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Original Research

The Modified Dmax Method is Reliable to Predict the Second Ventilatory Threshold in Elite Cross-Country Skiers

Fabre, Nicolas; Balestreri, Filippo; Pellegrini, Barbara; Schena, Federico

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Journal of Strength and Conditioning Research: June 2010 - Volume 24 - Issue 6 - p 1546-1552
doi: 10.1519/JSC.0b013e3181dc450a
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The capacity of an athlete to utilize an important part of his maximum oxygen uptake is a key issue for performance in long duration sports. This capacity, also called endurance, can be evaluated during laboratory or field incremental tests, determining the anaerobic threshold of an athlete. Thus, the work intensity corresponding to this threshold seems like one of the most important parameter to determine during a testing session. Then, knowing precisely this intensity, in terms of speed (ie, for runners), power (ie, for cyclists), and/or heart rate (HR) (ie, especially when speed and power are unusable like during cross-country ski activity because of snow conditions and field profile changes), athletes can perform some specific training sessions at this intensity to improve their endurance capacity and, therefore, their race performances.

The anaerobic threshold is principally determined examining, during an incremental test to exhaustion, the evolution of ventilatory parameters and/or blood lactate concentration. The ventilatory method, a noninvasive procedure, is used to determine the second ventilatory threshold (VT2, or ventilatory compensation point). Typically, the breakpoints of ventilatory equivalent of carbon dioxide (V̇E/V̇CO2), ventilatory equivalent of oxygen (V̇E/V̇O2), tidal partial pressure of carbon dioxide (PetCO2) and minute ventilation (V̇E) changes over time are determined by visual analysis (15,22,23). This method could be criticized for its lack of objectivity (4) because generally based on visual analysis. However, several reviewers with serious experience in this kind of evaluation can easily solve this issue, making VT2 as a standardized, validated, reliable, and individualized method for the determination of the anaerobic threshold. Moreover, VT2 seems as an useful training indicator and as a key factor of performance in endurance sports (1,7,13-15,17,22).

The estimation of the anaerobic threshold through the measurement of blood lactate concentration is more discussed and an important number of more or less valid methods has already been reported in the literature. Today, many trainers still use the training intensity corresponding to the fixed 4 mmol·L−1 lactate concentration value (12,21) to monitor the training of their athletes, whereas this method received many criticisms. Indeed, it does not take into consideration the individual variation of the lactatemia, and lactate concentrations are dependent on external factors such as test protocol or alimentation (9,20). The observation of 2 breakpoints in the lactate concentrations changes over the time during an incremental test (12,18) could resolve the problem of the individualization of the determination. However, this method required a sufficient number of points and for some authors, the blood lactate concentration increase as a continuous function in progressive exercise making impossible the observation of breakpoints (11). Finally, the DMAX method (5) has been proposed in cyclists (2) and later in runners (19). This method involves calculating the point that yields the maximal perpendicular distance to the straight line formed by the 2 end data points of the lactate vs time or workload curve. This method seemed like more sensitive and most strongly related to the performance when compared with the previous cited methods. Indeed, it seemed that the speed at the DMAX point was not significantly different from mean 10 km velocity and was more strongly correlated to 10 km velocity than the speed at the 4 mmol·L−1 lactate concentration point (19). During cycling (2), the power at DMAX point was highly correlated to 1-hour cycling performance and provided the best estimate 1-hour race pace in trained female.

Aforementioned, the DMAX method and its modified version (DMAX MOD) (2,8) have only been validated in activities like running (19) and cycling (2,5), but to our knowledge, no data are available for cross-country skiing activity. We hypothesized that one of these lactate threshold measurements (ie, DMAX and/or DMAX MOD) could be valid and reliable for cross-country skiers. If this is confirmed, cross-country skiers, coaches, and/or practitioners could have an individualized and objective method for the determination of the anaerobic threshold, which could be easily and confidently used in complement (in the case of doubts with the visual analysis of VT2) or instead of the ventilatory method.

