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Comparison of calculated and experimental power in maximal lactate-steady state during cycling

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Background The purpose of this study was the comparison of the calculated (MLSSC) and experimental power (MLSSE) in maximal lactate steady-state (MLSS) during cycling. Methods 13 male subjects (24.2 ± 4.76 years, 72.9 ± 6.9 kg, 178.5 ± 5.9 cm, V˙O2max: 60.4 ± 8.6 ml min−1 kg−1, V˙Lamax: 0.9 ± 0.19 mmol l-1 s-1) performed a ramp-test for determining the V˙O2max and a 15 s sprint-test for measuring the maximal glycolytic rate (V˙Lamax). All tests were performed on a Lode-Cycle-Ergometer. V˙O2max and V˙Lamax were used to calculate MLSSC. For the determination of MLSSE several 30 min constant load tests were performed. MLSSE was defined as the highest workload that can be maintained without an increase of blood-lactate-concentration (BLC) of more than 0.05 mmol l−1 min−1 during the last 20 min. Power in following constant-load test was set higher or lower depending on BLC. Results MLSSE and MLSSC were measured respectively at 217 ± 51 W and 229 ± 47 W, while mean difference was −12 ± 20 W. Orthogonal regression was calculated with r = 0.92 (p < 0.001). Conclusions The difference of 12 W can be explained by the biological variability of V˙O2max and V˙Lamax. The knowledge of both parameters, as well as their individual influence on MLSS, could be important for establishing training recommendations, which could lead to either an improvement in V˙O2max or V˙Lamax by performing high intensity or low intensity exercise training, respectively. Furthermore the validity of V˙Lamax -test should be focused in further studies.
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R E S E A R C H Open Access
Comparison of calculated and experimental power
in maximal lactate-steady state during cycling
Thomas Hauser
1*
, Jennifer Adam
1,2
and Henry Schulz
1
* Correspondence:
Thomas.Hauser@gmx.de
1
Chemnitz University of Technology,
Chemnitz, Germany
Full list of author information is
available at the end of the article
Abstract
Background: The purpose of this study was the comparison of the calculated (MLSS
C
)
and experimental power (MLSS
E
) in maximal lactate steady-state (MLSS) during cycling.
Methods: 13 male subjects (24.2 ± 4.76 years, 72.9 ± 6.9 kg, 178.5 ± 5.9 cm,
_
VO2max:
60.4 ± 8.6 ml min
1
kg
1
,
_
VLamax: 0.9 ± 0.19 mmol l
-1
s
-1
) performed a ramp-test for
determining the
_
VO2max and a 15 s sprint-test for measuring the maximal glycolytic rate
(
_
VLamax). All tests were performed on a Lode-Cycle-Ergometer.
_
VO2max and
_
VLamax were
used to calculate MLSS
C
. For the determination of MLSS
E
several 30 min constant load
tests were performed. MLSS
E
was defined as the highest workload that can be
maintained without an increase of blood-lactate-concentration (BLC) of more than
0.05 mmol l
1
min
1
during the last 20 min. Power in following constant-load test was
set higher or lower depending on BLC.
Results: MLSS
E
and MLSS
C
were measured respectively at 217 ± 51 W and 229 ± 47 W,
while mean difference was 12 ± 20 W. Orthogonal regression was calculated with
r = 0.92 (p < 0.001).
Conclusions: The difference of 12 W can be explained by the biological variability
of
_
VO2max and
_
VLamax . The knowledge of both parameters, as well as their individual
influence on MLSS, could be important for establishing training recommendations,
which could lead to either an improvement in
_
VO2max or
_
VLamax by performing high
intensity or low intensity exercise training, respectively. Furthermore the validity
of
_
VLamax -test should be focused in further studies.
Keywords: Maximal lactate-steady-state, Calculation, Lactate-production rate,
Elimination of lactate
Introduction
Over the last 35 years, incremental graded exercise tests have been established for de-
tecting endurance performance on the basis of a lactate-performance curve and the ap-
plication of several different lactate-threshold concepts [1]. Most of these lactate
concepts have the aim to approximate the power output achieved at maximal lactate-
steady-state (PMLSS), which is one criterion of endurance performance [1,2]. PMLSS
is defined as the highest workload where lactate-formation and lactate-elimination in the
muscle cell are maintained at a steady-state [2-4]. However, Hauser et al. [5] compared
the power at "onset of blood lactate accumulation" (OBLA) [6,7], the "individual anaer-
obic threshold" (IAT) [8] and the " + 1.5 mmol·l
1
lactate model" [9] with power in MLSS,
measured during 30-minutes constant load tests. They found high significant correlations
© 2014 Hauser et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
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stated.
Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25
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between OBLA and MLSS: r= 0.89 (mean difference 7.4 W); IAT and MLSS: r = 0.83
(mean difference 12.4 W), +1.5 mmol·l
1
lactate model and MLSS: r = 0.88 (mean differ-
ence 37.4 W). However, based on Bland-and-Altman, the comparison of power of all
threshold-concepts with power in MLSS showed large individual differences, which de-
ceive the high regression coefficients and small mean differences between these methods.
