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## Revista Brasileira de Medicina do Esporte

##
*Print version* ISSN 1517-8692

*On-line version* ISSN 1806-9940

### Rev Bras Med Esporte vol.12 no.2 Niterói Mar./Apr. 2006

#### http://dx.doi.org/10.1590/S1517-86922006000200003

**ORIGINAL ARTICLE**

**Characterization
of the blood lactate curve and applicability of the Dmax model in a progressive
protocol on treadmill**

**La caracterización de la curva del lactato sanguíneo
y la pertinencia del Dmax durante el protocolo progresivo en la cinta rodante
**

**Flávio
de Oliveira Pires ^{I}; Adriano Eduardo Lima Silva^{II}; João
Fernando Laurito Gagliardi^{I}; Ronaldo Vilela Barros^{I}; Maria
Augusta Peduti Dal' Molin Kiss^{I}**

^{I}Laboratory
of Sportive Performance – School of Physical Education and Sports –
São Paulo – University São Paulo (SP)

^{II}Laboratory of Morpho-Functional Researches – Center of Physical
Education, Physiotherapy and Sports Santa Catarina State University – Florianópolis
(SC)

**ABSTRACT**

**PURPOSE:**
To characterize the blood lactate ([La]) behavior along a progressive protocol
on treadmill, and to investigate the applicability of the Dmax model in detecting
the lactate threshold (LT) and the sportive performance.

**METHODS:** Twenty-seven male athletes of regional level performed the Heck
*et al.* protocol (1985) incremented every 3 minutes. The sportive output
was attained by the mean velocity of the 10 km-test. The first and second LT
were determined through visual analysis of the [La] (LTv1 and LTv2) curve, and
by interpolation of the velocity related to the 2.0 and 3.5 mmol.l^{-1}
concentrations (LT_{2.0} and LT_{3.5}). The Dmax model has identified
the LT in measured values (Dmax_{MED}), and was predicted by the polynomial
functions (Dmax_{POL}), the 2-segment linear (Dmax_{SEG}) and
the continuous exponential (Dmax_{EXP}). The characteristic of the blood
lactate along the incremental test was checked through 2-segment linear adjustments
and continuous exponential.

**RESULTS:** There was no significant difference between the sums of the
square residues of the curve adjustments, but there was a trend for a better
continuous exponential adjustment at 70.4% of the sampling. Although there was
no significant difference between the Dmax_{MED}, Dmax_{POL},
Dmax_{SEG}, and Dmax_{EXP}, the Dmax methods were higher than
the LTv1, lower than the LT_{3.5}, and were not different of the LT_{2.0}.
Every Dmax criteria were significantly lower than the mean velocity of the 10
km-test.

**CONCLUSIONS:** While the [La] trended to an exponential increase along
the progressive protocols on treadmill, the Dmax model presented evidences of
its applicability to detect the LT, but not for the sportive output.

**Keywords:**
Curve adjustments. Progressive protocol. Lactate threshold.

**RESUMEN **

**PROPÓSITO:** Este estudio tenía
como los objetivos, para caracterizar la conducta del lactato sanguíneo
([La]), durante el protocolo progresivo en la cinta rodante, y para
investigar la pertinencia del Dmax en el descubrimiento del umbral de lactato
(LL) y el ingreso deportivo. **
MÉTODOS:** Veintisiete atletas de nivel regional ejecutaron protocolo
de Heck et al. (1985), con incrementos cada 3 minutos. El ingreso deportivo
se obtuvo por la velocidad de la prueba de 10 km. El 1 y 2 LL sea cierto a través
del análisis visual de la curva del [La] (LLv1 y LLv2), y para
la interpolación en la velocidad con respecto a las concentraciones de
2,0 y 3,5 mmol.l

^{-1}(LL

_{2,0}y LL

_{3,5}). EL Dmax identificó LL en los valores moderados (Dmax

_{MED}), y se predijo por el polinomial de las funciones (Dmax

_{POL}), lineal de dos segmentos (Dmax

_{SEG}), y exponencial continuo (Dmax

_{EXP}). La característica del lactato sanguíneo durante la prueba incremental se verificó por los ajustes lineal de 2 segmentos y exponencial continuo.

**No había diferencia significante entre el sumatoria de los residuos cuadrados de los ajustes de la curva, sin embargo, había una tendencia continua de ajuste exponencial bueno en 70,4% de la muestra. Mientras que no había diferencia significante entre Dmax**

RESULTADOS:

RESULTADOS:

_{MED}, Dmax

_{POL}, Dmax

_{SEG}y Dmax

_{EXP}, el método Dmax es más grande que LLv1, más pequeño que LL

_{3,5}, y no presenta diferencia con el de LL

_{2,0}. Todo el criterio Dmax sea significativamente más pequeño que la velocidad elemento de la prueba de 10 km.

