Vol.:(0123456789)
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https://doi.org/10.1007/s00421-021-04780-8
ORIGINAL ARTICLE
Steady‑state ̇VO2 above MLSS: evidence that critical speed better 
represents maximal metabolic steady state in well‑trained runners
Rebekah J. Nixon1 · Sascha H. Kranen1 · Anni Vanhatalo1 · Andrew M. Jones1 
Received: 1 May 2021 / Accepted: 26 July 2021 
© The Author(s) 2021
Abstract
The metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical 
interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous 
with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated 
their ability to discriminate speeds at which ̇VO2 was stable over time from speeds at which a steady-state ̇VO2 could not be 
established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up 
to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. 
The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). 
Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS 
(P < 0.01); however, pulmonary ̇VO2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. 
In contrast, ̇VO2 increased significantly over time and reached ̇VO2 max at end-exercise at a speed ~ 0.4 km/h above CS 
(P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of ̇VO2 at a speed exceeding MLSS suggests 
that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the 
maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary ̇VO2.
Keywords Endurance · Physiology · Oxygen uptake · Performance · Lactate · Threshold
Introduction
In a pioneering study, Whipp and Wasserman (1972) 
reported that, for a given individual, exercise at different 
constant work rates evoked distinctive response profiles 
for pulmonary  O2 uptake ( ̇VO2 ). It is now recognised that, 
following the initial cardiopulmonary and fundamental 
phases, ̇VO2 might: (1) reach a rapid (i.e. within ~ 3 min 
of the onset of exercise) steady state; (2) reach a delayed 
(within ~ 10–20 min) steady state; or (3) not attain a steady 
state at all, but rather rise with time until the ̇VO2 max is 
attained, with task failure occurring shortly thereafter (Jones 
and Poole 2005; Whipp and Ward 1992). These charac-
teristic ̇VO2 response profiles are emblematic of exercise 
intensity domains which have been termed moderate, heavy 
and severe (Carter et al. 2002; Poole et al. 1988; Pringle 
et al. 2003; Wilkerson et al. 2004). These three exercise 
intensity domains have been considered to be partitioned by 
the lactate threshold (LT) or gas exchange threshold for the 
moderate-to-heavy intensity boundary, and the critical power 
(CP) or maximal lactate steady state (MLSS) for the heavy-
to-severe intensity boundary (Jones et al. 2010; Whipp and 
Wasserman 1972).
It has been established that the neuromuscular, metabolic, 
blood acid–base and pulmonary gas exchange responses dif-
fer in the three intensity domains, resulting in differences 
in the predominant causes of fatigue and the corresponding 
limitations to exercise performance (Black et al. 2017; Burn-
ley et al. 2012; Vanhatalo et al. 2016). The heavy-to-severe 
intensity boundary is particularly important for endurance 
exercise in that it will determine whether a particular power 
output or speed is, or is not, sustainable in a metabolic steady 
state. Accurately discriminating the boundary between the 
heavy-intensity and severe-intensity exercise domains is, 
therefore, of both scientific and practical interest (Burnley 
Communicated by Philip D. Chilibeck.
 * Andrew M. Jones 
 
a.m.jones@exeter.ac.uk
1 
Sport and Health Sciences, University of Exeter, St. Luke’s 
Campus, Heavitree Road, Exeter EX12LU, UK
/ Published online: 5 August 2021
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and Jones 2018; Jones and Vanhatalo 2017; Vanhatalo et al. 
2011).
As noted above, there are two principal approaches for 
the determination of the heavy-to-severe exercise intensity 
boundary. The first of these is based upon the well-known 
hyperbolic relationship between power (or speed) and time, 
with the asymptote of this relationship representing CP (or 
critical speed, CS) and the curvature constant (W´ or D´, 
for cycling and running, respectively) representing a finite 
amount of work that can be done, or distance that can be 
covered, above the CP or CS, respectively (Hughson et al. 
1984; Monod and Scherrer 1965; Moritani et al. 1981; Poole 
et al. 1988). Exercise performed above CP results in the 
development of a pronounced ̇VO2 ‘slow component’ that 
does not level off but which eventually drives ̇VO2 to its 
maximum value; simultaneously, the intramuscular concen-
tration of phosphocreatine (PCr) falls and the intramuscular 
concentrations of inorganic phosphate and  H+ rise inexora-
bly, to reach values that are presumably limiting to muscle 
function at the limit of tolerance (Black et al. 2017; Jones 
et al. 2008; Vanhatalo et al. 2016). Muscle and blood lactate 
concentrations are elevated and also display non-steady-state 
behaviour above CP, but are elevated (compared to resting 
values) but stable over time in the heavy-intensity domain 
below CP (Black et al. 2017; Vanhatalo et al. 2016). The 
second approach to determine the heavy-to-severe intensity 
boundary is based solely upon the blood lactate responses 
to continuous exercise and the identification of MLSS, with 
the latter being defined as the highest power or speed that 
can be sustained without a greater than 1 mM increase in 
blood lactate concentration between 10 and 30 min of exer-
cise (Beneke and von Duvillard 1996; Dekerle et al. 2003; 
Pringle and Jones 2002; Smith and Jones 2001).