Furthermore, it is problematical that lactate-threshold concepts are based solely on
the blood-lactate-concentration (BLC), which is mainly influenced by lactate forma-
tion, transport, diffusion and -elimination. Therefore, BLC may not represent the
true metabolic processes occurring within the muscle cell. Mader [10,11] and Bleicher
et al. [12] have previously suggested that the same lactate-performance-curve may
result from different combinations of maximal oxygen uptake (
_
VO2max
) and maximal
lactate production rate (
_
VLamax ). Furthermore, the shift of a lactate-performance curve
could also be achieved by changing
_
VO2max or
_
VLamax separately.
Indeed, Bleicher et al. [12] verified, that two different athletes, (soccer and track), had
exactly the same velocity for onset of blood lactate accumulation (OBLA) of 4.4 m s
1
,
yet the individual parameters of
_
VO2 max and
_
VLamax were higher for the soccer player
when compared to the track athlete (
_
VO2max : 70 vs. 63 ml min
1
kg
1
;
_
VLamax 0.93 vs.
0.65 mmol l
1
s
1
, respectively). That confirms, therefore that identical MLSS could be
originate by completely different combinations of
_
VO2max - and
_
VLamax -values. Using
either
_
VO2max,
_
VLamax or BLC alone, it is not possible to explain differences of PMLSS
between two athletes or the effects of training on the MLSS. As such, it would be bene-
ficial to understand, how MLSS is controlled by glycolysis and oxidative phosphoryl-
ation within the muscle cell.
To explain the metabolic background of MLSS, Mader and Heck [3] introduced A
theory of the metabolic origin of anaerobic threshold. The authors published a math-
ematical description of the metabolic response, based on measured values, exemplarily
for a single muscle cell. They focussed on the activation of glycolysis (as the lactate
production system) and on the oxidative phosphorylation (as the combustion system
for lactate). Mader and Heck [3] argued that on the basis of Michaelis-Menten kinetics,
it would be possible to calculate at the same time both, the rate of lactate-formation by
glycolysis and its rate of lactate elimination by the oxidative phosphorylation, depending
on a constant workload. These authors subsequently defined PMLSS as the crossing point
at which the lactate-formation (
_
VLass) exactly equates to the maximal-elimination-rate of
lactate (
_
VLaoxmax )asshowninFigure1.
The present study, therefore, hypothesised firstly that it would be possible to calculate
the PMLSS using the method by Mader and Heck [3] and secondly that knowledge of
_
VO2max and
_
VLamax (and their interaction) would help to better understand the mecha-
nisms of the MLSS. These outcomes could provide a benefit compared to lactate-
threshold concepts and to time-extensive 30 min constant-load tests.
Methods
Study sample
13 male subjects (age: 24.2 ± 4.76 yr, weight: 72.9 ± 6.9 kg, height: 178.5 ± 5.9 cm,
_
VO2max:
60.4 ± 8.6 ml·min
1
·kg
1
,
_
VLamax :0.9±0.19mmoll
-1
s
-1
) with different endurance levels
participated in this study (training volume: n = 4 between 10 and 14 hours/week, n = 7
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from 2 to 8 hours/week, n =2 no sport). All subjects were informed about the aims of the
study and subsequently provided written consent in accordance with the declaration of
Helsinki [13].
Procedure
All tests were performed on a Lode Excalibur Sport Ergometer (Lode, Groningen, NL).
At the beginning of this investigation subjects performed, in a random order, a
_
VLamax
test for detecting the maximal glycolytic rate and a
_
VO2max test for detecting the max-
imal aerobic performance. Using the method introduced by Mader and Heck [3],
PMLSS
C
was calculated on the basis of the individual
_
VO2max,
_
VLamax and body weight.
PMLSS
C
was used for the first constant-load-test and several 30 min constant load-tests
were undertaken to detect PMLSS
E
. Each test was performed on different days.
_
VLamaxtest
In order to detect
_
VLamax the subjects performed a sprint-test lasting 15 s which con-
sisted of a 12 min warm-up period with a constant load set at 1.5 times of the individ-
ual body weight, followed by a second exercise bout with a constant load of 50 W for ten
Figure 1 Presented are the parameters of grosslactate formation (
_
VLass). The maximal elimination
of lactate (
_
VLaoxmax ) and maximal-lactate-steady-state (PMLSS) independence of
_
VO2steady-state (
_
VO2ss). All
parameters are dictated by the
_
VO2steady-state (Figure modified from Mader and Heck [3]).
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minutes. Directly after finishing the warm up phase, two blood samples were obtained
from the earlobe in order to measure the lactate-concentration before the test. Follow-
ing a countdown of 3 s the subjects began pedalling maximally in the seated position,
with pedalling frequency being maintained at 130 rpm. The subjects had to retain the
power output as long as possible. Blood samples were then immediately drawn and at
every 60 s until the 9
th
min after the end of the test, to determine the maximum-post-
exercise-lactate.
_
VLamax was calculated according to Equation 1 [14]:
_
VLamax ¼LamaxPost LaPre
ttesttalac
Equation 1: Calculation of maximal glycolytic rate.
Abbreviations are as follows: La
maxPost
= Maximal Post Exercise Bloodlactate, La
Pre
=
Bloodlactate before test, t
test
= test duration = 15 sec, t
alac
= alactic time interval
The alactic time interval (t
alac
) was defined as the time from the beginning of the
sprint (0 sec) to when the maximum power decreases by 3.5%.
