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Influence of regression model and incremental testprotocol on the relationship between lactate thresholdusing the maximal-deviation method and performancein female runnersFabiana Andrade Machado a , Fbio Yuzo Nakamura b & Solange Marta Franzi De Moraes ca Department of Physical Education, State University of Maringa, Maring, Brazilb Department of Physical Education, State University of Londrina, Londrina, Brazilc Department of Physiologic Sciences, State University of Maringa, Maring, BrazilPublished online: 10 Jul 2012.

To cite this article: Fabiana Andrade Machado , Fbio Yuzo Nakamura & Solange Marta Franzi De Moraes (2012)Influence of regression model and incremental test protocol on the relationship between lactate threshold using themaximal-deviation method and performance in female runners, Journal of Sports Sciences, 30:12, 1267-1274, DOI:10.1080/02640414.2012.702424

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Influence of regression model and incremental test protocol on therelationship between lactate threshold using the maximal-deviationmethod and performance in female runners

FABIANA ANDRADE MACHADO1, FABIO YUZO NAKAMURA2, &

SOLANGE MARTA FRANZOI DE MORAES3

1State University of Maringa, Department of Physical Education, Maringa, Brazil, 2State University of Londrina,

Department of Physical Education, Londrina, Brazil, and 3State University of Maringa, Department of Physiologic Sciences,

Maringa, Brazil

(Accepted 30 May 2012)

AbstractThis study examined the influence of the regression model and initial intensity of an incremental test on the relationshipbetween the lactate threshold estimated by the maximal-deviation method and the endurance performance. Sixteen non-competitive, recreational female runners performed a discontinuous incremental treadmill test. The initial speed was setat 7 km h71, and increased every 3 min by 1 km h71 with a 30-s rest between the stages used for earlobe capillaryblood sample collection. Lactate-speed data were fitted by an exponential-plus-constant and a third-order polynomialequation. The lactate threshold was determined for both regression equations, using all the coordinates, excluding thefirst and excluding the first and second initial points. Mean speed of a 10-km road race was the performance index(3.04 + 0.22 m s71). The exponentially-derived lactate threshold had a higher correlation (0.98 r 0.99) andsmaller standard error of estimate (SEE) (0.04 SEE 0.05 m s71) with performance than the polynomially-derivedequivalent (0.83 r 0.89; 0.10 SEE 0.13 m s71). The exponential lactate threshold was greater than thepolynomial equivalent (P 5 0.05). The results suggest that the exponential lactate threshold is a validperformance index that is independent of the initial intensity of the incremental test and better than the polynomialequivalent.

Keywords: Dmax, endurance, exponential-plus-constant, third-order polynomial

Introduction

The lactate threshold has been used widely to predict

endurance performance, prescribe training intensity

and evaluate training effects (Allen, Seals, Hurley,

Ehsani, & Hagberg, 1985; Billat, 1996; Papadopou-

los, Doyle, & Labudde, 2006). There are several

techniques that can detect lactate thresholds (Davis,

Rozenek, DeCicco, Carizzi, & Pham, 2007; Tokma-

kidis, Leger, & Pilianidis, 1998; Thomas, Costes,

Chatagnon, Pouilly, & Busso, 2008). Specifically, the

maximal-deviation method (Dmax) proposed by

Cheng et al. (1992) can evaluate mechanisms that

underpin long-distance running and cycling perfor-

mance. In most studies, lactate threshold determined

by the maximal-deviation method was more highly

correlated with performance than the lactate thresh-

old values determined by other methods (Bishop,

Jenkins, & Mackinnon, 1998; Machado, de Moraes,

Peserico, Mezzaroba, & Higino, 2011; Nicholson &

Sleivert, 2001; Papadopoulos et al., 2006). Addi-

tionally, according to Morton, Stannard, and Kay

(2012), the lactate threshold determined by the

maximal-deviation method was the only one of seven

markers that was highly reproducible and could be

used alone to identify small but meaningful changes

in training status with sufficient statistical power.