**Mientras las [LA] tenderon a un aumento exponencial durante los protocolos progresivos en la cinta rodante, el Dmax ejemplar presentó evidencias de pertinencia mayor el descubrimiento de LL, pero no para rendimiento deportivo.**

CONCLUSIONES:

CONCLUSIONES:

**Palabras-clave:** Ajustes de la curva. Protocolo
progresivo. Umbral del lactato.

**INTRODUCTION**

The analysis of the blood lactate concentrations ([La]) curve
has supplied important subsidies to provide an understanding on
the phenomena related to the sportive output^{(1)}. Along
the 80's, Hughson *et al.* (1987)^{(2)} and Campbell
*et al.* (1989)^{(3)}, showed an exponential
increase in that variable along progressive protocols employing
mathematical curve adjustments, differently from prior studies
that checked a 3 or 4-segment curvilinear
characteristic^{(4,5)}. Nevertheless, Hughson and
co-workers^{(2)} and Campbell and
co-workers^{(3)} used ergometric bike protocols,
restricting the extrapolation of those results when a treadmill
was employed, as the behavior of that variable depends on the
motor pattern and the size of the recruited muscular
mass^{(6,7)}.

Still, the analysis of the blood lactate concentrations
enables the identification of one or two metabolic transition
zones that are dependant on the terminology and methodology
adopted, and which is commonly denominated lactate threshold
(LT)^{(5)}. This point has been investigated due to its
properties in detecting the level of the aerobic capability and
to predict the sportive output, since it theoretically represents
a maximal balance status in the [La] along constant
exercising^{(8,9)}. In fact, whenever methodologies to
identify the two metabolic transition zones are used, the second
point is frequently taken as reference for such
intensity^{(10)}. In this sense, several methods to allow
an objective^{(11,12)} and practice^{(13,14)}
determination of that spot were proposed, but the major part of
them has limitations and methodological implications.

In the 90's, Cheng
*et al.* (1992)^{(15)} suggested the Dmax model to determine the
LT (figure 1), under the supposition it would allow more
individualized identifications instead of using fixed and less subjective concentrations,
and less subjectives than visual analysis, since it makes objective calculations
of the intensity that considers every value contained in the curve^{(15)}.
Consequently, the point identified by the Dmax is directly connected to the
behavior of every curve of the blood lactate along the incremental test.

Despite the evidences of the validity of this
model^{(16-18)}, whenever is admitted the existence of
two metabolic transition zones, there are gaps related to which
of both transition zone is marked by such method.

Therefore, some speculations must be investigated from the
above mentioned statements. First, it is unknown in what extent
the [La] present an exponential increase along the progressive
tests on treadmill, since the previously observed exponential
characteristic^{(2,3)} was not confirmed by that type of
ergometric device. Second, considering that the Dmax model is
conditioned to the behavior of every [La] curve, it appears some
doubts as to its applicability to determine the LT and the
sportive performance, because although some studies applied that
method to adjusted data with polynomial
regression^{(19)}, others employed the continuous
exponential function^{(20)}, suggesting that the use of
different mathematical functions can generate distortions in the
intensity determined through that model.

Thus, the purpose of this paper was to characterize the blood lactate behavior along the progressive period on treadmill, and to check the applicability and consistency of the Dmax model in detecting the LT and the sportive output from measured and adjusted values by different mathematical functions.

**METHODS**

*Sampling*: Twenty-seven male athletes of regional level
(triathletes and marathon runners) participated in this study
(29.1 ± 5.4 years; 172.3 ± 8.1 cm; 67.2 ±
9.3 kg; 58.5 ± 10.8 ml.kg^{-1}.min^{-1})
after signing an informed consent term. This study was approved
by the ethics committee for studies in humans (EEFE-USP).

*Progressive protocol*: All subjects performed
incremental test on a Quinton^{®} model 2472
treadmill with initial velocity of 6.0 km.h^{-1} and 1.2
km.h^{-1} increments in each of the 3 minutes phase and
with 30 second pause to the blood collection^{(13)}.