CP and MLSS have often been considered to represent 
the same phenomenon and the terms are frequently used 
interchangeably. However, small but statistically significant 
differences between CP and MLSS, with CP being higher, 
are frequently reported (Dekerle et al. 2003, 2005; Mattioni 
Maturana et al. 2016; Pringle and Jones 2002; Smith and 
Jones 2001) and this has led to debate and over which of 
them should be considered the ‘gold standard’ (Jones et al. 
2019a). The rationale underpinning the specific defini-
tion of MLSS (i.e. less than a 1 mM increment in blood 
[lactate] between 10 and 30 min) is obscure and the pro-
tocol from which MLSS is derived, it has been argued, is 
methodologically biased towards an underestimation of the 
‘true’ maximal metabolic steady state (Jones et al. 2019a). 
Moreover, it has been proposed that using changes in blood 
[lactate] alone as a proxy index of muscle metabolic and 
respiratory homeostasis lacks precision and that the profile 
of pulmonary ̇VO2 represents a more reasonable ‘global’ 
index of physiological conditions which are steady state 
or non-steady state (Jones et al. 2019a). Nevertheless, it is 
feasible that modification of the definition of MLSS via dif-
ferent permutations of permissible blood [lactate] increment 
and the time over which lactate accumulates might result in 
closer agreement between MLSS and CP and enable better 
approximation of CP from measurements of blood [lactate] 
derived from submaximal exercise tests.
The purpose of the present study was to investigate, in 
well-trained runners, which of CS and MLSS better repre-
sent the highest speed at which ̇VO2 can be stabilised (i.e. 
maximal metabolic steady state). We hypothesised that: (1) 
CS would be significantly higher than MLSS; (2) CS would 
more closely approximate the maximal metabolic steady 
state, as defined via the behaviour of ̇VO2 ; and (3) modify-
ing the definition of MLSS would eliminate the difference 
between CS and MLSS.
Methods
Participants
Ten well-trained, competitive male athletes (runners 
n = 7, triathletes n = 3; mean ± SD age 22.8 ± 4.8 years, 
height 1.80 ± 0.05 m, body mass 73.7 ± 5.8 kg, ̇VO2 peak 
63.0 ± 4.0 mL/kg/min) volunteered to participate in this 
study. The participants gave written informed consent and 
completed and signed a PAR-Q form as a declaration of 
their eligibility to take part in the study. Participants had no 
known medical conditions that would inhibit their ability to 
perform strenuous exercise or cause them harm while doing 
so. The study adhered to the principles of the Declaration 
of Helsinki (2013) and was approved by the University of 
Exeter Sport and Health Sciences Ethics Committee.
Experimental design and general procedures
This experiment was designed to investigate the relationship 
between running speeds at MLSS and CS and to explore 
which of MLSS and CS provided the better approxima-
tion of the maximal metabolic steady state, as defined by 
the ability to separate running speeds at which ̇VO2 can, or 
cannot, be stabilised. To this end, following an initial step 
incremental treadmill test, participants completed a series 
of constant-speed treadmill runs of up to 30-min duration 
or to the limit of tolerance for the assessment of MLSS (3–5 
runs) and CS (4–6 runs). Tests for determination of MLSS 
and CS were numbered consecutively from 1. The order of 
tests was randomised for each participant in a counterbal-
anced manner, with five participants starting with a CS test 
and the other five starting with a MLSS test. The final lab 
visit involved participants running just above their CS to the 
limit of tolerance.
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The study had a single blind, counterbalanced and ran-
domised design and included 9–12 lab visits. Participants 
were instructed to avoid strenuous exercise for 24 h before, 
and caffeine and alcohol consumption for 12 h before, lab 
visits. Testing was completed at the same time of day (± 2 h) 
for each participant to minimise any influence of circadian 
rhythm. All participants were offered a familiarisation visit. 
Testing was completed within 3–6 weeks, with 2–4 tests per 
week and at least 24 h between tests. The treadmill (Wood-
way PPS 55 Sport, Woodway GmbH, Weil am Rhein, Ger-
many) was set to 1% incline for all tests (Jones and Doust 
1996). Pulmonary gas exchange was measured during all 
tests, with participants wearing a facemask connected to a 
calibrated Jaeger Oxycon Pro breath-by-breath ergospirom-
etry system (VIASYS Healthcare GmbH, Hoechberg, Ger-
many). Heart rate (HR) was also recorded during all tests 
(Polar T31 Heart rate strap, Finland). Blood [lactate] was 
measured during the incremental test and the MLSS deter-
mination tests. Blood was collected from a fingertip using 
a single use lancet. The first drop of blood was wiped using 
a clean tissue then the blood sample was collected in a cap-
illary tube and analysed enzymatically (YSI 2500 Lactate 
Analyser, YSI, Letchworth, UK).
