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

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.


Introduction
Over the last 35 years, incremental graded exercise tests have been established for detecting endurance performance on the basis of a lactate-performance curve and the application of several different lactate-threshold concepts [1]. Most of these lactate concepts have the aim to approximate the power output achieved at maximal lactatesteady-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][3][4]. However, Hauser et al. [5] compared the power at "onset of blood lactate accumulation" (OBLA) [6,7], the "individual anaerobic 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 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 difference −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 deceive 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 formation, −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 ( _ VO 2 max ) and maximal lactate production rate ( _ VLa max ). Furthermore, the shift of a lactate-performance curve could also be achieved by changing _ VO 2 max or _ VLa max 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 _ VO 2 max and _ VLa max were higher for the soccer player when compared to the track athlete ( _ VO 2 max : 70 vs. 63 ml min −1 kg −1 ; _ VLa max 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 _ VO 2 max -and _ VLa max -values. Using either _ VO 2 max , _ VLa max 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 beneficial to understand, how MLSS is controlled by glycolysis and oxidative phosphorylation 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 mathematical 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 ( _ VLa ss ) exactly equates to the maximal-elimination-rate of lactate ( _ VLa oxmax ) as shown in Figure 1. 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 _ VO 2 max and _ VLa max (and their interaction) would help to better understand the mechanisms of the MLSS. These outcomes could provide a benefit compared to lactatethreshold concepts and to time-extensive 30 min constant-load tests.

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 _ VLa max test for detecting the maximal glycolytic rate and a _ VO 2 max test for detecting the maximal aerobic performance. Using the method introduced by Mader and Heck [3], PMLSS C was calculated on the basis of the individual _ VO 2 max , _ VLa max 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.

VLa max −test
In order to detect _ VLa max the subjects performed a sprint-test lasting 15 s which consisted of a 12 min warm-up period with a constant load set at 1.5 times of the individual body weight, followed by a second exercise bout with a constant load of 50 W for ten 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. Following 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-postexercise-lactate. _ VLa max was calculated according to Equation 1 [14]: 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%.

_ VO 2 max −Test
Subjects performed a ramp-test for measuring _ VO 2 max 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 subjects reached physically exhaustion, complaints of shortness of breath, dizziness or other physical complaints that unabled them proceeding the test [15]. _ VO 2 max was calculated by the mean of all _ VO 2 -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 ( _ VLa ss ) and oxidative phosphorylation ( _ VO 2ss ) must be known [3,11]. Activation of _ VLa ss and _ VO 2ss can be separately expressed by using the Michaelis-Menten kinetics (Equation 2) that is generally characterised by the activation of a single enzyme depending on a substrate and the maximal performance of glycolysis and oxidative phosphorylation, which is represented by _ VLa max and _ VO 2 max respectively. The K M which represents 50% of maximal activity rate must also be known. It is mostly agreed that under nomoxic conditions the main regulating substrate (S) for the activation of _ VO 2ss and _ VLa ss 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 _ VO 2ss and _ VLa ss [11].
Step 2: Activation of oxidative phosphorylation ( _ VO 2ss ) According to Mader [11] and Heck [3] _ VO 2ss can be assessed by using Hill equation ) as a function of free ADP and _ VO 2 max . The 50%-activity-rate-constant of _ VO 2ss (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 _ VO 2 [3,11]. The exponent 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].
Step 3: Activation of glycolysis ( _ VLa ss ) _ VLa ss 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 activation of _ VLa ss as a function of free ADP and _ VLa max . The 50%-activity-rate-constant of _ VLa ss (Ks2) due to PFK at ADP 3 of 1.1 mmol/kg leads to Ks2 of 1.331 [3]. Step 4: Calculation of Lactate-elimination-rate depending on _ VO 2ss The oxidation of lactate primary occurs within the active muscle. _ VLa oxmax is a linear function (Equation 5) of the current _ VO 2 [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].
Equation 5: Calculation of maximal lactate elimination rate ( _ VLa oxmax )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 _ VLa ss and _ VO 2ss in a daily endurance performance analysis. For an application of the model as a tool of endurance performance testing, _ VLa ss and _ VO 2ss must be calculated without measuring the free ADP-concentration. This is possible when the mentioned equations are transposed from ADP in _ VO 2ss depended equations.
Step 5: Transformation from ADP depended equations into _ VO 2ss depended equations During training or testing, _ VO 2ss can easily be measured by spirometry-devices or determined by a calculation (Equation 6), which is based on a linear function between _ VO 2ss and the workload [3].
: Calculation for the activity of oxidative phosphorylation ( _ VO 2ss ) as dictated by workload (P) and bodyweight.
If _ VO 2ss is known or easily fit from 1 to _ VO 2 max , Equation 2 can be rearranged in Equation 7. Therefore ADP-concentration can be calculated for a special workload depending on _ VO 2ss and _ VO 2 max , in the form of: Step 6: Calculation of PMLSS C depending on _ VO 2ss The empirical determined values of _ VLa 2 max , _ VLa max 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 _ VLa ss ¼ _ VLa oxmax . By using Equation 9, _ VO 2ss in PMLSS can be calculated as: Equation 9: Calculation in the activity of glycolysis with respect to the activation oxidative phosphorylation ( _ VO 2ss ) and maximal glycolytic rate ( _ VLa max ). Only Equation 9 has to be used to calculate MLSS. However, there is no analytic solution for the calculation of _ VO 2ss 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 _ VO 2ss in PMLSS C could be determined, PMLSS C can be calculated by using Equation 10. Therefore the relation between _ VO 2 and 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 subsequent 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 bloodlactate-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 between variables was investigated using orthogonal regression and correlation. The level of significance was set at α = 0.05 for all analyses.

