Non‐Invasive Estimation of the Upper Boundary of the Severe Intensity Exercise Domain: The Maximal Accumulated Oxygen Deficit Method

ABSTRACT

The aim of this study was to evaluate whether the highest power output at which the predominant energy contribution is derived from the aerobic system (aerobic limit power: ALP), as estimated using maximal accumulated O₂ deficit (MAOD) method, corresponds to the upper boundary of the severe intensity exercise domain. Thirteen males completed: (i) a ramp incremental exercise test, (ii) four submaximal constant power exercise tests, and (iii) 6–7 maximal and at least one supramaximal constant power exercise tests. The upper boundary of the severe intensity exercise domain was estimated based on the linear relationship between the time to achieve $\dot{\mathrm{V}}$O_2max and the time to task failure (P_UPPERBOUND). The ALP was estimated by MAOD method, i.e. based on the difference between the predicted $\dot{\mathrm{V}}$O₂ demand derived from a linear regression line from submaximal exercise tests and the accumulated O₂ uptake calculated by integrated $\dot{\mathrm{V}}$O₂ data. The highest power output at which the aerobic energy contribution rate was still predominant (i.e., 50%+) was defined as the ALP. Based on the principal results, ALP estimated by MAOD was not significantly different from the P_UPPERBOUND (390 ± 58 vs. 387 ± 61; p = 0.16; effect size: 0.42) and they were closely aligned (r: 0.99; bias: 3 ± 7 W; standard error of estimation: 7 W; limits of agreement: −11–17 W). Consequently, ALP, as derived from the MAOD method, provides a non‐invasive alternative to accurately determine the P_UPPERBOUND with less physiological stress.

Highlights

• Aerobic limit power (ALP) can be estimated by maximal accumulated O₂ deficit (MAOD) method.

• MAOD‐derived ALP closely matched the upper boundary of the severe intensity exercise domain.

• MAOD‐derived ALP offers a non‐invasive alternative for identifying the upper boundary of the severe intensity exercise domain with less physiological stress.

1. Introduction

The boundary between the heavy and severe intensity exercise domains is defined by the critical power (CP) (Bull et al. 2000; Jones et al. 2010; Poole et al. 1988). CP represents the threshold power output below which a metabolic steady state can be attained (Brickley et al. 2002; Hill et al. 2002; Hill and Smith 1999; Jones et al. 2008, 2019). In contrast, when exercise is performed above CP, within the severe intensity exercise domain, blood lactate concentration ([lactate]) and $\dot{\mathrm{V}}$O₂ do not stabilise, but instead increase over time, with the $\dot{\mathrm{V}}$O_2max typically being attained at, or close to, task failure (Black et al. 2017; Gaesser and Poole 1996; Hill et al. 2002; Hill and Ferguson 1999; Hill and Stevens 2005; Jenkins and Quigley 1990; Jones et al. 2008; Sloniger et al. 1996).

The upper boundary of the severe intensity exercise domain is defined as the highest power output at which $\dot{\mathrm{V}}$O_2max can be achieved momentarily (P_UPPERBOUND) (Hill et al. 2002; Hill and Ferguson 1999). When the P_UPPERBOUND is exceeded, within the extreme intensity exercise domain, it is not possible to attain the $\dot{\mathrm{V}}$O_2max due to a very high exercise intensity which limits exercise duration (Burnley and Jones 2007; Hill et al. 2002). Thus, the accurate assessment of the P_UPPERBOUND is important for the prediction of exercise performance, training prescription and monitoring of fitness in athletes (Hill et al. 2002, 2024; Hill and Stevens 2005; Ozkaya et al. 2025; Peker et al. 2024). P_UPPERBOUND can be conventionally estimated by identifying the point where the linear relationship between the time to achieve $\dot{\mathrm{V}}$O_2max and the time to task failure intersects with the line of identity (Hill et al. 2002).