Thus, the present study was mainly designed to compare, in elite cross-country skiers, the capacity of the DMAX and DMAX MOD methods to accurately predict VT2. Moreover, because the fixed 4 mmol·L−1 lactate concentration point still remains the most commonly indicator used by trainers for monitoring training, we also compared results obtained with VT2, DMAX, and DMAX MOD methods with those corresponding to the 4 mmol·L−1 lactate threshold.


Experimental Approach to the Problem

This study was carried out to compare the capacity of 2 individualized descriptors of the lactate threshold (DMAX and DMAX MOD points) to accurately predict the VT2 which can be considered as a good predictor of the competitive intensity in elite cross-country skiers, but which requires a consistent experience for its determination. To do this, the the DMAX and DMAX MOD points plus the fixed 4 mmol·L−1 lactate concentration point, determined through a customised written program, were compared with the VT2 point determined by visual analysis, by examining 1-way analysis of variance (ANOVA) for repeated measurements results and, their relationships were evaluated using the Pearson correlation. Finally, Bland-Altman plots (3) were used to assess the agreement between the measurements.


Twenty-three elite cross-country skiers (12 males and 11 females) from the national Italian ski team involved during winter in European and/or World Cup cross-country ski races, were evaluated. Their mean ± SD age was 22 ± 4 years, height was 173 ± 8 cm, body mass was 65.1 ± 10.1 kg, and V̇O2peak was 66.7 ± 5.1 ml·min·kg−1. They were asked to refrain from ingesting caffeine or alcohol for at least 12 hours before testing, to eat a light meal 3 hours before testing and to not plan an exhaustive training session for at least 48 hours before testing. The study protocol complied with the declaration of Helsinki for human experimentation and was approved by the University ethical committee for human research. Possible risks and benefits were explained, and written informed consent was obtained from each subject before participation.


The skiers carried out an incremental cross-country roller-ski test with the diagonal stride technique. This test was performed during roller skiing on a large motor-driven treadmill (belt dimensions of 2.5 m × 3.5 m, Rodby, Sodertalje, Sweden) with a constant speed of 9 km·h−1 for females and 10 km·h−1 for males. The start slope was fixed at 2° and increased by 1° every 3-minute work period until exhaustion. This study took place during October when skiers had already reached a high volume of training especially in cross-country roller-skiing. During the test, subjects used the same pair of roller-skis (Ski Skett Nord CL, Sandrigo, Italy) and their own poles for the classical technique.

At the beginning of the test, the skier was secured by a safety harness, which was connected to an emergency brake suspended from a metal bracket above the treadmill. Each skier was fully familiarized with roller skiing on treadmill.

Physiological Measurements

Ventilatory Measurement

Values of minute ventilation (V̇E), tidal partial pressure of carbon dioxide (PetCO2), carbon dioxide output (V̇CO2) and oxygen uptake (V̇O2) were continuously measured by a portable breath-by-breath gas exchange measurement system (Cosmed K4b2, Rome, Italy). Gas analyzers were calibrated before each test with ambient air (O2: 20.93 % and CO2: 0.03 %) and a gas mixture of known composition (O2: 16.00 % and CO2: 5.00 %). An O2 analyzer with a polarographic electrode and a CO2 analyzer with an infrared electrode sampled expired gases at the mouth. The Cosmed K4b2 system is lightweight (800 g) with the main sample unit attached to the chest and the battery pack on the back. The facemask, that had a low dead space (70 mL), was equipped with a low resistance, bidirectional digital turbine (28 mm diameter). This turbine was calibrated before each test with a 3-L syringe (Cosmed, Rome, Italy). Facemasks allowed subjects to simultaneously breathe with mouth and nose, for more comfort. Heart rate was continuously measured via a wireless Polar-monitoring system (Polar Electro Oy, Kempele, Finland) and synchronized with the Cosmed system.

