RESEARCH ARTICLE
Oxygen uptake kinetics and speed-time
correlates of modified 3-minute all-out shuttle
running in soccer players
Mark Kramer1*, Rosa Du Randt1, Mark Watson2, Robert W. Pettitt3
1 Human Movement Science Department, Nelson Mandela University, Port Elizabeth, South Africa,
2 Psychology Department, Nelson Mandela University, Port Elizabeth, South Africa, 3 Rocky Mountain
University of Health Professions, Provo, Utah, United States of America
* mark.kramer@mandela.ac.za
Abstract
How parameters derived from oxygen uptake _VO2 kinetics relate to critical speed is not fully
understood, and how such parameters relate to more sport-specific performances, such as
shuttle running, has not been investigated. Therefore, the primary aims of the present stu-
dent were to examine the _VO2 kinetics during all-out linear and shuttle running and compare
physiological variables of all-out running to variables measured during a graded exercise
test (GXT). Fifteen male soccer players performed a graded exercise test (GXT) and the
_VO2 kinetics from a series of three different 3-min all-out tests (3MT’s) were evaluated.
_VO2max achieved during the GXT did not differ from maximal _VO2 achieved during the all-
out tests (F = 1.85, p = 0.13) (overall ICC = 0.65; typical error = 2.48 mlkg-1min-1; coefficient
of variation = 4.8%). A moderate, inverse correlation (r = -0.62, p = 0.02) was observed
between τ (14.7 ± 1.92 s) and CS (3.96 ± 0.52 ms-1) despite the narrow SD for τ. No differ-
ences (p > 0.05) were observed for any of the _VO2 kinetics between continuous and shuttle
running bouts. The linear running 3MT (r3MT) represents a viable surrogate to the GXT and
data beyond CS and D’ may be gleaned by using the bi-exponential speed-time model.
Introduction
Measurement of the oxygen uptake ( _VO2) responses to constant work exercise performed in
various intensity domains is well researched and understood [1–3], yet research where severe-
intensity exercise is performed using non-constant strategies (e.g. all-out running), has
received limited attention [4,5]. Successful performance in athletic activities is dependent on
the level of aerobic energy transfer, which in turn is governed by the magnitude and the time
course of pulmonary _VO2 and muscle O2 consumption [3]. Measurement of _VO2 kinetics can
therefore provide valuable insights pertaining to the ventilatory, cardiovascular and neuro-
muscular responses to a given exercise mode, duration and intensity [2,6,7].
The speed of the increase in the _VO2 response, represented by the primary phase time con-
stant τ and is reflective of muscle _VO2 kinetics [7], towards a steady state (or quasi steady-
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OPEN ACCESS
Citation: Kramer M, Du Randt R, Watson M, Pettitt
RW (2018) Oxygen uptake kinetics and speed-time
correlates of modified 3-minute all-out shuttle
running in soccer players. PLoS ONE 13(8):
e0201389. https://doi.org/10.1371/journal.
pone.0201389
Editor: Alessandro Moura Zagatto, Sao Paulo State
University - UNESP, BRAZIL
Received: February 20, 2018
Accepted: June 13, 2018
Published: August 21, 2018
Copyright: © 2018 Kramer et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: To enhance the
reproducibility of the results we have gladly
deposited our data in an online repository (https://
doi.org/10.7910/DVN/3JVSOH).
Funding: The authors received no specific funding
for this work.
Competing interests: The authors have declared
that no competing interests exist.
Abbreviations: _VO2, rate of pulmonary oxygen
uptake; _VCO2, rate of pulmonary carbon dioxide
state) therefore implicates the relative contribution of oxidative and non-oxidative metabolic
processes to energy transfer [6]. Greater depletion of high energy phosphates (primarily phos-
phocreatine [PCr]) and the anaerobic catabolism of glycogen to lactate is experienced when
_VO2 kinetics are slower and/or the amplitude of the _VO2 kinetics are greater [2,6,7]. Faster
_VO2 kinetic responses (i.e. smaller τ) are therefore indicative of healthy and/or fit individuals,
whereas slower responses (i.e. larger τ) are more representative of unfit or unhealthy individu-
als [7]. The extent to which the associated _VO2 kinetic parameters of male soccer players relate
to critical speed is presently not well understood. Furthermore, how such parameters relate to
more sport specific performances, such as all-out shuttle running, has not been investigated.
Modern trends in field sports, such as soccer and rugby, have shown increases in playing
intensity (i.e. time and distance spent running at speeds exceeding 21 kmhr-1), necessitating a
requisite increase in the physical fitness parameters of players [8–10]. High intensity perfor-
mance is characterized by the ability to sustain a high percentage of maximum oxygen uptake
( _VO2max), with the gas exchange threshold (GET) often being associated with an athlete’s
maximum sustainable intensity rate [7,10–12]. However, although the GET is a good predictor
of exercise performance, it is not reflective of the athlete’s competition specific intensity [13].