A recent study proposed a novel approach to the assessment of this threshold (i.e., the boundary between the severe and extreme intensity exercise domains) by reporting that the highest power output at which the predominant energy contribution (i.e., 50%+) to total energy turnover is derived from the aerobic energy system, termed the Aerobic Limit Power (ALP), coincides with the P_UPPERBOUND (Peker et al. 2024). It was demonstrated that once the ALP is exceeded, and exercise to task failure is performed within the extreme intensity domain, $\dot{\mathrm{V}}$O_2max cannot be attained, and anaerobic energy metabolism surpasses aerobic metabolism as the primary contributor to overall energy turnover.

In the study of Peker et al. (2024), ALP was determined by evaluating the $\dot{\mathrm{V}}$O₂ response during exercise, peak blood [lactate] during recovery, and the fast phase of recovery $\dot{\mathrm{V}}$O₂ kinetics in order to estimate energy contributions from the aerobic, glycolytic, and phospholytic systems, respectively (Beneke et al. 2002; di Prampero 1981; di Prampero and Ferretti 1999). However, another widely used method for estimating energy system contribution is the maximal accumulated O₂ deficit (MAOD), which is calculated as the difference between the estimated total O₂ cost and the accumulated O₂ uptake during exercise (Medbø et al. 1988; Medbø and Tabata 1989). While the energy contribution rates derived from the two methods are interchangeable (Bertuzzi et al. 2010; Hill 2023; Miyagi et al. 2017; Zagatto et al. 2016, 2017), MAOD is often preferred as a non‐invasive and useful alternative for the estimation of the aerobic and anaerobic energy contributions to exercise (Noordhof et al. 2010). It is therefore of interest to ascertain whether the ALP, when calculated using the MAOD method, corresponds to the P_UPPERBOUND. The purpose of this study was to evaluate whether the ALP, as determined by MAOD, coincides with the P_UPPERBOUND. It was hypothesised that ALP would closely align with the P_UPPERBOUND.

2. Methods

2.1. Participants

The study complied with the principles outlined in the Declaration of Helsinki (2013) and received ethical approval from university ethics committee (22‐9.1 T/3). Prior to testing, all participants provided written informed consent and underwent a medical screening to ensure their suitability to perform high‐intensity exercise. Thirteen healthy, physically active males volunteered to participate in the study (31 ± 8 years; 70 ± 6 kg; 1.77 ± 0.06 m). All participants were ostensibly free of cardiovascular, respiratory and neurological diseases, and musculoskeletal injuries. Prior to each test, participants were asked to avoid alcoholic and caffeinated beverages for a least 24 h and to refrain from strenuous physical activity during the same period. They were also asked to maintain consistent dietary and hydration habits and to arrive at the laboratory well‐rested. The participants completed exercise testing at a similar time of day (± 2 h).

2.2. Experimental Design

This study consisted of a total of 12–14 laboratory visits, each separated by 24–48 h, and was conducted over a 4–5‐week study period (Figure 1). A familiarisation session was conducted before the commencement of the main testing procedure to ensure accurate data collection. In the familiarisation sessions, participants selected their own cadence (between 70 and 90 rpm) and were instructed to maintain a fixed cadence throughout ramp incremental and constant power exercise tests. Then, at the second visit, participants performed a ramp incremental exercise test for the determination of $\dot{\mathrm{V}}$O_2max and its corresponding power output (P‐$\dot{\mathrm{V}}$O_2max). Subsequently, four constant power exercise tests at submaximal power outputs were performed to estimate $\dot{\mathrm{V}}$O₂ demand for the target power outputs in the severe or extreme intensity exercise domains, using the forward extrapolation method. During the subsequent visits, participants completed a series of constant power exercise tests to estimate P_UPPERBOUND and ALP determined by MAOD.

FIGURE 1.

Schematic illustration of the study experimental protocol. The familiarisation visit is not included, as the figure depicts only protocol‐specific procedures.

2.3. Equipment and Measurements

All exercise protocols were performed under standard laboratory condition (∼20°C, ∼21% O₂, ∼0.05% CO₂, and 50%–60% relative humidity). Exercise tests were performed on an electromagnetically braked cycle ergometer of which the saddle and handlebar were individually adjusted (Monark LC7, Vansbro, Sweden). Pulmonary gas exchange was measured breath‐by‐breath throughout all exercise tests (Cosmed Quark CPET, Rome, Italy). Prior to each exercise test, the system was calibrated using ambient air, a gas mixture of known concentration (16% O₂, 5% CO₂, and balanced N₂) and a precision 3‐L calibration syringe. The breath‐by‐breath $\dot{\mathrm{V}}$O₂ data were omitted when data points were four standard deviations (SD) outside the local mean (Lamarra et al. 1987). Then, the $\dot{\mathrm{V}}$O₂ data were processed through a 5‐breath rolling average smoothing procedure (Hill 2019).