Before all testing sessions, participants completed a 
standardised warm up which involved running for 5 min 
at 10 km/h and the opportunity to stretch. For CS predic-
tion tests > 18 km/h, participants also completed a 30–60 s 
‘strider’ at a speed above 10 km/h but below their LT. Time 
was recorded for all tests to the nearest second. Timing 
(Traceable Timer, Fisher Scientific, Loughborough, UK) 
started as participants let go of the treadmill handrails to 
transition to the moving belt and stopped when they stepped 
to the sides of the treadmill to end the test.
Initial incremental test
On their first visit to the laboratory, the participants com-
pleted a multi-stage incremental step test to the limit of tol-
erance. The test commenced with 3 min of standing rest 
during which pulmonary gas exchange, HR and blood [lac-
tate] were measured. The treadmill test then commenced 
at a speed of 10–12 km/h, depending on the ability of the 
participant. Every 3 min, the participant stopped running by 
stepping to the side of the treadmill belt for 30 s to facili-
tate the collection of a fingertip blood sample. Speed was 
increased by 1 km/h every 3 min until the participant could 
not complete a stage or declined the opportunity to start 
a new stage. The final completed stage was defined as the 
peak speed attained. ̇VO2 peak was defined as the highest 30 s 
mean value recorded during the test. The running speeds at 
LT (i.e. the first increase in blood [lactate] above baseline 
values of ~ 1 mM) and lactate turnpoint (LTP; i.e. a sudden 
and sustained second threshold increase in blood [lactate] 
at ~ 2.5–4 mM) were determined visually from plots of blood 
[lactate] against running speed by two experienced research-
ers (Jones 2007; Jones et al. 2021).
Determination of running speed at maximal lactate 
steady state
Participants ran at a constant (but different) speed for up 
to 30 min on 3–5 occasions (3 runs for four participants, 
4 runs for five participants and 5 runs for one participant). 
Every 5 min they stopped running and stepped to the sides 
of the treadmill belt for 15 s to enable the collection of a 
fingertip blood sample. The selection of test speeds was 
informed by the speed at LTP measured in the incremental 
test. Speeds used in the tests were subsequently varied by 
0.5 km/h and were continued until there was sufficient data 
to determine MLSS, which was defined as the highest speed 
which resulted in an increase of blood [lactate] of less than 
1 mM between 10 and 30 min (Beneke and von Duvillard 
1996; Jones and Doust 1998). If the increase in blood [lac-
tate] was ± 0.05 mM above or below 1 mM (an event that 
occurred in two participants), the test was repeated and the 
mean of the blood [lactate] at each time point during the two 
tests was calculated and used in the determination of MLSS.
In addition to the conventional definition of MLSS 
outlined above, different permutations of the criteria for 
the change in blood [lactate] (i.e., < 1.0 mM, < 1.5 mM 
and < 2.0 mM) and the time window over which changes 
in blood [lactate] were measured (i.e. 5–10 min, 5–15 min, 
5–20 min, 5–25 min, 5–30 min, 10–15 min, 10–20 min, 
10–25 min, 10–30 min, 15–20 min, 15–25 min, 15–30 min, 
20–25 min and 20–30 min), were applied to provide a modi-
fied MLSS assessment.
Determination of critical speed
The participants completed constant-speed runs to the limit 
of tolerance at speeds corresponding to 90%, 95%, 100% 
and 105% of the peak speed attained in the incremental test 
such that test duration was ~ 2–15 min. Pulmonary ̇VO2 was 
monitored throughout the tests to assess whether end-test 
values exceeded 95% of the peak value determined in the 
step incremental test. Test durations longer than 15 min were 
only included in the CS determination if ̇VO2 was greater 
than 95% of the respective peak value measured in the incre-
mental test. CS was subsequently calculated from two lin-
ear regression models, the distance–time and speed–1/time 
models, and the non-linear hyperbolic speed–time model. 
The standard errors (SE) associated with the CS and Dʹ 
estimates for each model were calculated using regression 
analysis. The coefficient of variation (CoV) for each CS and 
Dʹ estimate was then calculated by expressing the SE as % 
of the parameter estimate. For a model to be accepted, the 
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coefficient of variation (CoV) for the mathematical fit had 
to be < 5% for CS and < 10% for D´. The output from the 
model with the lowest error was used in subsequent analysis 
(Black et al. 2015). If the CoV was too high after the initial 
four tests, further tests were completed until the CoV criteria 
were met. In total, five participants completed four tests, 
two participants completed five tests and three participants 
completed six tests.
Following the assessment of CS and calculation of the 
95% confidence intervals (CI) surrounding the CS estimate 
for each individual, the participants completed a final test 
just above CS (i.e.  CS+ test) in which they ran to the limit 
of tolerance at the speed representing the upper bound of 
the 95% CI. The highest running speed that was used in the 
MLSS assessment but was below the lower bound of the 
95% CI for the CS estimate for each participant was identi-
fied and defined as  CS−.