Alternatively, critical power (for cycling) or critical speed (for running) has emerged as a more
viable substitute and has been found to be more consistent with high-intensity exercise [7].
Knowing and understanding specific speed thresholds and the physiological responses they
elicit therefore has important performance implications.
Exercise intensities performed at speeds below the lactate threshold (LT, or gas exchange
threshold [GET]) are defined as moderate, whereby a metabolic steady state is rapidly
achieved. Heavy intensity exercise is bounded by intensities above LT, but below critical power
(CP or the maximal lactate steady state [MLSS]), resulting in elevated but stable blood lactate
levels [2,7]. In fact, CP represents the highest _VO2 at which blood lactate and _VO2 can be stabi-
lized [2]. From a _VO2 kinetics perspective, the _VO2 in the heavy intensity domain exhibits a
‘slow component’ which represents an elevated _VO2 and results in a delayed steady state of
10–15 minutes or more depending on the relative power/speed within the heavy intensity
domain. Exercise in the severe domain is constrained to intensities above CP in which
_VO2max can be elicited [14]. Within the severe domain, the slow component causes _VO2 to
rise to maximum and blood lactate levels to rise exponentially until exercise is terminated
[2,10,14].
More specifically, CP has been found to be a robust parameter representative of a fatigue
threshold, placed approximately midway between GET and _VO2max, which demarcates the
heavy from the severe intensity domains [12]. The CP concept was first proposed by Monod
and Scherrer whereby maximal work rate and the time to exhaustion of a single muscle group
exhibited a hyperbolic relationship [15]. The curvature constant of the hyperbolic relationship
(termed W’; measured in kilojoules [kJ]) represents the maximum amount of work that can be
completed at intensities above CP. This same relationship has since been extended to whole
body exercise such as cycling [16,17], swimming [18,19], rowing [20,21], running [22,23] and
even field-based sports such as soccer and rugby [24–26].
What had initially held back the broader implementation of the CP concept was the
requirement of several exhaustive bouts over several days [12]. This limitation was overcome
in 2006 whereby it was evidenced that a 3-min all-out exercise test (3MT) for cycling was
found to accurately replicate the CP and W’ values obtained using the more cumbersome pro-
tocols [27]. When running is the preferred mode of exercise, the CP term is replaced with criti-
cal speed (CS; measured in ms-1 as opposed to watts), and W’ is replaced by D’ (measured in
meters, and is indicative of the maximum distance that can be covered at speeds above CS).
O2 kinetics and all-out running
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expulsion; HRmax, maximum heart rate; BF,
breathing frequency; _VE, minute ventilation; CP,
critical power; RER, respiratory exchange ratio; CS,
critical speed; GET, gas exchange threshold;
Δ50%, midpoint between GET and _VO2max; D’,
curvature constant of the speed-time relationship
for high-intensity exercise (maximum distance
covered at speeds above CS); r3MT, 3-minute
maximal run test; TE, typical error; ICC, intra-rater
correlation coefficient; CV, coefficient of variation;
O2, oxygen; CO2, carbon dioxide.
The same 3MT protocol has since been successfully applied to running (here referred to as
r3MT to differentiate it from the cycling version) resulting in the successful derivation of CS
and D’ [22,23]. The conventional r3MT requires athletes to run all-out in a straight line (or
around a track), and has even been used to derive CS and D’ parameters for soccer and rugby
players. Sports involving shuttle running, that incorporate multiple changes of direction, may
limit the ecological validity of the r3MT, and motivates a modification of the 3MT protocol to
incorporate all-out shuttle running. To our knowledge there is presently no research whether
modifications of the r3MT protocol would modify the physiological loading of athletes as mea-
sured by the _VO2 uptake kinetics as well as other physiological measures such as heart rate
(HR), breathing frequency (BF), minute ventilation ( _V E), or the respiratory exchange ratio
(RER). No studies, to the knowledge of the present authors, have measured the _VO2 kinetics
during the r3MT or modified versions thereof.
Similarly, given the nature of the r3MT speed-time curve, a wealth of information may be
overlooked when only CS and D’ parameters are considered. Factors such as maximal speed
achieved, rate of speed decay towards CS, and time to maximal speed are simply not reported
in the literature. In part, this is due to a lack of mathematical modeling that accurately repre-
sents the instantaneous changes in speed during the r3MT. Such modeling may lead to greater
insights into physiological factors governing high intensity running performance.