The maximal-deviation method is an objective

and graphical technique that identifies the point on a

lactate-intensity regression curve that is furthest

away from a straight line which connects the first

and last points of that curve. As the distance is

calculated perpendicularly from the line drawn

between the datum points, increasing the initial

intensity of an incremental exercise test leads to an

apparently higher lactate threshold (Janeba, Yaeger,

Correspondence: Fabiana Andrade Machado, State University of Maringa, Department of Physical Education, Av.Colombo, 5790, Block M 06, Maringa,

87020900 Brazil. E-mail:[email protected]

Journal of Sports Sciences, August 2012; 30(12): 12671274

ISSN 0264-0414 print/ISSN 1466-447X online 2012 Taylor & Francishttp://dx.doi.org/10.1080/02640414.2012.702424

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White, & Stavrianeas, 2010). However, it remains

unclear whether this procedure affects the relation-

ship between the lactate threshold and endurance

performance.

Additionally, the influence of the choice of

regression model on the lactate threshold estimate

is not known. The third-order polynomial equation

was adopted originally by Cheng et al. (1992) in

the development of the maximal-deviation method.

Bishop et al. (1998) also used this form of

equation to determine the lactate threshold, but

Nicholson and Sleivert (2001), for example, used

the exponential-plus-constant model, which is

supposed to improve the sensitivity with which

physiological changes in blood lactate concentra-

tion during progressive exercise can be investigated

(Hughson, Weisiger, & Swanson, 1987). The

major drawback of the third-order polynomial

model is that there is no theoretical justification

for its use to describe lactate responses and

adaptations to exercise.

As the lactate threshold determined by the max-

imal-deviation method was the most highly corre-

lated with performance and was the only highly

reproducible lactate threshold estimate in previous

studies, it is important to investigate both the

influence of the regression model and initial intensity

of the incremental test on the relationship between

the lactate threshold and performance. To our

knowledge, no previous study has investigated these

aspects of the maximal-deviation method. We

hypothesised that the impact of the initial intensity

on the relationship between the lactate threshold

determined by the maximal-deviation method and

the endurance performance will be smaller using an

exponential-plus-constant than a third-order poly-

nomial model. Thus, this study was conducted to

examine the influence of the regression model and

initial intensity of the incremental test on the

relationship between the lactate threshold deter-

mined by the maximal-deviation method and en-

durance performance.

Methods

Participants

Sixteen non-competitive, recreational female runners

of local standard with a minimum of two years of

training experience volunteered to take part in this

study. Of these, 13 completed the entire study and

10 were included for analysis. The 10-km running

times of the participants were between 45 and

65 min, with a pace between 2.5 and 3.5 m s71(*4560% of the world record). Characteristics ofthe participants (n 16) were age 42.2 + 7.5 years,stature 1.63 + 0.03 m, body mass 57.3 + 6.6 kg,

body mass index 21.6 + 2.1 kg m72, body fat20.4 + 4.1% and maximal oxygen uptake53.2 + 8.0 mL kg71 min71. The training char-acteristics of the participants (mean + s) wereexperience 3.1 + 1.9 years, frequency 2.6 + 0.5days week71 and distance 24.9 + 6.0 km week71. The experimental protocol was approved

by the local Ethics Committee (# 719/2010).

Incremental exercise test

Participants performed a discontinuous incremental

exercise test on a motorised treadmill (INBRA-

SPORT ATL, Porto Alegre, Brazil) with the

gradient set at 1%. Participants were instructed to

avoid consuming food 2 h before the maximal

exercise test, and to abstain from caffeine and

alcohol and to refrain from strenuous exercise for

48 h prior to testing. After a 5-min warm-up at

5 km h71, the initial treadmill speed was set at7 km h71, and this speed was increased by 1 km h71 between each of the 3-min successive stages.

Each stage was separated by a 30-s period of rest,

during which an earlobe capillary blood sample

(25 mL) was collected into a glass tube; from thesesamples, using single analysis, blood lactate was

determined by electroenzymatic methods (YSI

1500, Ohio, USA). Prior to operation, the YSI

1500 was calibrated using a 5 and a 15 mmol L71lactate standard solution according to the manufac-

turers instructions. Throughout the tests, pulmon-

ary gas-exchange variables were determined using a

portable gas analyser (MedGraphics VO2000, St.