2.4. Procedures

2.4.1. Ramp Incremental Exercise Tests

The ramp incremental exercise tests were comprised of a 4‐min baseline period, followed by an incremental phase of 30 W·min⁻¹. The ramp test was terminated at task failure (i.e., when cadence dropped > 10 rpm below the preferred cadence for more than 10 consecutive seconds), despite strong verbal encouragement. Gas exchange threshold (GET) was identified via the v‐slope method ($\dot{\mathrm{V}}$CO₂ vs. $\dot{\mathrm{V}}$O₂) (Beaver et al. 1986). The mean response time (MRT) was calculated using standard backward extrapolation and applied to GET (Boone et al. 2008). The highest 15‐s mean $\dot{\mathrm{V}}$O₂ and the corresponding power output were defined as $\dot{\mathrm{V}}$O_2max and P‐$\dot{\mathrm{V}}$O_2max, respectively, for each participant.

2.4.2. Submaximal Constant Power Exercise Tests

The participants were first required to complete a series of four submaximal constant power exercise tests at power outputs corresponding to 40%–70% of P‐$\dot{\mathrm{V}}$O_2max. Participants completed 4‐min of baseline cycling after which the target power outputs were applied immediately and maintained for 10 min. The steady state $\dot{\mathrm{V}}$O₂ responses at these four power outputs were calculated as the mean value over the last 1‐min of exercise. A linear regression line was plotted between the $\dot{\mathrm{V}}$O₂ responses and the power outputs, and then forward extrapolated to the target power outputs.

2.4.3. Estimation of P_UPPERBOUND

Following the submaximal constant power exercise tests, participants completed, on different days, four constant power exercise tests to task failure, ranging between 2 and 16 min, for the estimation of P_UPPERBOUND. For that purpose, the time to achieve $\dot{\mathrm{V}}$O_2max was calculated using nonlinear regression analysis (Sigma‐Plot 14.0, Systat Software Inc., San Jose, CA, USA) for each exercise test. The initial 20 s of exercise (i.e., cardio‐dynamic phase) was excluded from the analyses (Ozyener et al. 2001) and a mono‐exponential model was applied to describe the behaviour of $\dot{\mathrm{V}}$O₂ kinetics (Equation 1).

$${\dot{\mathrm{V}}\mathrm{O}}_{2\left(\mathrm{t}\right)}={\dot{\mathrm{V}}\mathrm{O}}_{2\text{baseline}}+{\mathrm{A}}_{\mathrm{p}}\times \left(1-{\mathrm{e}}^{-\left(\mathrm{t}-{\text{TD}}_{\mathrm{p}}\right)/{\tau }_{\mathrm{p}}}\right)$$ (1)

where $\dot{\mathrm{V}}$O_2(t) is time; $\dot{\mathrm{V}}$O_2baseline is baseline $\dot{\mathrm{V}}$O₂; A _p is primary phase amplitude; TD_p is the primary phase time delay; and τ _p is the time constant of the primary phase.

The maximum value of the $\dot{\mathrm{V}}$O₂ response was determined as the point where the amplitude of the mono‐exponential curve reached 99% (Hill et al. 2002). The point where the linear relationship between the time to achieve $\dot{\mathrm{V}}$O_2max and the time to task failure intersected with the line of identity was identified to estimate the time to task failure for the P_UPPERBOUND. Finally, P_UPPERBOUND was defined as the intersection of the hyperbolic relationship between the power output and the time to task failure with the estimated exercise duration (Hill et al. 2002).