Given that CS and D’ are mathematically derived parameters, the mathematical model
bears important consideration as variation in model selection will influence the parameter esti-
mates [28,29]. Although various mathematical models exist to derive both CP and W’ (or CS
and D’), none yet have attempted to model the r3MT. We introduce such a model in the pres-
ent study and compare the CS and D’ parameters derived to more traditional methods pro-
posed by Vanhatalo et al. [16] and Broxterman et al. [23].
The principal purpose of this study was therefore to characterize the _VO2 kinetics of linear
all-out running and contrast these to the _VO2 kinetics of all-out shuttle running of varying dis-
tances (i.e. 25-m and 50-m). We also distinguished the physiological parameters obtained
from all-out running to those obtained from a traditional laboratory-based GXT to determine
whether the physiological stresses imposed by the all-out tests were inherently different. Given
that the speed-time curve of linear all-out running has not been modeled before, but that such
modeling could provide important performance-related information that could be used for
intervention-based analyses, a secondary purpose of the study was therefore to determine
whether such a model could adequately characterize the speed-time curve. The model was
compared to traditional methods of analysis for deriving CS and D’, and extended to compare
the speed-time model parameters to those of the _VO2 kinetics.
Materials and methods
Ethics statement
The Research Ethics Committee for human test subjects of the Nelson Mandela University, in
accordance with the Code of Ethics of the World Medical Association (Declaration of Hel-
sinki), approved all procedures. All subjects provided written informed consent after having
the testing procedures explained both verbally and in written format.
Experimental overview
Subjects visited the testing facility on five separate occasions, with each visit separated by at
least 48 hours over a two-week period. The first visit was used to familiarize subjects with the
testing procedures prior to the start of experimentation. On the second visit subjects
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performed the incremental running test on a motorized treadmill (Woodway, USA) to deter-
mine _VO2max and GET, as well as the heart rate (HR), minute ventilation ( _V E), respiratory
exchange ratio (RER), breathing frequency (BF) and running velocities associated with these
parameters. On the third visit, after a standardized warm-up, subjects completed the r3MT on
a 400m outdoor track with a portable spirometer (Metamax 3B, Cortex Biophysik, Leipzig,
Germany), global positioning system (GPS, Cortex, Germany) and Polar H7 heart rate moni-
tor (Polar Electro Oy, FI-90440, Kempele, Finland) to determine peak values along with data
for subsequent modeling of the _VO2 kinetics. The fourth and fifth visits utilized the same
assessment set-up as that of the 3MT described previously, but the tests were modified to
incorporate all-out shuttle-like turns over 25-m or 50-m distances respectively on a designated
portion of the outdoor track to maintain the same surface kinetics. The sequence of the all-out
testing was counterbalanced to avoid an order effect.
Subjects
A total of 15 male soccer players volunteered for the study. The subjects had the following
characteristics (mean ± SD): age = 23.1 ± 3.1 years, height = 1.73 ± 0.06 m, and weight =
68.9 ± 8.6 kg. Subjects were recruited from the Nelson Mandela University first team soccer
club, were apparently healthy, had a minimum of one-year competitive playing experience,
were not taking any medications and were uninjured at the time of testing.
Procedures
Graded exercise test with verification protocol.
The system was calibrated prior to each
test using ambient air, with an assumed concentration of 20.94% O2 and 0.03% CO2, as well as
a gas of known O2 and CO2 concentrations of 15% and 5% respectively as per manufacturer’s
instructions. The turbine flowmeter was calibrated using a 3-L syringe (Metamax 3B, Cortex
Biophysik). Prior to the GXT, subjects completed a five-minute warm-up at 6–8 kmhr-1 on a
motorized treadmill (Woodway, 4Front, USA), followed by a five-minute rest period during
which subjects were encouraged to complete dynamic stretches. The ramp test began at 8
kmhr-1 at an incline of 1o and increased by 1 kmhr-1 every minute until exhaustion was
reached. Inspired and expired gas volume and concentrations were continuously sampled
breath-by-breath using an automated open circuit spirometry device (Metamax 3B, Cortex
Biophysik). Heart rate was continuously monitored throughout the test using short range
telemetry (Polar H7 HR monitor, Polar, Finland). A rating of perceived exertion (RPE), using
the original Borg scale [30], was used to monitor when athlete’s felt close to exhaustion. Strong
verbal encouragement was given throughout the test to ensure maximal effort. Once exhaus-
tion was reached, subject’s straddled the treadmill belt, upon which speed was returned to 6
kmhr-1 to allow for an active recovery period lasting 3-minutes. To determine whether a ‘true’
_VO2max was attained, a verification bout was utilized [31–34]. At the end of the 3-minute
active recovery period, the treadmill speed was increased to 2-stages below the speed reached
at the final stage of the primary _VO2max test, that is, if the test was initially terminated at 15
kmhr-1 using a 1 kmhr-1min-1 protocol, then the validation bout would be initiated at 13
kmhr-1 to validate the _VO2max value. The end-stage _VO2 reached during the verification
bout would need to be within 3% of the original bout to be deemed a ‘true’ _VO2max [33,34].