Paul, USA). Before each test, the VO2000 was

calibrated according to the manufacturers instruc-

tions, which consisted of performing an auto-

calibration routine on the oxygen (accuracy +0.1%) and carbon dioxide (accuracy + 0.2%)

analysers using room air and proprietary software.

Heart rate was also continuously recorded through-

out the tests (Polar, Kempele, Finland). The 620

Borg scale (Borg, 1982) was used to measure the

rating of perceived exertion during the test. Each

participant was encouraged to give maximum effort

until volitional exhaustion. The maximal effort was

deemed to be achieved if the incremental test met

three of the following criteria: 1) a plateau in oxygen

uptake with increases in speed (difference in oxygen

uptake 150 mL min71), 2) the highest respira-tory exchange ratio 1.15, 3) blood lactateconcentration higher than 8 mmol L71, 4) thehighest heart rate within + 10 beats min71 of age-predicted maximum heart rate (220-age) and 5)

maximal perception of effort greater than 18 in the

620 Borg rating of perceived exertion scale (British

Association of Sport Sciences, 1988; Howley,

Bassett Jr, & Welch, 1995).

1268 F. A. Machado et al.

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Determination of the lactate threshold from the

exponential-plus-constant regression equation

The lactate threshold was determined for each

participant from the blood lactate concentration

(mmol L71) and speed (m s71) data obtainedfrom the incremental exercise test (Cheng et al.,

1992). The data were fitted by the exponential

regression curve (Hughson et al., 1987):

LA s a b exp c s 1

where s is the speed in m s71, and [LA](s) is theblood lactate concentration (mmol L71) as a func-tion of speed (m s71); a, b and c are the functionparameters that were determined by non-linear

regression with Statistical Package for the Social

Sciences (SPSS) 17.0 software (SPSS Inc., USA).

The point on the regression curve that yielded the

maximal perpendicular distance to the straight line

connecting the first and last point of this curve was

considered to be the speed at the lactate threshold

determined by the maximal-deviation method

(Figure 1).

The maximal perpendicular distance, which re-

presents the exponential lactate threshold, occurs at

the point where the slope of the exponential-plus-

constant curve is equal to the slope of the straight

line that connects the first and last point of this

curve. Because the slope of the curve is obtained

from the first derivative of the exponential-plus-

constant equation, the following equation was used:

exponential lactate threshold

ln exp c sf exp c si = c sf c si f gf g=c2

where ln is the natural logarithm, c is the

parameter of the exponential-plus-constant equation

and si and sf are the initial and final speeds of the

incremental exercise test, respectively. The final

speed was considered to be that of the last

completed stage.

Determination of the lactate threshold from the third-

order polynomial regression equation

The lactate threshold was determined for each

participant from the blood lactate concentration

(mmol L71) and speed (m s71) data obtainedfrom the incremental exercise test (Cheng et al.,

1992). The data were fitted by the third-order

polynomial regression curve (Cheng et al.,

1992):

LA s d0 d1 s d2 s2 d3 s3 3

where s is the speed in m s71, and [LA](s) is theblood lactate concentration (mmol L71) as afunction of speed (m s71); d0, d1, d2 and d3 areparameters that were determined by non-linear

regression with the SPSS 17.0 software (SPSS Inc.,

USA).

The polynomial lactate threshold occurs at the

point where the slope of the third-order polynomial

curve is equal to the slope of the straight line that

connects the first and last points of this curve.

Because the slope of the curve is obtained from the

first derivative of the polynomial equation, the

following equation was used:

polynomial lactate threshold

d2 d22 3 d3 d1 D n o

= 3 d3 4

where d1, d2 and d3 are the function parameters of

the third-order polynomial equation. Delta (D) is theslope of the straight line connecting the first and last

points of this curve:

Figure 1. Lactate threshold determined by the maximal-deviation method from the exponential-plus-constant (left) and third-order

polynomial (right) models for one participant. The calculated lactate threshold was different for the same data: 3.4 m s71 (exponential-plus-constant) and 3.2 m s71 (third-order polynomial).