2.4.4. Estimation of ALP

The ALP based on the MAOD method was defined as the highest power output at which the predominant energy contribution is derived from the aerobic energy system (Peker et al. 2024). For this purpose, the initial exercise test was performed at 105% of P‐$\dot{\mathrm{V}}$O_2max and the power output was increased by 5% until anaerobic energy metabolism contributed 50%+. The tests were terminated when participants' cadence fell by more than 10 rpm below their preferred cadence for more than 10 s, despite strong verbal encouragement. The highest 15‐s mean $\dot{\mathrm{V}}$O₂ was recorded for each trial.

The net energy contribution of the aerobic energy pathway (W_AER) has typically been calculated by subtracting resting $\dot{\mathrm{V}}$O₂ area from exercise $\dot{\mathrm{V}}$O₂ area integrated over time (Åstrand 1981; Beneke et al. 2002; Bertuzzi et al. 2007; Ozkaya et al. 2014). However, for the estimation of the anaerobic energy contribution based on MAOD (W_ANE), $\dot{\mathrm{V}}$O₂ demand for the target power output is calculated by linear extrapolation of the $\dot{\mathrm{V}}$O₂ versus power output relationship for the four submaximal power outputs from a fixed y‐intercept (Medbø et al. 1988; Medbø and Tabata 1989; Weber and Schneider 2001). The y‐intercept was accepted as 8.2 mL·min⁻¹⋅kg⁻¹ (Hill 2023). The total VO₂ cost of the exercise (i.e., mL·kg⁻¹) was calculated as the product of the estimated $\dot{\mathrm{V}}$O₂ demand and the time to task failure (Hill 2023). W_ANE was calculated as the difference between the total O₂ cost and the accumulated O₂ uptake (Medbø et al. 1988; Medbø and Tabata 1989; Noordhof et al. 2010; Weber and Schneider 2001) (Figure 2). Absolute W_ANE was reduced by 10% to correct for the contribution of body oxygen stores to the energy supply (Bertuzzi et al. 2010; Medbø et al. 1988). The absolute contribution from the energy systems as derived from the MAOD method was denoted in quantitative terms in kJ and mL·kg⁻¹. The total energy expenditure during constant power exercise (W_TOTAL) was calculated as the sum of the energy derived from W_AER and W_ANE (i.e., W_AER + W_ANE). The relative contributions of the energy systems were then derived by dividing W_AER (W_AER%) and W_ANE (W_ANE%) by W_TOTAL. The relative contribution of each energy system at the P_UPPERBOUND was predicted through interpolation using data obtained from exercise tests performed just below and just above the threshold.

FIGURE 2.

Principle of the maximal accumulated O₂ deficit method. In panel A, a linear regression line is constructed based on the relationship between the $\dot{\mathrm{V}}$O₂ responses and the power outputs obtained from four submaximal constant power exercise tests continued for 10 min. This regression line is then extrapolated forward to estimate $\dot{\mathrm{V}}$O₂ demands for targeted higher‐intensity power outputs. In panel B, accumulated O₂ deficit is calculated as the difference between the total O₂ cost and the accumulated O₂ uptake.

2.5. Statistical Analyses

All statistical analyses were performed using SPSS Statistics 26 (IBM Corp, Armonk, NY, USA). Results are presented as mean ± SD. Differences between power output, $\dot{\mathrm{V}}$O₂ response, time to task failure, absolute and relative energy contributions of each energy pathway measured from the exercise tests were assessed by repeated measures ANOVA. When sphericity was violated, the Greenhouse‐Geisser correction was applied. Pairwise comparisons were conducted with Bonferroni adjustment for multiple comparisons. Paired sample t tests were performed to examine the difference between P_UPPERBOUND and ALP determined by MAOD. Effect size (ES) was calculated using Cohen's d, with magnitude interpreted as trivial (0–0.19), small (0.20–0.49), medium (0.50–0.79) and large (≥ 0.80) (Cohen 1992). A Pearson product‐moment correlation was computed to evaluate the relationship between P_UPPERBOUND with the ALP based on MAOD method. Additionally, standard error of estimation (SEE) was used to examine the accuracy of estimations of the P_UPPERBOUND and ALP (Hopkins 2000). Bland‐Altman analysis (mean of difference ± 1.96 SD) was used to examine the agreement between P_UPPERBOUND and ALP (Bland and Altman 1986). Statistical significance was accepted at p < 0.05.

