From a physiological perspective, speed of locomotion in endurance sports such as running and cycling is primarily related to the maximal aerobic metabolic rate (MR) (i.e., maximum oxygen uptake, V.O2max), its fractional utilization, and the energy cost of movement. Although aerobic energy provision is the primary source of energy supply in endurance sports, anaerobic energy provision is also involved (Joyner and Coyle, 2008). Due to the limited capacity of the anaerobic energy supply, the relative anaerobic contribution to exercise decreases with duration (Gastin, 2001). For example, in 800 and 1500-m track running (lasting ∼2.1 and ∼4.4 min, respectively), the relative contribution of anaerobic metabolism decreases from ∼40 to ∼14% in trained runners (Duffield et al., 2005a,b). In addition, many endurance races are often performed head-to-head, making anaerobic energy provision crucial for the success of breakaways and final end-spurts.

Although aerobic energy provision can be quantified during exercise by using measures of oxygen consumption and carbon dioxide production, the quantification of anaerobic energy provision is more complicated. Several different methods of quantifying anaerobic capacity (AnC) have been used (Noordhof et al., 2013), but the gold standard procedure is probably the direct method first described by Bangsbo et al. (1990) for single-leg knee extension exercise. However, this sophisticated invasive method is not applicable for traditional whole-body endurance modalities such as running or cycling, where many large muscle groups are involved in locomotion (Noordhof et al., 2010). Therefore, indirect estimates of anaerobic energy production are commonly used, such as the maximal accumulated oxygen deficit (MAOD) method (Medbø et al., 1988) or the gross efficiency (GE) method (Serresse et al., 1988; Noordhof et al., 2011; Andersson and McGawley, 2018). The MAOD method identifies a supramaximal total average oxygen uptake (V.O2) requirement calculated from a linear relationship between submaximal V.O2 and speed (or power output). Due to the effect of increasing submaximal exercise intensity on substrate utilization (Shaw et al., 2014) and the different energy equivalents for fat and carbohydrate oxidation (Weir, 1949), a speed (or power output) vs. MR relationship should be more appropriate (Andersson and McGawley, 2018). By contrast, for the GE method, the supramaximal total metabolic requirement can be calculated by dividing the supramaximal power output by GE determined from a single submaximal exercise bout. For both methods, the anaerobic MR during supramaximal exercise can be calculated by subtracting the instantaneous aerobic MR from the total required instantaneous MR, with the AnC calculated as the anaerobic MR integrated over time (Andersson and McGawley, 2018; Andersson et al., 2020).

The main limitations of the linear regression method are related to the range of exercise intensities included in the submaximal linear relationship, the number, and duration of the submaximal stages, and whether a continuous or discontinuous submaximal protocol is used (Noordhof et al., 2010). In addition, the effect of including a baseline value of MR in the linear regression model is equivocal and might differ for exercise modalities (Bangsbo, 1992, 1996; Noordhof et al., 2011; Andersson and McGawley, 2018; Andersson et al., 2020). For instance, Andersson et al. (2020) showed for diagonal-stride treadmill roller-skiing that the inclusion of a resting baseline value of MR (i.e., the Y-intercept value) was likely to result in an underestimated supramaximal metabolic requirement and AnC compared to no inclusion of a baseline Y-intercept value. However, Noordhof et al. (2011) showed no such difference when including a fixed Y-intercept value for cycle ergometry exercise.

Due to the difficulties in determining external work during running, the GE method can be considered inappropriate for determining AnC for running exercise. Therefore, most previous studies that have estimated AnC during treadmill running have used the MAOD approach (Medbø et al., 1988; Ramsbottom et al., 1994; Craig and Morgan, 1998; Spencer and Gastin, 2001; Hill et al., 2002) while the GE approach has been more commonly used during cycle ergometry exercise to estimate anaerobic work capacity and/or anaerobically attributable power output (Serresse et al., 1988; Foster et al., 2003; de Koning et al., 2005; Hettinga et al., 2006). An alternative method that can be used to estimate the AnC for treadmill roller-skiing or running is the gross energy cost (GEC, J⋅kg^–1⋅m^–1) method, which is conceptually similar to the GE method and has recently been employed for estimating AnC during diagonal-stride treadmill roller-skiing (Andersson and McGawley, 2018). In this study, both the GE and GEC methods resulted in identical values of AnC and are, thus, conceptually similar when applied to treadmill exercise in a laboratory where air drag is negligible. Therefore, the GEC concept may potentially be used as an alternative to the GE approach when estimating AnC during supramaximal running on a treadmill. A potential limitation of the GEC (or GE) method is the assumption that GEC (or GE) is speed (or power output) independent (Batliner et al., 2018; Andersson et al., 2020). Based on the linear regression between speed (or power output) and MR, as used in the modified MAOD method, GEC (or GE) is only constant when the Y-intercept is zero. For relationships with a positive Y-intercept, GEC will always decrease (or GE will increase) with increasing exercise intensity due to the diminishing effect of the Y-intercept value (Ettema and Lorås, 2009; Batliner et al., 2018). However, when a wide range of exercise intensities are used and combined with a resting baseline value in the linear MAOD regression, a positive Y-intercept would be expected (Noordhof et al., 2011), which in theory would explain the disagreement between the MAOD and GE methods (Andersson et al., 2020).