Lactate Measurement

Finger-tip capillary blood (20 μL) was sampled in the last 20 s of each 3-min work stage following a puncture made using a lancet (Heinz-Herenz, Germany), without stopping the treadmill and immediately at the end of the incremental test. During the sample, the skier placed his/her left hand on the lateral hand-bar of the treadmill continuing to ski with only 1 pole (ie, the right one). The blood sample was then immediately mixed with a lysing stabilizing agent in a safe-lock vial. Blood lactate concentration was determined using a Biosen C-Line Sport Analyser (EKF Diagnostics, Magdeburg, Germany). Before blood analysis, the analyzer was calibrated with standard 12 mmol·L−1 solution.

Data Analysis

Ventilatory Threshold Determination

Two blinded and experienced investigators determined individually the second VT2 (or ventilatory compensation point) by visual analysis of the breakpoints of ventilatory equivalent of carbon dioxide (V̇E/V̇CO2), ventilatory equivalent of oxygen (V̇E/V̇O2), tidal partial pressure of carbon dioxide (PetCO2) and minute ventilation (V̇E) changes over time, with an increase in both V̇E/V̇CO2 and V̇E/V̇O2 and a decrease in PetCO2 (15,22,23). If a difference was observed between the results of the 2 investigators, a third 1 was asked to do the analysis.

Lactate Thresholds Determination

Three different descriptors (Figure 1) were determined thanks to a customised written program (LabView 7.1, National Instruments, Austin, TX, USA): (1) 4 mM, corresponding to the 4 mmol·L−1 fixed blood lactate concentration (10,2) DMAX, identified as the point on the third order polynomial curve that yielded the maximal perpendicular distance to the straight line formed by the 2 end data points, and (3) DMAX MOD, a modified DMAX method, identified as the point on the third order polynomial curve that yielded the maximal perpendicular distance to the straight line formed by the point preceding an increase of lactate concentration greater than 0.4 mmol·L−1 and the final lactate point (2).

Figure 1
Figure 1:
The 3 methods used to determine lactate threshold: 4 mM, the 4 mmol·L−1 fixed blood lactate concentration(10); DMAX, individualized lactate threshold measurement identified as the point on the third order polynomial curve that yielded the maximal perpendicular distance to the straight line formed by the 2 end data points; DMAX MOD, a modified DMAX method, identified as the point on the third order polynomial curve that yielded the maximal perpendicular distance to the straight line formed by the first point preceding an increase of lactate concentration greater than 0.4 mmol·L−1 and the final lactate point. Schematic figure based on data from a subject of the study.

Statistical Analysis

Values presented are expressed as mean ± SD. They were checked for normal distribution using the Kolmogoroff-Smirnov test. A 1-way ANOVA for repeated measurements was chosen to test for differences between methods. If data distribution fails the normality and/or with unequal variance, a RM ANOVA on ranks was systematically performed. When overall difference was found, the Tukey post hoc test was used for specific comparisons. The Pearson product-moment zero-order correlation coefficient demonstrated any significant relationship between the VT2 and the various lactate thresholds. Finally, Bland-Altman plots (3) were used to assess the agreement between the measurement of HR at VT2 and HR at DMAX, DMAX MOD, and 4 mM. Difference between the values measured from 2 methods on y axis was plotted against their averages on x axis. Limits of agreement involved the mean difference between 2 methods ± 2 SD. Statistical significance was accepted at p ≤ 0.05. Data were analyzed with the software package SigmaStat version 3.5 (SPSS Inc., Chicago, IL, USA)


Mean data for the relevant physiological data observed are presented in Table 1.

Relevant physiological results observed (mean ± SD [min-max], n = 23).

VT2 was detected in 100% of the subjects. Both independent researchers were in agreement for VT2 detection in 21 (91%) of the tests. In those 2 cases where the opinion of a third observer was assessed for VT2 detection, there always existed agreement with 1 of the 2 other researchers. VT2 was then detected based on this agreement.

Comparisons Between Measurements

The 1-way RM ANOVA showed significant difference for HR between the measurements (p < 0.001). The Tukey multiple comparison procedure revealed that HR at DMAX (176.1 ± 7.6 bpm) was significantly lower than HR at VT2, at DMAX MOD and at 4 mM (p < 0.001). Nonsignificant differences were found between HR at VT2 (180.4 ± 8.0 bpm) and HR at DMAX MOD (180.1 ± 8.0 bpm, p = 0.953), between HR at VT2 and HR at 4 mM (180.3 ± 8.2 bpm, p = 1.000) and between HR at DMAX MOD and HR at 4 mM (p = 0.972).