3. Results

$\dot{\mathrm{V}}$O_2max was 55 ± 6 mL·min⁻¹⋅kg⁻¹ and P‐$\dot{\mathrm{V}}$O_2max corresponded to 356 ± 52 W. The $\dot{\mathrm{V}}$O₂ at GET was 34 ± 4.5 mL·min⁻¹ kg⁻¹, corresponding to 62 ± 7% $\dot{\mathrm{V}}$O_2max and 178 ± 42 W (50 ± 7% P‐$\dot{\mathrm{V}}$O_2max) after applying the MRT correction.

Exercise performance and $\dot{\mathrm{V}}$O₂ parameters derived from the submaximal constant power exercise tests are reported in Table 1. Two of the submaximal exercise tests were performed below and the other two were performed just above the GET for each participant. The slope and coefficient of determination (R ²) of the linear regression line between $\dot{\mathrm{V}}$O₂ and power output of the four submaximal tests were 11.8 ± 0.8 mL·min⁻¹⋅W⁻¹ and 0.99 ± 0.01, respectively.

TABLE 1.

Exercise performance and $\dot{\mathrm{V}}$O₂ parameters derived from the submaximal constant power output exercise tests.

Variables	Power output (W)	$\dot{\mathbf{V}}$O2 (mL·min−1⋅kg−1)
40% P‐$\dot{\mathrm{V}}$O2max	142 ± 21	33 ± 4
50% P‐$\dot{\mathrm{V}}$O2max	178 ± 26	39 ± 4
60% P‐$\dot{\mathrm{V}}$O2max	214 ± 31	45 ± 4
70% P‐$\dot{\mathrm{V}}$O2max	249 ± 36	50 ± 4

A comparison of group means for $\dot{\mathrm{V}}$O₂, power output and time to task failure between P_UPPERBOUND, ALP and ALP + 5% is presented in Table 2. The highest $\dot{\mathrm{V}}$O₂ achieved at ALP (54 ± 6 mL·min⁻¹⋅kg⁻¹) was not different from $\dot{\mathrm{V}}$O_2max (55 ± 6 mL·min⁻¹⋅kg⁻¹; p = 0.36). In contrast, the highest $\dot{\mathrm{V}}$O₂ achieved at ALP + 5% was significantly lower than $\dot{\mathrm{V}}$O_2max (Δ: 4 ± 3 mL·min⁻¹⋅kg⁻¹; p < 0.001), as expected. ALP was successfully calculated for each participant with a mean of 54 ± 3 for W_AER% and 46 ± 3 for W_ANE%. However, when ALP was exceeded, that is during the ALP + 5% exercise test, the predominant contribution obtained from the energy systems shifted with the contribution from W_AER% and W_ANE% calculated as 49 ± 2 and 51 ± 2%, respectively (Figure 3 and Table 3). Finally, ALP derived from the MAOD method was not different from the P_UPPERBOUND (390 ± 58 vs. 387 ± 61; p = 0.16; ES: 0.42) (Figure 4). They were strongly correlated (r: 0.99) and demonstrated close agreement as shown in the Bland‐Altman analysis (bias: 3 ± 7 W; SEE: 7 W; limits of agreement: −11–17 W) (Figure 5).

TABLE 2.

Comparison of power output, $\dot{\mathrm{V}}$O₂ response, and time to task failure values across P_UPPERBOUND, ALP, and ALP + 5% exercise.

Variables	PUPPERBOUND	ALP	ALP + 5%
Power output (W)	387 ± 61 a	390 ± 58 a	409 ± 60
$\dot{\mathrm{V}}$O2 (mL·min−1⋅kg−1)	—	54 ± 6 a	51 ± 5
Time to task failure (s)	122 ± 21 a	128 ± 13 a	104 ± 12

Abbreviations: ALP: the highest power output at which predominant energy contribution is derived from the aerobic energy system; ALP + 5%: constant power output exercise test performed 5% above the ALP; P_UPPERBOUND: the method to predict the upper boundary of the severe intensity exercise domain (Hill et al. 2002).

^a Denotes significant differences compared to ALP + 5%, p < 0.05.

FIGURE 3.

