Vol.:(0123456789)
1 3
European Journal of Applied Physiology (2023) 123:573–583 
https://doi.org/10.1007/s00421-022-05084-1
ORIGINAL ARTICLE
Modeling lactate threshold in young squad athletes: influence of sex, 
maximal oxygen uptake, and cost of running
Sanghyeon Ji1  · Sebastian Keller1,2,3  · Lukas Zwingmann1  · Patrick Wahl1 
Received: 5 July 2022 / Accepted: 20 October 2022 / Published online: 21 November 2022 
© The Author(s) 2022, corrected publication 2022
Abstract
Purpose This study aimed to investigate: 1. The influence of sex and age on the accuracy of the classical model of endurance 
performance, including maximal oxygen uptake ( ̇VO2peak ), its fraction  (LT2%), and cost of running (CR), for calculating 
running speed at lactate threshold 2 (vLT2) in young athletes. 2. The impact of different CR determination methods on the 
accuracy of the model. 3. The contributions of ̇VO2peak ,  LT2%, and CR to vLT2 in different sexes.
Methods 45 male and 55 female young squad athletes from different sports (age: 15.4 ± 1.3 years; ̇VO2peak : 51.4 ± 6.8 
mL ⋅ kg−1 ⋅ min−1 ) performed an incremental treadmill test to determine ̇VO2peak ,  LT2%, CR, and vLT2. CR was assessed at 
a fixed running speed (2.8 m ⋅ s−1 ), at lactate threshold 1 (LT1), and at 80% of ̇VO2peak , respectively.
Results Experimentally determined and modeled vLT2 were highly consistent independent of sex and age (ICC ≥ 0.959). The 
accuracy of vLT2 modeling was improved by reducing random variation using individualized CR at 80% ̇VO2peak (± 4%) 
compared to CR at LT1 (± 7%) and at a fixed speed (± 8%). 97% of the total variance of vLT2 was explained by ̇VO2peak , 
 LT2%, and CR. While ̇VO2peak and CR showed the highest unique (96.5% and 31.9% of total R2 , respectively) and common 
(– 31.6%) contributions to the regression model,  LT2% made the smallest contribution (7.5%).
Conclusion Our findings indicate: 1. High accuracy of the classical model of endurance performance in calculating vLT2 in 
young athletes independent of age and sex. 2. The importance of work rate selection in determining CR to accurately predict 
vLT2. 3. The largest contribution of ̇VO2peak and CR to vLT2, the latter being more important in female athletes than in 
males, and the least contribution of  LT2%.
Keywords Maximal metabolic steady state · Performance diagnostics · Aerobic capacity · Endurance performance · 
Running economy · Youth athletes
Abbreviations
calLT2 
 Calculated speed corresponding to lactate 
threshold 2
calLT2fix 
 Calculated speed corresponding to lactate 
threshold 2 determined using cost of running 
determined at a fixed speed of 2.8 m ⋅ s−1
calLT2LT1 
 Calculated speed corresponding to lactate 
threshold 2 determined using cost of running 
determined at lactate threshold 1
Communicated by Michael I. Lindinger.
Sanghyeon Ji, Sebastian Keller have contributed equally to this 
work.
 * Sanghyeon Ji 
 
s.ji@dshs-koeln.de
 
Sebastian Keller 
 
s.keller@dshs-koeln.de
 
Lukas Zwingmann 
 
zwingmann.lukas@gmail.com
 
Patrick Wahl 
 
p.wahl@dshs-koeln.de
1 
Department of Exercise Physiology, German Sport 
University, Cologne, Germany
2 
German Research Centre of Elite Sport, German Sport 
University, Cologne, Germany
3 
Department of Molecular and Cellular Sports Medicine, 
Institute of Cardiovascular Research and Sports Medicine, 
German Sport University, Cologne, Germany
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calLT280%  Calculated speed corresponding to lactate 
threshold 2 determined using cost of running 
determined at 80% of maximal oxygen uptake
C 
 Cost of movement
CR 
 Cost of running
CRfix 
 Cost of running determined at a fixed speed of 
2.8 m ⋅ s−1
CRLT1 
 Cost of running determined at lactate threshold 
1
CR80% 
 Cost of running determined at 80% of maximal 
oxygen uptake
LT1 
 Lactate threshold 1 (first rise in blood lactate 
concentration)
LT2% 
 Fractional utilization of maximal oxygen 
uptake at lactate threshold 2
ICC 
 Intra-class correlation coefficient
LT2 
 Lactate threshold 2
̇VO2peak 
 Maximal oxygen uptake
̇VO2 
 Oxygen uptake
vLT2 
 Running speed corresponding to lactate thresh-
old 2
Introduction
Endurance performance depends on a complex interplay 
of various metabolic and mechanical determinants (Joyner 
and Coyle 2008). While aerobic capacity, i.e., maximal oxy-
gen uptake ( ̇VO2peak ) and its fraction at a disproportion-
ate 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 move-
ment [C]) depends on the proportion of mechanical power 
output that contributes to progression (the higher the propor-
tion, the more economical the locomotion) (Minetti 2004). 
Together, these three parameters have been shown to accu-
rately 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.    
Recently, 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, respec-
tively. 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 
(1)
Endurance performance = LT2% ⋅
̇VO2peak
C
.
prediction (showing high correlations with endurance per-
formance) (Faude et al. 2009). Interestingly, in both dis-
ciplines, Støren et al. (2014) and Støa et al. (2020) found 
a strong dependence of LT2 on ̇VO2peak 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 ̇VO2peak 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 pre-
scription for endurance training.
