medicina
Article
Comparison and Performance Validation of Calculated and
Established Anaerobic Lactate Thresholds in Running
Sanghyeon Ji 1,2
, Aldo Sommer 1,3, Wilhelm Bloch 1,3 and Patrick Wahl 4,*


Citation: Ji, S.; Sommer, A.; Bloch,
W.; Wahl, P. Comparison and
Performance Validation of Calculated
and Established Anaerobic Lactate
Thresholds in Running. Medicina
2021, 57, 1117. https://doi.org/
10.3390/medicina57101117
Academic Editor: Jan Bilski
Received: 15 September 2021
Accepted: 12 October 2021
Published: 16 October 2021
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1
The German Research Centre of Elite Sport, German Sport University Cologne, 50933 Cologne, Germany;
hyeon7748@gmail.com (S.J.); a.sommer@dshs-koeln.de (A.S.); w.bloch@dshs-koeln.de (W.B.)
2
Department of Sports Medicine and Exercise Physiology, Institute of Sport Sciences,
Goethe University Frankfurt, 60487 Frankfurt, Germany
3
Department of Molecular and Cellular Sport Medicine, Institute of Cardiology and Sports Medicine,
German Sport University Cologne, 50933 Cologne, Germany
4
Institute of Interdisciplinary Exercise Science and Sports Medicine, Medical School Hamburg,
20457 Hamburg, Germany
*
Correspondence: patrick.wahl@medicalschool-hamburg.de; Tel.: +49-40-361-226-43209
Abstract: Background and Objectives: This study aimed to compare the calculated running veloc-
ity at the anaerobic lactate threshold (cLTAn), determined by a mathematical model for metabolic
simulation, with two established threshold concepts (onset of blood lactate accumulation (OBLA;
4 mmol·L−1) and modiﬁed maximal deviation method (mDmax)). Additionally, all threshold con-
cepts were correlated with performance in different endurance running events. Materials and Methods:
Ten sub-elite runners performed a 30 s sprint test on a cycle ergometer adjusted to an isokinetic mode
set to a cadence of 120 rpm to determine maximal lactate production rate (VLamax), and a graded
exercise test on a treadmill to determine maximal oxygen uptake (VO2max). Running velocities at
OBLA, mDmax, and cLTAn were then compared with each other, and further correlated with running
performance over various distances (3000 m, 5000 m, and 10,000 m). Results: The mean difference
in cLTAn was −0.13 ± 0.43 m·s−1 and −0.32 ± 0.39 m·s−1 compared to mDmax (p = 0.49) and
OBLA (p < 0.01), respectively. cLTAn indicated moderate to good concordance with the established
threshold concepts (mDmax: ICC = 0.87, OBLA: ICC = 0.74). In comparison with other threshold
concepts, cLTAn exhibited comparable correlations with the assessed running performances (cLTAn:
r = 0.61–0.76, mDmax: r = 0.69–0.79, OBLA: r = 0.56–0.69). Conclusion: Our data show that cLTAn
can be applied for determining endurance performance during running. Due to the consideration
of individual physiological proﬁles, cLTAn offers a physiologically justiﬁed approach to assess an
athlete’s endurance performance.
Keywords: aerobic capacity; anaerobic capacity; maximal lactate production rate; exercise testing;
endurance performance; metabolism
1. Introduction
Determination of the blood lactate response during exercise is among the most widely
used performance diagnostic tools [1,2]. Blood lactate concentration increases above the
resting value with increasing exercise intensity. However, as long as exercise is performed at
a constant exercise intensity under a certain intensity threshold, blood lactate concentration
remains constant, physiologically known as a steady-state condition [3,4]. At a certain
exercise intensity, a minor increment in the workload induces an accelerated blood lactate
accumulation and subsequent fatigue-related metabolic consequences, such as the negative
impact of hydrogen ion accumulation (acidosis) on muscle function and performance [4–7].
This considerable point has been deﬁned as the anaerobic lactate threshold (LTAn), which is
generally considered to be a good indicator of individual aerobic endurance performance
and can be used for prescribing endurance training intensities [8,9].
Medicina 2021, 57, 1117. https://doi.org/10.3390/medicina57101117
https://www.mdpi.com/journal/medicina
Medicina 2021, 57, 1117
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In recent decades, researchers have developed several concepts to determine LTAn.
Most LTAn concepts are usually applied to lactate performance curves derived from graded
incremental exercise tests [8]. Most existing LTAn concepts use either ﬁxed lactate con-
centrations [4,10] or inﬂection points [11,12] as their determination criteria. However,
these criteria are derived either arbitrarily or empirically from the graphical analysis of
the lactate performance curve. Moreover, LTAn has shown to be strongly dependent on
the applied test protocol [13,14] and on the athlete’s training status [15], which is critical
because there is no clear standardized test procedure deﬁned, which thus hinders accurate
data interpretation and comparison. Therefore, the physiological background and the
validity/reliability/comparability of these LTAn concepts have been questioned [8].