Estimation of ALP based on the maximal accumulated O₂ deficit method. In panel A and B, aerobic and anaerobic energy contribution rates are presented, calculated by subtracting the accumulated O₂ uptake from the estimated total O₂ cost during ALP and ALP + 5% exercise. When ALP is exceeded, the anaerobic energy contribution, as determined by the maximal accumulated O₂ deficit method, becomes predominant. Note that this figure was generated by considering group averaged $\dot{\mathrm{V}}$O₂ responses according to percentage of total exercise duration. ALP: the highest power output at which predominant energy contribution is derived from the aerobic energy system; and ALP + 5%: constant power output exercise test performed 5% above the ALP.

TABLE 3.

Parameters associated with the absolute energy contributions calculated for P_UPPERBOUND, ALP and ALP + 5% exercise.

Variables	PUPPERBOUND	ALP	ALP + 5%
WAER (mL·kg−1)	89 ± 10 a	85 ± 7 a	65 ± 10
WAER (kJ)	130 ± 15 a	125 ± 15 a	96 ± 17
WANE (mL·kg−1)	73 ± 8 b	73 ± 7 b	69 ± 9
WANE (kJ)	108 ± 14 b	108 ± 14 b	101 ± 16
WTotal (mL·kg−1)	162 ± 16 a	158 ± 12 a	134 ± 19
WTotal (kJ)	238 ± 27 a	233 ± 26 a	197 ± 33

Abbreviations: ALP: the highest power output at which predominant energy contribution is derived from the aerobic energy system; ALP + 5%: constant power output exercise test performed 5% above the ALP; P_UPPERBOUND: the method to predict the upper boundary of the severe intensity exercise domain (Hill et al. 2002); W_AER: the net energy contribution of the aerobic energy pathway; W_ANE: the net energy contribution of the anaerobic energy pathway; W_Total: the sum of the energy derived from the W_AER and W_ANE.

^a Denotes significant differences compared to ALP + 5%, p < 0.001.

^b Denotes significant differences compared to ALP + 5%, p < 0.01.

FIGURE 4.

Comparison of P_UPPERBOUND and ALP values in terms of individual values (solid lines) and group mean (dashed bold line). There was no significant difference between P_UPPERBOUND and ALP (p = 0.16; ES: 0.42). P_UPPERBOUND: the method to predict the upper boundary of the severe intensity exercise domain (Hill et al. 2002); and ALP: the highest power output at which the predominant energy contribution is derived from the aerobic energy system.

FIGURE 5.

Correlation and Bland‐Altman analyses of P_UPPERBOUND and ALP. In panel A, solid lines represent the best‐fit linear regression, while dashed lines indicate the line of identity. In panel B, Bland‐Altman plots illustrate the agreement between P_UPPERBOUND and ALP determined by the maximal accumulated O₂ deficit method. The differences in power output (y‐axis) are plotted against the mean power output of both measures (x‐axis), showing the mean bias (dashed line) and the 95% limits of agreement (solid lines). P_UPPERBOUND: the method to predict the upper boundary of the severe intensity exercise domain (Hill et al. 2002); and ALP: the highest power output at which predominant energy contribution is derived from the aerobic energy system.

4. Discussion

This study is the first to investigate whether the ALP determined by MAOD is associated with the upper boundary of the severe intensity exercise domain, that is, P_UPPERBOUND. The principal results showed that the relative aerobic and anaerobic contributions at the ALP determined by MAOD were 54% and 46%, respectively, while there was a shift to a predominantly anaerobic contribution, that is, 49% and 51%, when the ALP + 5% was performed. It was also demonstrated that the ALP determined by MAOD closely aligns with the P_UPPERBOUND. This novel approach using the MAOD method may provide a non‐invasive alternative for assessing the boundary between the severe and extreme intensity exercise domains with fewer maximal tests and therefore less physiological stress compared to the P_UPPERBOUND method.