Influence of regression model on Dmax 1269

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D LA final LA initial

= sf si 5

where [LA]initial and [LA]final are the initial and

final lactate concentrations estimated by the third-

order polynomial equation ([LA](s) d0 d1s d2s2 d3s3) for the initial (si) and final (sf) speeds,respectively.

Influence of the initial speed of the incremental test

To examine the influence of the initial speed of the

incremental test on the relationship between the

lactate threshold determined by the maximal-devia-

tion method and performance, speed at the lactate

threshold was determined in three ways: 1) using all

the coordinates, 2) excluding the first point and 3)

excluding the first and second points. This proce-

dure simulates varying the initial intensity of the

incremental test.

Relationship between the lactate threshold and

performance

All of the participants in this study competed the

same local 10-km road race, that took place within

one month period of laboratory testing. The

participants continued their regular training (fre-

quency 2.6 + 0.5 day week71 and distance24.9 + 6.0 km week71) between the test and therace. This local race takes place annually in April on

the paved streets of the city, and local runners direct

their training to have optimal performance in this

competition. The race began at 17:00 h on a sunny

day with relatively low humidity (approximately

40%) and a temperature of 308C. There were threehydration points along the course of the race.

Participants were encouraged to give their best

performance. Three runners had problems during

the race and did not finish. The race times of the

remaining runners were recorded, and their mean

10-km running speed from the road race was

calculated in m s71. Thereafter, the relationshipbetween 10-km running speed and variations of the

lactate threshold were examined.

Statistical analyses

Data are presented as the mean + s. Data wereanalysed using SPSS 17.0 software (SPSS Inc.,

USA). The Shapiro-Wilk test verified normality of

the data distributions. The speeds were compared

using one-way within-groups analysis of variance

(ANOVA) with a Bonferroni post hoc test. The

relationship between the speeds was examined using

Pearsons correlation coefficient. The standard error

of estimate (SEE) and the relative SEE, i.e. (SEE

expressed as a percentage of the mean of the outcome

measure) were used to examine the relationship

between the lactate threshold and 10-km road-race

performance. Additionally, the exponentially- and

polynomially-derived lactate thresholds were com-

pared by the technical error of measurement (TEM).

The magnitude of differences (effect size) was

calculated for significant differences and was inter-

preted as small ( 0.2), moderate (*0.5) and large (0.8) according to Cohen (1988). Statistical signifi-

cance was set at P 5 0.05.

Results

Three of the 13 participants who finished the entire

study completed just six stages in the incremental

test and were not included in the results to avoid

determining the lactate threshold excluding the first

and second points with only four points. The physical

and training characteristics (mean + s) of the re-maining participants (n 10) were age 41.2 +6.2 years, height 1.63 + 0.03 m, body mass57.5 + 4.8 kg, body mass index 21.6 + 1.9 kg m72, body fat 20.8 + 3.9%, experience 3.3 + 1.6years, training frequency 2.7 + 0.5 days week71and distance 23.3 + 5.6 km week71.

Maximal effort indices (mean + s) are as follows(n 10): maximal oxygen uptake 55.0 + 5.5 mL kg71 min71, respiratory exchange ratio 1.13 +0.10, peak blood lactate concentration 7.3 +2.3 mmol L71, 620 Borg rating of perceivedexertion 18.8 + 1.5 and maximum heart rate187 + 10 beats min71. All of the participantsmet at least three of the maximum-effort criteria.

Mean performance time during the 10-km road

race was 55:03 + 03:50 (min:s). The participantsfinished the race in between 49 and 60 min.

Mean speed during the road race was 3.04 +0.22 m s71.

Table I presents the exponential and polynomial

lactate threshold values (m s71) and their relation-ships with the 10-km road-race performance. The

exponential lactate threshold was greater when the

initial points were excluded. The exponential lactate

threshold excluding the first and second points was

greater than the exponential lactate threshold using

all the coordinates (P 5 0.05; effect size 4.5),exponential lactate threshold excluding the first point

(P 5 0.05; effect size 4.3) and polynomial lactatethreshold excluding the first and second points

(P 5 0.05; effect size 1.2). Furthermore, theexponential lactate threshold excluding the first point