Statistical analysis
Analyses were performed using IBM SPSS Statistics 26.0 
(Chicago, IL, USA). A two-tailed paired Students t test was 
used to analyse the difference between the running speeds 
at MLSS and CS. One-way repeated measures ANOVA 
were used to assess differences between peak values of ̇VO2 
attained during the CS determination trials and the incre-
mental test, and also between the running speeds at conven-
tional MLSS, modified MLSS and CS. Two-way ANOVA 
with repeated measures across condition and time (5, 10, 
15, 20, 25 and 30 min) was used to assess differences in the 
blood [lactate] response for running speeds at MLSS and 
the speed 0.5 km/h above MLSS (termed  MLSS+). Two-
way ANOVA with repeated measures across condition and 
time (10 and 30 min < CS and 5 min and end-exercise > CS) 
was also used to assess differences in the ̇VO2 response for 
running speeds at MLSS,  MLSS+,  CS− and  CS+. When 
sphericity was violated, the significance of F-ratios was 
adjusted using the Greenhouse–Geisser procedure and sig-
nificant interaction and main effects were followed up using 
LSD post hoc tests. Linear regression analysis using Pearson 
product moment was carried out to determine the relation-
ship between CS and D´ and the relationship between the 
running speeds at conventional MLSS, modified MLSS, and 
CS. Significance was set at P < 0.05 and results are reported 
as mean ± SD.
Results
The LT and LTP occurred at 14.5 ± 1.2 and 16.8 ± 1.0 km/h, 
respectively, and the peak speed attained in the incremental 
test was 19.6 ± 1.3 km/h. The ̇VO2 peak achieved during the 
incremental test was 4.65 ± 0.47 L/min or 63.0 ± 4.0 mL/kg/
min.
The times to exhaustion (s) in the CS prediction trials 
performed at 90%, 95%, 100% and 105% of the peak speed 
attained in the incremental treadmill test were 801 ± 219, 
500 ± 146, 388 ± 112 and 185 ± 33 s. The mean ̇VO2 peak 
attained during the CS trials (4.92 ± 0.58 L/min) was not 
significantly different from the peak value achieved during 
the step incremental test (P = 0.28). The CS and D´ were 
16.4 ± 1.3 km/h and 216 ± 79 m, respectively, and the CoV 
was 0.8 ± 0.7% for CS and 7 ± 3% for D´.
Following the calculation of CS and the associated 95% 
CI, participants completed a final test to the limit of tolerance 
at a speed just (~ 2.4%) above CS (i.e. at 16.8 ± 1.3 km/h; 
 CS+). The time to the limit of tolerance at this speed was 
17.0 ± 4.6 min and there was a strong positive correlation 
with D´ (r = 0.82, P < 0.01).
Comparison of critical speed and running speed 
at maximal lactate steady state
The determination of MLSS is shown for a representa-
tive participant in Fig. 1 and the determination of CS is 
shown in Fig. 2. There was a significant difference between 
CS and conventionally determined MLSS (16.4 ± 1.3 vs 
15.2 ± 1.0 km/h, respectively; P < 0.001). Different permu-
tations of the permitted blood [lactate] increase, and the time 
window over which [lactate] increased, resulted in different 
estimates for speed at MLSS (Fig. 3). Of all of the 45 per-
mutations of blood [lactate] increment and time window that 
were considered, only the criterion of a < 2.0 mM increase in 
blood [lactate] between 10 and 20 min produced an MLSS 
value (15.9 ± 0.9 km/h) that was not significantly different 
from CS (Fig. 3).
The conventional MLSS was significantly correlated 
with modified MLSS (r = 0.80, P < 0.01) and CS (r = 0.96, 
P < 0.001) and the modified MLSS was significantly cor-
related with CS (r = 0.80, P < 0.01).
Behaviour of blood [lactate] and oxygen uptake 
in the proximity of MLSS and CS
There was a significant main effect by time (F = 13.7, 
P = 0.005) and by condition (F = 38.1, P < 0.001), and a 
significant interaction effect (F = 14.1, P < 0.001) on blood 
[lactate] across MLSS and  MLSS+ trials. Post hoc tests 
showed significant differences in blood [lactate] between 
MLSS and  MLSS+ trials at 10, 15, 20, 25 and 30 min 
(P < 0.05 for all; Fig. 4A). The change in blood [lactate] 
between 10 and 30 min was significantly greater during the 
run at  MLSS+ compared to the run at MLSS (P < 0.001; 
Fig. 4A). During the MLSS run, blood [lactate] remained 
stable (2.1 ± 1.0, 2.3 ± 0.6 and 2.6 ± 1.0 mM at 10, 20 and 
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30 min, respectively) whereas, during the  MLSS+ run, 
blood [lactate] increased with time (2.7 ± 1.0, 3.4 ± 1.2 and 
4.4 ± 1.3 mM at 10, 20 and 30 min, respectively).
