Modeling lactate threshold in young squad athletes: influence of sex, maximal oxygen uptake, and cost of running

Endurance performance depends on a complex interplay of various metabolic and mechanical determinants (Joyner and Coyle 2008). While aerobic capacity, i.e., maximal oxygen uptake (\(\dot{V}\mathrm{O}_{2}\text{peak}\)) and its fraction at a disproportionate increase in the speed-lactate curve that can be sustained over a longer period (LT2_%) (Farrell et al. 1979; McLaughlin et al. 2010; Støa et al. 2020) represent the main metabolic determinants, movement economy (or energy cost of movement [C]) depends on the proportion of mechanical power output that contributes to progression (the higher the proportion, the more economical the locomotion) (Minetti 2004). Together, these three parameters have been shown to accurately predict endurance performance according to formula (1) (Joyner 1991; McLaughlin et al. 2010). For example, McLaughlin et al. (2010) found that in well-trained distance runners, 95.4% of the variation in 16-km running time could be explained by these variables.systematic analysis of validitRecently, Støren et al. (2014) and Støa et al. (2020) used the same equation to model the work rate corresponding to lactate threshold 2 (LT2) in cycling and running, respectively. Representing the highest work rate that still elicits a metabolic steady state, LT2 depicts an important parameter for endurance exercise prescription (indicating the upper boundary of the heavy intensity domain) and performance prediction (showing high correlations with endurance performance) (Faude et al. 2009). Interestingly, in both disciplines, Støren et al. (2014) and Støa et al. (2020) found a strong dependence of LT2 on \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C as well as a high agreement between calculated and measured work rates corresponding to LT2. Based on these observations, they concluded that training prescription may focus either on improving \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) for example using high intensity interval training or on improving C for example by implementing maximal strength training (Støa et al. 2020). Therefore, this model could represent a way to individualize exercise prescription for endurance training.

So far, however, the model applies only to adult well-trained to elite cyclists (Støren et al. 2014) and to adult recreational to elite long-distance runners (Støa et al. 2020), but not to other sport disciplines or age groups. Especially for young well-trained athletes, the model could represent an option to individualize training prescriptions based on the physiological profiles and thus use limited training time as efficiently as possible (Støa et al. 2020). However, it must first be investigated whether the model is dependent on age, since only adult athletes have been studied so far (Støa et al. 2020; Støren et al. 2014). Further, potential differences between sexes need to be considered, as sex specific prerequisites such as body composition could influence physiological characteristics such as aerobic capacity (Besson et al. 2022). In addition, the influence of the methods used to calculate C (model predictor) and LT2 (criterion) are unknown. With regard to LT2, there are a large number of studies that have investigated the agreement of different methods to determine LT2 with the underlying physiological concept of a maximal metabolic steady state but have yielded heterogeneous results [e.g., Faude et al. (2009)]. Regarding the LT2 determination method used by Støren et al. (2014) and Støa et al. (2020) (i.e., warm-up blood lactate concentration + 2.3 \(\hbox {mmol} \cdot \hbox {L}^{-1}\)), to the best of our knowledge, no systematic analysis of validity showing the absolute level of agreement with maximal metabolic steady state has been published. Therefore, re-calculating the model with a threshold concept that validly represents maximal metabolic steady state seems warranted.