_
VO2max Test
Subjects performed a ramp-test for measuring
_
VO2max breath-by-breath (Oxycon Pro,
Jäger, Höchberg, Germany) which included a warm up of 10 minutes at a constant load
corresponding to 1.5 times of the participants body-weight, followed by a period of
2 min at a constant load of 50 W. The workload at the beginning of the test was set to
50 W for 2 min and was increased by 25 W every 30 s. The test was finished when sub-
jects reached physically exhaustion, complaints of shortness of breath, dizziness or other
physical complaints that unabled them proceeding the test [15].
_
VO2max was calculated
by the mean of all
_
VO2-values measured within the last 30s of the test.
Calculation of PMLSS
C
Step 1: Biochemical elementary background
In order to identify PMLSS
C
, the activity of glycolysis (
_
VLass) and oxidative phosphoryl-
ation (
_
VO2ss) must be known [3,11]. Activation of
_
VLass and
_
VO2ss can be separately
expressed by using the Michaelis-Menten kinetics (Equation 2) that is generally charac-
terised by the activation of a single enzyme depending on a substrate and the maximal
performance of glycolysis and oxidative phosphorylation, which is represented by
_
VLamax
and
_
VO2max respectively. The K
M
which represents 50% of maximal activity rate must
also be known.
_
V0¼
_
Vmax
1þKM=S½
n
Equation 2: Elementary equation of Michaels-Menten-kinetics, where activation of
an enzyme-substrate-complex (
_
V0) depends on maximal performance (
_
Vmax ), 50%-
activity-constant (K
M
)andsubstrate(S).
It is mostly agreed that under nomoxic conditions the main regulating substrate (S) for
the activation of
_
VO2ss and
_
VLass is the level of free ADP concentration [3,11,16,17]. With
an increase of the workload and therefore a higher demand of ATP, ADP-concentration
rises exponentially within the muscle towards
_
VO2ss and
_
VLass [11].
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Step 2: Activation of oxidative phosphorylation (
_
VO2ss)
According to Mader [11] and Heck [3]
_
VO2ss can be assessed by using Hill equation
(Equation 2) as a function of free ADP and
_
VO2max . The 50%-activity-rate-constant of
_
VO2ss (Ks1) is related to the exponent of ADP, which must be greater than 1.0 [3,11,18]
otherwise it is not possible to calculate an appropriate activation of
_
VO2[3,11]. The expo-
nent may reside in the range of 1.4 to 2 [17]. In the present paper an exponent of 2 was
used, which leads to a 50% activity constant related to free ADP-concentration of
0.2512 mmol/kg of (0.2512)
2
mmol/kg [3]. Therefore Ks1 was set to (ADP)
2
= (0.2512)
2
=
0.0631 [3,19].
_
VO2ss ¼
_
VO2max
1þKs1=ADP½
2
Equation 3: Transformed equation of Michaels-Menten-kinetics to calculate the acti-
vation of oxidative phosphorylation (
_
VO2ss)depending on maximal oxygen uptake
(
_
VO2max), 50%-activity-constant (Ks1) and substrate (ADP).
Step 3: Activation of glycolysis (
_
VLass)
_
VLass mainly depends on the activation of the enzyme phosphofructokinase (PFK), which
is activated by free ADP and AMP [3,11,18,20]. AMP amplifies the activity of glycolysis in
addition to ADP which leads to an exponent of 3 [3,11]. Equation 4 describes the activa-
tion of
_
VLass as a function of free ADP and
_
VLamax . The 50%-activity-rate-constant of
_
VLass (Ks2) due to PFK at ADP
3
of 1.1 mmol/kg leads to Ks2 of 1.331 [3].
_
VLass ¼
_
VLamax
1þKs2=ADP½
3
Equation 4: Transformed equation of Michaels-Menten-kinetic to calculate the acti-
vation of glycolysis (
_
VLass) - depending on maximal glycolytic rate (
_
VLamax ), 50%-activity-
constant (Ks2) and substrate (ADP) (Figure 2).
Step 4: Calculation of Lactate-elimination-rate depending on
_
VO2ss
The oxidation of lactate primary occurs within the active muscle.
_
VLaoxmax is a linear
function (Equation 5) of the current
_
VO2[3,21]. Furthermore it not only depends on the
amount of oxidized pyruvate/lactate per unit O
2
, which lies at 0.02049 mmol lactate/ml
O
2
but also on the distribution volume that was set to 0.4 in the present paper [3].
_
VLaoxmax ¼lactateequivalent
lactate distribution volume
_
VO2ss ¼0:02049
0:4
_
VO2ss
Equation 5: Calculation of maximal lactate elimination rate (
_
VLaoxmax )depending on
lactate equivalent, lactate distribution volume and activity of oxidative phosphorylation.
However, there is no simple procedure to measure ADP-concentration and thus the
activity rates of
_
VLass and
_
VO2ss in a daily endurance performance analysis. For an ap-
plication of the model as a tool of endurance performance testing,
_
VLass and
_
VO2ss
must be calculated without measuring the free ADP-concentration. This is possible
when the mentioned equations are transposed from ADP in
_
VO2ss depended equations.
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Step 5: Transformation from ADP depended equations into
_
VO2ss depended equations
During training or testing,
_
VO2ss can easily be measured by spirometry-devices or de-
termined by a calculation (Equation 6), which is based on a linear function between
_
VO2ss and the workload [3].