There were significant main effects by time (F = 15.9, 
P = 0.003) and by condition (F = 21.5, P < 0.001), and a 
significant interaction effect (F = 4.3, P = 0.029) on ̇VO2 
for running speeds at MLSS,  MLSS+,  CS− and  CS+. Post 
hoc analysis revealed that ̇VO2 during MLSS was lower 
than in  MLSS+,  CS− and  CS+ (P = 0.001, P = 0.004 and 
P < 0.001, respectively), and ̇VO2 during  CS+ was greater 
than in MLSS,  MLSS+ and  CS− (P < 0.001, P = 0.012 and 
P < 0.001, respectively), while there was no difference 
between  MLSS+ and  CS− (P = 0.38). ̇VO2 did not change 
between 10 min and end-exercise during the runs at MLSS, 
 MLSS+ or  CS− (P = 0.10, P = 0.26, P = 0.78, respectively) 
(Fig. 4B and C). During the run at  CS+, however, ̇VO2 
increased significantly between 5 min and the limit of tol-
erance (P < 0.001; Fig. 4C). The ̇VO2 peak measured at the 
limit of tolerance in the  CS+ run (4.67 ± 0.41 L/min) was 
not significantly different from ̇VO2 peak measured in the 
step incremental test; however, the end-exercise ̇VO2 in the 
MLSS,  MLSS+ and  CS− runs were all significantly lower 
than ̇VO2 peak measured in the step incremental test (P < 0.05; 
Fig. 4B and C).
Discussion
The principal findings of the present study are that: (1) CS 
is higher than the speed at MLSS; (2) running at a speed 
0.5 km/h above MLSS (i.e.  MLSS+) results in a significant 
increase in blood [lactate] between 10 and 30 min, but no 
significant change in ̇VO2 over the same time frame; (3) run-
ning at a speed ~ 0.4 km/h above CS (i.e.  CS+), but not at a 
speed ~ 0.5 km/h below CS (i.e.  CS−), results in a significant 
increase in ̇VO2 over time with peak ̇VO2 attained at the limit 
of tolerance; and (4) in the current data set, defining the 
MLSS as a < 2 mM increment in blood [lactate] between 10 
and 20 min, as opposed to a < 1 mM increment between 10 
and 30 min as per the conventional definition, eliminates the 
difference between MLSS and CS. These findings are con-
sistent with our experimental hypotheses. We interpret the 
results to indicate that, while MLSS differentiates running 
speeds for which the blood [lactate] response is steady state 
vs. non-steady state, it underestimates the maximal meta-
bolic steady state as represented by the ability, or inability, to 
stabilise ̇VO2 during exercise. In contrast, running at a speed 
just above, but not just below, CS results in a rising ̇VO2 
profile until the limit of tolerance is reached, indicating that 
CS provides a more appropriate representation of maximal 
metabolic steady state.
Consistent with our hypothesis, CS was significantly 
higher than the speed at MLSS. This finding is in agreement 
with several other studies which have found CS or CP to be 
higher than MLSS, both for running and cycling (Dekerle 
et al. 2003, 2005; Mattioni Maturana et al. 2016; Pringle 
and Jones 2002). In the present study, CS was ~ 8% higher 
than MLSS, which is broadly consistent with previous com-
parisons: for example, 4% in Smith and Jones (2001), 9% in 
Pringle and Jones (2002), 16% in Dekerke et al. (2003), 5% 
in Dekerke et al. (2005) and 1% in Keir et al (2015). While 
differences in experimental protocol including the number 
and duration of prediction trials, the sensitivity of MLSS 
determination (which is a function of the power or speed 
increments between trials), and the mathematical models 
used to calculate CP or CS may explain some of the discrep-
ancy (Bishop et al. 1998; Black et al. 2015; Mattioni Matu-
rana et al. 2018), it is now clear that while CP and MLSS 
Fig. 1  Maximal lactate steady-
state (MLSS) assessment in a 
representative individual. MLSS 
was identified as the highest 
speed where the increase in 
blood [lactate] did not exceed 
1 mM between 10 and 30 min
0
5
10
15
20
25
30
0.0
0.5
1.0
1.5
2.0
2.5
15.0 km/h
15.5 km/h 
16.0 km/h
Time (min)
Blood [lactate] (mmol/L)
MLSS
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have historically been considered to represent broadly the 
same phenomenon, there is limited agreement in practice.
The tendency for CP to be higher than MLSS has led to 
the interpretation that CP overestimates the maximal meta-
bolic steady state, with the assumption that MLSS represents 
the ‘gold standard’ and that a blood [lactate] steady state 
reflects a ̇VO2 steady state (e.g. Iannetta et al. 2018; Pringle 
and Jones 2002). However, the physiological rationale for 
the accepted definition of MLSS (i.e. the highest power or 
speed at which blood [lactate] does not increase by more 
than 1 mM between 10 and 30 min of exercise, equivalent to 
a 0.05 mM increment in blood [lactate] per min) is obscure 
and apparently arbitrary (Jones et al. 2019a). It has been 
pointed out that reliance on blood [lactate] alone as a proxy 
for the existence of muscle metabolic and systemic homeo-
stasis is hazardous; that absolute blood [lactate] is influenced 
by exercise-induced haemoconcentration and modifications 
to substrate metabolism (Tanaka 1991); and that human, 
technical and instrument error in the collection and analy-
sis of capillary blood samples for [lactate] (Morton et al. 