The P_UPPERBOUND is estimated from data obtained during severe intensity exercise tests performed to task failure and modelling of $\dot{\mathrm{V}}$O₂ kinetics. It is based on the linear relationship between the time to achieve $\dot{\mathrm{V}}$O_2max and the time to task failure (Hill et al. 2002). However, studies have shown that some individuals display $\dot{\mathrm{V}}$O₂ kinetics that deviate from the expected response, being either slower or faster, leading to discrepancies in the regression slope between these two variables (Caputo and Denadai 2008; Ozkaya et al. 2025; Peker et al. 2024). Furthermore, aerobic training status has been shown to affect the relationship between the time to achieve $\dot{\mathrm{V}}$O_2max and the time to task failure, as the exercise tests performed to task failure must be completed within the severe intensity domain (Caputo and Denadai 2008). The reliability of such tests is higher when performed by individuals who are familiar with maximal efforts (Caputo and Denadai 2008). Although rare, variability in the time to task failure during severe intensity exercise can influence the accuracy of the regression model as reflected in the R ² values (Caputo and Denadai 2008; Peker et al. 2024). In contrast, ALP estimated by MAOD is determined from the relationship between the steady state $\dot{\mathrm{V}}$O₂ responses and the power outputs during submaximal exercise tests of just 10 min duration. In this respect, it can be said that the MAOD method overcomes the labour‐intensive nature of measuring the P_UPPERBOUND.

The threshold intensity that separates the severe from the extreme intensity exercise domain is important in understanding limitations to exercise tolerance, developing athletic performance and monitoring physical fitness status (Norouzi et al. 2022; Turnes, Aguiar, Cruz, Lisbôa, et al. 2016; Turnes, Aguiar, Cruz, Lisbôa, et al. 2016). A valid and practical method to define the severe‐to‐extreme intensity exercise domain boundary may enable the development of more rigorous approaches for the prescription of, and differentiation between, high‐intensity and sprint interval training (Bossi, Cole, et al. 2023; Bossi, Cole, et al. 2023; Ozkaya et al. 2023, 2025; Peker et al. 2024). Although the P_UPPERBOUND clearly defines that boundary and is based on sound theoretical foundations (Hill et al. 2002, 2024; Hill and Stevens 2005), this threshold intensity has, regrettably, not received the attention it deserves for more than 2 decades. A recently published study has revived attention to this threshold intensity and provided it with a new conceptual framework (Peker et al. 2024). Peker et al. (2024) emphasised that the upper boundary of the severe intensity exercise domain is also the highest power output at which the predominant energy contribution is derived from the aerobic energy pathways. The present study extends these findings by showing that the ALP, when calculated using the MAOD concept, also represents the P_UPPERBOUND, thereby providing a non‐invasive alternative for the calculation of ALP. The results of the present study reinforce the notion that ALP is not only a novel threshold intensity but also a robust, versatile and non‐invasive alternative for estimation of the upper boundary of the severe intensity exercise domain. Moreover, the majority of the available methodologies aimed at delineating the upper boundary of the severe intensity exercise domain ultimately identify a unique power output with respect to the concept of $\dot{\mathrm{V}}$O_2max (Caputo and Denadai 2008; Hill et al. 2002). However, it is now understood that $\dot{\mathrm{V}}$O_2max can be achieved for all severe intensity power outputs above CP such that there is no single power output at which $\dot{\mathrm{V}}$O_2max occurs (Azevedo et al. 2023; Iannetta et al. 2019; Poole and Jones 2017). Conversely, the concept of ALP, defined as the highest power output at which the predominant energy contribution remains aerobic, may offer a more progressive and physiologically relevant framework, particularly in relation to identification of the severe‐to‐extreme intensity exercise domain boundary.

In the original study proposing the concept of the ALP (Peker et al. 2024), the energy system contributions to total energy turnover were calculated based on analysis of $\dot{\mathrm{V}}$O₂ kinetics during exercise, peak blood [lactate] and the fast component of recovery $\dot{\mathrm{V}}$O₂ kinetics. An advantage of the former method is that it enables estimation of the separate phospholytic and glycolytic energy contributions to the total anaerobic contribution (Beneke et al. 2002; Bertuzzi et al. 2010; Hill 2023; Miyagi et al. 2017; Peker et al. 2024; Zagatto et al. 2016, 2017). In contrast, the MAOD method provides an estimate of the entire anaerobic contribution, that is the sum of the phospholytic and glycolytic energy contributions (Medbø et al. 1988; Medbø and Tabata 1989). Separate analyses of the phospholytic and glycolytic energy contributions are not required to determine the threshold intensity that distinguishes the severe from the extreme intensity exercise domain.