At present, a limited number of studies have compared different AnC estimates generated by the MAOD and GE methods (Noordhof et al., 2011; Andersson and McGawley, 2018; Andersson et al., 2020). The overall conclusion of these studies is that the different methods should not be used interchangeably, due to the relatively high within-participant disagreement. However, there is sparse information explaining this disagreement or the typical errors associated with the different AnC estimates generated by the MAOD and GEC/GE concepts. To date, there is, to our knowledge, only one study that has provided any methodological interpretation of the within-participant disagreement between the GE and MAOD methods, which was related to the individual variation in the Y-intercept values for the MAOD regression (Andersson et al., 2020). Given this sparsity of methodological inquiry, the current study aimed to compare estimates of anaerobic capacities generated during a 4-min running performance time trial (TT) using four different models: the 5 × 4-min MAOD method with the inclusion of a baseline Y-intercept value (5+Y_LIN) and without the inclusion of a baseline Y-intercept value (5-Y_LIN), and two GEC methods using the average GEC based on the 5 × 4-min submaximal exercise intensities (GEC_AVG) and using the last exercise intensity only (GEC_LAST).

The submaximal speeds, physiological responses, and two various concepts of energy cost (i.e., GEC and net energy cost) at the five submaximal stages are shown in Table 1. The GEC remained unchanged (∼4.39 J⋅kg^–1⋅m^–1) between all submaximal stages (F_1.48,56 = 0.84, P = 0.413, and η² = 0.004) whereas the net energy cost increased by ∼4.4% from the first to the last submaximal stage (F_1.55,56 = 11.0, P < 0.001, and η² = 0.048).

The mean ± SD speed and MR during the five submaximal stages and the TT, together with the regression lines (based on the mean values), are displayed in Figure 1A for the 5+Y_LIN and 5-Y_LIN models. The mean ± SD values of GEC and the GEC calculated from the 5+Y_LIN and 5-Y_LIN models are displayed in Figure 1B. The 4-min TT was completed at an average speed of 4.7 ± 0.4 m⋅s^–1 (17.0 ± 1.5 km⋅h^–1). The V.O2peak was 58 ± 6 mL⋅kg^–1⋅min^–1 (4.2 ± 0.9 L⋅min^–1), with an RER of 1.14 ± 0.05. The peak ventilation rate, peak heart rate, and peak blood lactate concentration were 148 ± 26 L⋅min^–1, 183 (IQR = 177–188) beats⋅min^–1, and 11.0 ± 2.1 mmol⋅L^–1, respectively. The RPE measured immediately after the TT was 19 (IQR = 18–19).

The estimated total MRs during the TT (including the aerobic and anaerobic contributions) and the AnC values are shown in Figures 1C,D, respectively, for the four different computational methods. In Figure 1D it can be seen that the estimated AnC was considerably lower for the 5+Y_LIN model compared to the three other models (i.e., 5-Y_LIN, GEC_AVG, and GEC_LAST).

The data presented in Table 2 show that the SEE was approximately twice as large for the 5+Y_LIN vs. the 5-Y_LIN regression model. Also, the Y-intercept value was considerably higher for the 5+Y_LIN model, which resulted in a regression slope (i.e., a delta energy cost) that was ∼10% lower for the 5+Y_LIN model than for the 5-Y_LIN model. The root mean square error for the relative difference between GEC calculated from the speed-MR regression and the GEC measured during the five submaximal stages was 1.8 ± 0.8% for the 5+Y_LIN and 0.8 ± 0.3% for the 5-Y_LIN model (P < 0.001, Hg_av = 1.6). The average GEC during the TT was ∼3.7% lower for the 5+Y_LIN compared to the other three models, which resulted in an ∼3.9% lower required MR during the TT for the 5-Y_LIN model (see Table 2). This explains the ∼26% lower estimated AnC for the 5+Y_LIN model (illustrated in Figure 1D).