Lactate production and removal are ongoing processes, which are closely related
to metabolic rate but not necessarily to oxygen delivery [5,6,16,17]. There is a continual
exchange of lactate between various organs and cells, which can be used as an energy source
for oxidative energy production and/or as a major precursor to gluconeogenesis [5,17].
This emphasizes the complexity of metabolic processes behind blood lactate concentrations
during exercise or other conditions. Limiting interpretation solely to blood lactate kinetics
in response to graded exercise tests allows only scarce insight into the complex metabolic
processes of total energy production [18,19].
In 1984, Mader [20] suggested that the lactate performance curve and the correspond-
ing exercise intensity at LTAn may be inﬂuenced by aerobic (maximal oxygen uptake;
VO2max) or anaerobic (glycolytic) capacity (maximal lactate production rate; VLamax) sepa-
rately [20]. Further research conﬁrmed this assumption and showed that different com-
binations of VO2max and VLamax can result in two identical lactate performance curves
with equal LTAn [18]. In a more differentiated approach, Mader and Heck [3] proposed a
mathematical simulation model of energy production processes in skeletal muscle. Using
Michaelis–Menten kinetics, these researchers described the activation of glycolysis as a
lactate production system and the oxidative phosphorylation as a combustion system, both
depending on the total metabolic rate [3]. Based on this theoretical construct, the term
“maximal steady-state of blood lactate (MLSS)” was introduced (as another concept of
LTAn), at which the extent of lactate formation by glycolysis is exactly equal to the maximal
elimination rate of lactate by combustion. Thus, no lactate accumulation in blood lactate
over time occurs (Figure 1) [3]. Thereby, it was suggested that accelerated accumulation of
blood lactate during exercise is due to the saturation of the combustion system (oxidative
phosphorylation) [3], which was later veriﬁed by subsequent investigations of lactate
kinetics during exercise [6,21]. As this mathematical model considers both the maximal
aerobic and anaerobic capacities for the determination of LTAn, it provides differentiated
information about the energetic background of LTAn, as well as the physiological proﬁle of
an athlete [18].
Based on Mader’s approach, Hauser et al. [22] applied the mathematical model to
calculate the power output at MLSS during cycling using individual VO2max- and VLamax-
values and demonstrated a signiﬁcant correlation with the experimental determined MLSS,
and high reliability in the estimation of MLSS [23]. However, there is a lack of knowledge
regarding the transferability of the model to running. Furthermore, the calculation method
in the previous study [22] has only been compared to the empirically determined MLSS,
but not to the actual athlete’s competition performance, which is an essential aspect for a
practical application of a laboratory testing parameter [8]. Therefore, this study aimed to
calculate running velocity at LTAn using individual VO2max and VLamax and an adapted
mathematical method initially described by Mader and Heck [3] and Hauser et al. [22].
The calculated LTAn (cLTAn) was then compared with other established experimentally
determined LTAn concepts. Additionally, we aimed to validate cLTAn against the athlete’s
recent performance in endurance running events.
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Medicina 2021, 57, x FOR PEER REVIEW 
3 of 12 
 
 
 
Figure 1. An exemplary description of the mathematical model for metabolic simulation, presenting 
the gross lactate formation (VLass) and the maximal lactate elimination rate (VLaoxmax) depending on 
exercise intensity [22]. Maximal lactate steady state (MLSS) is defined as the exercise intensity at 
which the lactate formation is exactly equal to elimination. VO2max = maximal oxygen uptake; VLamax 
= maximal lactate production rate; Ks4 = individual constant value of the relationship between oxy-
gen demand and running velocity. 
Based on Mader’s approach, Hauser et al. [22] applied the mathematical model to 
calculate the power output at MLSS during cycling using individual VO2max- and VLamax-
values and demonstrated a significant correlation with the experimental determined 
MLSS, and high reliability in the estimation of MLSS [23]. However, there is a lack of 
knowledge regarding the transferability of the model to running. Furthermore, the calcu-
lation method in the previous study [22] has only been compared to the empirically de-
termined MLSS, but not to the actual athlete’s competition performance, which is an es-
sential aspect for a practical application of a laboratory testing parameter [8]. Therefore, 
this study aimed to calculate running velocity at LTAn using individual VO2max and VLamax 
and an adapted mathematical method initially described by Mader and Heck [3] and 
Hauser et al. [22]. The calculated LTAn (cLTAn) was then compared with other established 
experimentally determined LTAn concepts. Additionally, we aimed to validate cLTAn 
against the athlete’s recent performance in endurance running events. 