2012; Tanner et al. 2010) at just two discrete time points 
(10 and 30 min), along with poor day-to-day reproducibility 
Fig. 2  Pulmonary ̇VO2 responses to four severe-intensity prediction 
trials at speeds ranging from 17.0 to 21.0 km/h (Panel A), and the 
critical speed (CS) and D´ estimation in a representative participant 
using distance–time (Panel B), speed–1/time (Panel C) and speed–
time models (Panel D). The model with the lowest sum of coefficients 
of variation (CoV) for CS and D´ for each participant was selected 
for analysis. The dashed line indicates the ̇VO2 peak measured in the 
initial step incremental test in panel A, and the speed-asymptote (CS) 
in panel D 
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of [lactate] during MLSS assessment (Hauser et al. 2013), 
could result in either false positives or false negatives (Jones 
et al. 2019a). Moreover, the use of discrete powers or speeds 
in the MLSS assessment procedure will inevitably result in 
an underestimation of the actual maximal metabolic steady 
state (Jones et al. 2019a), the extent of which will depend 
on the sensitivity of the measurements, with tests typically 
differing by 20–30 W for cycling and 0.5 or 1.0 km/h for 
running.
Methodological strengths of the present study included 
that: at least three (and frequently 4 or 5) 30-min trials 
were used in the assessment of MLSS; the trials were 
separated by relatively small (0.5 km/h) running speed 
increments; and, where the increase in blood [lactate] 
was within 0.05 mM of meeting the criterion of a 1 mM 
increase (an event that occurred in two participants), the 
test was repeated and the mean response was used in 
subsequent analysis. These elements of the study design 
provide a high level of confidence in the precision of 
MLSS determination. An important finding in the pre-
sent study was that, while MLSS partitioned a running 
speed at which blood [lactate] did not change between 10 
and 30 min from a running speed at which blood [lactate] 
increased significantly over the same time frame, it did not 
separate steady state from non-steady-state ̇VO2 responses. 
Specifically, at the speed immediately (0.5 km/h) above 
that which was identified as representing MLSS, ̇VO2 did 
not change significantly between 10 and 30 min. Other 
recent studies also indicate that MLSS does not reflect the 
maximum power or speed at which ̇VO2 can be stabilised. 
For example, Bräuer and Smekal (2020) measured MLSS 
from 4 to 6 30-min cycle exercise tests in 45 participants 
and reported stable ̇VO2 over the last 10 min of exercise at 
both MLSS and at a power output above MLSS. Similarly, 
Iannetta et al (2018) found that when participants cycled at 
10 W above the power output established as representing 
MLSS, a ̇VO2 steady state was manifest. Such results are 
insightful because it is known that, in the steady state, pul-
monary ̇VO2 closely reflects skeletal muscle ̇VO2 (Grassi 
et al. 1996; Krustrup et al. 2009). Moreover, pulmonary 
̇VO2 and intramuscular [PCr] profiles are closely related 
both when steady states can be attained and when slow 
components in the responses are manifest (Rossiter et al. 
2002). Collectively, these findings indicate that MLSS, 
as conventionally defined, does not represent the maxi-
mal metabolic steady state, which is more appropriately 
defined in relation to the ability to stabilise pulmonary ̇VO2 
and thus skeletal muscle ̇VO2 and [PCr] (Grassi et al. 1996; 
Rossiter et al. 2002).
In contrast, when the athletes in the present study ran 
at a speed just above CS  (CS+, 16.8 ± 1.3 km/h, calculated 
according to the 95% CI surrounding the estimate of CS), 
̇VO2 increased significantly beyond 5 min, and the end-
exercise ̇VO2 was not different from the ̇VO2 peak measured 
Speed (km/h)
10-30 min
10-20 min
15-30 min
20-30 min
10-30 min
10-20 min
15-30 min
20-30 min
10-30 min
10-20 min
15-30 min
20-30 min
>1.0 mM
>1.5 mM
>2.0 mM
*
*
*
*
*
*
*
*
*
*
*
Fig. 3  Different permutations of the maximal lactate steady state 
(MLSS) definition including < 1.0, < 1.5 and < 2.0  mM blood 
[lactate] increase, over time intervals of 10–30  min, 10–20  min, 
15–30  min and 20–30  min, and the critical speed (dashed bar). 
Note that, for clarity, not all of the MLSS permutations are shown. 
All MLSS permutations were lower than CS (*P < 0.05), except 
for the < 2.0 mM increase in blood [lactate] between 10 and 20 min 
(MLSS = 15.9 ± 0.9 km/h)
European Journal of Applied Physiology (2021) 121:3133–3144 
3139
 
1 3
Fig. 4  Panel A: blood [lactate] 
responses at the established 
maximal lactate steady state 
(MLSS, 15.2 ± 0.9 km/h) 
and at the speed immedi-
ately above MLSS  (MLSS+; 
15.7 ± 0.9 km/h). Panel B: 
pulmonary ̇VO2 responses 
during exercise at MLSS and 
 MLSS+; note that ̇VO2 did not 
change significantly between 
10 and 30 min. Panel C: ̇VO2 at 
the speeds immediately below 
CS  (CS−, 15.9 ± 0.9 km/h) 
and above CS  (CS+, 
16.8 ± 1.3 km/h). ̇VO2 did not 
change significantly between 10 
and 30 min at  CS− but increased 
between 5 min and end-exercise 
for  CS+ (P < 0.05). The dashed 
line in panels B and C indicates 
the group mean ̇VO2 peak meas-
ured in the step incremental 
test. Error bars indicate standard 
deviations. *End-exercise ̇VO2 
significantly different from 
̇VO2 peak measured in the step 
incremental test (P < 0.05)
European Journal of Applied Physiology (2021) 121:3133–3144 
3140
 
1 3
in the maximal incremental test. When the highest speed 
below CS the athletes ran at  (CS−, 15.9 ± 0.9 km/h) was 
considered, ̇VO2 was not significantly different between 10 
and 30 min. Therefore, when the athletes ran at a speed 
that was ~ 6 s per km slower than CS, ̇VO2 was in steady 
state and the prescribed 30 min of exercise was completed, 
whereas when the athletes ran at a speed that was ~ 5 s 
per km faster than CS, a ̇VO2 steady state could not be 
achieved and exercise tolerance was limited to ~ 17 min, 
indicative of exercise within the severe-intensity domain 
(Black et al. 2017; Poole et al. 1988).