All individual regression lines between speed and MR are shown in Figures 2A,B for the 5+Y_LIN and 5-Y_LIN models, respectively. The GEC calculated from the two regression equations (GEC_REG) for the five submaximal speeds and the TT speed is presented in Figures 2C,D for the 5+Y_LIN and 5-Y_LIN models, respectively, whereas the directly measured GEC is presented in Figure 2E. It can be seen that the inclusion of a Y-intercept value in the linear regression (i.e., the 5+Y_LIN model) resulted in a decline in GEC with increasing speed for all participants, which deviates from the somewhat mixed speed-GEC patterns presented in Figures 2D,E. The within-participant disagreement in estimated AnC for the four different models is illustrated in Figure 2F.

Comparisons of the AnC estimates from the 4-min TT using the four different models are presented in Figure 3. As shown in Figures 3A–C, the 5+Y_LIN model generated anaerobic capacities that were ∼19 kJ⋅kg^–1 lower than the 5-Y_LIN, GEC_AVG, and GEC_LAST models, whereas the mean difference between the 5-Y_LIN, GEC_AVG, and GEC_LAST models was approximately zero (Figures 3D–F). The typical errors for the respective comparisons were generally high, with exception of the 5+Y_LIN vs. GEC_AVG model (see Figure 3).

The variation in Y-intercept values for the 5-Y_LIN model was highly related to the variation in the AnC estimates between the 5-Y_LIN and GEC_AVG models (r² = 0.990; Figure 4B), as well as between the 5-Y_LIN and GEC_LAST models (r² = 0.956; Figure 4D). This explains the relatively large typical errors and 95% limits of agreements for the AnC differences observed for the 5-Y_LIN vs. GEC_AVG and GEC_LAST models (shown in Figures 3E,F), and the small typical error and 95% limits of agreement for the 5+Y_LIN vs. GEC_AVG model (shown in Figure 3B).

Supplementary data based on two alternative polynomial models and three alternative linear models are provided in the Supplementary Tables 1, 2.

The main findings of the current study were that the total required MR during the 4-min TT was ∼3.9% lower when a baseline MR was included in the linear model (i.e., 5+Y_LIN) compared to no inclusion of a baseline MR (i.e., 5-Y_LIN) and the two GEC models (i.e., GEC_AVG and GEC_LAST). The significantly higher Y-intercept in the 5+Y_LIN model resulted in a significantly lower slope of the regression line and a higher SEE. The average AnC was ∼26% lower for the 5+Y_LIN model vs. the three other models (i.e., 5-Y_LIN, GEC_AVG, and GEC_LAST). Although the estimated anaerobic capacities for the 5-Y_LIN, GEC_AVG, and GEC_LAST models were very similar on a group level, the within-participant variation was relatively high, as indicated by the typical errors that ranged between 0.07 and 0.16 kJ⋅kg^–1. The 5+Y_LIN model demonstrated smaller typical errors when compared with the GE_AVG and GE_LAST models than when compared with the 5-Y_LIN model, which was highly related to the considerably larger between-participant variation in Y-intercept values for the 5-Y_LIN model.