Gas exchange data were reduced to 10-second averages for the estimation of the GET using
the following criteria: (1) the first disparate increase in _VCO2 in the _VCO2 vs. _VO2 plot using
the V-slope method [35,36]; (2) an increase in _V E= _VCO2 with no increase in _V E= _VO2; and (3)
the first increase in end-tidal O2 tension with no fall in end-tidal CO2 tension. _VO2max was
O2 kinetics and all-out running
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determined using the highest _VO2 average over a 30-second period during the GXT, with vali-
dation of the ‘true’ _VO2max measured with the verification bout. Oxygen uptake, HR, _V E, BF
and speed at Δ50% were calculated from the initial GXT data as the midpoint between GET
and _VO2max data. The speed at GET (sGET), Δ50% (sΔ50%) and at _VO2max (s _VO2max)
were linearly interpolated at 1-minute preceding the sample [22]. The verification bout was
used to determine whether a ‘true’ _VO2max was reached. Only two subjects failed to be within
the 3% cut-off (3.9% and 4.1% respectively) and were subsequently asked to re-do the test
within a one-week period. On re-testing, both subjects managed to be within the requisite cut-
off and were subsequently retained for analysis.
Three-minute all-out running tests.
In the third session subjects completed the r3MT on
an outdoor 400 m tartan sprinting track with minimal wind conditions and a clear sky. After
10–15 minutes of active warm-ups and dynamic stretching, subjects were fitted with a portable
spirometer and global positioning sensor (GPS) sampling at 1 Hz (Metamax 3B, Cortex Bio-
physik) along with a chest strapped wireless HR monitor (H7, Polar, Finland). The GPS system
connects directly to the portable spirometer thereby allowing speed data collection that is con-
gruent with the breath-by-breath data. Subjects were instructed to run all-out with maximal
effort throughout the entirety of the test. Although verbal encouragement was provided
throughout the test, subjects were neither informed of the elapsed time nor time remaining to
discourage pacing. Subjects were instructed to stop once 3 minutes and 5 seconds had elapsed
to ensure full GPS coverage. The same procedures, sprinting track, equipment and principles
were applied to the modified 3MT’s (25-m and 50-m shuttle 3MT) during the fourth and fifth
sessions, each test being separated by at least 48 hours. The modified 3MT’s, unlike the con-
ventional r3MT, incorporated 180o turns over distances of 25-m or 50-m, and were therefore
deemed more “sport specific” for activities such as soccer, rugby, and hockey given that the
modified tests would require significant accelerations and decelerations for each shuttle. The
number of turns required would be inversely proportional to the distance of the shuttle, in
other words, 25-m shuttles would require more turns compared to 50m shuttles in the given
time. The modified all-out shuttle test has been validated by comparing CS and D’ against sev-
eral distance time-trials [37].
Assessment of oxygen uptake kinetics.
For each subject and each 3MT test, breath-by-
breath _VO2 data were linearly interpolated to give one value per second (averaging increment
of 1 s), which were then time aligned to the start of the test.
The oxygen uptake (O2) kinetics were modeled using a mono-exponential function [2,3,38]
expressed as:
_VO2ðtÞ ¼ _VO2ðBLÞ þ A1  ð1 where t is the time, S(t) is the speed at a given time, S0 is the y-asymptote (also defined as CS),
Ag is the growth amplitude of the exponential, Ad is the decay amplitude of the exponential, tc
is the time offset between exponential growth and decay, τg is the time constant of the expo-
nential growth term and τd is the time constant of the exponential decay term. Unconstrained
non-linear regression by least sum of squares (OriginPro 2017 [version 94E], OriginLab, USA)
was used to determine all the coefficients.
From the bi-exponential speed (S0) model, the CS is represented by the S0 term, peak speed
can be determined by summing the S0 and Ad terms, and D’ can be determined by integration
of the model at speeds above CS (see Fig 1).
Critical speed values were obtained as the average speed of the final 30-seconds for each all-
out test [22,37]. Speeds for all tests were sampled at 1Hz, allowing for comparable fidelity of
Fig 1. Bi-exponential speed-time (S0) model and parameters of the r3MT for a representative subject.
https://doi.org/10.1371/journal.pone.0201389.g001
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speed-time data for the 25m 3MT and 50m 3MT to that of Saari, et al. [37]. It is important to
note however, that greater precision of shuttle speed data should be obtained, and that the val-
ues presented should interpreted with some mindfulness.