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 between 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 between MLSS and OBLA and individual anaerobic threshold of r = 0.92 and r = 0.87, respectively. 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 _ VO 2 max and _ VLa max on MLSS, as well as their combined effects. This can be highlighted for subjects with similar _ VO 2 max 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 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, SDstandard deviation, _ VLa max -maximal lactat production rate, _ VO 2 max -maximum oxygen consumption at maximum load.
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 _ VO 2 max , but differences in _ VLa max 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 second in contrast to subject 12. When related to the same _ VO 2 max , 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 _ VO 2 max and _ VLa max 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 _ VO 2 max and _ VLa max as previously suggested by Bleicher et al. [12]. Therefore the knowledge of _ VO 2 max and _ VLa max 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 positive correlation between _ VO 2 max and PMLSS exists, which incidentally was confirmed in the present study, and highlights the importance of _ VO 2 max concerning PMLSS. The determination of _ VO 2 max 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, _ VLa max must have a significant influence on PMLSS. In the present investigation _ VLa max shows no correlation with PMLSS E , which was probably caused by the small range of _ VLa max values measured in this investigation. Furthermore, the missing correlation between _ VLa max 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 example, in the present study _ VLa max was measured by a sprint-test lasting 15 s. It is possible that testing _ VLa max by using a test duration lower than 15 s would lead to higher maximal glycolytic rates and therefore on the basis of the same _ VO 2 max to a lower PMLSS [3,12,14].
Hauser [24] showed, that _ VLa max increases by 8% when measured using a 13 s sprint-test compared to a 15 s sprint-test. If the present _ VLa max of 0.91 mmol·l −1 ·s −1 would be increased 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 _ VLa max 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 underestimated by a mean by 4 -5 W. Consequently, it is possible that PMLSS E does not represent 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 −7 W.
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 _ VO 2 and power output (Ks4) has an important 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 interindividual basis [3], and only a theoretical increase of Ks4 by 2.5% would lead to a 224 W decrease in PMLSS C . In addition, the day-to-day variability of _ VO 2 max and _ VLa max also has important influences on PMLSS, with a mean within-subject variation of 5.6% of _ VO 2 max leading to deviations in PMLSS C of ± 30 W [25]. In contrast, the biological variability of _ VLa max 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 _ VO 2 max and _ VLa max 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 _ VO 2 max or _ VLa max by performing high intensity or low intensity exercise training, respectively.