*Data collection and analysis*: During the 30 final
seconds of each stage, 25 µl of arterialized blood were
collected from the ear lobule (previously prepared with
Finalgon^{®}), which was stored in microtubes
containing 50 µl of sodium fluoride and stored at
10ºC for later analysis in a Yellow
Springs^{®} Model 2000 lactate analyzer. The attained
[La] had the velocity plotted to identify the LT (expressed in
km.h^{-1}).

*Identification of the lactate threshold*: The
1^{st} and 2^{nd} lactate thresholds (LT1 and
LT2) were identified through visual analysis of the blood lactate
curve from a mean observation performed by three researchers.
While the LT1 was determined at the increase point of the [La]
related to the resting values (1^{st} interruption of the
curve's linearity), the LT2 was determined by the intensity where
the [La] presented a sudden and continuing increase
(2^{nd} interruption of the curve's linearity). Whenever
necessary, LT1 or LT2 were approximated according to other
criteria^{(21)}.

The LT1 and LT2 were also identified by
interpolation^{(6)} of the velocity corresponding to the
fixed lactate concentrations of 2.0 and 3.5 mmol.l^{-1},
and they are representatives of the LT1 and LT2,
respectively^{(10,13)}. For a better understanding on the
terms, the visually attained LT1 and LT2 will be called LTv1 and
LTv2, and the LT1 and LT2 attained by the use of fixed
concentrations will be called LT_{2.0} and
LT_{3.5}.

The LT was also determined at the point where the [La]
presented an increase __>__ at 1.0 mmol.l^{-1(19)}. Such
criterion was treated herein as L1.0, and it was used because it
allows the identification of only one metabolic transition
zone.

At last, the Dmax^{(15)} model has identified the LT
at the most distant perpendicular point between the [La] values
contained in the curve, and a regression line was traced between
the first and the last value of that curve.

*Adjustments in the blood lactate curve:* The
characterization of the blood lactate curve in function of the
velocity was verified following the 2-segment linear mathematical
functions, and the continuous exponential variating between 7 and
11 points. Later, the Dmax model was calculated in measured data
(Dmax_{MED}), and in adjusted data using the 2-segment
linear (Dmax_{SEG}), the continuous exponential
(Dmax_{EXP}), and the 3^{rd} order polynomial
(Dmax_{POL}) functions.

The 2-segment linear adjustment^{(22)} was attained by
linear regression equation with an initially unknown intercept
calculated from every possible visual intersection points between
segments. The intercept that better divided the curve in two
theoretically linear segments was assumed as the higher
R^{2} value and the lower sum of the square residues
(SRQ). Thus, the curve segments were predicted by the following
equations:

where *y* is the predicted value for the [La], *a*
is the intercept for both segments, *b1* and *b2* are
respectively, the inclination of the 1^{st} and
2^{nd} segments, and *c* is the tangent between both
segments.

The exponential characteristic of the [La] along the
progressive tests was tested by the continuous exponential
function^{(2)}, through the following equation:

where *y* is the predicted value for [La], *x* is
the velocity, *e* is the residual error, *a, b,* and
*c* are minimized estimates of the SRQ between measured and
predicted values for the [La], and *exp(x)* is the maximized
estimate of the correlation coefficient between variables
*x* and *y*.

The 3^{rd} order polynomial function was used to
attenuate the noises contained in the rough values of the [La],
without changing the initial characteristics of the curve,
allowing one of the variations for the Dmax model
(Dmax_{POL}). The equation generated was the
following:

where *y* is the predicted value for the [La], *b1,
b2,* and *b3* are the inclination's constants of the
curve; *x* is the velocity, and *a* is the
intercept.

*Sportive output:* After a lower than 30 days interval
from the progressive protocol, the sampling performed a 10
km-test on a 400-meter race track. The mean time and velocity of
the 10 km-test (VM_{10km}) were recorded.

*Statistical analysis:* After verifying the data
distribution (Shapiro-Wilk's) it was attained the significance of
the differences between the assessed variables using the
Friedman's Anova along with the Wilcoxon (*post* hoc)
signalization test for matched pairs. The association between
variables was attained using the Spearman Rank test. In every
analysis (SPSS version 1.0) it was adopted 5% significance level
(p < 0.05).

**RESULTS**

Every calculation used the mean and standard deviation as central trend and dispersion measurements, respectively. For eventual comparisons, a few data related to the 10 km-test and the SRQ between the mathematical functions of adjustment are also presented as mean and standard deviation.