Statistical analyses
The Statistica (version 10.1) software package was used for statistical data analysis. Data are
presented as mean ± SD unless otherwise stated. All data were assessed for normality using the
Shapiro-Wilk test, and all data were found to conform to normality. A one-way analysis of var-
iance (ANOVA) with repeated measures was used to compare maximum _VO2 values, _V E;
HRmax RER, and BF, for each test (GXT, verification bout, r3MT, 25m 3MT and 50m 3MT),
followed by a post-hoc Scheffe´ test for instances where the null-hypotheses were rejected. The
parameter estimates for the _VO2 kinetics (A, δ, and τ) for all three 3MT’s were analysed using
a one-way ANOVA, followed by post-hoc Scheffe´ testing for significant differences. Simple lin-
ear regression was used to compare parameter estimates of the _VO2 kinetics and bi-exponen-
tial speed-time models. Relative consistency between tests was assessed using the intraclass
correlation coefficient (ICC α), whereas absolute consistency was evaluated using coefficient
of variation (CV%) and typical error (TE) [39]. The fit of the S0-model to the raw data was
evaluated using the coefficient of determination (r2) and the standard error of the estimate
(SEE). Statistical significance was accepted at a level of p < 0.05.
Results
Graded exercise test
Consistent peak _VO2 values (i.e. within 3%) in the incremental and verification bouts would
provide support that a ‘true’ _VO2max was reached. Relative _VO2max values (mlkg-1min-1)
between the GXT and the verification bout did not differ significantly (t = 1.73, p = 0.11), and
were internally consistent (CV% = 1.7, TE = 0.88 mlkg-1min-1), thereby indicating the
achievement of a true _VO2max. A summary of the physiological parameters obtained from the
GXT are presented in Table 1.
Comparison in terms of graded and all-out running tests
Table 1 displays the physiological data from the GXT and all-out running performances. No
significant differences were found between absolute or relative _VO2max; _V E, or BF for all
physiological tests. Peak values for HR in the all-out tests were lower than the GXT. The RER
values were higher during the all-out tests compared to the GXT. From Table 1 above it is evi-
dent that CS derived from the r3MT was not significantly different from speed at Δ50%
(t = 0.90, p = 0.39) and there was strong internal consistency observed between the two metrics
(CV% = 6.8, TE = 0.27 ms-1).
The parameter estimates for the _VO2 uptake kinetics for each of the all-out tests are pre-
sented in Table 2 (see also Fig 2). No significant differences for any of the parameter estimates
could be detected, implying a potentially similar physiological response for each of the all-out
tests, at least from a muscle-metabolic and cardiopulmonary perspective. The averaged maxi-
mal oxygen uptake obtained for the all-out shuttle tests are presented in Fig 2A together with
the 95% confidence interval (CI) for the GXT. An example of the modeled _VO2 uptake kinetics
for the 25m 3MT is presented in panel B of Fig 2 (R2 = 0.97, representing the average goodness
of fit for all subjects).
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The r3MT speed-time (S0) model
In alignment with the methods described by Vanhatalo et al. [16] and Broxterman et al. [23]
for deriving CS from an all-out test (i.e. the average speed of the final 30-seconds of the all-out
test), the S0 parameter in the present study was compared to the average speed in the final
30-seconds of the r3MT and evaluated for absolute and relative consistency. With a TE of 0.09
ms-1, CV of 2.3%, and ICC α of 0.97, the S0 parameter derived from the S0-model is indeed
reflective of CS determined via the methods proposed by Vanhatalo et al. [16] and Broxterman
et al. [23]. The same was true for the D’ parameter, which is defined as the area under the
curve, but above CS during an all-out test. The D’ parameter would traditionally be
Table 1. Peak values of the GXT and all-out tests.