Regarding model predictors, \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and LT2_% represent physiologically well-defined constructs, albeit dependent on test protocol and determination method (Faude et al. 2009; Midgley et al. 2007), whereas determination of cost of running (C_R) is still strongly debated (Barnes and Kilding 2015; Lundby et al. 2017). This controversy is mainly related to the question of whether or not C_R is independent of the running speed and therefore different external work rates have been studied (Iaia et al. 2009; Jones and Doust 1996; Lacour and Bourdin 2015; Svedenhag and Sjödin 1994). In contrast to the common approach of measuring oxygen uptake (\(\dot{V}\mathrm{O}_{2}\)) at a fixed submaximal speed (e.g., 12 \(\hbox {km} \cdot \hbox {h}^{-1}\)) to ensure achievement of a metabolic steady-state (Barnes and Kilding 2015), Støa et al. (2020) assessed \(\dot{V}\mathrm{O}_{2}\) at a fix percentage (i.e., 70%) of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) calculated from the linear relationship between submaximal running speeds and the corresponding \(\dot{V}\mathrm{O}_{2}\) values. However, apart from the fact that the linearity of the \(\dot{V}\mathrm{O}_{2}\) response to exercise is controversial (DiMenna and Jones 2009), from a physiological point of view both assessment methods bear the risk to obtain heterogeneous metabolic responses due to inter-individual variability. For example, Scharhag-Rosenberger et al. (2010) reported a large variability in blood lactate response at a work rate corresponding to 60% and 75% of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\). Similarly, measuring \(\dot{V}\mathrm{O}_{2}\) at a fixed submaximal speed (e.g., 12 \( \hbox {km} \cdot \hbox {h}^{-1}\)) will most likely elicit different metabolic responses in differently trained individuals. Since such divergent internal metabolic responses may impact inter-individual comparability, assessing C_R at a distinct submaximal metabolic anchor such as the first rise in blood lactate levels (LT1) might be a more individualized option.

Due to the potential impact of the cited methodological aspects as well as participant characteristics including sporting background, age, and sex on the accuracy of the model, the aims of the present study were to investigate: 1. The accuracy of the model, originally applied to adult runners by Støa et al. (2020), in young athletes of different disciplines depending on age and sex. In contrast to Støa et al. (2020), a validated threshold concept was used as a criterion. 2. The impact of different methods to determine C_R on the accuracy of the model. 3. The influence of LT2_%, \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), and C_R on the running speed at LT2 (vLT2) in young athletes depending on sex.

Table 1 summarizes the characteristics of the athletes. Both in absolute and relative terms, male athletes had a higher \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) compared to female athletes (\(p <0.001\)). Regardless of the method used (in terms of both running speed and expression), male athletes showed poorer C_R (\(p <0.001\)) but better vLT2 (\(p <0.001\)) than female athletes. No sex difference was found for LT2_% (\(p =0.999\)). The running speeds corresponding to LT1 were 3.00 ± 0.33 \(\hbox {m} \cdot \hbox {s}^{-1}\) and 2.70 ± 0.18 \(\hbox {m} \cdot \hbox {s}^{-1}\), and those corresponding to 80% \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\)were 3.29 ± 0.39 \(\hbox {m} \cdot \hbox {s}^{-1}\) and 2.92 ± 0.22 \(\hbox {m} \cdot \hbox {s}^{-1}\) in male and female athletes, respectively. In addition, minute ventilation was significantly higher in male than in female athletes at all submaximal running speeds used for C_R assessment (at LT1: 77.2 ± 14.6 \(\hbox {L} \cdot \hbox {min}^{-1}\) vs. 63.2 ± 8.3 \(\hbox {L} \cdot \hbox {min}^{-1}\), at 80% of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\): 89.3 ± 19.8 \(\hbox {L} \cdot \hbox {min}^{-1}\) vs. 70.9 ± 8.8 \(\hbox {L} \cdot \hbox {min}^{-1}\), \(p <0.001\)), except at a running speed of 2.8 \(\hbox {m} \cdot \hbox {s}^{-1}\) (108.6 ± 35.3 \(\hbox {L} \cdot \hbox {min}^{-1}\) vs. 97.4 ± 26.0 \(\hbox {L} \cdot \hbox {min}^{-1}\), \(p = 0.069\)).

The mean differences along with limits of agreement between _calLT2_fix, _calLT2_LT1, and _calLT2_80% vs. vLT2 are shown in the Bland-Altman plots (Fig. 2) and in Table 2. All modeled thresholds showed excellent concordance with vLT2 (Table 2).

Since C_R80% provided the model with the highest accuracy due to the smallest limits of agreement (i.e., _calLT2_80% ± 4% vs. and _calLT2_fix ± 7% and ± 8%, respectively), it was used for further regression analyses. The relationships between vLT2 and the three physiological variables were presented both for the whole sample and separated by sex in Table 3.

