2002; Caputo and Denadai 2004; Hill and Stevens 2005). This criterion was utilized for two reasons: (1) to individualize the day-to-day biological variability on VO₂max values; (2) not to assume fixed values or fixed percentages of only one test, such as VO₂max obtained in incremental test (VO₂max_INC) minus 2.1 ml kg⁻¹ min⁻¹ (Billat et al. 1999), or 95% of VO₂max_INC (Billat et al. 2000). The utilization of only one value of VO₂max (e.g., VO₂max_INC) minus a fixed value can only add to biological variability when used as a reference value for testing on different days, hence it will not be able “to offset” biological variation effect. In order to minimize this effect, it was utilized for each subject the mean of four VO₂max values subtracted by its biological variability (i.e., one TEM). Therefore, our criterion seemed to obtain a more robust and individualized VO₂max, increasing the accuracy of determining I _HIGH and T _LOW using only one transition. Nevertheless, other experimental designs could obtain a high precision to determine I _HIGH and T _LOW from averaging repeated bouts.

In conclusion, the present study has shown that the aerobic training status affects the validity of the proposed models for estimating both T _LOW and I _HIGH. The relationship between the TAVO₂max and T _lim was not valid to estimate ET _LOW, irrespective of aerobic training status. This relationship appeared to be affected mainly by the slower VO₂ response in the individuals with lower aerobic fitness, which resulted in the lower estimated ET _LOW. The exercise intensity estimated from CP model seems to be dependent on exercise duration, suggesting that the model is indirectly affected by aerobic status, since actual and estimated T _LOW are reduced via an increase in aerobic fitness. For participants in the present study, depending on the aerobic fitness, the highest intensity and the shortest duration that would permit attainment of VO₂max were, respectively, 117–129% IVO₂max and ∼2–3.5 min, on average. These variables might be interesting to prescribe high-intensity interval training, mainly in high trained athletes.