GXT
Verification
GET
Δ50%
r3MT
25m 3MT
50m 3MT
ANOVA Statistics
(F, p)
_VO2 (Lmin-1)
3.45 ± 0.29
3.42 ± 0.25
2.65 ± 0.27
3.05 ± 0.26
3.56 ± 0.35
3.71 ± 0.38
3.69 ± 0.33
F = 2.545,
p = 0.065
_VO2max
(mlkg-1min-1)
50.46 ± 3.95
49.91 ± 4.05
38.67 ± 3.89
44.57 ± 3.66
51.96 ± 4.56
53.59 ± 4.80
53.03 ± 5.17
F = 1.847,
p = 0.130
_V E (Lmin-1)
126.61 ± 16.92
127.19 ± 18.19
73.63 ± 15.88
100.12 ± 15.22
132.81 ± 15.03
138.34 ± 16.69
137.65 ± 16.90
F = 1.646,
p = 0.173
BF (breathsmin-1)
57.87 ± 15.63
59.80 ± 13.43
44.07 ± 15.93
50.97 ± 15.44
60.93 ± 10.72
61.27 ± 8.97
60.60 ± 10.13
F = 0.192,
p = 0.942
HRmax
(beatsmin-1)
189 ± 4
189 ± 5
165 ± 8
177 ± 5
183 ± 6c,d
179 ± 5a,b
182 ± 4a,b
F = 10.260,
p < 0.001
RER
1.12 ± 0.05
1.02 ± 0.04
0.94 ± 0.03
1.03 ± 0.03
1.25 ± 0.12a,c,d
1.30 ± 0.08a,b
1.30 ± 0.07a,b
F = 39.255,
p < 0.001
End-stage speed
(ms-1)
4.66 ± 0.36
4.10 ± 0.36
3.14 ± 0.32
3.90 ± 0.31a
3.96 ± 0.52a
3.10 ± 0.36
a,b,d
3.66 ± 0.45a
F = 29.928,
p < 0.001
Values are mean ± SD. GXT (graded exercise test); GET (gas exchange threshold); 3MT (3-minute all-out run test); 25-m 3MT (3-minute all-out shuttle run test over
25-m distances); 50-m 3MT (3-minute all-out shuttle run test over 50-m distances); _V_O2max (maximal rate of pulmonary oxygen uptake); _V_
E (minute ventilation); BF
(breathing frequency); HR (heart rate); RER (respiratory exchange ratio).
a significantly different from GXT
b significantly different from r3MT
c significantly different from 25m 3MT
d significantly different from 50m 3MT
 p < 0.05
 p < 0.01
 p < 0.001.
Note: verification data was not included in the all-out comparison as this data was used merely to verify the GXT data.
https://doi.org/10.1371/journal.pone.0201389.t001
Table 2. Parameter estimates for the _VO2 response for the all-out tests.
r3MT
25m 3MT
50m 3MT
ANOVA Statistics (F, df, p)
_VO2ðBLÞ (mlkg-1min-1)
14.30 ± 5.92
16.34 ± 4.77
12.57 ± 5.63
F = 1.792, p = 0.179
A (mlkg-1min-1)
37.39 ± 7.59
34.69 ± 7.01
38.15 ± 8.55
F = 0.827, p = 0.444
Asymptote (mlkg-1min-1)
51.69 ± 4.68
51.03 ± 4.70
50.72 ± 5.19
F = 0.154, p = 0.858
τ (s)
14.67 ± 1.92
17.42 ± 4.75
14.92 ± 3.38
F = 2.765, p = 0.075
δ (s)
0.54 ± 0.31
0.56 ± 0.32
0.47 ± 0.17
F = 0.439, p = 0.647
Values are mean ± SD. _VO2ðBLÞ (baseline _VO2); τ time constant of the exponential function; δ is the time delay of the exponential function.
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determined from the raw speed-time data in the absence of a mathematical model, and may
therefore capture ‘noise’ inherent in raw data [16, 23]. As such, a comparison of both methods
(i.e. the S0-model compared to raw data), yielded a TE of 12.31 m, CV of 7.2% and an ICC α of
0.93, again indicating strong agreement and consistency. The fit of the modeled speed data to
the raw speed data showed a very strong fit (r2 = 0.91 and SEE = 0.40 ms-1). This would imply,
at the very least, that the S0-model is justifiably comparable to the ‘traditional’ methods, and
may supersede these methods due to additional information gleaned from the model.
The S0-model provides a total of 6 parameters (Table 3). The CS is evidenced by the S0
term, whereas the time at which peak speed (Smax) is attained is reflected by the tc term. The
magnitude of the decay amplitude, which indicates the decline in speed from peak speed to
CS, is indicated by the Ad parameter, and the decay time constant, reflected by τ, represents
the amount of time necessary to achieve 63% of Ad. Finally, an approximation of the peak
speed attained is reflected by the Smax parameter, which consists of a summation of the S0 and
Ad terms (see Fig 1).
Fig 2. Oxygen uptake for all 3 all-out tests. Panel A: dotted grey lines represent 95% CI of _VO2max derived from the lab-based GXT; Panel B: indicates the
summarized parameter estimates of the mono-exponential equation derived for the 25m 3MT for the squad of athletes.
https://doi.org/10.1371/journal.pone.0201389.g002
Table 3. Parameter estimates for the r3MT S0-model.