Entering \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), LT2_%, and C_R80% into the multiple linear regression model was able to explain 97%, 97%, and 95% of the variance in vLT2 for all, male, and female athletes, respectively (Table 3). Based on the selection criteria in the stepwise selection procedure, sex and age were not included in the final multiple regression model.

According to the commonality analysis, \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) showed the highest unique contribution to the total regression \(R^2\) followed by C_R80% and LT2_% regardless of the analyzed subset. Regarding the common effects, all sets of predictors showed a negative commonality coefficient, indicating the presence of suppression effects. The most noticeable suppression effect was observed between \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C_R80%, which was at – 31.6% in the whole sample. This was more pronounced in the female (– 51.7%) compared to the male subset (– 19.5%). The detailed results of the commonality analyses are depicted in Fig. 3.

The present study investigated the accuracy of the classical model with the physiological variables (i.e., \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), LT2_%, and C_R), applied in previous studies (McLaughlin et al. 2010; Støa et al. 2020; Støren et al. 2014), in determining vLT2 as an indicator of endurance performance in young squad athletes of different disciplines, ages, and sexes. We found an excellent accordance between the modeled and experimentally determined vLT2 (ICC \(\ge\) 0.959) with a very low systematic bias (mean difference ± limits of agreement \(\le\) 0.07 ± 0.32 \(\hbox {m} \cdot \hbox {s}^{-1}\)) independent of sex and age, supporting the applicability of _calLT2 to assess aerobic endurance performance also in young athletes. Furthermore, the accuracy of vLT2 modeling was improved, when C_R was determined by individualized approaches (especially C_R80%) rather than at a fixed speed (i.e., C_Rfix) (Fig. 2). According to the stepwise regression and commonality analyses, \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) is the most important factor for vLT2 in both sexes, followed by C_R, whereas LT2_% has the least influence (Fig. 3).

In the present investigation, C_R determined by different methods showed very high similarity with each other (Table 1). However, the application of individualized approaches, particularly C_R80%, further improved the accuracy of the model for calculating vLT2 as reflected by the lower variation (i.e., limits of agreement) compared to the other methods assessing C_R (Table 2 and Fig. 2). Especially in a heterogeneous sample as in our study, measuring \(\dot{V}\mathrm{O}_{2}\) at a fixed running speed (i.e., C_Rfix) results in different metabolic responses (e.g., percent utilization of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and substrate utilization) and thus impairs the inter-individual comparability of C_R. This might have contributed to the lower accuracy of _calLT2_fix compared to the other methods (i.e., larger random variation). To compensate for inter-individual variability in metabolic response, we suggested to assess C_R at a specific submaximal metabolic anchor, i.e., LT1. However, incorporating C_RLT1 in the model (i.e., _calLT2_LT1) did not considerably improve its accuracy in calculating vLT2 as compared to C_R80%. This result can be explained in part by the fact that the running speed at LT1 (2.84 ± 0.30 \(\hbox {m} \cdot \hbox {s}^{-1}\)) was similar to 2.8 \(\hbox {m} \cdot \hbox {s}^{-1}\) (running speed for C_Rfix) and significantly lower than that at 80% of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) (3.09 ± 0.36 \(\hbox {m} \cdot \hbox {s}^{-1}\)). Although it is now widely established that C_R is independent of the respective running speed (Di Prampero et al. 2009; Shaw et al. 2014), there are still conflicting findings indicating an increased or decreased C_R with the running speed (Iaia et al. 2009; Jones and Doust 1996; Lacour and Bourdin 2015; Svedenhag and Sjödin 1994). Assessing C_R at high relative running speed is likely to represent typical movement patterns (e.g., stride length and frequency) and to consider the individual metabolic demand, especially near to LT2. In this regard, it can be speculated that the running speed at 80% of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) may have better represented the inter-individual variation in running energetics and/or mechanics near LT2 compared to the running speed at LT1, thereby increasing the accuracy of the computational model. This is supported by the previous suggestion of Lacour and Bourdin (2015) that athletes’ performance may be more accurately predicted from C_R determined at high relative running speed.