(m s71) was greater than the exponential lactatethreshold using all the coordinates (P 5 0.05; effectsize 4.3) and polynomial lactate threshold exclud-ing the first point (P 5 0.05; effect size 1.4).Additionally, the exponential lactate threshold using

all the coordinates was significantly higher than the


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polynomial lactate threshold using all the coordinates

(P 5 0.05; effect size 1.0). The regression model(exponential-plus-constant versus third-order poly-

nomial) influenced the apparent lactate threshold, in

which the exponential lactate threshold was greater

than the polynomial equivalent (P 5 0.01). Theinitial intensity of the incremental test also influ-

enced the identified lactate threshold (P 5 0.001),producing higher values for the lactate threshold with

the exclusion of the initial points. Thus, the

regression model and the initial intensity of the

incremental test affected the lactate threshold

intensity.

The correlation between the exponential lactate

threshold and the 10-km road-race performance was

high (0.98 r 0.99; P 5 0.001), and the correla-tion was practically unaltered by excluding the first

or the first and second points. The correlation

between the polynomial lactate threshold and the

10-km road-race performance was systematically

smaller than the correlation between the exponential

lactate threshold and the 10-km road-race perfor-

mance and decreased slightly from 0.89 (polynomial

lactate threshold using all the coordinates) to 0.83

(polynomial lactate threshold excluding the first and

second points). Additionally, although the mean

difference (bias) between the exponential lactate

threshold and the 10-km road-race performance

increased with the exclusion of the initials points,

the standard error of estimate remained practically

unchanged (0.040.05 m s71), independent of theinitial intensity of the incremental test. The standard

error of estimate for the relationship between the

polynomial lactate threshold and 10-km road-race

performance was greater than that for the exponen-

tial lactate threshold.

The exponential lactate thresholds using all the

coordinates, excluding the first point and excluding

the first and second points were highly correlated

with each other (0.99 r 1.00; P 5 0.001),

indicating high inter-correlation between the expo-

nential lactate threshold indices. The inter-correla-

tion between the polynomial lactate threshold indices

was high (0.96 r 0.98; P 5 0.001) but slightlysmaller than the inter-correlation between the

exponential lactate threshold indices. The correla-

tions between exponential and polynomial lactate

threshold using all the coordinates (r 0.88;P 5 0.001), excluding the first point (r 0.89;P 5 0.001) and excluding the first and secondpoints (r 0.81; P 5 0.01) were not as high as theintra-modelling method indices. The absolute and

relative technical errors of measurement between

exponential- and polynomial-derived lactate thresh-

olds using all the coordinates (0.15 m s71; 4.9%),excluding the first point (0.18 m s71; 5.9%) andexcluding the first and second points (0.19 m s71;6.1%) were greater than the coefficient of variation

(CV) of the maximal-deviation method reported by

Morton, Stannard, and Kay (2012) during incre-

mental exercises on a cycle ergometer (CV 3.8%).Figure 2 illustrates the relationships between 10-km

road-race performance lactate threshold for the

exponential-plus-constant (left) and third-order poly-

nomial (right) regression equations. The relationship

(left) was systematically shifted to the right when the

initial points were excluded, but the correlation

between road-race performance and the exponential

lactate threshold remained practically unchanged.

The relationship (right) was also shifted to the right

for the third-order polynomial equation, but the

points were not as clustered around the regression

line as for the 10-km road-race performance and

exponential lactate threshold relationship (left).

Discussion

The major findings of this study were that the

polynomial lactate threshold underestimated the

equivalent exponentially-determined lactate threshold

Table I. Relationship between the lactate threshold using the maximal-deviation method and 10-km road-race performance (n 10)

Protocol

Exponential Polynomial

Lactate threshold

(m s71) rSEE

(m s71) SEE (%)Lactate threshold

(m s71) rSEE

(m s71)SEE

(%)