2. Materials and Methods 
2.1. Subjects 
Ten sub-elite male middle- and long-distance runners (age = 19.2 ± 3.5 years, body 
mass = 65.8 ± 5.8 kg, height = 181.7 ± 5.2 cm, VO2max = 69.8 ± 6.7 mL∙kg−1 min−1, VLamax = 0.39 
± 0.09 mmol L−1 s−1) participated in this study. Prior to signing the written informed con-
sent of the investigation, all participants were informed about the experimental proce-
dures. The protocols used in this investigation were approved by the Ethics Committee of 
the university and are in line with the Declaration of Helsinki. 
 
 
Figure 1. An exemplary description of the mathematical model for metabolic simulation, presenting
the gross lactate formation (VLass) and the maximal lactate elimination rate (VLaoxmax) depending
on exercise intensity [22]. Maximal lactate steady state (MLSS) is deﬁned as the exercise intensity
at which the lactate formation is exactly equal to elimination. VO2max = maximal oxygen uptake;
VLamax = maximal lactate production rate; Ks4 = individual constant value of the relationship
between oxygen demand and running velocity.
2. Materials and Methods
2.1. Subjects
Ten sub-elite male middle- and long-distance runners (age = 19.2 ± 3.5 years, body
mass = 65.8 ± 5.8 kg, height = 181.7 ± 5.2 cm, VO2max = 69.8 ± 6.7 mL·kg−1 min−1,
VLamax = 0.39 ± 0.09 mmol L−1 s−1) participated in this study. Prior to signing the
written informed consent of the investigation, all participants were informed about the
experimental procedures. The protocols used in this investigation were approved by the
Ethics Committee of the university and are in line with the Declaration of Helsinki.
2.2. Design
The present investigation consisted of two different performance tests completed on
a single day. The body mass was measured before the performance testing (Tanita Corp.,
Tokyo, Japan). Participants were instructed to arrive in the laboratory in a rested, 2 h
postprandial, and well-hydrated state. They were ordered to avoid strenuous exercise for
at least 24 h before the test.
First, the participants performed a 30 s isokinetic sprint test on a cycle ergometer
with subsequent measurements of whole-blood lactate concentration for the determination
of VLamax. After a 60 min break, a graded exercise test on a treadmill (second test) was
performed to determine VO2max and running velocity at the onset of blood lactate accumu-
lation (OBLA; 4 mmol·L−1) [4] and at the modiﬁed maximal deviation point (mDmax) [24].
The cLTAn was determined according to the calculation scheme described by Mader and
Heck [3], as well as by Hauser et al. [22], and subsequently compared with OBLA and
mDmax. To evaluate the validity of cLTAn, OBLA, and mDmax as indicators of endurance
performance, running velocities at each concept were compared with the participant’s per-
formance (average velocity (m·s−1)) over various distances (3000 m, 5000 m, and 10,000 m).
Medicina 2021, 57, 1117
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One participant did not provide performance data, so only data from nine participants
were included in correlation analysis.
2.3. Isokinetic Sprint Test and VLamax Determination (Performance Capacity of Glycolysis)
The participants ﬁrst performed a 10 min standardized warm-up at 1.5 W kg−1 body
mass. After an additional passive rest for 5 min, a 30 s sprint test was performed on a cycle
ergometer adjusted to an isokinetic mode set to a cadence of 120 rpm [25,26]. Participants
were instructed to perform the test in a sitting position and were verbally encouraged
throughout the test to achieve and maintain maximal effort. After the sprint, participants
took a rest in a sitting position for 10 min. Immediately before sprint testing, as well as
every minute after the sprint bout (1′–10′), 20 µL of capillary blood was taken from the
earlobe for lactate analysis (Biosen C-line; EKF Diagnostic Sales, Magdeburg, Germany).
The VLamax was calculated using the following equation [27]:
VLamax (mmol L−1 s−1) = ([La]peak − [La]rest) · (texerc − talac)−1
(1)
where Lapeak (mmol L−1) is the peak post-exercise lactate concentration, Larest (mmol L−1)
is the resting lactate concentration, texerc (s) is the duration of exercise, and talac (s) is the
period at the beginning of exercise in which no lactate formation is assumed. According to
Heck et al. [27], talac was set to 5.5 s for all participants.
2.4. Graded Exercise Running Test and VO2max and LTAn Determination
The graded exercise test was performed on a treadmill (Woodway, Weil am Rhein,
Germany), which started at 2.4 m s−1 and increased by 0.4 m s−1 every 5 min until volitional
exhaustion was reached. After each step of the graded exercise test, a 30 s rest was given for
blood sampling. Furthermore, heart rate (HR) (H7, Polar Electro Oy, Kempele, Finland) and
breath-by-breath expired gases (Cortex Metalyzer II, Leipzig, Germany) were continuously
measured throughout the test. The VO2max corresponded to the highest value measured
(moving average of 30 s) during the test.
Blood lactate concentrations during the incremental tests were plotted against running
velocity and then ﬁtted by a third-order polynomial function. Running velocity at OBLA
was set as the point at which blood lactate concentration reached 4 mmol·L−1 [4]. mDmax
was identiﬁed as the point on the third-order polynomial 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
was equal to 1.00 [24].