Regarding the criterion, Støren et al. (2014) and Støa et al. (2020) used a threshold concept with a warm-up level of blood lactate concentration plus a fixed absolute value (2. 3 \(\hbox {mmol} \cdot \hbox {L}^{-1}\)) to determine LT2 as an estimate of maximal metabolic steady state. Although such an approach has been repeatedly used in previous studies as an established indicator of endurance performance [e.g., Helgerud et al. (1990, 2009)], there is no explicit study assessing its systematic bias and absolute agreement compared to the underlying physiological concept of a maximal metabolic steady state apart from unpublished work [i.e., Helgerud et al. (1990)], which is crucial for ensuring the validity of a threshold concept (Faude et al. 2009). In addition, the increase in blood lactate concentrations of a certain fixed value might not always be equally meaningful, since it is highly affected by various factors (e.g., test protocols, training- and nutrition-status) (Svedahl and MacIntosh 2003). In contrast, we applied a mathematical model for determining inflection points as a determination criteria for LT2, which is based on blood lactate kinetics rather than absolute concentrations (Zwingmann et al. 2019). Even though the use of mathematical models for LT2 determination has been criticized by some authors because of the lacking physiological fundamental (Janeba et al. 2010), its validity for estimating the maximal lactate steady state has been verified by systematic analyses (Jamnick et al. 2018; Zwingmann et al. 2019).

In the present study, the stepwise regression analysis showed that 97% of the total variance (males: 97%, females: 95%) in vLT2 in young squad athletes of different disciplines was explained by \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), LT2_%, and C_R, supporting that these are the three primary physiological factors influencing aerobic endurance performance (McLaughlin et al. 2010). The single most important determinant of vLT2 independent of sex was \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), which is in accordance with previous research (McLaughlin et al. 2010; Støa et al. 2020; Støren et al. 2014), emphasizing the importance of aerobic energy supply during prolonged weight-bearing exercise such as running. Therefore, especially in heterogeneous samples as in the present study, endurance performance is strongly related to \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\). Likewise, the lower values observed in the young female compared to the male athletes are in accordance with previous studies and are likely related to body composition (i.e., greater percentage of body fat) and oxygen carrying capacity (i.e., lower hematocrit levels) (Besson et al. 2022).

Based on the commonality analysis, C_R, being the second major factor influencing vLT2, seems to act as a suppressor which purifies the “irrelevant” variance of other independent variables (i.e., negative common effects), and thus improves their contribution to the regression model. In particular, the pronounced suppression effect of C_R in combination with \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) (– 19.5% to – 51.7% of total \(R^2\)) can emphasize the crucial role of the interaction between maximal aerobic capacity and movement economy for endurance performance (Joyner and Coyle 2008). Indeed, in the present investigation, C_R separately exhibited only negligible to low correlation with vLT2 (r = – 0.359 to – 0.003), but its incorporation into the regression model in addition to \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) resulted in a significantly improved \(R^2\) with a significant (standardized) beta weight in both the whole group and the male and female subgroups (see Table 3). Furthermore, the product of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C_R (expressing maximal aerobic speed) has been demonstrated to be a very good predictor for 16-km time trial performance (\(R^2\) = 0.94) and vLT2 (\(R^2\) = 0.85) in competitive runners (McLaughlin et al. 2010; Støa et al. 2020). Interestingly, the unique (56.3% vs. 37.9%) and common effects (– 51.7% vs. – 19.5%) of C_R on the total \(R^2\) were distinctly higher in female than in male athletes implying the greater impact of C_R in determining endurance performance in females. Further, female athletes showed lower C_R values independent of the determination method. This is an interesting finding which contributes to the debate whether or not there are sex differences regarding C_R(Besson et al. 2022). While some authors argue that sex differences in C_R disappear when expressed as relative intensities (i.e., as percentage of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) or lactate threshold) (Fletcher et al. 2013; Helgerud et al. 1990), our data indicate that, at least in young athletes, females exhibit lower values whether expressed as absolute (C_Rfix) or relative (C_R80% and C_RLT1) values.  Besides differences in anthropometric dimensions (e.g., body height, see Table 1), the lower C_R in female athletes might be due to neuromuscular characteristics of the lower extremities such as lower-body stiffness or Achilles moment arm length as shown for well-trained distance runners (Barnes et al. 2014). Furthermore, since we observed significantly higher minute ventilation at the speed corresponding to 80% of \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) in male compared to female athletes, it can be assumed that the differences in C_R may be attributed, at least in part, to increased demands of breathing. Thus, it has been shown earlier that running economy was improved by training induced decrease in minute ventilation (Franch et al. 1998). Nonetheless, it should be noted that our study did not take into account hormonal changes related to the phase of the menstrual cycle in female athletes, which is known to affect C_R (Besson et al. 2022; Dokumacı and Hazır 2019).