There are several problems associated with the various methods used to estimate the AnC (Noordhof et al., 2010, 2013). Based on previous validation data on supine one-legged dynamic knee-extensor exercise a high agreement between the indirect MAOD method and a more sophisticated direct measurement was observed (Bangsbo et al., 1990), which indicates that the MAOD method might be valid for whole-body exercise as well. When using the MAOD method several previous studies have either used a forced Y-intercept of 5 mL⋅kg^–1⋅min^–1, a resting V.O2 measured at baseline, or an arbitrary value in the linear regression (Medbø et al., 1988; Russell et al., 2000, 2002; Bickham et al., 2002). This procedure has been suggested to increase the precision of the estimated V.O2 demand (Medbø et al., 1988; Russell et al., 2000; Noordhof et al., 2011). However, the use of a Y-intercept value in the linear regression between speed (or power output) and MR (or V.O2) can only be justified if it is reasonably aligned with the submaximal stages of exercise. In the current study, the inclusion of a Y-intercept value in the linear regression resulted in a significantly lower required MR, GEC, and AnC during the TT (see Figure 1). Moreover, compared to the 5-Y_LIN model, the 5+Y_LIN regression model demonstrated a significantly lower slope (3.85 vs. 4.32 W⋅kg^–1 per m⋅s^–1) and a higher Y-intercept (1.69 vs. 0.18 W⋅kg^–1), which together indicate that the included Y-intercept value changed the regression equation noticeably. The SEE was considerably larger for the 5+Y_LIN than the 5-Y_LIN model, which indicates a worse fit of the regression line when a baseline MR (i.e., resting value) was added. These results suggest that the total metabolic requirement and the estimated AnC are likely to be underestimated when including a baseline MR (i.e., a modeled Y-intercept) in the linear relationship between speed and MR for treadmill running exercise. Interestingly, some previous studies have shown GEC or gross oxygen cost (i.e., VO₂ consumed per unit of distance) to be speed independent (on a group level) (Fletcher et al., 2009; Helgerud et al., 2010; Shaw et al., 2014), indicating a zero Y-intercept for the linear regression between speed and MR (or V.O2). This because GEC or gross oxygen cost would only be speed independent if the Y-intercept is zero, which is also similar for GE and the regression between power output and MR (Batliner et al., 2018; Andersson et al., 2020). Moreover, using a forced Y-intercept in the linear regression model has been observed to generate unreasonably low values of estimated AnC in running compared to cycling (Hill et al., 2002). Also, the linearity of the regression has been questioned for treadmill running (Bangsbo, 1996; Hill, 1996; Hill and Vingren, 2011). This, together with the current findings, conflicts with the traditional view that a baseline value (i.e., a Y-intercept) should be included in the linear regression when estimating the AnC during treadmill running (Medbø et al., 1988; Russell et al., 2000; Noordhof et al., 2011).

Even though it is well known that the energy equivalent per unit of VO₂ differs considerably between fats and carbohydrates (Weir, 1949), most previous studies have used expressions of oxygen cost for determining running (or movement) economy without considering the potential influence of substrate utilization (Conley and Krahenbuhl, 1980; Daniels and Daniels, 1992; Duffield et al., 2005b; Helgerud et al., 2010). This is of particular relevance when studying heterogeneous participants or evaluating the effect of exercise intensity on running economy (Fletcher et al., 2009; Shaw et al., 2014). Due to the aforementioned factors, the current study employed two linear regression models that were based on submaximal MR, rather than submaximal V.O2, to estimate the total metabolic requirement. The two linear models were also used on a second-by-second basis to estimate the instantaneous total metabolic requirement, which, compared to the traditional MAOD concept described by Medbø et al. (1988), can provide more detailed information regarding the anaerobic energy distribution during exercise. This is also an essential aspect when comparing different pacing strategies and/or repeated performances (Hettinga et al., 2006; Andersson et al., 2016).

To facilitate the comparison between the four different models, GEC during the TT was calculated from the regression equations for the 5+Y_LIN and 5-Y_LIN models and average values were similar for the 5-Y_LIN, GEC_AVG, and GEC_LAST models, and higher than the 5+Y_LIN model (Table 2). In the current study, GEC was observed to be speed independent on a group level, which explains the similar estimated average anaerobic capacities for the 5-Y_LIN, GEC_AVG, and GEC_LAST models as shown in Figure 1. However, individual data show that GEC derived from the individual 5-Y_LIN regressions, as well as the directly measured GEC, were not speed independent (see Figures 2D,E), which explains the generally high disagreement observed between the different models used for estimating the AnC (see Figure 2F). Interestingly, the inclusion of a baseline MR as a Y-intercept had a relatively large effect on the GEC values calculated from the linear regression equation (see Figure 2C vs. Figure 2E). The disagreement for GEC derived from the regression equation vs. directly measured GEC was also higher for the 5+Y_LIN than the 5-Y_LIN model as indicated by the significantly higher root mean square error. The disagreement in GEC values at the TT speed, i.e., the disagreement in GEC values computed from the 5+Y_LIN and 5-Y_LIN regressions and the GEC_AVG and GEC_LAST, helps to explain the variability in the estimated anaerobic capacities between the different computational models (see Figure 2). As shown in Figure 3, the typical errors were fairly high for all the four models compared and the 5+Y_LIN generated significantly lower values of AnC in comparison to 5-Y_LIN, GE_AVG, and GE_LAST. Inclusion of a baseline resting MR as a Y-intercept in the linear model compared to no baseline resulted in a large mean difference and typical error for the 5+Y_LIN vs. 5-Y_LIN model (Figure 3A). Based on the inconsistent individual speed vs. GEC relationships demonstrated in Figure 2E, it is likely that the use of the 5+Y_LIN, GE_AVG, and GE_LAST models are less reliable than the 5-Y_LIN model for estimating AnC. Therefore, to create a more robust linear relationship between speed and MR for treadmill running, it is probably wise to include some additional submaximal stages rather than adding a Y-intercept.