All the coordinates 3.11 + 0.21{ 0.98** 0.05 1.5% 2.96 + 0.30 0.89** 0.10 3.4%Exclusion of the

first point

3.20 + 0.20{{ 0.99** 0.04 1.3% 2.98 + 0.30 0.89** 0.10 3.4%

Exclusion of the

first and second points

3.28 + 0.18{{{ 0.98** 0.04 1.3% 3.07 + 0.29# 0.83* 0.13 4.2%

Note: r, Pearsons correlation coefficient; SEE, standard error of estimate; SEE (%), standard error of estimate expressed as a percentage of

mean speed for the road race; {P 5 0.05 for the polynomial (using all the coordinates); {{P 5 0.05 for the exponential (using all thecoordinates) and polynomial (excluding the first point); {{{P 5 0.05 for the exponential (using all the coordinates and excluding the firstpoint) and polynomial (excluding the first and second points); #P 5 0.05 for the polynomial (using all the coordinates and excluding thefirst point); *Statistical significance is P 5 0.01; **Statistical significance is P 5 0.001.


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for all conditions involving original or excluded initial

intensities. Moreover, the exponential lactate thresh-

old had higher correlation and smaller standard error

of the estimate with 10-km road-race performance

than the polynomial lactate threshold. Additionally,

the correlation between the exponential lactate thresh-

old and the 10-km road-race performance was nearly

independent of the initial intensity of the incremental

test.

The maximal-deviation method is a graphical

technique that depends on the shape of the lactate-

intensity curve and the initial and final intensities of

that curve. The final intensity can be controlled by

guaranteeing that maximum effort has been exerted

(e.g., strong verbal encouragement). The traditional

criteria to check for maximal effort are a plateau in

oxygen uptake despite a continued increase in

exercise intensity, high concentrations of blood

lactate in the minutes after the exercise test (peak

blood lactate 8.0 mmol L71), a respiratory ex-change ratio greater than 1.15, a final heart rate

within + 10 beats min71 of age-predicted max-imum and a rating of perceived exertion greater than

18 in Borgs 620 scale (British Association of Sport

Sciences, 1988; Howley et al., 1995). Using these

criteria, it is unlikely that researchers, coaches and

practitioners will not achieve the maximum lactate

point. Nevertheless, the lactate threshold as deter-

mined by the maximal-deviation method requires

athletes to exert maximally during an incremental

test. In some cases, athletes are limited in their ability

to do so (Marcora, Bosio, & de Morree, 2008;

Marcora, Staiano, & Manning, 2009). Therefore, the

method can fail to determine the lactate threshold.

Thus, as a practical application, athletes should use

another method to estimate the lactate threshold

when they do not meet the maximum physiological

and perceived effort criteria. Accordingly, the effects

of acute changes in the final lactate point by

experimental manipulations (e.g., muscle fatigue or

mental fatigue (Marcora et al., 2008, 2009) should

be tested in the future.

Appropriate setting of the initial intensity of the

incremental test is highly dependent on the experi-

ence of the researchers, coaches and practitioners.

Unfortunately, for the maximal-deviation method,

there is no standard for determining this intensity.

This is the main shortcoming of the maximal-

deviation method because it is known that the lactate

threshold increases with an increase in the initial

intensity of the incremental test (Janeba et al., 2010).

The lactate threshold increased systematically when

initial points were excluded both for the exponential-

plus-constant and third-order polynomial regression

models. Thus, the lactate threshold determined by

the maximal-deviation method is dependent on the

initial intensity of the incremental test, and exclusion

of the initial points will increase the apparent lactate

threshold. Additionally, the regression model (ex-

ponential-plus-constant versus third-order polyno-

mial) influenced the identified lactate threshold. The

polynomially-derived lactate threshold was lower

than the exponentially-derived equivalent. Figure 1

shows the exponential and polynomial lactate thresh-

old from one participant in whom the polynomial

lactate threshold underestimated the exponential

lactate threshold by 5.9% (0.2 m s71).The occurrence of a unique threshold point over

the range of the lactate-intensity curve was ques-

tioned by Tokmakidis et al. (1998), who reported

that various lactate threshold indices were well

correlated with performance. For example, they

found that intensities equivalent to a blood lactate

concentration of 4 mmol L71 did not have a highercorrelation with performance than 5, 6, 7 or even

8 mmol L71. That does not mean that a fixedlactate concentration of 5 or 8 mmol L71 can beused in training despite its high correlation with

performance, but rather suggests that these points

can be used as valid performance markers. In

contrast to the variation in lactate threshold (using

the maximal-deviation method) with the initial

intensity, the correlation and standard error of

estimate between the lactate threshold and the

Figure 2. Plots of 10-km road-race performance versus lactate threshold estimated by the maximal-deviation method indices from the

exponential-plus-constant (left) and third-order polynomial (right) models (n 10).