2.5. Calculation of Running Velocity at cLTAn
To determine cLTAn, the oxidative and glycolytic energy production depending on
exercise intensity must initially be known, which can be expressed as the activity of
oxidative phosphorylation (VO2ss) and glycolysis (VLass), respectively [3]. The theoretical
background of the applied equations and constants is explained in detail by previous
publications [3,22].
According to Mader and Heck [3], the implementation of the metabolic simulation
model requires knowing the free ADP concentration, which is the main regulating substrate
for the activation of VO2ss and VLass. Since there is no simple and practical procedure
for measuring free ADP concentration, the ADP-dependent equations in the previous
study were transposed into VO2ss-dependent equations [22]. On this occasion, the term
“VO2ss” represents the steady-state oxygen consumption at a constant work rate [3,22].
Hauser et al. [22] calculated the VO2ss in relation to exercise intensity based on the assump-
tion of a linear relationship between oxygen demand (VO2) and workload. Thereby, a
constant value for VO2 per 1 W (Ks4 = 11.7 mL O2 W−1) was used for all participants based
on the data of previous cycling experiments [3,28]. However, it should be noted that VO2
in running is more affected by an athlete’s exercise economy (i.e., metabolic cost at a given
workload) than in cycling. Running economy was shown to be inﬂuenced by several physi-
Medicina 2021, 57, 1117
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ological and biomechanical factors [29], which can lead to greater inter-individual variation
in comparison to the cycling economy due to weight-bearing activity [30]. Therefore, it is
necessary to determine Ks4 (mL kg−1·min−1 per 1 m·s−1 running velocity) individually,
by plotting VO2 during incremental tests against running velocity. The Ks4 corresponded
to the slope of linear regression (y = mx + b) between VO2 and running speed (Figure 2).
 
study were transposed into VO2ss dependent equations [22]. On this occasion, the term 
“VO2ss” represents the steady-state oxygen consumption at a constant work rate [3,22]. 
Hauser et al. [22] calculated the VO2ss in relation to exercise intensity based on the assump-
tion of a linear relationship between oxygen demand (VO2) and workload. Thereby, a con-
stant value for VO2 per 1 W (Ks4 = 11.7 mL O2 W−1) was used for all participants based on 
the data of previous cycling experiments [3,28]. However, it should be noted that VO2 in 
running is more affected by an athlete’s exercise economy (i.e., metabolic cost at a given 
workload) than in cycling. Running economy was shown to be influenced by several phys-
iological and biomechanical factors [29], which can lead to greater inter-individual varia-
tion in comparison to the cycling economy due to weight-bearing activity [30]. Therefore, 
it is necessary to determine Ks4 (mL kg−1∙min−1 per 1 m∙s−1 running velocity) individually, 
by plotting VO2 during incremental tests against running velocity. The Ks4 corresponded 
to the slope of linear regression (y = mx + b) between VO2 and running speed (Figure 2). 
 
Figure 2. An exemplary description of the determination of the individual Ks4 (constant value of 
the relationship between oxygen demand and running velocity). The slope of the regression line 
corresponds to Ks4. From this equation, Ks4 for this runner is 12.1 mL∙kg−1∙min−1 per 1 m∙s−1. 
After determining the individual Ks4, the VO2ss in relation to running velocity was 
calculated with Equation (2). 
VO2ss (mL kg−1 min−1) = V Ks4 + VO2rest 
(2)
where v (m s−1) is the running velocity, VO2rest (mL kg−1 min−1) is the resting oxygen uptake, 
and Ks4 is the constant value of the relationship between oxygen demand and the running 
velocity (i.e., mL kg−1 per 1 m s−1 running velocity). 
Figure 2. An exemplary description of the determination of the individual Ks4 (constant value of
the relationship between oxygen demand and running velocity). The slope of the regression line
corresponds to Ks4. From this equation, Ks4 for this runner is 12.1 mL·kg−1·min−1 per 1 m·s−1.
After determining the individual Ks4, the VO2ss in relation to running velocity was
calculated with Equation (2).
VO2ss (mL kg−1 min−1) = V Ks4 + VO2rest
(2)
where v (m s−1) is the running velocity, VO2rest (mL kg−1 min−1) is the resting oxygen
uptake, and Ks4 is the constant value of the relationship between oxygen demand and the
running velocity (i.e., mL kg−1 per 1 m s−1 running velocity).
By knowing VO2ss (from resting level to VO2max), it is possible to calculate VLass
(lactate formation) as a function of VO2ss, as demonstrated in the following equation:
VLass (mmol L−1 min−1) =
60 ·
.
VLamax
1 + (
Ks2
s
Ks1·
.
VO2ss
.
VO2max−
.