In the same way, a statistical significant difference was found for blood lactate concentration between the measurements (p < 0.001). The post hoc tests revealed that the blood lactate concentration corresponding at DMAX (3.03 ± 0.5 mmol·L−1) was lower than the lactatemia observed with the three other methods (p < 0.001). The blood lactate concentration corresponding at VT2 (4.16 ± 0.8 mmol·L−1) was not significantly different with DMAX MOD (3.94 ± 0.6 mmol·L−1, p = 0.250) and with 4mM (4.00 ± 0.0 mmol·L−1, p = 0.539).

Relationships and Agreement Between Measurements

As shown in Figure 2, HR at VT2 was strongly correlated with HR at 4mM (r = 0.93, p < 0.001), HR at DMAX (r = 0.97, p < 0.001) and especially with HR at DMAX MOD (r = 0.99, p < 0.001). However, despite the strong correlation between HR at VT2 and HR at DMAX, Figure 2F also revealed that data do not fit with the line of identity. Bland-Altman plot (Figure 2E), showed that HR measured with DMAX method underestimated HR measured with the VT2 method. Finally and more interestingly, the Bland-Altman plots permitted to observe that the DMAX method and particularly the DMAX MOD method had consistently and appreciably smaller limits of agreement (2 SD −0.2 to −8.5 bpm and −2.5 to 2.0 bpm, respectively) as compared with the 4 mM method (2 SD −5.9 to 5.8 bpm), underlining an important variability in the HR measurement with the 4 mM method when this method is compared with the VT2 method.

Figure 2
Figure 2:
Heart rate measured at the second VT2 compared with heart rate measured at DMAX MOD (A and B), 4 mM (C and D) and DMAX (E and F). Plots B, D, and F represent the regression analyses with the line of identity (dotted diagonal) and the regression line (thick line). Plots A, C, and E represent Bland-Altman (3) plots with the dashed line showing mean difference (systematic bias) between methods and the 2 extreme lines showing the limits of agreement (2 SD around the mean). Note that the between-method limits of agreement were narrower for the DMAX MOD method (panel A). SEE = standard error of the estimate; VT2 = ventilatory threshold.


The aim of this study was to compare the capacity of mainly designed to compare the capacity of the DMAX method and its modified version (DMAX MOD) to accurately predict the second VT2 in elite cross-country skiers. This threshold, also named ventilatory compensation threshold, can be identified as the second breakpoint in the ventilation response mainly explained by an acidosis (pH decrease) as bicarbonate is overwhelmed by the growing production of lactate (22). After the publication of Wasserman and McIlroy (23), the use of ventilation and gas exchange techniques to determine the onset of metabolic acidosis has become widespread in the literature and has an obvious attraction in cardiorespiratory evaluations as noninvasive and useful index of exercise performance (15,16,22). Thus, we choose the second VT2 as a reference to evaluate the suitability of different lactate threshold measurements, especially the DMAX and DMAX MOD methods. One could say that detection of VT2 is too much subjective to be valid (4), however, more than 1 reviewer with serious experience in this kind of evaluation (many years of practice in athletes testing) help to solve this issue.

Otherwise, in most of the protocols that were carried out regarding the determination of the anaerobic threshold and its utility for training, intensity was often set according to the speed or the power corresponding to the anaerobic threshold. But, giving the particularity of the cross-country skiing activity during which skiers are unable to determine their training intensity using speed (as, for example, a runner on a track might) because of variations of snow conditions and field profile, HR and/or exercise perception are the only parameters available for setting training intensity at or near anaerobic threshold. In this way, we choose to compare methods according to the HR value corresponding to the different points measured.