**Quality of the curve adjustments**

The 3^{rd} order polynomial adjustment was not
included in the residual analysis, once it does not have a
theoretical basis that justifies its application in the attempt
to describe the assessed phenomenon. As to the 2-segment linear
adjustment, eight individuals presented the 2^{nd}
segment adjusted in only two points. There was no significant
difference between the SRQ of the continuous exponential
adjustment and the 2-segment linear adjustment's SRQ (0.11
± 0.18 mmol.l^{-1} vs. 0.09 ± 0.07
mmol.l^{-1} mean and standard deviation values). Upon an
individual comparison of the SRQ, 19 out of 27 analyzed
individuals (70.4%) presented trend for a better continuous
exponential adjustment. The 2-segment linear adjustment presented
a trend for improvement in seven individuals (25.9%), while one
individual (3.7%) showed an identical residual value between both
mathematical functions. The ten first runners in the 10 km-test
showed a trend for a better continuous exponential
adjustment.

**Dmax and different methods to identify the LT**

Four individuals
did not attain the 2.0 and/or 3.5 mmol.l^{-1} concentration values along
the incremental test. There were no significant differences between variations
in the Dmax model, whether applied on measured and/or adjusted values by three
different mathematical functions (table 1).

Related to the other methods, it was found no significant differences between any Dmax criterion and the LT

_{2.0}and LT

_{1.0}(p between 0.06 and 0.09). However, while Dmax

_{MED}and Dmax

_{EXP}were different from LTv2, the same was not observed in the Dmax

_{POL}and Dmax

_{SEG}. Every Dmax criterion was higher than LTv1 and lower than LT

_{3.5}(table 1). Interestingly, LT1 and LT2 attained through fixed concentrations were higher than LT1 and LT2 attained through visual analysis (LT

_{2.0}> LTv1 and LT

_{3.5}> LTv2).

Dmax_{MED},
Dmax_{SEG}, Dmax_{EXP}, and Dmax_{POL} presented a correlation
coefficient that varied between 0.57 and 0.80 (p < 0.01). Table
2 shows the association level between the Dmax criteria and other methods.

**Dmax and sportive output**

The time of the test and the VM_{10km} were 37.8
± 3.2 minutes, and 16.0 ± 1.3 km.h_{-1},
respectively.

Every Dmax variation,
as well as other identification methods for the LT was significantly lower than
the VM_{10km}. On the other hand, only the Dmax_{EXP} were significantly
correlated to the VM_{10km} (r = 0.68) (table 2).

**DISCUSSION**

Historically, conceptual and methodological problems limitate a broadest definition to the phenomena related to the lactate metabolism while exercising. That approach is expressly linked to the different models used to investigate them, and our paper reinforces such premise.

The major contribution this paper supplied was the trend for an exponential increase in the [La] related to the workload observed in 70.4% of the assessed sampling. In that case, the absence of a significant difference between the SRQ of the mathematical functions may be conditioned to some factors.

First, differently
from studies verifying a better exponential adjustment in the [La]^{(2,3)},
the protocol employed here has generated a lower amount of points per curve.
As the continuous exponential function (figure 2) predicts
the blood lactate values with progressive correction minimizing the SRQ maximizing
the correlation coefficient between the x and y^{(2)} values, such lower
amount of points could be one of the reasons for the absence of differences
between the mathematical functions.

In fact, the duration of the protocol can influence the curve
behavior of the [La] in the incremental test^{(23)}.

Second, the 2-segment
linear adjustment (figure 3) was calculated using four
to nine points in the first segment, and two to four points in the second segment.
As it is demanded at least seven points to achieve a successful curve adjustment^{(24)},
this would be a limitation to the present investigation, as that mathematical
function splits the curve in two theoretically linear and partially independent
segments. Thus, even observing between 7 and 11 points to analyze each total
curve, it could there have been a "best" adequation of the data to the segmented
linear function by the simple division of the curve in two segments. The difficulties
in using such mathematical adjustment were previously mentioned^{(25)}.

A descriptive approach helps to understand our results. The features of the blood lactate increase along the progressive protocol must pursue associations with the sportive output, since the best places in a 10 km-test trended to present an exponential increase in the [La].

Such behavior was also observed as to the PVE, with the
highest values generated by the majority of individuals with
trend for a better continuous exponential adjustment (12
individuals). Although we must be careful, it is reasonable to
expect that individuals with a higher aerobic fitness level, also
present a higher trend for an exponential increase of the [La]
due to the workload^{(26)}.