VO2ss
3 )
(3)
where VLamax (mmol L−1·s−1) is the maximal glycolytic rate, VO2max (mL kg−1 min−1)
is the maximal oxygen uptake, VO2ss (mL kg−1 min−1) is the steady-state oxygen con-
sumption, and Ks1 and Ks2 are the 50% activity rate constant of oxidative phosphorylation
(0.0631) and glycolysis (1.331), respectively [22].
Furthermore, the maximal lactate elimination rate (VLaoxmax) which depends on VO2ss
can also be calculated based on the experimentally estimated value of lactate equivalent
(i.e., the amount of oxidized lactate per unit O2), lactate distribution volume [3], and using
the following equation:
VLaoxmax

mmol L−1 min−1
=
lactate-equivalent
lactate distribution volume ·VO2ss = 0.02049
0.4
·VO2ss
(4)
where VLaoxmax (mmol L−1 min−1) is the maximal lactate elimination rate as a function of
the steady-state oxygen consumption (VO2ss; mL kg−1 min−1) [22].
Medicina 2021, 57, 1117
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According to Hauser et al. [22], lactate-equivalent and lactate distribution volume were
set to 0.02049 mmol lactate per 1 mL O2 and 0.4 L H2O per kg body weight, respectively.
Thus, simulating the simultaneous lactate formation and elimination depending on the
metabolic rate or running speed can be carried out based on the individual VO2max and
VLamax value, as well as body weight. cLTAn is deﬁned as the running velocity at which
the lactate formation is exactly equal to elimination (i.e., VLass = VLaoxmax).
2.6. Statistical Analysis
For statistical analysis of the data, the software IBM SPSS version 24 (Chicago, IL,
USA) was used. Descriptive statistics of the data are presented as means ± standard devi-
ation (±SD). The normal distribution and the variance homogeneity were veriﬁed using
the Shapiro–Wilk test and Mauchly test of sphericity, respectively. Statistically relevant
differences between the three LTAn concepts were determined using one-way repeated
measure ANOVA with Bonferroni correction for post hoc tests. Statistical differences were
considered to be signiﬁcant for p ≤ 0.05. To estimate the practical relevance, effect sizes
(partial eta squared, ηp2) were calculated for the main effect. According to Cohen [31],
a ηp2 ≥ 0.01 indicates small effects, ≥0.059 medium effects, and ≥0.138 large effects. To
display the concordance between the LTAn concepts, Bland–Altman plots were constructed.
Furthermore, the intra-class correlation coefﬁcients (ICC) were calculated based on a
single-measure two-way mixed-effects model. For evaluating the degree of agreement
between cLTAn vs. OBLA or mDmax, the “absolute agreement” type of analysis (ICC (2,1))
was chosen. For the comparison of each LTAn concept vs. 3000 m, 5000 m, or 10,000 m,
we chose the “consistency” type of analysis (ICC (3,1)). According to Koo and Li [32],
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. Pearson’s correlations were also calculated and
interpreted as follows: 0.0–0.3 = negligible, 0.3–0.5 = low, 0.5–0.7 = moderate, 0.7–0.9 = high,
and 0.9–1.0 = very high [33].
3. Results
Individual values of maximal metabolic performance tests and individual running
velocities at each LTAn concept are presented in Table 1.
Table 1. Body mass, maximal oxygen uptake (VO2max), maximal lactate production rate (VLamax), constant value of
the relationship between oxygen demand and running velocity (Ks4), and running velocity at the onset of blood lactate
accumulation (OBLA), at the modiﬁed maximal deviation method (mDmax) and the calculated anaerobic lactate threshold
(cLTAn) for each participant.
Participant
Body
Mass (kg)
VO2max
(mL kg−1·min−1)
VLamax
(mmol L−1 s−1)
Ks4
(mL kg−1·min−1
per 1 m s−1)
OBLA
(m s−1)
mDmax
(m s−1)
cLTAn
(m s−1)
1
59.2
74.6
0.38
12.1
5.19
4.93
4.70
2
64.4
70.0
0.32
12.1
4.97
4.65
4.42
3
64.4
80.3
0.33
13.2
-
5.12
4.87
4
72.6
68.0
0.33
11.8
4.43
4.16
4.38
5
72.3
65.4
0.42
11.3
4.54
4.43
4.20
6
68.5
62.3
0.46
10.7
4.31
4.37
3.99
7
59.1
80.1
0.31
14.2
4.53
4.33
4.53
8
73.2
67.4
0.55
10.8
4.77
4.52
4.31
9
58.4
68.7
0.33
11.0
4.94
4.61
4.72
10
65.4
60.8
0.50
11.0
4.13
3.97
3.66
Mean ± SD
65.8 ± 5.8
69.8 ± 6.7
0.39 ± 0.09
11.8 ± 1.1
4.65 ± 0.35
4.44 ± 0.28 *
4.32 ± 0.34 *
* signiﬁcantly different compared to OBLA (p < 0.01).