Parameters
r3MT
S0 (ms-1)
3.96 ± 0.52
tc (s)
7.67 ± 2.54
Ag (ms-1)
19.13 ± 7.76
τg (s)
12.01 ± 8.83
Ad (ms-1)
5.28 ± 0.78
τd (s)
36.95 ± 12.66
Smax (ms-1)
9.24 ± 0.70
Values are mean ± SD. S0 (critical speed); tc (time delay); Ag (growth amplitude); τg (growth time constant); Ad (decay
amplitude); τd (decay time constant); Smax = (S0 +Ad) (peak speed).
https://doi.org/10.1371/journal.pone.0201389.t003
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The link between the _VO2 uptake kinetics and the S0-model is presented in Fig 3A. We
investigated a potential link between τ derived from the _VO2 uptake kinetics the CS derived
from the r3MT S0 model. The regression analysis (Fig 3B) yielded a moderate, inverse correla-
tion (Fig 3B).
Discussion
A surprising finding of the current study was the lack of a significant difference in _VO2 kinet-
ics of all three all-out tests. Whether athletes performed a continuous straight-line sprint with-
out directional changes (r3MT), or whether athletes sprinted all-out with 180o turns every
25-m or 50-m respectively, there were no appreciable differences in _VO2max; _V E, BF, or in
parameter estimates of the _VO2 kinetic responses such as _VO2ðBLÞ, A, asymptote, τ or δ
(Tables 1 and 2). Given that _VO2 kinetics are reflective of muscle metabolic processes [2,3],
this would imply that the physiological, and perhaps neuromuscular, loading of linear and
shuttle all-out running are similar. This is an important finding in that, for shuttle running,
each change of direction requires substantial braking forces followed by propulsive forces,
thereby challenging the force and endurance capacities of the leg musculature [40]. Repeated
directional changes would therefore increase the aerobic demand of the legs, with a concomi-
tantly greater level of muscle deoxygenation and fatigue development [40,41]. Conversely,
speeds during shuttle running are typically lower compared to straight line running (due to
the directional changes), which in turn would lower muscle deoxygenation and fatigue devel-
opment [40]. The present study therefore lends credence to the latter body of evidence in that
_VO2 kinetics were not significantly different (eluding to the muscle metabolic processes), and
HRmax being lower during shuttle running compared to linear running.
Also noteworthy, the _VO2max values achieved in the laboratory were consistently repro-
duced in all three field-based tests. Attainment of _VO2max during the r3MT is consistent with
existing literature [7,12], although much of this has focused almost exclusively on the cycling
3MT. A novel finding therefore lies in the attainment of _VO2max even during the all-out
Fig 3. O2 kinetics and regression analysis. (Panel A) O2 kinetics and speed-time relationship of the r3MT; (Panel B) regression analysis of the O2 kinetics time constant.
https://doi.org/10.1371/journal.pone.0201389.g003
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shuttle tests, perhaps hinting at the robustness of the 3MT methodology in taxing the requisite
bioenergetic pathways.
Within the all-out bouts, _VO2max was achieved within 90-seconds, specifically ~74 s for
the r3MT, ~87 s for the 25m 3MT, and ~75 s for the 50m 3MT, and stayed near constant for
the remainder of the tests despite exponential decay in speed that would asymptote in the
attainment of CS and a commensurate depletion of D’. These findings are congruent with
research by Vanhatalo et al. [42], whereby _VO2max was reached within ~72 s during a 3-min
all-out cycling test. The attainment, and maintenance, of _VO2max despite a commensurate
exponential decrease in running speed is indicative, in part, of a progressive loss of muscle effi-
ciency [42]. This progressive loss has been attributed to a higher phosphate cost of force gener-
ation (i.e. mechanistic basis of fatigue) rather than a greater O2 cost of oxidative of ATP
production (i.e. energy supply basis of fatigue] [42].
The rapid attainment of _VO2max during all three 3MT’s can be explained by the fact that
speeds above CS lead to substantial decreases in arterial pH, as evidenced by the high RER
achieved for all 3MT’s, evoking a dramatic increase in _V E primarily due to increases in BF,
hence increasing the O2 cost of breathing [3,4,7]. The lack of significant differences in _VO2
uptake kinetics or physiological correlates, such as _VO2max; _V E and BF, between the three
all-out tests warrants further investigation (i.e. perhaps investigating the energetics associated
with all-out running and/or a muscle-blood profile). From a neurological perspective differ-
ences between straight-line running and shuttle running exist [41–44]. All-out sprint exercise
requires maximal recruitment of available motor-units thereby requiring increased mitochon-
drial respiration; hence the increased _VO2 uptake towards maximum within 90-seconds of all-
out effort [4]. Changes in muscle phosphocreatine (PCr) concentrations, which serve as an
indicator of muscle metabolic perturbations, decrease exponentially during the first 30-sec-
onds of all-out activity, after which the rate of utilization tends to asymptote towards a pseudo
‘steady-state’ [3,4]. The muscle metabolic perturbations therefore reach very high levels during
such activities, which may in part explain the fatigue experienced during all-out running.