The main finding of this study was that among the 3 lactate threshold measurements tested, the DMAX MOD method seemed like the more reliable to predict the VT2 in elite cross-country skiers. However and whatever the method used, HR was highly correlated (with still the higher r-value for DMAX MOD method) with HR at VT2. But, the Bland-Altman analysis revealed that, (1) the DMAX method underestimated the HR at VT2 (mean HR difference of about 4 bpm) but had narrow limits of agreement and that, (2) despite the same HR mean value, the 4 mM method provided consistently and appreciably larger limits of agreement compared with the DMAX MOD and DMAX methods. This last point implies that using the HR corresponding to the 4 mM point to individually monitor athletes training, trainers run the risk of making important errors, even though no significant differences in mean HR values compared with VT2 and a strong relationship with HR at VT2 are present. Indeed, fixed levels of blood lactate concentrations can vary widely inter and intrasubject (Table 1, the high range of lactate values obtained with the individualized threshold measurements). These variations in lactate levels may be induced by factors including nutrition, prior stress, and muscle fibre distribution (6). Consequently and as shown in the present study, it is more effective for training monitoring and/or for performance predicting, to use a method derived from lactate kinetics than from absolute values.

Our results underlining a better precision of an individualized vs fixed lactate concentration method to predict anaerobic threshold are consistent with the studies that previously tested these methods (2,8,19). However and unlike the present study, Bishop et al. (2) observed a stronger relationship to the performance with DMAX than with DMAX MOD. This discrepancy could be explained by the fact that the performance test carried out in the study of Bishop et al (2) was a 1-hour time trial which corresponds to a lower exercise intensity than the intensity at VT2 (intensity usually maintained no longer than 50 minutes (7)). The intensity at DMAX point effectively is always lower than the intensity at DMAX MOD point. In the same way, Nicholson and Sleivert (19) showed no significant difference between the running speed at the DMAX point and the speed on a 10-km running time trial. The training level of the subjects tested may be an explicative reason for this difference with our result. In fact, Nicholson and Sleivert (19) have tested subjects “actively engaged in running” with a middle-ranking regional running level (ie, mean 10-km velocity of 3.77 m·s−1 equivalent to a total time of 44 minutes to cover the distance), whereas we tested elite skiers regularly engaged in international competitions, thus, physiologically and psychologically more suited to enduring high exercise intensities.

In summary, this study has shown that the DMAX MOD lactate threshold measurement is extremely accurate to predict the second VT2 in elite cross-country skiers. Thus, this method can be easily and confidently used by practitioners in complement (in the case of doubts with the visual analysis of ventilatory parameters) or instead of the VT2 determination. The DMAX method underestimate the HR at VT2 and so, seems like not valid for monitoring training at or near VT2 intensity but could remain a good marker of aerobic endurance because of its strong relationship with VT2 and the narrow limits of agreements when compared with VT2. Finally, the fixed lactate concentration method (4 mM) should be cautiously applied as proposed by Vallier et al (22), because of its not negligible error risk for a precise individualized monitoring training in elite athletes.

Practical Applications

From a practical point of view, a precise determination of the intensity close to competitive intensity is needed for skiers and/or coaches to optimize training load and increase race performances. Indeed, the determination of this intensity is useful for skiers and/or coaches because it is a key factor of performance in elite endurance athletes (15). This intensity represents the capacity of the athletes to utilize an important part of their maximum oxygen consumption (ie, endurance). To improve their endurance capacity and, therefore, their race performances, skiers have to perform some specific training sessions (usually interval training sessions) precisely at the intensity corresponding to VT2 (14) to obtain significant training-induced adaptations (ie, shift in VT2 toward higher workload). Now, it seems that this intensity can precisely and individually be determined using the DMAX MOD method in good to high level skiers, without using expensive gas exchange analyzers. Moreover, the determination of the DMAX MOD point is not human related, thus the error-risk to precisely determinate this point is reduced and requires less experience than for the determination of VT2.


The authors gratefully acknowledge the assistance of all those who took part in this study, particularly all the subjects from the national Italian ski team and their coaches.


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anaerobic threshold; lactate; respiratory compensation threshold; roller-ski

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