So far, however, the model applies only to adult well-
trained to elite cyclists (Støren et al. 2014) and to adult rec-
reational 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 dif-
ferences between sexes need to be considered, as sex spe-
cific prerequisites such as body composition could influence 
physiological characteristics such as aerobic capacity (Bes-
son 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 physiologi-
cal 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 mmol ⋅ 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, ̇VO2peak and  LT2% repre-
sent physiologically well-defined constructs, albeit depend-
ent on test protocol and determination method (Faude et al. 
2009; Midgley et al. 2007), whereas determination of cost 
of running (CR) is still strongly debated (Barnes and Kilding 
2015; Lundby et al. 2017). This controversy is mainly related 
to the question of whether or not CR 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 ( ̇VO2 ) at a fixed submaximal speed (e.g., 12 km ⋅ h−1 ) 
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to ensure achievement of a metabolic steady-state (Barnes 
and Kilding 2015), Støa et al. (2020) assessed ̇VO2 at a fix 
percentage (i.e., 70%) of ̇VO2peak calculated from the linear 
relationship between submaximal running speeds and the 
corresponding ̇VO2 values. However, apart from the fact that 
the linearity of the ̇VO2 response to exercise is controver-
sial (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 ̇VO2peak . Simi-
larly, measuring ̇VO2 at a fixed submaximal speed (e.g., 12 
km ⋅ h−1 ) will most likely elicit different metabolic responses 
in differently trained individuals. Since such divergent inter-
nal metabolic responses may impact inter-individual com-
parability, assessing CR 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 sport-
ing 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 CR on the accuracy 
of the model. 3. The influence of  LT2%, ̇VO2peak , and CR on 
the running speed at LT2 (vLT2) in young athletes depend-
ing on sex.
Materials and methods
Participants
The study sample consisted of young squad athletes from 
the federal state of North Rhine-Westphalia, Germany (n = 
248). All of them participated in regular training and official 
competitions in various sports (including endurance type 
individual sports and team, racket, as well as combat sports) 
on regional to national levels. All athletes gave their assent, 
and informed consent was obtained from their parents or 
legal guardians. The experimental procedures were approved 
by the local ethics committee (approval number 67/2020) 
and was conducted in accordance with the Declaration of 
Helsinki.
To ensure validity and comparability, only data that 
met the following criteria were included for further 
analysis: (a) age < 19 years; (b) exhaustion (see below 
for determination of ̇VO2peak ); (c) valid determination 
of LT1 and LT2 using the modified maximal deviation 
method (see below); (d) number of stages completed dur-
ing the incremental step test > three (e) running speed 
at 80% of ̇VO2peak ≥ 2.4 m ⋅ s−1 (i.e., within the speed 
range used in the incremental test). If athletes had multi-
ple performance diagnostic visits, only data from the first 
visit were used. A total of 100 athletes (45 males and 55 
females) were finally included in the present study. The 
athlete’s anthropometric characteristics and disciplines 
are presented in Table 1 and Fig. 1, respectively.
Procedures
In this cross-sectional study, all athletes completed an incre-
mental step test to determine endurance performance as part 
of a larger performance check-up for young squad athletes at 
a local performance diagnostic center between January 2018 
and January 2022.
All tests were performed under constant laboratory 
conditions on a treadmill (h/p/cosmos,  saturn® 250/100, 
Traunstein, Germany) with an incline of 1% simulating air 
resistance. Following a two-minute resting measurement in 
standing position, the initial speed was set to 2.4 m ⋅ s−1 and 
increased by 0.4 m ⋅ s−1 every 5 min to ensure attainment 
of metabolic steady state conditions. Between the stages, 
short resting periods (30 s) were allowed for capillary blood 
sampling (20 μL ) and tests were performed until volitional 
exhaustion.
Throughout the test, breathing gases  (Metalyzer®3B; 
Cortex Biophysik GmbH, Leipzig, Germany) and heart rate 
(Polar H7 Sensor; Polar Electro, Kempele, Finland) were 
recorded every second and averaged over 30 s. The spirom-
eter was calibrated weekly with a reference gas (5%  CO2 and 
15%  O2) and before each test with ambient air and with a 
3-L syringe, according to the manufacturer’s specifications. 
Immediately after the test, blood lactate concentrations were 
determined (Biosen C-line; EKF Diagnostic Sales, Magde-
burg, Germany).
Parameters
Blood lactate concentrations during the incremental step test 
were plotted against running speed and then fitted by a third-
order polynomial function. vLT2 was identified as the point 
on the lactate performance curve that yielded the maximal 
perpendicular distance to a straight line formed by the peak 
lactate point and by the point of the first rise in blood lactate 
concentration at which the slope of the fitted lactate curve 
equaled 1.00 (LT1). This method has recently been shown to 
be a valid estimate of maximal lactate steady state in running 
(Zwingmann et al. 2019).
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̇VO2peak corresponded to the highest measured 30-s 
moving average of ̇VO2 during the test. Exhaustion was 
verified using the following criteria (Midgley et al. 2007): 
respiratory exchange ratio ≥ 1.10, heart rate ≥ 95% of age 
predicted maximum, blood lactate concentration ≥ 8 mmol 
·  L–1, and volitional exhaustion.
All spirometric data were averaged over the last third of 
each stage to ensure that a steady state was achieved at least 
in the submaximal stages (i.e., ≤ vLT2) (Whipp and Was-
serman 1972).