Repeated measures ANOVA showed a signiﬁcant difference between LTAn concepts
with a large effect (p < 0.01, η2p = 0.63). Post hoc analysis using Bonferroni correction
revealed that running velocity at OBLA was signiﬁcantly higher compared to cLTAn and
mDmax (p < 0.01). No signiﬁcant difference was found between running velocity at cLTAn
and mDmax (p = 0.49). The cLTAn indicated a high correlation with OBLA (r = 0.83,
Medicina 2021, 57, 1117
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r2 = 0.70, p < 0.01) and mDmax (r = 0.81, r2 = 0.65, p < 0.01). Between OBLA and mDmax,
there was a very high correlation (r = 0.94, r2 = 0.89, p < 0.001).
According to the Bland–Altman Plots (Figure 3), the mean difference in cLTAn was
−0.13 ± 0.43 m·s−1 and −0.32 ± 0.39 m·s−1 compared to mDmax and OBLA, respectively.
The intraclass correlation coefﬁcient comparing cLTAn with mDmax showed a good agree-
ment (ICC = 0.87), whereas a moderate agreement was shown between cLTAn and OBLA
(ICC = 0.74).
 
0
65.
60.8
0.50
.0
. 3
3.9
3.66
Mean ± SD 
65.8 ± 5.8 
69.8 ± 6.7 
0.39 ± 0.09 
11.8 ± 1.1 
4.65 ± 0.35 
4.44 ± 0.28 * 
4.32 ± 0.34 * 
* significantly different compared to OBLA (p < 0.01). 
Repeated measures ANOVA showed a significant difference between LTAn concepts 
with a large effect (p < 0.01, η2p = 0.63). Post hoc analysis using Bonferroni correction re-
vealed that running velocity at OBLA was significantly higher compared to cLTAn and 
mDmax (p < 0.01). No significant difference was found between running velocity at cLTAn 
and mDmax (p = 0.49). The cLTAn indicated a high correlation with OBLA (r = 0.83, r2 = 
0.70, p < 0.01) and mDmax (r = 0.81, r2 = 0.65, p < 0.01). Between OBLA and mDmax, there 
was a very high correlation (r = 0.94, r2 = 0.89, p < 0.001). 
According to the Bland–Altman Plots (Figure 3), the mean difference in cLTAn was 
−0.13 ± 0.43 m∙s−1 and −0.32 ± 0.39 m∙s−1 compared to mDmax and OBLA, respectively. The 
intraclass correlation coefficient comparing cLTAn with mDmax showed a good agreement 
(ICC = 0.87), whereas a moderate agreement was shown between cLTAn and OBLA (ICC = 
0.74). 
 
 
(a) 
(b) 
Figure 3. Bland–Altman Plots: differences in running velocity at calculated anaerobic lactate thresh-
old (cLTAn) vs. modified maximal deviation method (mDmax; (a)) and onset of blood lactate accu-
mulation (OBLA; (b)). The solid lines indicate the mean difference; the dotted lines indicate the 
limits of agreement (mean ± 1.96 SD); the dashed lines represent the fitted linear regression. 
The mean running velocities over the distances of 3,000 m, 5,000 m, and 10,000 m 
were 5.65 ± 0.29 m s−1, 5.37 ± 0.26 m s−1, and 5.03 ± 0.26 m s−1, respectively. cLTAn and 
mDmax indicated moderate to high correlations with running performance over all 
Figure 3. Bland–Altman Plots: differences in running velocity at calculated anaerobic lactate threshold (cLTAn) vs. modiﬁed
maximal deviation method (mDmax; (a)) and onset of blood lactate accumulation (OBLA; (b)). The solid lines indicate the
mean difference; the dotted lines indicate the limits of agreement (mean ± 1.96 SD); the dashed lines represent the ﬁtted
linear regression.
The mean running velocities over the distances of 3000 m, 5000 m, and 10,000 m
were 5.65 ± 0.29 m s−1, 5.37 ± 0.26 m s−1, and 5.03 ± 0.26 m s−1, respectively. cLTAn
and mDmax indicated moderate to high correlations with running performance over all
distances observed (cLTAn: 0.61 < r < 0.76, 0.37 < r2 < 0.58, p < 0.05; mDmax: 0.69 < r < 0.79,
0.48 < r2 < 0.62, p < 0.05), whereby OBLA had the poorest correlations (0.56 < r < 0.69,
0.32 < r2 < 0.48, p ≤ 0.09) compared to other concepts in most cases (Figure 4a). The
intraclass correlation (Figure 4b) also revealed good concordance of cLTAn (ICC = 0.75–0.86)
and mDmax (ICC = 0.82–0.88) with running performance over all distances observed,
whereas OBLA showed only moderate concordance (ICC = 0.68–0.80) in most cases.