The main justification for this suggestion is the changes in
the blood lactate accumulation features after a physical
training^{(23)}. Along with the incremental test,
individuals presenting a better aerobic conditioning are
successful in keeping themselves during a prolonged period of low
[La], thus delaying the beginning of the progressive increase of
that variable^{(1,8,14,27)}, and this could generate an
exponential increase in the blood lactate curve. This behavior
seems to be connected to the higher capability of the tamponage
system^{(28)}, to the better removal^{(28,29)},
and/or a lower lactate production rate^{(30)} in
individuals performing exercises.

Another important contribution granted by this investigation was the confirmation of the applicability and consistency of the Dmax model in determining the LT both in measured and in adjusted values. On the other hand, even with no significant differences, the points attained by the variations in the Dmax model were not kept away in the same way compared to other methods used.

However, some divergences between methods to identify the LT
were previously observed^{(16,17,19,20)}, and these can
be related to different methodologies adopted to obtain such
intensity^{(31)}.

Unlike prior studies^{(19,20)}, it was observed that
the Dmax model was unable to detect the sportive output, because
besides the significant difference between the velocities
attained through that method and the VM_{10km}, we have
noticed low correlation levels between these variables. Our
results confirm the supposition that the LT has a higher
predictive power in long endurance tests^{(8,19,32,33)},
suggesting that the PVE and the blood lactate peak attained in
incremental tests is a more sensitive variable to detect the
sportive output in short term tests, with lower or equal to 10 km
distances^{(34)}. Thus, the lack of capability in
detecting the sportive output in such type of test should not be
conditioned to that specific model, but instead to the
physiological phenomenon it represents.

This and other investigations^{(15-17)} allow us to
suppose that the Dmax is closest to the L1.0 and away from
LT_{3.5} and/or the 4.0 mmol.l^{-1} threshold.
This supposition is justified by the trend to the overestimation
of the LT when the fixed [La] is used mainly in individuals with
higher aerobic fitness levels^{(12,13)}, as the
individuals assessed in this and other
investigations^{(16,17)} were recreational and/or
competitive aerobic athletes.

Additionally, when it is assumed that there is a curvilinear
relationship between the [La] and the workload^{(4,22)},
this criterion can be arbitrary and less sensitive to identify
such intensity^{(25)}.

However, considering the existence of two metabolic transition
zones^{(5,10)}, it is not possible to conclude to which
one the Dmax model is the marker. For instance, although it was
noted no difference between any Dmax criterion and the
LT_{2.0}, the Dmax_{MED} and the
Dmax_{EXP} were significantly different from LTv2 (p =
0.03), although the same behavior as to the Dmax_{POL}
and Dmax_{SEG} was not observed. This makes difficult to
interpret our findings, since theoretically, the LT_{2.0}
and the LTv2 are considered markers for different metabolic
transition zones^{(5,10)}.

In fact, the theoretical model suggesting two metabolic
transition zones is based on classic studies using visual
analysis of the lactate curve^{(25,35-37)} and/or fixed
[La]^{(13,25,26,35)} in order to obtain the LT. Thus, the
identification for two distinct intensities is allowed by the
arbitrarity of the fixed [La] method or by the high level of
subjectivity and dependence when the researcher is interpreting
using the visual method^{(11,12)}. Considering the
limitations of these classic methods, it could be suggested the
existence of a continuously manifested sole metabolic transition
zone^{(21)}.

In fact, a better exponential adjustment in the blood lactate
curve observed in prior studies^{(2,3)}, and the trend
for a better continuous exponential adjustment observed here
would be the evidence for the presence of only one metabolic
transition zone.

Despite the limitations of the present study, it was observed trends for an exponential behavior in the blood lactate curve along the progressive protocol on treadmill. On the other hand, it was noted evidences on the applicability and consistency of the Dmax model in determining the LT intensity both in measured and in adjusted values. Nevertheless, this method was not effective in detecting the sportive output on a 10 km-test, suggesting that the exponential characteristic of the [La] curve in that case can be a phenomenon that may help to understand the performance in those tests. Further studies must confirm this suggestion.

**THANKFULNESS**

We wish to thank to Prof. Doctor Fernando Roberto de Oliveira and Professor Cláudio Romero Marinho for their contributions along the elaboration of the study.

*All the authors declared there is not any potential
conflict of interests regarding this article.*

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**Correspondence
to:**

Flávio de Oliveira Pires

Rua Acalanto de Bartira, 166, Jd. Bonfiglioli, Butantã

05358160 – São Paulo, SP.

Phone: (11) 3731-3071, fax: (11) 3763-2588

E-mail: piresfo@usp.br

Received in 24/11/04.

Final version received in 30/7/05.

Approved in 3/11/05.