LT2% was determined by dividing ̇VO2 corresponding to 
LT2 by ̇VO2peak.
To determine CR, ̇VO2 at three different work rates was 
divided by the respective running speeds: (1) a fixed run-
ning speed of 2.8 m ⋅ s−1 (CRfix); (2) the running speed 
corresponding to LT1 (CRLT1); and (3) the running speed 
corresponding to 80% of ̇VO2peak as calculated from the 
linear regression from running speed and ̇VO2 ( R2 ≥ 0.92) 
(CR80%). Since extrapolation outside the measured values 
would have been necessary for several participants to deter-
mine 70% of ̇VO2peak in accordance with Støa et al. (2020), 
80% was chosen instead being always within the measuring 
range (except for two participants, which were excluded, 
see above) and giving the same CR according to Helgerud 
et al. (2009). Independent of the work rate used, CR was 
Table 1  Descriptive 
anthropometric and 
physiological characteristics 
(mean ± standard deviation) of 
the participants
̇VO2peak maximal oxygen uptake, CR cost of running, CRfix CR determined at a fixed speed of 2.8 m ⋅ s−1 , 
CRLT1 CR determined at lactate threshold 1, CR80% CR determined at 80% of ̇VO2peak , LT2% fractional uti-
lization of ̇VO2peak , vLT2 running speed at lactate threshold 2, calLT2fix calculated vLT2 determined using 
CRfix, calLT2LT1 calculated vLT2 determined using CRLT1, calLT280% calculated vLT2 determined using 
CR80%
Variable
All (N = 100)
Males (N = 45)
Females (N = 55)
p (m vs. f)
Anthropometrics
 Age [y]
15.4 ± 1.3
15.8 ± 1.4
15.2 ± 1.1
0.013
 Height [cm]
172.8 ± 9.1
175.2 ± 10.5
170.9 ± 7.3
0.019
 Body mass [kg]
62.3 ± 11.8
63.6 ± 14.6
61.2 ± 8.9
0.303
̇VO2peak
 [mL ⋅ min−1]
3182 ± 639
3561 ± 735
2871 ± 304
< 0.001
 [mL ⋅ kg−1 ⋅ min−1]
51.4 ± 6.8
56.4 ± 5.9
47.3 ± 4.3
< 0.001
Oxygen CR
 CRfix [mL · kg−1 · m −1]
0.223 ± 0.020
0.232 ± 0.021
0.216 ± 0.017
< 0.001
 CRLT1 [mL · kg−1 · m −1]
0.222 ± 0.020
0.230 ± 0.020
0.216 ± 0.018
< 0.001
 CR80% [mL · kg−1 · m −1]
0.222 ± 0.018
0.229 ± 0.018
0.216 ± 0.016
< 0.001
Energy CR
 CRfix[J ⋅ kg−1 ⋅ m−1]
4.84 ± 0.44
5.02 ± 0.46
4.70 ± 0.37
< 0.001
 CRLT1 [ J ⋅ kg−1 ⋅ m−1]
4.82 ± 0.43
4.98 ± 0.43
4.68 ± 0.38
< 0.001
 CR80% [ J ⋅ kg−1 ⋅ m−1]
4.84 ± 0.40
5.00 ± 0.39
4.71 ± 0.35
< 0.001
Lactate threshold
  LT2% [%]
87.0 ± 2.6
87.0 ± 2.9
87.0 ± 2.4
0.999
 vLT2 [ m ⋅ s−1]
3.38 ± 0.39
3.61 ± 0.41
3.19 ± 0.24
< 0.001
 calLT2fix [ m ⋅ s−1]
3.34 ± 0.38
3.54 ± 0.42
3.18 ± 0.25
< 0.001
 calLT2LT1 [ m ⋅ s−1]
3.36 ± 0.41
3.58 ± 0.44
3.18 ± 0.27
< 0.001
 calLT280% [ m ⋅ s−1]
3.36 ± 0.39
3.58 ± 0.43
3.18 ± 0.24
< 0.001
Fig. 1  Number of athletes included in the study, separated by sex and 
sport discipline
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specified as oxygen cost in mL · kg−1 · m −1 and as energy 
cost in J ⋅ kg−1 ⋅ m−1 using the respiratory exchange ratio 
(Péronnet and Massicotte 1991) to take into account poten-
tial differences in substrate use (Barnes and Kilding 2015). 
In addition to CR, minute ventilation was determined at the 
three different running speeds.
Based on Eq. 1 (Støa et al. 2020; Støren et al. 2014), 
vLT2, as an indicator of endurance performance, was cal-
culated using individual ̇VO2peak ,  LT2%, and each of three 
differently determined values of CR (using CRfix: calLT2fix, 
using CRLT1: calLT2LT1, using CR80%: calLT280%).
Statistical analysis
The Statistical Package for the Social Sciences (version 27.0, 
IBM SPSS, Chicago, IL) was used for statistical analysis. 
All results were interpreted as significant for 훼 = 0.05 . For 
all data, normal distribution and homogeneity of variance 
were verified using the Shapiro-Wilk test and Levene’s test, 
respectively. Differences between male and female athletes 
were determined using independent sample t-tests.
Correlations between physiological parameters (model 
predictors and criteria) were determined using Pearson’s 
correlation coefficient r. These were interpreted as follows: 
< 0.30 = negligible, 0.30–0.50 = low, 0.50–0.70 = moderate, 
0.70–0.90 = high, and > 0.90 = very high (Mukaka 2012). 