 
 
(a) 
(b) 
 
Figure 4. Correlations (a) and intraclass correlation coefﬁcients (b) of the running velocity at onset of blood lactate
accumulation (OBLA), modiﬁed maximal deviation method (mDmax), and calculated anaerobic lactate threshold (cLTAn)
compared to average running velocity over 3000 m (v3000), 5000 m (v5000), and 10,000 m (v10,000); * p < 0.05.
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4. Discussion
The purpose of this study was to determine cLTAn in running by adapting the mathe-
matical model for metabolic simulation previously described by Mader and Heck [3] and
Hauser et al. [22]. cLTAn demonstrated moderate to good concordance with the established
concepts in determining the running velocity at LTAn. Although cLTAn provided lower
running velocity compared to mDmax and OBLA, the correlation of cLTAn with the en-
durance running performance was similar compared to mDmax and even better compared
to OBLA.
One of the relevant criteria for the practical application of a laboratory test parameter is
its relationship with competitive performance. A comprehensive review by Faude et al. [8]
demonstrated moderate to high correlations (r = 0.66–0.92) between various LTAn concepts
and performance in endurance running competitions and therefore justiﬁed the practical
application of those concepts in sports diagnostics. Even though cLTAn did not indicate
signiﬁcantly superior results, its good concordance (ICC = 0.75–0.86) with mDmax and
OBLA, as well as comparable correlations (r = 0.61–0.76) with competition performance, can
support its applicability as a valid indicator to assess an athlete’s endurance performance.
The metabolic simulation model (cLTAn) incorporates the inﬂuence of individual
VO2max, VLamax, and Ks4 on LTAn, as well as their combined effects [18,22]. This could
enable a more differentiated approach in the interpretation of the endurance performance
of an athlete. The individually determined Ks4 values are dependent on individual exercise
economy, expressed by the relationship between energy demand and running velocity [29].
Especially in well-trained athletes with similar VO2max, running economy has been shown
to be a crucial indicator of distance running performance [29,34,35]. The consideration of
individual physiological proﬁles allows speciﬁc explanations of how equal and/or differ-
ent endurance performance can be achieved regarding the interplay of single metabolic
parameters [18]. For instance, participants 3 and 7 in our study showed similar aero-
bic and anaerobic capacities (VO2max: 80.3 vs. 80.1 mL kg−1·min−1, VLamax: 0.33 vs.
0.31 mmol L−1 s−1); however, participant 3 displayed a much higher speed at LTAn regard-
less of the used LTAn concept (Table 1) and, consequently, better performance compared to
participant 7 (e.g., 10,000 m running time: 30 vs. 32 min). In this case, the performance dif-
ferences could be explained by much lower Ks4 (13.2 vs. 14.2 mL kg−1 min−1 per 1 m s−1).
A recent training study used the metabolic simulation-model-detected training-induced
changes in single performance capacities (i.e., VO2max and VLamax). The authors reported
speciﬁc explanations of changes in endurance performance (MLSS) [36], which highlights
the potential for the practical application of the model.
Despite the moderate to good agreement with other LTAn concepts, cLTAn systemat-
ically provides lower running velocities in our study (Figure 3). This discrepancy could
be attributed to the underrated VO2max by using a graded exercise test. The main reason
we used a graded incremental protocol, instead of a ramp protocol, was to concurrently
determine OBLA and mDmax, as well as the relationship between steady-state oxygen
demand and running velocity (i.e., individual Ks4). However, the mean time to exhaustion
of our test protocol was ~38 min, which is signiﬁcantly longer than the “optimal” test
duration for assessing VO2max, as suggested by previous studies [37–39]. Sperlich et al. [40]
reported that VO2max, achieved with the same graded exercise test protocol as in our study,
was signiﬁcantly lower (on average 2 mL min−1 kg−1) than assessed by incremental tests
with shorter test duration (ranged from 7–11 min). Hauser [28] showed that a theoretical
25% increase in VO2max (and constant VLamax, and Ks4) leads to a 44% increase in calcu-
lated MLSS in cycling. Indeed, cLTAn is increased by ~0.2 m s−1 when the participant’s
VO2max is increased by 2 mL min−1 kg−1 (and constant values of VLamax, and Ks4), and
thus the difference between running speed at cLTAn and the other LTAn is reduced (data
not presented). To solve the underestimation of VO2max, further work should use a VO2max
veriﬁcation bout [41,42] or a combined step- and ramp-exercise protocol [43]. Such proto-
cols could ensure the appropriate determination of VO2max and the individual Ks4 at the
same time, as two core parameters of the metabolic simulation model.