_
VO2ss ¼PKs4ðÞþbodyweight
_
VO2rest

bodyweight
Equation 6: Calculation for the activity of oxidative phosphorylation (
_
VO2ss) as dic-
tated by workload (P) and bodyweight.
If
_
VO2ss is known or easily fit from 1 to
_
VO2max , Equation 2 can be rearranged in
Equation 7. Therefore ADP-concentration can be calculated for a special workload de-
pending on
_
VO2ss and
_
VO2 max, in the form of :
ADP½¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ks2
_
VO2ss
_
VO2max
_
VO2ss

2
s
Equation 7: Calculation of free ADP-concentration with respect to activated oxida-
tive phosphorylation (
_
VO2ss) and maximal oxygen uptake (
_
VO2max ).
After replacing the term ADP in Equation 3 with the right term of Equation 7,
_
VLass
can be calculated as a function of
_
VO2ss using Equation 8.
_
VLass ¼60
_
VLamax
1þKs2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ks1
_
VO2ss
_
VO2max
_
VO2ss
q
0
@1
A
3
Equation 8: Calculation of glycolysis activity with respect to activated oxidative phos-
phorylation (VO
2ss
) and maximal glycolytic rate (
_
VLamax ).
Furthermore,
_
VLaoxmax can also be calculated as demonstrated in Equation 5.
Figure 2 Steady-state activation and 50% activity rate of oxidative phosphorylation (
_
VO2ss, Ks1 = 0.0631)
and glycolysis (
_
VLass, Ks2 = 1.331). Data expressed as percentage of
_
VO2max and
_
VLamax respectively, with
respect to free ADP concentration (mmol/kg
m
). Modification from Mader and Heck [3].
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Step 6: Calculation of PMLSS
C
depending on
_
VO2ss
The empirical determined values of
_
VLa2 max ,
_
VLamax and body weight are needed in
order to calculate PMLSS
C
. MLSS is defined at the power at which lactate formation
exactly equates to the maximal lactate elimination rate. Mathematically, this means
_
VLass ¼
_
VLaoxmax . By using Equation 9,
_
VO2ss in PMLSS can be calculated as:
0¼
_
VLass
_
VLaoxmax ¼60
_
VLamax
1þKs2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ks1
_
VO2ss
_
VO
2 max
_
VO
2ss
q
0
@1
A
3
0:02049
Volrel
_
VO2ss
Equation 9: Calculation in the activity of glycolysis with respect to the activation oxi-
dative phosphorylation (
_
VO2ss) and maximal glycolytic rate (
_
VLamax).
Only Equation 9 has to be used to calculate MLSS. However, there is no analytic so-
lution for the calculation of
_
VO2ss in Equation 9. Therefore, a numerical approximation
such as the numerical interval bisection method or multiple mathematical optimized
methods, has to be used, as implemented in computer software. If
_
VO2ss in PMLSS
C
could be determined, PMLSS
C
can be calculated by using Equation 10.
PMLSSC¼
_
VO2ss bodyweight

bodyweight
_
VO2rest

Ks4
Equation 10: Calculation of power in MLSS (PMLSS
C
) depending on the activity of
oxidative phosphorylation (
_
VO2ss), bodyweight and oxygen/workload-constant (Ks4).
Therefore the relation between
_
VO2and power expressed as Ks4 must be known. In
the present paper Ks4 was set to a constant value of 11.7 O
2
/W [3].
Constant load tests
Subjects performed at least two 30 min constant load exercise tests at a cadence of
7080 rpm for determination the PMLSS
E
[2]. The first constant-load test according
to PMLSS
C
started after a warm-up of 3 minutes at a power corresponding to 60% of
the PMLSS
C
rate. Blood samples were taken during rest, after 4 and 8 min, and at subse-
quent 2 min intervals until the end of the test. The PMLSS
E
was defined as the highest
workload that can be maintained without an increase of blood-lactate-concentration of
more than 0.05 mmol·l
1
·min
1
during the last 20 minutes of the test. Depending on blood-
lactate-concentration, power in the next constant load test was set higher or lower by 10 W.
Statistical analysis
All data were analyzed using the software SPSS version 14. Descriptive statistics were
calculated from the data (means, standard deviations (SD), minimum and maximum
values). Normal distribution was verified using the Shapiro-Wilk-Test. Relationship be-
tween variables was investigated using orthogonal regression and correlation. The level
of significance was set at α= 0.05 for all analyses.
Results
Descriptive values of
_
VLamax ,
_
VO2max , bodyweight, PMLSS
C
and PMLSS
E
are presented
inTable1.Furthermore,highsignificant correlation between PMLSS
E
and PMLSS
C
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(r = 0.92; p < 0.001) (Figure 3) and PMLSS
E
and
_
VO2max (r = 0.84; p < 0.001) were found.
_
VLamax shows no correlation with PMLSS
E
(r = 0.2; p > 0.05). The mean difference be-
tween PMLSS
C
and PMLSS
E
was 12 W ± 20 W.
Discussion
The aim of the present investigation was to compare the calculated and experimentally
determined power output in MLSS. The comparison of PMLSS
C
and PMLSS
E
showed a
highly significant correlation (0.92), with only a mean difference of 12 W ± 20 W between
the two methods. The results of the present paper accords to previous comparisons be-
tween the different lactate-concepts and MLSS. It is well known that different lactate
threshold concepts approximate in average MLSS rather well. Van Schuylenbergh et al.