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performance was little changed when the initial

points of the incremental test were excluded. This

outcome occurred mainly with the exponential

lactate threshold, for which the correlation with 10-

km road-race performance remained high. The

correlation between the polynomial lactate threshold

and road-race performance was less than that

between the exponential lactate threshold and the

10-km road-race performance. Thus, the exponential

lactate threshold can be considered a consistent and

valid performance index because it remained nearly

unchanged when the initial points were excluded.

Bishop et al. (1998) compared lactate threshold

estimations. The lactate threshold estimated by the

maximal-deviation method was the most highly

correlated with performance. The group examined

six commonly used lactate measures in trained

female cyclists. Mean power output for a 1-h cycling

challenge was 183 + 19 W, and the polynomiallactate threshold using the maximal-deviation meth-

od was 178 + 24 W. Of the six lactate measurescompared, power output at the polynomial lactate

threshold using the maximal-deviation method was

most highly correlated with the 1 h challenge

(r 0.84; P 5 0.001), followed by the lactatethreshold at 4 mmol L71 (r 0.81; P 5 0.001)and peak power output (r 0.81; P 5 0.001).Because Bishop et al. (1998) used the third-order

polynomial regression model, we believe that this

high correlation would have been even higher if they

had used the exponential-plus-constant model.

Considering that ours is the first study to examine

the relationship between equations and lactate

threshold estimations with performance, further

studies will be necessary to confirm this trend.

The standard error of estimate between the

exponential lactate threshold and the 10-km road-

race performance remained practically unchanged

when the initial points were excluded. The standard

error of estimate was substantially smaller for the

relationship between the exponential lactate thresh-

old and 10-km road-race performance than for the

polynomial lactate threshold equivalent. Once the

data are fitted to the equation to generate the least

sum-of-squares error, the third-order polynomial

equation will be adjusted to the minimum error

irrespective of the physiological meaning of the

lactate response to exercise. The exponential-plus-

constant regression equation is less influenced by the

location of the coordinate points and better describes

the physiological lactate response to exercise, as

reported by Hughson et al. (1987). Thus, because

the exponentially-derived lactate threshold produced

the smallest standard error of the estimate with 10-

km road-race performance, it is a better indicator of

endurance performance than the polynomially-de-

rived measure.

It must be emphasised that this study simulated

the influence of the initial speed of the incremental

test on the lactate threshold determined by the

maximal-deviation method by excluding the first and

the first and second points of the lactate-speed curve.

Because the initial speed influences the shape of the

lactate-speed curve and peak speed during the

incremental tests, further studies are needed to

analyse these influences on the maximal-deviation

method.

Conclusions

In summary, both the regression model and initial

intensity of the incremental test influenced the lactate

threshold determined by the maximal-deviation

method. The polynomially-derived lactate threshold

underestimated the exponentially derived equivalent.

The correlation between the exponential lactate

threshold and 10-km road-race performance was

independent of the initial intensity of the incremental

test. Additionally, the exponential lactate threshold

had a higher correlation and smaller standard error of

estimate with 10-km road-race performance than the

polynomial lactate threshold. Thus, despite the small

final sample size, which is a limitation of this study, the

exponential lactate threshold is a valid performance

index that is independent of the initial intensity of the

incremental test. It is better than the polynomial

lactate threshold for this purpose. Smaller correlations

occur when using the polynomial, irrespective of the

initial speed adopted in the incremental test. Because

this was the first study to examine the relationship

between running performance and the lactate thresh-

old determined by the maximal-deviation method

using two regression models, further studies are

required to confirm our findings in other groups of

differing standard. We anticipate that in research and

training this study will contribute to the use both of

the maximal-deviation method and the exponential-

plus-constant regression model rather than the third-

order polynomial model for the determination of the

lactate threshold by the maximal-deviation method.

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