These data indicate that CS provides a rather precise 
demarcation of the highest running speed at which ̇VO2 can 
be stabilised. This observation is consistent with several pre-
vious studies which indicate that CP or CS is the metabolic 
threshold which partitions severe-intensity exercise, which, 
by definition, is characterised by an inexorable increase in 
̇VO2 to its peak value at the limit of tolerance, from heavy-
intensity exercise, during which a ̇VO2 steady state can still 
be achieved (Jones et al. 2010; Poole et al. 2016; Whipp 
1994). It has been established from muscle biopsy studies 
that these characteristic ̇VO2 profiles during exercise per-
formed above and below CP are associated with correspond-
ing steady-state or non-steady-state responses in skeletal 
muscle PCr and lactate concentrations (Black et al. 2017; 
Vanhatalo et al. 2016). These findings are reinforced by non-
invasive 31P-magnetic resonance spectroscopy assessment of 
the skeletal muscle metabolic responses, which demonstrate 
striking differences in the profiles of PCr, inorganic phos-
phate and pH for exercise performed just above, compared 
to just below, CP (Jones et al. 2008). These differences in 
the rates of substrate utilisation and metabolite accumula-
tion likely underpin observations that the rate and nature 
of neuromuscular fatigue development also differ according 
to the intensity of the exercise task relative to CP (Black 
et al. 2017; Burnley et al. 2012; Dinyer et al. 2020; Pethick 
et al. 2020). Finally, it is pertinent to note that simultaneous 
assessment of the responses of muscle [lactate] and blood 
[lactate] during heavy-intensity and severe-intensity exercise 
reveal that the former may be stable while the latter rises 
(Jones et al. 2019b), suggesting differences in the dynamics 
of lactate accumulation in the muscle and blood compart-
ments. These observations clearly indicate that a maximum 
blood [lactate] steady state will likely underestimate the 
maximal metabolic steady state as determined by muscle 
[lactate], as well as the responses of other muscle ions and 
metabolites, and ̇VO2.
The evaluation of CP or CS is not without its challenges, 
ideally requiring 3–5 maximal efforts on separate days, 
although this burden can be alleviated in athletes through 
the use of recent training or competition data (Jones and 
Vanhatalo 2017; Karsten et al. 2015; Smyth and Muniz-
Pumares 2020). In some situations, estimating CP or CS 
from submaximal exercise tests may be considered prefer-
able to direct assessment. While it is clear from both the 
present study and from earlier studies that the conventional 
protocol and criteria for MLSS assessment underestimates 
the maximal metabolic steady state, it is possible that adjust-
ments to these factors might enable a closer approximation 
of CP or CS. In the present study, we calculated the running 
speed at MLSS using a variety of permutations of absolute 
increments in blood [lactate] (e.g. 1.0, 1.5 and 2.0 mM) and 
the time frame over which such increments were consid-
ered. Of these permutations, we found that modifying the 
criteria to a 2 mM increment in blood [lactate] between 
10 and 20 min increased the group mean running speed at 
MLSS from 15.2 to 15.9 km/h and eliminated the difference 
between MLSS and CS. This approach does not, however, 
circumvent other limitations to relying solely on measure-
ments of blood [lactate] for the assessment of the maximal 
metabolic steady state and might be considered to be just 
as obscure and arbitrary as the conventional definition of 
MLSS. At the present time, therefore, we favour direct 
assessment of CP or CS if precision is required in scientific 
studies or for training prescription.
By definition, exercise in the severe-intensity domain 
should result in the attainment of ̇VO2 peak at or shortly before 
the limit of tolerance is reached (Hill et al. 2002; Jones et al. 
2010; Poole et al. 1988; Whipp 1994). It should be appreci-
ated, however, that CP and CS are estimated mathematically 
from several prediction trials and there will inevitably be 
some error, both computational and biological (e.g. day-
to-day variability), surrounding the estimates (Black et al. 