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Another potential contributing factor to the difference between cLTAn and other LTAn
concepts could be the run-nonspeciﬁc test procedure for the assessment of VLamax and
its inﬂuence on cLTAn. The cycling sprint test is an established anaerobic test for nearly
all sports disciplines. Thus, we determined the participant’s VLamax using an isokinetic
cycle sprint [22,23,36,44]. However, the peak post-exercise lactate concentration, which
is a key parameter for the estimation of VLamax, is dependent on the exercise modality
used in tests [44]. Unfortunately, up to now no established running-speciﬁc test procedure
for VLamax determination exists. Just recently, Quittmann et al. [45] attempted to measure
VLamax and sprint performance parameters using a running sprint test. However, this
study used ﬁxed distances, rather than a ﬁxed time for the sprint test, which might inﬂuence
VLamax determination. Whether and how VLamax estimation and cLTAn determination
would be affected by applying a running-speciﬁc anaerobic test procedure remain to
be clariﬁed.
Since VO2ss contributes as a core parameter to the calculation of both the lactate
formation and elimination rate at any given running velocity, it is necessary to determine
VO2ss (from resting level to VO2max) as precisely as possible. For the determination of VO2ss,
the relationship between oxygen demand and running velocity (Ks4) plays an important
role [3]. In contrast to the previous study in cycling [22], we individually determined the
Ks4 value considering the inter-individual variation in the running economy. Typically, it
is assumed that there is a linear relationship between VO2 and workload. This has been
supported by several investigations indicating a nearly invariant oxygen cost of transport
(calculated by dividing oxygen uptake by running velocity, mL kg−1 km−1) over a range of
running speeds (2.0–4.0 m s−1) [46,47]. However, these studies investigated the individual
running energetics only from the start of exercise until LTAn intensity and not till exhaustion.
Daniels and Daniels [48] suggested that the metabolic demand of running is not exclusively
dependent on running speed and can vary with an athlete’s specialized background. They
found that most of the 800–1500 m specialists in their study showed an equal oxygen cost
of transport over all intensities examined. In contrast to that, the specialists in longer
distances (3000 m—marathon) mostly showed an increased oxygen cost of transport at
exercise intensities above 70% of VO2max [48]. These ﬁndings emphasize the importance of
considering the individual running energetics over all possible test speeds to assess the
performance difference between athletes. To what extent the running energetics, especially
near the LTAn intensity, differ between athletes, and how they affect the LTAn, is unclear.
With respect to the previous model in cycling [22], we, therefore, decided to use the Ks4
from a linear ﬁt to calculate VO2ss in our study. However, there is abundant space for
further progress in analyzing the relationship between metabolic rate and running velocity
and its inﬂuence on cLTAn determination. For instance, a curvilinear ﬁt suggested by
Batliner et al. [49] might better assess the inter-individual difference in running energetics,
especially around and above the LTAn intensity, which might consequently lead to an
improved performance prediction of cLTAn.
In addition to the above methodological limitations, it is important to note that our
data did not address the basic variability and reproducibility of each physiological measure
(VO2max, VLamax, and Ks4), which are also relevant quality criteria for the application of the
cLTAn. However, previous research in cycling already demonstrated a very high reliability
for both VO2max and VLamax, as well as the calculated MLSS from these two parameters [23].
Further studies with a longitudinal analysis in running should be carried out to investigate
the reliability and sensitivity of the single performance tests and metabolic simulation
model for detecting performance changes.
5. Practical Applications
The present study suggests that the mathematical model for metabolic simulation
could be applied to assess an athlete’s endurance performance in running by considering
multiple physiological parameters. Considering multiple physiological measures, the
metabolic simulation model (cLTAn) provides an insight into the complex interplay of
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single metabolic systems and their inﬂuence on endurance performance. This allows
a differentiated interpretation of the athlete’s performance, which could be useful for
establishing training interventions targeting and eliminating speciﬁc weaknesses in the
physiological proﬁle of an athlete.
6. Conclusions
The metabolic simulation model considers different metabolic parameters to evaluate
an athlete’s performance proﬁle. In determining running velocity at LTAn, the metabolic
simulation model (cLTAn) revealed a moderate to good agreement with other established
concepts. However, the velocity at cLTAn was lower with regard to the other LTAn concepts.
With regard to the compared LTAn concepts, comparable and partially better correlations
between cLTan and the endurance performance of sub-elite middle- and long-distance
runners were found.
Author Contributions: Conceptualization, P.W.; methodology, S.J., A.S. and P.W.; formal analysis,
S.J.; investigation, S.J., A.S. and P.W.; resources, P.W. and W.B.; data curation, S.J., A.S. and P.W.;
writing—original draft preparation, S.J.; writing—review and editing, S.J., A.S. and P.W.; visualization,
S.J.; supervision, P.W. and W.B. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: The study was conducted according to the guidelines of the
Declaration of Helsinki and approved by the Ethics Committee of German Sport University Cologne
(approval code: 146/2021; approval date: 4 October 2021).
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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Comparison and Performance Validation of Calculated and Established Anaerobic Lactate Thresholds in Running.
Ji, Sanghyeon,Sommer, Aldo,Bloch, Wilhelm,Wahl, Patrick