Intra-class correlation coefficients (ICC) were calculated 
based on a single measure absolute agreement, two-way 
mixed model, to examine the agreement between the meth-
ods for determining CR and between vLT2 and the modeled 
threshold estimates. According to Koo and Li (2016), the 
degree of agreement was interpreted as follows: < 0.50 = 
poor, 0.50–0.75 = moderate, 0.75–0.90 = good, and > 0.90 
= excellent. In addition, a Bland-Altman analysis was per-
formed to assess the concordance between vLT2 and the 
modeled threshold estimates.
Multiple regression analysis using bi-directional step-
wise selection procedure (criteria: probability of F to enter 
≤ 0.05, probability of F to remove ≥ 0.10) was performed to 
estimate the association between vLT2 (dependent variable) 
and the three physiological variables ̇VO2peak ,  LT2%, and 
CR (independent variables). In addition, sex and age were 
included as independent variables to assess the influence of 
these anthropometric variables on the accuracy of the model.
To better understand the regression model, we addition-
ally assessed the contributions of each predictor (independ-
ent variable) to the regression R2 using a commonality 
analysis using R [R Core Team (2021), Version 4.1.2, yhat 
package] (Nathans et al. 2012; Ray-Mukherjee et al. 2014). 
In this way, it can be determined how much variance in the 
dependent variable is uniquely explained by a single predic-
tor, independent of all other predictors (unique effects) and 
how much variance in the dependent variable is shared by 
a combination of the predictors (common effects). Further, 
negative commonality coefficients may indicate improved 
overall predictive power of the model associated with the 
suppressor variable, which removes some irrelevant vari-
ance or error in other variable(s) in the common effect, thus 
increasing the variance contributions of other variable(s) to 
the regression R2 (Nathans et al. 2012; Pandey and Elliott 
2010). All analyses were performed both for the whole sam-
ple and for the male and female subsets.
Results
Table 1 summarizes the characteristics of the athletes. Both 
in absolute and relative terms, male athletes had a higher 
̇VO2peak compared to female athletes ( p < 0.001 ). Regard-
less of the method used (in terms of both running speed and 
expression), male athletes showed poorer CR ( p < 0.001 ) but 
better vLT2 ( p < 0.001 ) than female athletes. No sex differ-
ence was found for  LT2% ( p = 0.999 ). The running speeds 
corresponding to LT1 were 3.00 ± 0.33 m ⋅ s−1 and 2.70 
± 0.18 m ⋅ s−1 , and those corresponding to 80% ̇VO2peak
were 3.29 ± 0.39 m ⋅ s−1 and 2.92 ± 0.22 m ⋅ 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 CR assessment (at 
LT1: 77.2 ± 14.6 L ⋅ min−1 vs. 63.2 ± 8.3 L ⋅ min−1 , at 80% 
of ̇VO2peak : 89.3 ± 19.8 L ⋅ min−1 vs. 70.9 ± 8.8 L ⋅ min−1 , 
p < 0.001 ), except at a running speed of 2.8 m ⋅ s−1 (108.6 ± 
35.3 L ⋅ min−1 vs. 97.4 ± 26.0 L ⋅ min−1 , p = 0.069).
The mean differences along with limits of agreement 
between calLT2fix, calLT2LT1, and calLT280% 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 CR80% provided the model with the highest accu-
racy due to the smallest limits of agreement (i.e., calLT280% 
± 4% vs. and calLT2fix ± 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 ̇VO2peak ,  LT2%, and CR80% into the multiple 
linear regression model was able to explain 97%, 97%, and 
95% of the variance in vLT2 for all, male, and female ath-
letes, 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, ̇VO2peak showed 
the highest unique contribution to the total regression R2 
followed by CR80% and  LT2% regardless of the analyzed 
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subset. Regarding the common effects, all sets of predictors 
showed a negative commonality coefficient, indicating the 
presence of suppression effects. The most noticeable sup-
pression effect was observed between ̇VO2peak and CR80%, 
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.
Discussion
The present study investigated the accuracy of the classi-
cal model with the physiological variables (i.e., ̇VO2peak , 
 LT2%, and CR), applied in previous studies (McLaughlin 
et al. 2010; Støa et al. 2020; Støren et al. 2014), in deter-
mining vLT2 as an indicator of endurance performance 
in young squad athletes of different disciplines, ages, and 
sexes. We found an excellent accordance between the mod-
eled and experimentally determined vLT2 (ICC ≥ 0.959) 
with a very low systematic bias (mean difference ± limits 
of agreement ≤ 0.07 ± 0.32 m ⋅ s−1 ) independent of sex and 
age, supporting the applicability of calLT2 to assess aero-
bic endurance performance also in young athletes. Fur-
thermore, the accuracy of vLT2 modeling was improved, 
when CR was determined by individualized approaches 
(especially CR80%) rather than at a fixed speed (i.e., CRfix) 
(Fig. 2). According to the stepwise regression and com-
monality analyses, ̇VO2peak is the most important factor 
for vLT2 in both sexes, followed by CR, whereas  LT2% has 
the least influence (Fig. 3).