Although MAOD is regarded by some as the gold standard for estimating energy system contributions to exercise (Hill 2023; Medbø et al. 1988; Noordhof et al. 2010), it has also attracted criticism regarding its methodological assumptions and practical implementation (Bangsbo 1998; Ozyener et al. 2003). An important consideration in the calculation of MAOD‐derived ALP is the inclusion of an appropriate number of submaximal constant power exercise tests to produce the linear regression model that is used for the estimation of the accumulated O₂ deficit at the target power output (Noordhof et al. 2010). It has been suggested that at least 10 submaximal exercise tests should be performed to accurately estimate the $\dot{\mathrm{V}}$O₂ demand at any targeted power output (Noordhof et al. 2010; Zagatto et al. 2017). However, several studies have reported no statistical difference between different energy calculation methods using fewer submaximal exercise tests (Bertuzzi et al. 2010; Hill 2023; Miyagi et al. 2017; Zagatto et al. 2016). Indeed, in our study, we accurately estimated individual $\dot{\mathrm{V}}$O₂ demand for ALP using four submaximal exercise tests for each participant and this number of exercise test sessions appears to be appropriate to accurately estimate ALP and P_UPPERBOUND.

Secondly, in addition to the number of exercise sessions, it is known that the intensity at which they are performed is also important. Specifically, Bangsbo et al. (1993) reported that the $\dot{\mathrm{V}}$O₂ response at higher submaximal intensities exceeded that predicted by linear extrapolation from lower submaximal intensities, indicating that the relationship is not linear. Therefore, it has been stated that using this relationship may lead to an underestimation of the true accumulated O₂ deficit during supramaximal exercise (Bangsbo 1998). Nonetheless, in our study, the linear regression line between $\dot{\mathrm{V}}$O₂ and power output of the four submaximal tests demonstrated a high R ² and sufficient regression slope (0.99 ± 0.01 and 11.8 ± 0.8 mL·min⁻¹⋅W⁻¹, respectively).

Thirdly, a conceptual limitation of the MAOD method concerns its implicit assumption that the O₂ deficit reflects purely anaerobic energy contribution. However, several studies have demonstrated that the accumulated O₂ deficit also includes an aerobic component, as reflected in the change of body oxygen stores such as those in venous blood and muscle tissue (Medbø et al. 1988; Ozyener et al. 2003). To account for this, absolute accumulated O₂ deficit values were reduced by 10% to correct for the contribution of body oxygen stores to the energy supply in our study (Bertuzzi et al. 2010; Medbø et al. 1988; Weber and Schneider 2001).

The participant cohort in the present study consisted exclusively of males. Unfortunately, only male participants responded to the announcements throughout the experimental process of the study. The participants were relatively homogenous in terms of their physical activity status and represent a population group that is likely to benefit from measurement of ALP and P_UPPERBOUND. The extent to which our findings can be generalised to other populations, including elite athletes, females, older adults, and clinical groups, remains unclear and requires further investigation. Moreover, further studies are required to determine whether MAOD‐derived ALP provides a similarly accurate estimate of the upper boundary of the severe intensity exercise domain in other exercise modalities such as running.

5. Conclusion

We have proposed a novel approach for estimating the ALP, which coincides with the upper boundary of the severe intensity exercise domain, using the MAOD method. By analysing the linear relationship between the steady state $\dot{\mathrm{V}}$O₂ response and the power output from a series of submaximal exercise tests, estimating the total O₂ cost during severe and extreme intensity exercise bouts and calculating the accumulated O₂ consumed and O₂ deficit, it was possible to identify a distinct and individualised threshold intensity for each participant. The ALP determined by MAOD closely aligned with the independently established P_UPPERBOUND. Therefore, the determination of ALP by the MAOD method offers a non‐invasive alternative for identifying the upper boundary of the severe intensity exercise.

Funding

This study was financially supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK‐1002 program; project code: 220S455).

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.