[22] published highly significant correlations between MLSS and OBLA and the Dmax
method (r = 0.94 and r = 0.89, respectively). Heck [4] also evaluated correlations be-
tween MLSS and OBLA and individual anaerobic threshold of r = 0.92 and r = 0.87, re-
spectively. However, as already mentioned, the investigation of Hauser et al. [5] showed
large individual differences comparing power of threshold-concepts with power in MLSS.
Therefore the calculation method is at least as useful the application of lactate-concepts
to detect MLSS.
In contrast to lactate-concepts, however, by using the calculation method it is also
possible to show the influence of individual
_
VO2 max and
_
VLamax on MLSS, as well as
their combined effects. This can be highlighted for subjects with similar
_
VO2max values,
for example subject 5 and 12 at 61.0 and 62.7 ml·min
1
·kg
1
respectively. Using the
classical interpretation, endurance performance of these subjects would be nearly the
Table 1 Results of maximum metabolic performance tests and calculated and experimental
power in maximal lactate-steady state
Subject
_
VLamax
(mmol·l
1
·s
1
)
_
VO2max
(ml·min
1
·kg
1
)
Bodyweight
(kg)
PMLSS
C
(W)
PMLSS
E
(W)
Difference
PMLSS
C
-PMLSS
E
(W)
1 0.87 70.4 58.8 233 233 0
2 0.67 69.7 70.65 294 244 50
3 0.78 68.4 78.65 305 295 10
4 0.89 64.8 70.00 246 266 20
5 1.39 61.0 66.2 182 172 10
6 0.74 60.0 62.7 208 198 10
7 1.02 55.8 76.65 207 187 20
8 0.98 48.0 71.9 157 147 10
9 0.98 56.6 80.1 224 204 20
10 1.07 71.3 75.8 291 271 20
11 0.74 47.1 78.55 184 144 40
12 0.94 62.7 78.35 258 278 20
13 0.81 49.0 79.00 190 180 10
x± s 0.91 ± 0.18 60.4 ± 8.6 72.9 ± 6.8 229 ± 47 217 ± 51 12 ± 20
min 1.39 71.3 80.1 305 295 50
max 0.67 47.1 58.8 157 144 20
Abbreviations are as follows: min - minimum, max - maximum, PMLSS
C
- power in calculated maximal lactate-steady-state,
PMLSS
E
- power in experimental maximal lactate-steady-state, SD standard deviation,
_
VLamax - maximal lactat production
rate,
_
VO2max - maximum oxygen consumption at maximum load.
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same, yet interestingly PMLSS
E
of subject 5 and 12 were completely different (172 vs.
278 W). To explain this difference of 106 W, it is not possible to use only
_
VO2max , but
differences in
_
VLamax of both subjects (1.39 vs. 0.94 mmol·l
1
·s
1
) is also required.
Therefore, subject 5 produces significantly more lactate within the muscle cell per sec-
ond in contrast to subject 12. When related to the same
_
VO2max , this higher lactate
production rate leads to a reduction of MLSS [10,12].
On the other hand it also seems pertinent to focus on subjects with the same PMLSS
E,
for example subject 5 and 13 (172 vs. 180 W). It is essential to mention that
_
VO2max and
_
VLamax values of these subjects are completely different (61 vs. 49 ml·min
1
·kg
1
and 1.39
vs. 0.81 mmol·l
1
·s
1
, respectively). This particular example explains, why individuals with
the same MLSS could originate by completely different combinations of
_
VO2max and
_
VLamax as previously suggested by Bleicher et al. [12]. Therefore the knowledge of
_
VO2max and
_
VLamax and the application of the calculation method could help for a better
interpretation of MLSS.
Limitations
The reason for the overestimation of PMLSS
C
is likely caused by methodological as
well as physiological aspects related to its calculation. It is well known, that a high posi-
tive correlation between
_
VO2max and PMLSS exists, which incidentally was confirmed
Figure 3 Correlation and orthogonal regression of PMLSS
E
and PMLSS
C
(r = 0.92; p 0.001).
Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25 Page 9 of 12
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in the present study, and highlights the importance of
_
VO2max concerning PMLSS. The
determination of
_
VO2max is a valid test procedure and well established in performance
and clinical diagnostics [23]. However, Mader and Heck [3], Bleicher et al. [12], Heck
and Schulz [14] and Mader [11] showed that on a theoretical basis,
_
VLamax must have
a significant influence on PMLSS. In the present investigation
_
VLamax shows no correl-
ation with PMLSS
E
, which was probably caused by the small range of
_
VLamax values
measured in this investigation. Furthermore, the missing correlation between
_
VLamax
and PMLSS
E
as well as the overestimation of PMLSS
C
may have been caused by the
methodological procedure in determining the maximal anaerobic performance. For ex-
ample, in the present study
_
VLamax was measured by a sprint-test lasting 15 s. It is possible
that testing
_
VLamax by using a test duration lower than 15 s would lead to higher maximal
glycolytic rates and therefore on the basis of the same
_
VO2max to a lower PMLSS [3,12,14].