In the present investigation, CR determined by differ-
ent methods showed very high similarity with each other 
(Table 1). However, the application of individualized 
approaches, particularly CR80%, 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 CR (Table 2 and Fig. 2). Espe-
cially in a heterogeneous sample as in our study, measur-
ing ̇VO2 at a fixed running speed (i.e., CRfix) results in 
different metabolic responses (e.g., percent utilization of 
̇VO2peak and substrate utilization) and thus impairs the 
Table 2  Mean difference (± limits of agreement) and intra-class cor-
relation coefficients (ICC) between running speed at lactate thresh-
old 2 (vLT2) vs. calculated lactate threshold 2 using the oxygen cost 
of running at a fixed running speed of 2.8 m ⋅ s−1 (calLT2fix), at lac-
tate threshold 1 (calLT2LT1), and at 80% of maximal oxygen uptake 
(calLT280%)
CI confidence interval
All (N = 100)
Males (N = 45)
Females (N = 55)
Mean difference 
[ m ⋅ s−1]
ICC (95% CI)
Mean difference 
[ m ⋅ s−1]
ICC (95% CI)
Mean difference 
[ m ⋅ s−1]
ICC (95% CI)
calLT2fix
– 0.04 ± 0.26
0.968 (0.950–0.979) – 0.07 ± 0.32
0.955 (0.908–0.977) – 0.02 ± 0.18
0.962 (0.934–0.978)
calLT2LT1
– 0.02 ± 0.22
0.979 (0.968–0.986) – 0.03 ± 0.25
0.976 (0.956–0.987) – 0.01 ± 0.20
0.959 (0.929–0.976)
calLT280% – 0.02 ± 0.12
0.993 (0.988–0.996) – 0.02 ± 0.13
0.992 (0.983–0.996) – 0.02 ± 0.11
0.986 (0.975–0.992)
Fig. 2  Bland-Altman Plots: differences between calculated running 
speed a at lactate threshold 2 determined by oxygen cost of running 
at a fixed running speed of 2.8 m ⋅ s−1 (calLT2fix), b at lactate thresh-
old 1 (calLT2LT1), and c at 80% of maximal oxygen uptake (calLT280%) 
vs. running speed at lactate threshold 2 (vLT2) determined by modi-
fied maximal deviation method. The individual data of male (N = 45) 
and female (N = 55) athletes are presented by blue cycles and red 
triangles, respectively; the solid line indicates mean difference; the 
dashed lines indicate the limits of agreement (mean ± 1.96 standard 
deviation); the dotted line represents the fitted linear regression
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European Journal of Applied Physiology (2023) 123:573–583 
1 3
inter-individual comparability of CR. This might have 
contributed to the lower accuracy of calLT2fix compared 
to the other methods (i.e., larger random variation). To 
compensate for inter-individual variability in metabolic 
response, we suggested to assess CR at a specific submaxi-
mal metabolic anchor, i.e., LT1. However, incorporating 
CRLT1 in the model (i.e., calLT2LT1) did not considerably 
improve its accuracy in calculating vLT2 as compared to 
CR80%. This result can be explained in part by the fact that 
the running speed at LT1 (2.84 ± 0.30 m ⋅ s−1 ) was similar 
to 2.8 m ⋅ s−1 (running speed for CRfix) and significantly 
lower than that at 80% of ̇VO2peak (3.09 ± 0.36 m ⋅ s−1 ). 
Although it is now widely established that CR is independ-
ent of the respective running speed (Di Prampero et al. 
2009; Shaw et al. 2014), there are still conflicting findings 
indicating an increased or decreased CR with the running 
speed (Iaia et al. 2009; Jones and Doust 1996; Lacour and 
Bourdin 2015; Svedenhag and Sjödin 1994). Assessing CR 
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 ̇VO2peak may have better repre-
sented 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 computa-
tional model. This is supported by the previous suggestion 
of Lacour and Bourdin (2015) that athletes’ performance 
Table 3  Model summary resulting from stepwise multiple regression analyses using the modeled running speed corresponding to lactate thresh-
old 2 as dependent variable and classical physiological parameters as independent variables
Beta beta coefficient, SE standard error, Std. Beta standardized beta coefficient, r correlation coefficient to the running speed at lactate threshold 
2, R2 coefficient of determination, Adj. R2 adjusted coefficient of determination, ̇VO2peak maximal oxygen uptake, CR80% cost of running deter-
mined at 80% of ̇VO2peak , LT2% fractional utilization of ̇VO2peak
Model
Variable
Beta
SE
Std. Beta
t
p
r
R2
Adj. R2
F
p
Analysis 1: All (N = 100)
 1
(Constant)
1.033
0.176
5.877
< 0.001
0.650
0.646
181.73
< 0.001
̇VO2peak
0.046
0.003
0.806
13.481
< 0.001
 2
(Constant)
2.894
0.153
18.890
< 0.001
0.899
0.897
431.55
< 0.001
̇VO2peak
0.063
0.002
1.113
29.378
< 0.001
Oxygen CR80%
– 12.409
0.802
– 0.586
– 15.471
< 0.001
 3
(Constant)
– 0.388
0.226
– 1.718
0.089
0.971
0.970
1086.10
< 0.001
̇VO2peak
0.065
0.001
1.142
56.078
< 0.001
0.806
Oxygen CR80%
– 14.491
0.449
– 0.685
– 32.244
< 0.001
– 0.003
LT2%
0.042
0.003
0.283
15.585
< 0.001
0.175
Analysis 2: Males (N = 45)
 1
(Constant)
0.625
0.389
1.606
0.116
0.581
0.571
59.63
< 0.001
̇VO2peak
0.053
0.007
0.762
7.722
< 0.001
 2
(Constant)
3.076
0.325
9.473
< 0.001
0.876
0.871
149.03
< 0.001
̇VO2peak
0.062
0.004
0.888
15.949
< 0.001
Oxygen CR80%
– 12.827
1.280
– 0.558
– 10.024
< 0.001
 3
(Constant)
– 0.407
0.369
– 1.105
0.276
0.967
0.965
402.69
< 0.001
̇VO2peak
0.062
0.002
0.895
30.818
< 0.001
0.762
Oxygen CR80%
– 14.858
0.694
– 0.646
– 21.396
< 0.001
– 0.359
LT2%
0.045
0.004
0.313
10.643
< 0.001
0.170
Analysis 3: Females (N = 55)
 1
(Constant)
1.588
0.277
5.737
< 0.001
0.390
0.379
33.92
< 0.001
̇VO2peak
0.034
0.006
0.625
5.824
< 0.001
 2
(Constant)
2.806
0.191
14.665
< 0.001
0.813
0.806
112.92
< 0.001
̇VO2peak
0.064
0.004
1.173
14.946
< 0.001
Oxygen CR80%
– 12.143
1.121
– 0.851
– 10.836
< 0.001
 3
(Constant)
– 0.177
0.274
– 0.649
0.519
0.949
0.946
318.67
< 0.001
̇VO2peak
0.065
0.002
1.189
28.831
< 0.001
0.625
Oxygen CR80%