In a previous study, Andersson et al. (2020) demonstrated for the first time that the between-participant variation in Y-intercept values is related to the disagreement between the MAOD and GE concepts for estimating AnC. Not surprisingly, a similar finding was observed here when using GEC instead of GE, with the value of the Y-intercept of the 5-Y_LIN model being linearly related to the mean difference in anaerobic capacities between the 5-Y_LIN vs. the two GEC models (see Figures 4B,D). However, the strength of the same relationships decreased considerably for the 5+Y_LIN vs. the two GEC models (see Figures 4A,C). This was most likely due to: (1) the substantially reduced between-participant variation in the modeled Y-intercept values when including a baseline MR (i.e., a resting value); and (2) the disagreement between measured GEC and calculated GEC based on the 5+Y_LIN regression for the submaximal stages being significantly higher for the 5+Y_LIN model, as based on the higher root mean square error.

The current study is to our knowledge the first that has compared the GEC concept for estimating AnC with the more traditional MAOD method. In theory, the GEC_LAST model is very similar to the GE concept used for estimating anaerobically attributable work or AnC (Noordhof et al., 2011; Andersson and McGawley, 2018). If assuming a linear regression between power output, or speed (for running), vs. MR with a modeled Y-intercept that is similar to the resting MR, GE would increase with higher power output while an inverse relationship would be the case for the GEC of treadmill running vs. speed (Andersson and McGawley, 2018; Andersson et al., 2020). This is simply explained by the fact that the relative contribution of the baseline resting MR to the total MR decreases with higher exercise intensity (Ettema and Lorås, 2009). Due to this, both GE and GEC at supramaximal exercise intensities can be estimated from a linear regression equation between submaximal power output, or speed (for running), and MR (as shown in Figures 2A–D). Therefore, a linear regression model used for estimating AnC can also be employed as a method for estimating GEC (or GE) during high-intensity exercise. In contrast, the GEC based on the GEC_LAST or GEC_AVG models for estimating AnC can be converted to a linear regression between speed and MR where the Y-intercept would always be zero and with the slope representing the GEC_LAST or GEC_AVG. For exercise using a fixed GE value for estimating AnC (Noordhof et al., 2011), it is simply the same analogy, but the linear regression between power output and MR would be best described as a slope representing the reciprocal value of GE combined with a zero Y-intercept (Andersson et al., 2020).

In the current study, the estimated anaerobic capacities were relatively low and for the four models combined, approximately one-third of the theoretical maximum proposed by Saltin (1990). However, somewhat similar values of anaerobic capacities have been observed previously for level running (Olesen, 1992; Sloniger et al., 1997). In previous literature, uphill running has also been shown to generate higher anaerobic capacities than level running, which is explained at least in part by the lower amount of activated muscle mass in the lower extremities (Olesen, 1992; Sloniger et al., 1997). It is also plausible that the degree of linearity of the relationship between submaximal speed and MR is different for running on different slopes (Olesen, 1992). For instance, Hill et al. (2002) observed unreasonably large differences in anaerobic capacities between running and cycling, with ∼39% lower values of AnC in running when employing the same MAOD method and using a forced Y-intercept of 5 mL⋅kg^–1⋅min^–1 as suggested by Medbø et al. (1988). Hill et al. (2002) proposed that these differences were mainly a computational effect, i.e., employing a linear regression on a relationship that was more upwardly curvilinear in running than in cycling. In the current study where running was analyzed, the inclusion of a measured and modeled (i.e., not forced) Y-intercept in the MAOD model resulted in a 25% lower value of AnC compared to no inclusion. A similar finding has been observed for uphill diagonal-stride roller-skiing (Andersson and McGawley, 2018; Andersson et al., 2020). These findings suggest that the inclusion of a Y-intercept value in the linear regression equation is likely to underestimate the AnC while running or roller-skiing (diagonal-stride) on a treadmill as it underestimates the GEC (or overestimates GE for roller-skiing) during a maximal TT. However, the inclusion of a Y-intercept might be more relevant for cycling exercise where technique is likely to be more robust over a larger range of intensities, and might thus be better aligned with a measured Y-intercept than running or roller-skiing. For instance, Figure 2E shows large individual variability in GEC vs. speed, which indicates that the effect of speed on running biomechanics and GEC is highly individual, and adding a measured Y-intercept may change the speed-GEC relationship considerably as shown in Figure 2.