Hauser [24] showed, that
_
VLamax increases by 8% when measured using a 13 s sprint-test
compared to a 15 s sprint-test. If the present
_
VLamax of 0.91 mmol·l
1
·s
1
would be in-
creased by 8%, the PMLSS
C
would have been 224 W. The bias between PMLSS
C
and
PMLSS
E
would only be 7 W, which could from a practical point of view be neglected.
Therefore test procedures of
_
VLamax must receive greater focus in future investigations.
Another reason for the differences between the two methods could be the defined
interval of 10 W between two constant-load tests, which was used because of time and
economic reasons. Using the interval of 10 W it is possible, that PMLSS
E
is underesti-
mated by a mean by 4 - 5 W. Consequently, it is possible that PMLSS
E
does not repre-
sent the PMLSS exactly. The possible increase of PMLSS
E
of 4 - 5 W would lead to a
decrease in the difference between PMLSS
C
and PMLSS
E
of 7W.
In addition, physiological reasons for differences could be based on the biological
variability of the parameters and constants that were used in the calculation. As pointed
out by Mader and Heck, the relation between
_
VO2and power output (Ks4) has an im-
portant influence on PMLSS [3]. Again according to Mader and Heck [3] Ks4 was set to
11.7 O
2
/W in the present study. This relation corresponds exactly to the determined
mean value of Ks4 used with the cycle ergometer. However, Ks4 varies on an interindivid-
ual basis [3], and only a theoretical increase of Ks4 by 2.5% would lead to a 224 W de-
crease in PMLSS
C
. In addition, the day-to-day variability of
_
VO2max and
_
VLamax also has
important influences on PMLSS, with a mean within-subject variation of 5.6% of
_
VO2max
leading to deviations in PMLSS
C
of ± 30 W [25]. In contrast, the biological variability of
_
VLamax still remains unknown.
Conclusion
The mathematical method introduced by Mader and Heck [3] for the determination of
PMLSS represents an accurate method similar to that of previous lactate-threshold
concepts. In contrast to lactate-threshold concepts, however, this novel calculation
method is based on
_
VO2max and
_
VLamax that can be used for explaining the origin of
PMLSS and therefore the metabolic response. The knowledge of both parameters, as
well as their individual influence on MLSS, could be important for establishing training
recommendations, which could lead to either an improvement in
_
VO2max or
_
VLamax by
performing high intensity or low intensity exercise training, respectively.
Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25 Page 10 of 12
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Ethical standards
The experiments comply with the current laws of the country. The study was proved
by Ethics Commission.
Abbreviations
ADP: Adenosine diphosphate; AMP: Adenosine monophosphate; ATP: Adenosine triphosphate; AT: Anaerobic
threshold; BLC: Blood-lactate-concentration; BW: Body weight; CLa
rest
: Blood-lacate-concentration during rest;
CP: Crossing point; Dmax method: Lactate threshold concept; IAT: Individual anaerobic threshold; Ks1: 50%-activity
constant of oxidative phosphorylation; Ks2: 50%-activity constant of glycolysis; Ks4: Oxygen/workload equivalent;
MaxPostLa: Maximum post excercise blood lactate concentration; MLSS: Maximal lactate-steady-state; MLSSc: Calculated
maximal lactate steady-state; MLSS
E
: Experimental maximal lactat steady-state; OBLA: Onset of blood lactate accumulation;
PMLSS: Power in maximal lactate-steady-state; PMLSS
C
: Power in calculated maximal lactate-steady-state; PMLSS
E
: Power in
experimental maximal lactate-steady-state; PFK: Phosphofructokinase; P
max
: Maximal power; rpm: Revolutions per minute;
RER: Respiratory exchange ratio; SD: Standard deviation; t
alac
: Alactic time intervall;
_
VLamax: Maximum lactate production
rate;
_
VLass: Gross lactate formation/activation of glycolysis;
_
VLaoxmax: Maximal elimination-rate of lactate;
_
VO2ss: Activation of
oxidative phosphorylation;
_
VO2max: Maximum oxygen uptake;
_
VLassnet:Netlactate formation.
Competing interest
The authors declare that they have no conflict of interest.
Authorscontributions
Data collection: TH, JA, Manuscript: TH, JA, HS. All authors read and approved the final manuscript.
Acknowledgements
The authors would like to thank Steffi Hallbauer and Jörg Kersten for their assistance in the laboratory and Scott
Bowen for their help.
Funding
The publication coast of this article were founded by the German Research Foundation/DFG (Geschäftszeichen INST
270/219-1) and the Chemnitz University of Technology in the funding programme Open Access Publishing.
Author details
1
Chemnitz University of Technology, Chemnitz, Germany.
2
Department of Internal Medicine/Cardiology, University of
Leipzig, Heart Centre, Leipzig, Germany.
Received: 5 February 2014 Accepted: 16 May 2014
Published: 27 May 2014
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doi:10.1186/1742-4682-11-25
Cite this article as: Hauser et al.:Comparison of calculated and experimental power in maximal lactate-steady state
during cycling. Theoretical Biology and Medical Modelling 2014 11:25.