– 14.330
0.617
– 1.004
– 23.208
< 0.001
– 0.094
LT2%
0.039
0.003
0.396
11.725
< 0.001
0.283
580
 
European Journal of Applied Physiology (2023) 123:573–583
1 3
may be more accurately predicted from CR 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 mmol ⋅ 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 indica-
tor 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 physi-
ological 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 (Zwing-
mann 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 ̇VO2peak ,  LT2%, and CR, 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 ̇VO2peak , 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 ̇VO2peak . 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, CR, 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 CR in combination with 
̇VO2peak (– 19.5% to – 51.7% of total R2 ) can emphasize 
the crucial role of the interaction between maximal aero-
bic capacity and movement economy for endurance per-
formance (Joyner and Coyle 2008). Indeed, in the present 
investigation, CR 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 
̇VO2peak resulted in a significantly improved R2 with a sig-
nificant (standardized) beta weight in both the whole group 
and the male and female subgroups (see Table 3). Further-
more, the product of ̇VO2peak and CR (expressing maximal 
aerobic speed) has been demonstrated to be a very good 
predictor for 16-km time trial performance ( R2 = 0.94) and 
vLT2 ( R2 = 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 CR on 
the total R2 were distinctly higher in female than in male 
athletes implying the greater impact of CR in determining 
endurance performance in females. Further, female athletes 
showed lower CR values independent of the determination 
method. This is an interesting finding which contributes to 
the debate whether or not there are sex differences regarding 
CR(Besson et al. 2022). While some authors argue that sex 
differences in CR disappear when expressed as relative inten-
sities (i.e., as percentage of ̇VO2peak 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 (CRfix) or relative (CR80% 
Fig. 3  Graphical summary of commonality analyses for the modeled 
running speed at lactate threshold 2 (LT2) within all (N = 100), male 
(N = 45) and female (N = 55) athletes. The percentage contribution 
of each unique predictor to the total regression effect (i.e., R2 ) is pre-
sented by the black filled arrows; the dashed lines and external solid 
lines represent the common effects of two and all predictors in R2 , 
respectively. ̇VO2peak : maximal oxygen uptake; CR80%: cost of run-
ning determined at 80% of ̇VO2peak ;  LT2%: fractional utilization of 
̇VO2peak at LT2.
581
European Journal of Applied Physiology (2023) 123:573–583 
1 3
and CRLT1) values.  Besides differences in anthropometric 
dimensions (e.g., body height, see Table 1), the lower CR in 
female athletes might be due to neuromuscular character-
istics 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 ̇VO2peak in male compared 
to female athletes, it can be assumed that the differences in 
CR 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 min-
ute 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 CR (Besson et al. 2022; 
Dokumacı and Hazır 2019).
Besides sex-specific differences in CR, it is unclear why 
CR had a greater impact on vLT2 determination in young 
female athletes than in males. However, beside the afore-
mentioned 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 fib-
ers 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 CR 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 actu-
ally profit more than male athletes from an improvement 
in CR.
In contrast to ̇VO2peak and CR, we found no sex differ-
ence 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 stud-
ies 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 endur-
ance 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 per-
formance (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 aero-
bic endurance performance (i.e., vLT2) in young athletes of 
different disciplines.
Due to the high accuracy in estimating vLT2, the pro-
posed model allows to draw conclusions about the limiting 
factors (mainly ̇VO2peak and CR) 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 effi-
ciently as possible. Thus, depending on the individual physi-
ological prerequisites, training prescription may focus either 
on improving ̇VO2peak for example using high intensity 
interval training or on improving CR for example by imple-
menting explosive- and maximal-strength training (Røn-
nestad 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 physiologi-
cal predictors actually lead to the intended changes in endur-
ance performance.
Conclusion
In conclusion, the classical model using ̇VO2peak , CR, and 
 LT2% to determine vLT2 is also suitable for assessing endur-
ance performance in young squad athletes of different dis-
ciplines, ages, and sexes. The accuracy of the model was 
further improved by an individual determination of CR (in 
particular CR80%). ̇VO2peak and CR were found to have the 
most important contributions in determining vLT2. While in 
young female athletes, the impact of CR on endurance per-
formance appeared to be greater than that in male athletes, 
 LT2% was generally found to have the least impact on vLT2 
determination.
Acknowledgements The authors would like to thank Anja Habbig, 
Paulina Heumann, Till Kämpfer, Simon Kohne, Christian Manunzio, 
Inga Schifferdecker, Aldo Sommer, and Sarah Strütt for their enthusi-
astic contribution to data collection from 2018 to 2022.
