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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

Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and

reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication

waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise

stated.

Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25

http://www.tbiomed.com/content/11/1/25

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

Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25 Page 2 of 12

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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.

_

VLamax−test

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 “gross”lactate 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

ttest−talac

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 participant’s 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 ¼lactate‐equivalent

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 :

ADP½¼

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

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

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

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

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

70–80 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

Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25 Page 7 of 12

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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).

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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

http://www.tbiomed.com/content/11/1/25

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:“Net”lactate formation.

Competing interest

The authors declare that they have no conflict of interest.

Authors’contributions

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

References

1. Heck H, Beneke R: 30 Years of Lactate Thresholds –what remains to be done? Dt Z Sportmed 2008, 59:297–302.

2. Beneke R: Methodological aspects of maximal lactate steady state-implications for performance testin. Eur J

Appl Physiol 2003, 89(1):95–99.

3. Mader A, Heck H: A theory of the metabolic origin of "anaerobic threshold". Int J Sports Med 1986, 7(1):45–65.

4. Heck H: Laktat in der Leistungsdiagnostik. Schorndorf: Hofmann; 1990.

5. Hauser T, Adam J, Schulz H: Comparison of selected lactate threshold parameters with maximal lactate‐steady‐state

in cycling. Int J Sport Med 2013. Epub ahead of print.

6. Jones AM, Doust JH: The validity of the lactate minimum test for determination of the maximal lactate steady

state. Med Sci Sports Exerc 1998, 30(8):1304–1313.

7. Sahlin K, Harris RC, Nylind B, Hultman E: Lactate content and pH in muscle obtained after dynamic exercise.

Pflugers Arch 1976, 367(2):143–149.

8. Sjödin B, Jacobs I: Onset of blood lactate accumulation and marathon running performance. Int J Sports Med

1981, 2(1):23–26.

9. Dickhuth H-H, Yin L, Niess A, Röcker K, Mayer F, Heitkamp HC, Horstmann T: Ventilatory, lactate-derived and

catecholamine thresholds during incremental treadmill running: relationship and reproducibility. Int J Sports

Med 1999, 20(2):122–127.

10. Mader A: Eine Theorie zur Berechnung der Dynamik und des steady state von Phosphorylierungszustand und

Stoffwechselaktivität der Muskelzelle als Folge des Energiebedarfs. Köln: Dt. Sporthochschule; 1984.

11. Mader A: Glycolysis and oxidative phosphorylation as a function of cytosolic phosphorylation state and

power output of the muscle cell. Eur J Appl Physiol 2003, 88(4–5):317–338.

12. Bleicher A, Mader A, Mester J: Zur Interpretation von Laktatleistungskurven - experimentelle Ergebnisse mit

computergestützten Nachberechnungen. Spectrum der Sportwissenschaften 1998, 10:92–104.

13. Harriss DJ, Atkinson G: Update–Ethical standards in sport and exercise science research. Int J Sports Med 2011,

32(11):819–821.

14. Heck H, Schulz H: Diagnostics of anaerobic power and capacity. Dt Z Sportmed 2002, 53:202–212.

15. Mader A, Liesen H, Heck H, Phillipi H, Rost R, Schürch P, Hollmann W: Zur Beurteilung der sportartspezifischen

Ausdauerleistungsfähigkeit im Labor. Dt Z Sportmed 1976, 27:80–88. 109–112.

16. Chance B, Williams GR: Respiratory enzymes in oxidative phosphorylation. I. Kinetics of oxygen utilization.

J Biol Chem 1955, 217(1):383–393.

17. Mader A, Heck H: Energiestoffwechselregulation, Erweiterungen des theoretischen Konzepts und seiner

Begründungen. Nachweis der praktischen Nützlichkeit der Simulation des Energiestoffwechsels. In

Hauser et al. Theoretical Biology and Medical Modelling 2014, 11:25 Page 11 of 12

http://www.tbiomed.com/content/11/1/25

Brennpunktthema Computersimulation: Möglichkeiten zur Theoriebildung und Ergebnisinterpretation. Edited by Mader A,

Allmer H. Sankt Augustin: Academia-Verl; 1996:124–162.

18. Newsholme EA, Start C: Regulation in metabolism. London: Wiley & Sons; 1973.

19. Barstow TJ, Buchthal SD, Zanconato S, Cooper DM: Changes in potential controllers of human skeletal muscle

respiration during incremental calf exercise. J Appl Physiol 1994, 77(5):2169–2176.

20. Krause U, Wegener G: Control of adenine nucleotide metabolism and glycolysis in vertebrate skeletal muscle

during exercise. Experientia 1996, 52(5):396–403.

21. Donovan CM, Brooks GA: Endurance training affects lactate clearance, not lactate production. Am J Physiol

1983, 244(1):83–92.

22. Van Schuylenbergh R, Vanden Eynde B, Hespel P: Correlations Between Lactate and Ventilatory Thresholds and

the Maximal Lactate Steady State in Elite Cyclists. Int J Sports Med 2004, 25(06):403–408.

23. Weltman A, Snead D, Stein P, Seip R, Schurrer R, Rutt R, Weltman J: Reliability and Validity of a Continuous

Incremental Treadmill Protocol for the Determination of Lactate Threshold, Fixed Blood Lactate

Concentrations, and V

̇

O

2max

.Int J Sports Med 1990, 11(01):26–32.

24. Hauser T: Untersuchungen zur Validität und Praktikabilität des mathematisch bestimmten maximalen Laktat-steady-states

bei radergometrischen Belastungen [abstract]. TU-Chemnitz: Chemnitz; 2012.

25. Katch VL, Sady SS, Freedson P: Biological variability in maximum aerobic power. Med Sci Sports Exerc 1982,

14(1):21–25.

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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