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Chapter
In diesem Kapitel wird zunächst die Entwicklung der zahlreich existierenden Laktatschwellenkonzepte in chronologischer Reihenfolge tabellarisch dargestellt. Danach werden die einzelnen Schwellenkonzepte – basierend auf der jeweiligen Primärliteratur – grafisch veranschaulicht und die Bestimmungsmethode erläutert. Es folgt eine vergleichende exemplarische Betrachtung ausgewählter Schwellenkonzepte. Als „goldener Standard“, an dem sich zahlreiche Schwellenkonzepte orientieren, wird das maximale Laktat-Steady-State im Zusammenhang mit dem Crossing Point erklärt. Danach werden einzelne Schwellenkonzepte verschiedenen Kategorien zugeordnet, und es wird aufgezeigt, dass basislaktatorientierte Konzepte keine biochemische Grundlage haben. Am Ende des Kapitels wird auf die Frage eingegangen, welches Schwellenkonzept das „richtige“ und welches das „beste“ ist.
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The kinetic body motions have guided the core-shell fabrics of wearable bioelectronics to be elastoplastic. However, the polymeric electrodes follow the trade-off relationship between toughness and stretchability. To this end, the stress dissipation encoded silk fibroin electrode is proposed as the core electrode of wearable bioelectronics. Significantly, the high degree of intrinsic stress dissipation is realized via an amino acid crosslink. The canonical phenolic amino acid (i.e., tyrosine) of silk fibroin is engineered to bridge the secondary structures. A sufficient crosslink network is constructed when tyrosine is exposed near the amorphous strand. The stress dissipative tyrosine crosslink affords 12.5-fold increments of toughness (4.72 to 58.9 MJ m⁻³) and implements the elastoplastic silk fibroin. The harmony of elastoplastic core electrodes with shell fabrics enables the wearable bioelectronics to employ mechanical performance (elastoplasticity of 750 MJ m⁻³) and stable electrical response. The proposed wearable is capable of assisting the effective workouts via triboelectricity. In principle, active mobility with suggested wearables potentially relieves muscular fatigues and severe injuries during daily fitness.
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Primed-continuous infusion of [2-3H]- and [U-14C]lactate was used to study the effects of endurance training (running 2 h/day at 29.4 m/min up a 15% gradient) on lactate metabolism in rats. Measurements were made under three metabolic conditions: rest (Re), easy exercise (EE, 13.4 m/min, 1% gradient) and hard exercise (HE, 26.8 m/min, 1% gradient). Blood lactate levels in trained animals increased from 1.0 +/- 0.09 mM in Re to 1.64 +/- 0.21 in EE and 2.66 +/- 0.38 in HE. Control animals also demonstrated an increase in blood lactate with increasing work rate, but values were 1.93 +/- 0.21 and 4.62 +/- 0.57 mM at EE and HE, respectively. Lactate turnover rates (RtLA) measured with [U-14C]lactate increased from 214.0 +/- 17.0 mumol.kg-1.min-1 in Re to 390.3 +/- 31.6 in EE and 518.1 +/- 56.4 in HE. No significant differences in RtLA were observed between controls and trained animals under any condition. Identical relationships between RtLA and exercise or training were obtained with [2-3H]lactate; however, the values obtained were consistently 90% higher than those observed with [U-14C]lactate. Metabolic clearance rate (MCR) for 14C was not significantly different in Re between controls and trained animals (180.6 +/- 27.7 ml.kg-1.min-1). Metabolic clearance of lactate in trained animals was 37 and 107% greater than in controls during EE and HE, respectively. Results indicate that the effect of endurance training is not on production of lactate but on its clearance from the blood.
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In 1976, the aerobic-anaerobic threshold first defined a point on the lactate power curve as a) a transition from aerobic to partly anaerobic energy metabolism, b) an indicator of aerobic performance and c) a means of predicting exercise intensities in endurance training. Subsequent threshold concepts detected selected changes of the lactate power curve either based upon theories concerning lactate formation and utilisation or on empirical training observations. Studies on the highest steady state of lactate during prolonged constant workload, termed maxLass or MLSS, support the idea of a transition from aerobic to partly anaerobic energy metabolism. The shape of the lactate power curve and corresponding thresholds are testing-protocol dependent. Thresholds as well as performances at other arbitrarily-selected points on the lactate power curve correlate comparably well with MLSS power and maximum endurance performance. There is no consistent theory or experimental evidence for an interrelationship between MLSS, MLSS exercise intensity and aerobic performance, nor that thresholds indicate superior training intensities. Mechanisms linking lactate concentrations with specific training effects remain unclear. There is no need for new lactate threshold concepts. Existing data should be used to identify reference values in order to adjust lactate performance testing to biomedical standards. Prospective and observatory training studies should advance knowledge regarding the meaning of specific lactate concentrations for achieving defined training effects. Computer modelling appears to be underused in developing and testing hypotheses on complex effects related to new findings at (sub-)cellular level and their meaning for exercise testing, lactate power curve and training.