In a previous study by Hill and Vingren (2011), the relationship between speed and MR was found to be upwardly curvilinear for running but linear for cycle ergometry. In order to make a thorough evaluation of the linearity of the data in the current study, the results generated by two alternative polynomial models and three alternative linear models were compared with the conventional 5-Y_LIN and GEC_LAST models, and these data are presented as Supplementary Tables. The results in Supplementary Table 1 reveal that the AnC estimates were not significantly different for the five alternative models when compared to the conventional 5-Y_LIN and GEC_LAST models, indicating that the submaximal relationship between speed and submaximal MR for the five submaximal stages can be considered linear. The results in Supplementary Table 2 also reveal that the agreements between the two polynomial models and the other models were relatively poor. Interestingly, the comparison between the AnC estimates for the 5-Y_POL vs. 5-Y_LIN models resulted in a high typical error (0.20 kJ⋅kg^–1). This indicates that polynomial models can be problematic to use on data that are mainly linear due to the issue of so-called overfitting, which has also been observed previously for diagonal-stride roller-skiing (Andersson et al., 2020).

In the current study, a mixed group of female and male recreational, endurance-trained athletes was recruited. It is possible that between-participant variability in physiological characteristics could have an impact on the agreement between the different models that were used to estimate AnC, and that such variability could be higher for a mixed-sex athlete group. For example, it is possible that between-participant variation in a physiological variable such as V.O2max could influence the agreement between the GEC_LAST and 5-Y_LIN models of estimating AnC. This is because the relative influence of the baseline (i.e., resting) MR on GEC becomes smaller with increasing exercise intensity, and V.O2max is directly related to the participant’s highest absolute submaximal exercise intensity. However, the range in V.O2max was relatively small in the current study and as a result, it is unlikely that sex differences per se would have influenced the results to a major extent.

This study aimed to compare four different models of estimating AnC during high-intensity treadmill running and to methodologically examine the agreement between the four models. Two of the four models were based on a linear relationship between submaximal speed and MR (i.e., 5+Y_LIN and 5-Y_LIN) and two were based on a fixed GEC value (i.e., GEC_AVG and GEC_LAST). The GEC_AVG and GEC_LAST models were introduced because of the similarities to the GE concept that has been used for estimating AnC/work capacity during cycling (Serresse et al., 1988; Noordhof et al., 2011).

The main findings of the current study were that GEC was found to be speed independent on a group level and that 5-Y_LIN, GEC_AVG, and GEC_LAST generated similar values of AnC, while the 5+Y_LIN model generated ∼26% lower values of AnC. The lower anaerobic capacities estimated with the 5+Y_LIN could be related to the significantly lower slope of the regression line and the higher Y-intercept value, which resulted in a lower GEC value (based on the regression equation) during the 4-min TT effort. Although the 5-Y_LIN, GEC_AVG, and GEC_LAST generated similar values of AnC, they should not be used interchangeably due to the profound individual variability, as indicated by the large typical errors and the large SEM. The 5-Y_LIN model might be the most reliable and valid model out of the four models that were studied and as such, this model is recommended for estimating AnC during treadmill running exercise. This is because GEC was not observed to be speed independent on an individual basis and GEC calculated from the 5-Y_LIN linear regression equation was more similar to the directly measured GEC at the five submaximal intensities.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by The Regional Ethical Review Board of Umeå University, Umeå, Sweden. The patients/participants provided their written informed consent to participate in this study.

EA and KM designed the study. KM, EA, and GB were responsible for the data collection, drafted the final manuscript, approved the final version to be published, and agreed to be accountable for all aspects of the work. EA analyzed and interpreted the data, and wrote the first draft of the manuscript. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.