2015; Mattioni Maturana et al. 2018). For this reason, asking 
participants to exercise to the limit of tolerance exactly at the 
computed CP or CS can result in wide variability in both the 
physiological responses and the time to the limit of tolerance 
due to some participants being below and others being above 
the CP or CS (Pethick et al. 2020; see Jones et al. 2019a 
for review). Indeed, the notion of exercising at the CP (or 
CS) is vacuous because the asymptote of the power–time 
relationship represents the power that lies exactly between 
those powers at which W´ is utilised and those powers at 
which it is not; that is, it defines the threshold separating the 
heavy-intensity and severe-intensity domains and the inher-
ent steady-state or non-steady-state physiological behaviour 
that defines those domains; and therefore, it is erroneous 
to define CP as the highest power at which steady-state 
responses are observed. In the present study, we employed 
several approaches to minimise the error surrounding the CS 
estimate including: having the athletes complete at least 4 
and up to 6 prediction trials; ensuring that the athletes ran to 
the limit of tolerance during all prediction trials, as validated 
by there being no significant difference in ̇VO2 peak achieved 
in the prediction trials compared to the maximal incremental 
test; and applying all three standard mathematical models 
European Journal of Applied Physiology (2021) 121:3133–3144 
3141
 
1 3
and choosing the output from the model with the least error 
for each individual (Black et al. 2015). Together, these 
approaches resulted in CoV that were appreciably lower for 
both CS (0.8 ± 0.7%) and D´ (7 ± 3%) than the degree of 
error which has been suggested to be acceptable (< 5% for 
CS and < 10% for D´; Hill 1993).
The experimental procedures employed in the present 
study also ensured that the 95% CI surrounding CS were 
relatively narrow (i.e. group mean of ± 0.4 km/h). Our study 
participants, therefore, ran very close to, but very slightly 
above, their CS to the limit of tolerance as a validation that 
CS represents the heavy-to-severe exercise intensity bound-
ary. It should be acknowledged that, while the group mean 
CS was estimated to be 16.4 km/h, when the 95% CI is taken 
into account, the ‘actual’ CS could have occurred anywhere 
between 16.0 and 16.7 km/h. We took appropriate measures 
to minimise errors arising from biological factors and math-
ematical modelling, but it is important to note that it is not 
possible to entirely eliminate the error margin surrounding 
any physiological threshold estimate (Pethick et al. 2020). It 
should also be appreciated that this range of speeds within 
which the CS resides represents an error of only ± 4–5 s per 
km (~ 2%).
The time to the limit of tolerance at  CS+ (17.0 ± 4.6 min) 
was closely correlated with the athletes’ D´ (r = 0.82). This 
indicates that when an exercise task is relativized to ath-
letes’ CS values, then the energetic reserve or work capacity 
above CS becomes an important factor determining exercise 
tolerance. Within the limitations of the present study (i.e. 
the error margin surrounding the estimation of CS), these 
results also reveal that the longest an athlete can run at a con-
stant speed and still attain ̇VO2 peak is approximately 17 min. 
Therefore, assuming an even pace is employed throughout 
the race to minimise the time taken to complete the distance 
(Fukuba and Whipp, 1999), it appears likely that athletes 
will attain ̇VO2 peak during a 5000 m race (since this will 
be at the lower end of the severe-intensity domain) but not 
during a 10,000 m race (which is positioned at the upper end 
of the heavy-intensity domain). These results highlight an 
important conceptual issue: it is inappropriate to consider 
peri-CS (or CP) exercise to be ‘fatigueless’, or to be sustain-
able indefinitely or for some arbitrary time period such as 
60 min; indeed, this might be considered a misinterpreta-
tion of the original descriptions of the concept (Monod and 
Scherrer 1965). Rather, contemporary understanding is (or, 
at least, in our view, should be) that CS separates exercise 
domains within which: (1) physiological (including muscle 
metabolic and cardiorespiratory) responses are differenti-
ated by steady-state vs. non-steady-state behaviour; and (2) 
the predominant determinants of fatigue are altered, with 
exercise tolerance > CS being predictable as a function of 
CS and D´.
In conclusion, this study affirms that CS occurs at a 
higher speed than MLSS in well-trained runners. An impor-
tant novel finding was that a ̇VO2 steady state was elicited 
when the athletes ran at a speed which was above MLSS but 
below CS, whereas a ̇VO2 steady state could not be attained 
when they ran at a speed which was just above CS. These 
results indicate that CS, rather than MLSS, provides a better 
representation of the maximal metabolic steady state.
Author contributions AMJ conceived and designed the research. RJN 
and SHK conducted the experiments. RJN and AV analysed the data. 
RJN and AMJ wrote the manuscript. All the authors read and approved 
the manuscript.
Declarations 
Conflict of interests The authors have no conflicts of interest to de-
clare.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long 
as you give appropriate credit to the original author(s) and the source, 
provide a link to the Creative Commons licence, and indicate if changes 
were made. The images or other third party material in this article are 
included in the article’s Creative Commons licence, unless indicated 
otherwise in a credit line to the material. If material is not included in 
the article’s Creative Commons licence and your intended use is not 
permitted by statutory regulation or exceeds the permitted use, you will 
need to obtain permission directly from the copyright holder. To view a 
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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Steady-state [Formula: see text] above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners.
Nixon, Rebekah J,Kranen, Sascha H,Vanhatalo, Anni,Jones, Andrew M