Thesis
Das maximale Laktat-steady-state (MLSS) gilt als ein physiologischer Parameter der Ausdauerleistungsfähigkeit. Bereits in den 1980er Jahren entwickelte Mader (1984) auf Basis der Michaelis-Menten-Kinetik eine Berechnungsmethode zur Bestimmung der Leistung im MLSS. Diese Methode setzt die Kenntnis der maximalen Reaktionsgeschwindigkeiten von Glykolyse und Atmung voraus. Die Goldstandard-Methode zur Ermittlung der Leistung im MLSS sind mehrere 30-minütige konstante Dauerbelastungen. Das hauptsächliche Ziel der vorliegenden Arbeit bestand in dem Vergleich der berechneten mit der empirisch ermittelten Leistung im MLSS. 57 männliche Probanden unterzogen sich zunächst in randomisierter Reihenfolge einem Test zur Bestimmung der maximalen Laktatbildungsrate sowie der maximalen Sauerstoffaufnahme. Im Anschluss absolvierten die Testpersonen mehrere 30 minütige Dauertests zur empirischen Ermittlung der Leistung im MLSS. Die ermittelten Ergebnisse zeigen, dass zwischen beiden Testmethoden eine hochsignifikante Korrelation (r = 0,89; p< 0,001) sowie eine mittlere Differenz von -13 Watt vorliegt. Ausgehend von den ermittelten Ergebnissen kann der Schluss gezogen werden, dass die Leistung im MLSS, ermittelt unter Verwendung der Methode nach Mader (1984) im Mittel mit der empirisch ermittelten Leistung im MLSS sehr gut übereinstimmt. Neben der angeführten Hauptstudie, wurde in der vorliegenden Arbeit weiterhin die Reliabilität und Tag-zu-Tag-Variabilität der Leistung im MLSS, der Einfluss der Testdauer auf die Laktatbildungsrate sowie die Praktikabilität der berechneten Leistung im MLSS in einem Einzelzeitfahren näher untersucht.
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Anaerobic threshold as a basic criterion of training recommendation can be estimated by various parameters. The purpose of this study was to investigate the relationship and the reproducibility of ventilatory, lactate-derived and catecholamine thresholds of an incremental treadmill exercise. Therefore, 11 male subjects underwent two incremental treadmill tests within 7 days. The lactate threshold (LT) was determined at the lowest Value of the lactate-equivalent (ratio lactate/performance). The individual anaerobic threshold (IAT) was calculated at LT + 1.5 mmol/L lactate. The ventilatory thresholds, using mass-spectrometry, were defined by the V-slope method (AT) and at the deflection point of end-tidal CO2 (ET-CO2) concentration (RCP). The thresholds of epinephrine (TE) and norepinephrine (TNE) were calculated in the manner of LT. The running velocities were highly reproducible at LT (test-retest correlation coefficient r = 0.90), IAT (r = 0.97), AT (r = 0.88) and RCP (r = 0.95). By contrast TE (r = 0.49) and TNE (r = 0.46) showed a poor reproducibility. TE and TNE occurred 5 - 11 % below LT and AT with a low correlation to LT and AT. LT was found 4 % below AT, both were correlated with r = 0.70 (p < 0.01, test 1) and r = 0.95 (p < 0.01, test 2). IAT occurred 7 - 8% above RCP, in both tests a close correlation was found between IAT and RCP of r = 0.97 (p < 0.01). In summary, the ventilatory and lactate-derived thresholds show a high and similar reproducibility, but the catecholamine threshold does not. In the present exercise protocol, there are systematic differences between the lactate-derived and ventilatory thresholds, in spite of a close relationship, and these must be taken into account in recommendations derived for training.
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The aim of the present investigation was to compare power at “onset of blood lactate accumulation” (OBLA), “individual anaerobic threshold” (IAT) and “+1.5 mmol ∙ l⁻¹ lactate model” with power in maximal lactate steady state (MLSS) in cycling. However, there is a lack of studies concerning the absolute individual differences between different lactate parameters and MLSS. A total of 57 male participants performed several 30-min constant-load tests to determine MLSS by measuring blood lactate concentration (BLC). Depending on BLC, power was increased or decreased by 10 W in the following 30-min test. For detecting power at different threshold parameters, an incremental test was performed that began at 40 W and increased by 40 W every 4 min. Highly significant correlations were found between OBLA and MLSS: r=0.89 (mean difference −7.4 W); IAT and MLSS: r=0.83 (mean difference 12.4W), “+1.5 mmol ∙ l⁻¹ lactate model” and MLSS: r=0.88 (mean difference −37.4W). On average, the parameters of OBLA and IAT approximate MLSS with no significant differences. The “+1.5 mmol ∙ l⁻¹ lactate model” underestimates MLSS significantly. Based on Bland-and-Altman, the comparison of power of all threshold parameters with power in MLSS shows great individual differences despite the high regression coefficients and low mean differences between these methods.
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Testing procedures for the assessment of anaerobic energy metabolism during muscular work have not yet gained the relevance of tests assessing maximal aerobic power. The diagnosis of aerobic power allows one, through the choice of an adequate testing protocol, to design a test that mainly measures the power of aerobic metabolism by means of indicators like VO2max and lactate. With regard to tests for the assessment of anaerobic power and capacity, however, alactic, lactic, and oxidative components of energy expenditure as a whole cannot be differentiated by means of simple parameters (e.g., lactate and time until exhaustion). By means of computer simulations of energy metabolism for supramaximal loads with durations until exhaustion of about 10 s and 60 s as well as the isolated variation of the concentration of muscle phosphocreatine, the maximal rate of lactate production, and the maximal aerobic power (VO2max), the influence of the single components on energy metabolism as a whole is presented in a semi-quantitative way. Subsequent testing procedures for the measurement of alactic and lactic power as well as alactic and lactic capacity are presented. Finally critical-power method and method for the determination of maximal accumulated O2 deficit are described in greater detail, because both methods are widely discussed in contemporary international literature.