Funding Open Access funding enabled and organized by Projekt 
DEAL.
Declarations 
Conflicts of interest The authors declare no conflict of interest. No 
funding was received to assist with the preparation of this manuscript.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long 
as you give appropriate credit to the original author(s) and the source, 
582
 
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provide a link to the Creative Commons licence, and indicate if changes 
were made. The images or other third party material in this article are 
included in the article's Creative Commons licence, unless indicated 
otherwise in a credit line to the material. If material is not included in 
the article's Creative Commons licence and your intended use is not 
permitted by statutory regulation or exceeds the permitted use, you will 
need to obtain permission directly from the copyright holder. To view a 
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References
Barnes KR, Kilding AE (2015) Running economy: measurement, 
norms, and determining factors. Sports Med Open. https:// doi. 
org/ 10. 1186/ s40798- 015- 0007-y
Barnes KR, Mcguigan MR, Kilding AE (2014) Lower-body determi-
nants of running economy in male and female distance runners. 
J Strength Cond Res 28(5):1289–1297. https:// doi. org/ 10. 1519/ 
jsc. 00000 00000 000267
Besson T, Macchi R, Rossi J, Morio CYM, Kunimasa Y, Nicol 
C, Millet GY (2022) Sex differences in endurance run-
ning. Sports Med 52(6):1235–1257. https:// doi. org/ 10. 1007/ 
s40279- 022- 01651-w
DiMenna FJ, Jones AM (2009) “linear’’ versus “nonlinear’’ vo2 
responses to exercise: reshaping traditional beliefs. J Exerc 
Sci Fit 7(2):67–84. https:// doi. org/ 10. 1016/ S1728- 869X(09) 
60009-5
Di Prampero PE, Salvadego D, Fusi S, Grassi B (2009) A simple 
method for assessing the energy cost of running during incre-
mental tests. J Appl Physiol 107(4):1068–1075. https:// doi. org/ 
10. 1152/ jappl physi ol. 00063. 2009
Dokumacı B, Hazır T (2019) Effects of the menstrual cycle on running 
economy: oxygen cost versus caloric cost. Res Q Exerc Sport 
90(3):318–326. https:// doi. org/ 10. 1080/ 02701 367. 2019. 15998 00
Farrell PA, Wilmore JH, Coyle EF, Billing JE, Costill DL (1979) 
Plasma lactate accumulation and distance running performance. 
Med Sci Sports 11(4):338–344
Faude O, Kindermann W, Meyer T (2009) Lactate threshold con-
cepts: how valid are they? Sports Med 39(6):469–490. https:// 
doi. org/ 10. 2165/ 00007 256- 20093 9060- 00003
Fletcher JR, Pfister TR, MacIntosh BR (2013) Energy cost of running 
and achilles tendon stiffiness in man and woman trained runners. 
Physiol Rep 1(7):e00178. https:// doi. org/ 10. 1002/ phy2. 178
Franch J, Madsen K, Djurhuus MS, Pedersen PK (1998) Improved 
running economy following intensified training correlates with 
reduced ventilatory demands. Med Sci Sports Exerc 30(8):1250–
1256. https:// doi. org/ 10. 1097/ 00005 768- 19980 8000- 00011
Helgerud J, Ingjer F, Strømme SB (1990) Sex differences in perfor-
mance-matched marathon runners. Eur J Appl Physiol Occup 
Physiol 61(5–6):433–439. https:// doi. org/ 10. 1007/ bf002 36064
Helgerud J, Støren Ø, Hoff J (2009) Are there differences in running 
economy at different velocities for well-trained distance run-
ners? Eur J Appl Physiol 108(6):1099–1105. https:// doi. org/ 10. 
1007/ s00421- 009- 1218-z
Iaia FM, Hellsten Y, Nielsen JJ, Fernström M, Sahlin K, Bangsbo J 
(2009) Four weeks of speed endurance training reduces energy 
expenditure during exercise and maintains muscle oxidative 
capacity despite a reduction in training volume. J Appl Physiol 
106(1):73–80. https:// doi. org/ 10. 1152/ jappl physi ol. 90676. 2008
Jamnick NA, Botella J, Pyne DB, Bishop DJ (2018) Manipulating 
graded exercise test variables affects the validity of the lactate 
threshold and v.o2peak. PLoS One 13(7):e0199794. https:// doi. 
org/ 10. 1371/ journ al. pone. 01997 94
Janeba M, Yaeger D, White R, Stavrianeas S (2010) The dmax 
method does not produce a valid estimate of the lactate thresh-
old. J Exerc Physiol Online 13(4):50–57
Jones AM, Doust JH (1996) A 1% treadmill grade most accurately 
reflects the energetic cost of outdoor running. J Sports Sci 
14(4):321–327. https:// doi. org/ 10. 1080/ 02640 41960 87277 17
Joyner MJ (1991) Modeling: optimal marathon performance on the 
basis of physiological factors. J Appl Physiol 70(2):683–687. 
https:// doi. org/ 10. 1152/ jappl. 1991. 70.2. 683
Joyner MJ, Coyle EF (2008) Endurance exercise performance: the 
physiology of champions. J Physiol 586(1):35–44. https:// doi. 
org/ 10. 1113/ jphys iol. 2007. 143834
Koo TK, Li MY (2016) A guideline of selecting and reporting intra-
class correlation coefficients for reliability research. J Chiropr 
Med 15(2):155–163. https:// doi. org/ 10. 1016/j. jcm. 2016. 02. 012
Lacour J-R, Bourdin M (2015) Factors affecting the energy cost 
of level running at submaximal speed. Eur J Appl Physiol 
115(4):651–673. https:// doi. org/ 10. 1007/ s00421- 015- 3115-y
Lundby C, Montero D, Gehrig S, Hall UA, Kaiser P, Boushel R, 
Madsen K (2017) Physiological, biochemical, anthropometric, 
and biomechanical influences on exercise economy in humans. 