Besides sex-specific differences in C_R, it is unclear why C_R had a greater impact on vLT2 determination in young female athletes than in males. However, beside the aforementioned factors (e.g., anthropometric, neuromuscular, and cardio-respiratory), there are sex-specific differences related to substrate oxidation during exercise and muscle tissue characteristics (e.g., proportion of type I muscle fibers and muscle capillarization), that could affect male and female athletes differently in terms of submaximal energy metabolism (Besson et al. 2022). These differences may partly explain why C_R appears to have a stronger influence on endurance performance in young female compared to male athletes, similar to the previous findings of Støa et al. (2020) in adult runners. In this context, future longitudinal studies might investigate whether female athletes can actually profit more than male athletes from an improvement in C_R.

In contrast to \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C_R, we found no sex difference in LT2_% (87.0 ± 2.9% vs. 87.0 ± 2.4%) with a very low inter-individual variation (coefficient of variation \(=\) 3%). These results are in line with previous investigations indicating no difference in LT2_% between well-trained male and female runners (McLaughlin et al. 2010) as well as between elite, national, and recreational runners (Støa et al. 2020). Further, the LT2_%-values in the previous studies with adult recreational and elite runners (72–93%) are in a similar range to those in the current study (80–94%). Taken together, it seems plausible to assume that LT2_% does not vary substantially depending on the aerobic endurance level. Moreover, the minor contribution of LT2_% to the regression model for determining vLT2 in the present study (Fig. 3) provides further support for the assumption that LT2_% is not a major factor affecting aerobic endurance performance (McLaughlin et al. 2010; Støa et al. 2020; Støren et al. 2014). Nonetheless, further studies need to investigate whether long-term adaptations of LT2_% lead to altered aerobic endurance performance (i.e., vLT2) in young athletes of different disciplines.

Due to the high accuracy in estimating vLT2, the proposed model allows to draw conclusions about the limiting factors (mainly \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C_R) of endurance performance of young athletes of various disciplines and both sexes, and may therefore guide future training design. Since total time to improve endurance capacity in technically or tactically demanding sports is limited especially in young athletes with a restricted schedule, this time needs to be utilized as efficiently as possible. Thus, depending on the individual physiological prerequisites, training prescription may focus either on improving \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) for example using high intensity interval training or on improving C_R for example by implementing explosive- and maximal-strength training (Rønnestad and Mujika 2013; Støa et al. 2020). Future studies should use the predictors to model endurance performance longitudinally, e.g., over one or multiple seasonal cycles to examine whether training induced changes in the physiological predictors actually lead to the intended changes in endurance performance.

In conclusion, the classical model using \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\), C_R, and LT2_% to determine vLT2 is also suitable for assessing endurance performance in young squad athletes of different disciplines, ages, and sexes. The accuracy of the model was further improved by an individual determination of C_R (in particular C_R80%). \(\dot{V}\mathrm{O}_{2}\mathrm{peak}\) and C_R were found to have the most important contributions in determining vLT2. While in young female athletes, the impact of C_R on endurance performance appeared to be greater than that in male athletes, LT2_% was generally found to have the least impact on vLT2 determination.