Scand J Med Sci Sports 27(12):1627–1637. https:// doi. org/ 10. 
1111/ sms. 12849
McLaughlin JE, Howley ET, Bassett DR, Thompson DL, Fitzhugh 
EC (2010) Test of the classic model for predicting endurance 
running performance. Med Sci Sports Exerc 42(5):991–997. 
https:// doi. org/ 10. 1249/ mss. 0b013 e3181 c0669d
Midgley AW, McNaughton LR, Polman R, Marchant D (2007) Cri-
teria for determination of maximal oxygen uptake. Sports Med 
37(12):1019–1028. https:// doi. org/ 10. 2165/ 00007 256- 20073 
7120- 00002
Minetti AE (2004) Passive tools for enhancing muscle-driven motion 
and locomotion. J Exp Biol 207(8):1265–1272. https:// doi. org/ 
10. 1242/ jeb. 00886
Mukaka M (2012) Statistics corner: a guide to appropriate use of 
correlation in medical research. Malawi Med J 24(3):69–71
Nathans LL, Oswald FL, Nimon K (2012) Interpreting multiple 
linear regression: a guidebook of variable importance. Pract 
Assess Res Eval 17(1):9. https:// doi. org/ 10. 7275/ 5fex- b874
Pandey S, Elliott W (2010) Suppressor variables in social work 
research: ways to identify in multiple regression models. J Soc 
Soc Work Res 1(1):28–40. https:// doi. org/ 10. 5243/ jsswr. 2010.2
Péronnet F, Massicotte D (1991) Table of nonprotein respiratory 
quotient: an update. Can J Sport Sci 16(1):23–29
R Core Team (2021) R: A language and environment for statistical 
computing. R Foundation for Statistical Computing, Vienna, 
Austria
Ray-Mukherjee J, Nimon K, Mukherjee S, Morris DW, Slotow 
R, Hamer M (2014) Using commonality analysis in multiple 
regressions: a tool to decompose regression effects in the face 
of multicollinearity. Methods Ecol Evol 5(4):320–328. https:// 
doi. org/ 10. 1111/ 2041- 210X. 12166
Rønnestad BR, Mujika I (2013) Optimizing strength training for run-
ning and cycling endurance performance: a review. Scand J Med 
Sci Sports 24(4):603–612. https:// doi. org/ 10. 1111/ sms. 12104
Scharhag-Rosenberger F, Meyer T, Gäßler N, Faude O, Kindermann 
W (2010) Exercise at given percentages of VO2max: hetero-
geneous metabolic responses between individuals. J Sci Med 
Sport 13(1):74–79. https:// doi. org/ 10. 1016/j. jsams. 2008. 12. 626
Shaw AJ, Ingham SA, Folland JP (2014) The valid measure-
ment of running economy in runners. Med Sci Sports Exerc 
46(10):1968–1973. https:// doi. org/ 10. 1249/ mss. 00000 00000 
000311
Støa EM, Helgerud J, Rønnestad BR, Hansen J, Ellefsen S, Støren Ø 
(2020) Factors influencing running velocity at lactate threshold in 
583
European Journal of Applied Physiology (2023) 123:573–583 
1 3
male and female runners at different levels of performance. Front 
Physiol. https:// doi. org/ 10. 3389/ fphys. 2020. 585267
Støren Ø, Rønnestad BR, Sunde A, Hansen J, Ellefsen S, Helgerud J 
(2014) A time-saving method to assess power output at lactate 
threshold in well-trained and elite cyclists. J Strength Cond Res 
28(3):622–629. https:// doi. org/ 10. 1519/ JSC. 0b013 e3182 a73e70
Svedahl K, MacIntosh BR (2003) Anaerobic threshold: the concept 
and methods of measurement. Can J Appl Physiol 28(2):299–323. 
https:// doi. org/ 10. 1139/ h03- 023
Svedenhag J, Sjödin B (1994) Body-mass-modified running economy 
and step length in elite male middle-and long-distance runners. 
Int J Sports Med 15(06):305–310. https:// doi. org/ 10. 1055/s- 2007- 
10210 65
Whipp BJ, Wasserman K (1972) Oxygen uptake kinetics for various 
intensities of constant-load work. J Appl Physiol 33(3):351–356. 
https:// doi. org/ 10. 1152/ jappl. 1972. 33.3. 351
Zwingmann L, Strütt S, Martin A, Volmary P, Bloch W, Wahl P (2019) 
Modifications of the dmax method in comparison to the maxi-
mal lactate steady state in young male athletes. Phys Sportsmed 
47(2):174–181. https:// doi. org/ 10. 1080/ 00913 847. 2018. 15461 03
Publisher's Note Springer Nature remains neutral with regard to 
jurisdictional claims in published maps and institutional affiliations.

Modeling lactate threshold in young squad athletes: influence of sex, maximal oxygen uptake, and cost of running.
Ji, Sanghyeon,Keller, Sebastian,Zwingmann, Lukas,Wahl, Patrick