Although this may serve as a viable explanation for the exponential speed decrements, other
evidence is suggestive of a mechanistic fatigue basis, rather than an energy supply limitation
[42].
The CS derived from the S0-model was comparable to the laboratory-based sΔ50%, a find-
ing consistent with previous investigations using all-out cycling [16] and running [22]. When
coupled with the field-based _VO2max data, the implications of the present analyses are that
the physiological parameters derived from the r3MT were similar to those obtained from the
laboratory-based GXT, meaning that the r3MT may serve as a potential surrogate for the GXT
as a measure of aerobic fitness for athletic population groups using portable spirometry.
A potential link between the parameter estimates derived from the _VO2-kinetics and the
S0-model was also established, with a moderate, inverse relationship between τ and the CS
attained during the r3MT (Fig 3). Such a result indicates that individuals with lower time con-
stants had higher overall CS values; in other words, those who exhibited a faster time to
_VO2max could sustain a higher overall CS. The τ is representative of muscle-metabolic pro-
cesses, whereby intensity-dependent _VO2 closely mirrors the intramuscular [PCr] kinetics in
an inverse relationship (i.e. dramatic decreases in [PCr] and other metabolites drive the respi-
ratory response), with the magnitude of the response being dependent on the proximity of the
intensity to CS [3,45,46]. The CS parameter attained at the end of an all-out test is reliant on
primarily peripheral fatigue related factors such as reduced [PCr], elevated [Pi] and reduced
pH [12,46]. It is important to note however, that at intensities above CS, additional factors
O2 kinetics and all-out running
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may contribute to fatigue (e.g. central fatigue [impaired muscle activation, efficiency]), which
could explain some of the exponential speed decay, and may account for some of the unex-
plained variance between the τ and CS parameter comparisons (i.e., the τ parameter from the
S0-model may be measuring a unique physiological characteristic) [42]. Future investigators
may wish to evaluate experimental interventions (e.g., manipulation of inspired O2, adapta-
tions to training) on the τ parameter from the S0-model.
The present study presents the first link between a parameter estimate derived from _VO2
kinetics and that derived from the S0-model, tentatively hinting at the utility of the model to
provide potentially useful insights to the underlying mechanics of the r3MT (Fig 3B). Future
research should therefore focus on probing differences in CS and D’ between the three differ-
ent versions of the r3MT, as would investigations pertaining to the energetics of turning. In
other words, do turning and turning frequencies tend to tax the body to a greater extent com-
pared to straight-line running? It is hypothesized at this stage that the peak speeds attained for
each of the three tests would be distinctive, and that the number of turns would be vastly dif-
ferent especially for the 25m 3MT compared to the 50m 3MT [47]. It is inferred therefore that
differences in speed and turn quantity may be inversely proportional which may explain the
overall similar physiological loads between tests obtained in the present study. It is acknowl-
edged that all-out running, which is non-constant, may limit the utility of spirometry to detect
the underlying physiological loads imposed on the human body. Investigating the kinetic ener-
getics of turning may therefore provide insights that differentiate all-out shuttle turning from
linear all-out running, whereas at this stage, no discernible differences between the various all-
out modalities were apparent.
Conclusions
The practical findings for the study were four-fold. Firstly, all three 3MT’s yielded _VO2max
values similar to laboratory-based assessments implying that the r3MT’s may provide a suit-
able estimate of _VO2 uptake within a three-minute time frame, as well as providing additional
parameters such as CS and D’. Secondly, no significant differences in _VO2 kinetics could be
detected using present methods implying that 25-m or 50-m all-out shuttles could provide a
useful alternative for determining _VO2 uptake kinetics within the severe-intensity domain.
Thirdly, the introduction of a bi-exponential S0-model may provide useful insights into under-
lying mechanics of the r3MT. The model may be useful in comparing the different r3MT’s
based on the notion that accurate measurements of speed can be made for the all-out shuttle
versions of the r3MT. Finally, the _VO2 time constant, or τ, is inversely related to CS, implying
that underlying fatigue mechanisms may be similar; but, further inquiry into the all-out meth-
odology is recommended.
Author Contributions
Conceptualization: Mark Kramer, Robert W. Pettitt.
Data curation: Mark Kramer.
Formal analysis: Mark Kramer, Robert W. Pettitt.
Investigation: Mark Kramer.
Methodology: Mark Kramer, Rosa Du Randt, Mark Watson, Robert W. Pettitt.
Supervision: Robert W. Pettitt.
Visualization: Mark Kramer.
O2 kinetics and all-out running
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Writing – original draft: Mark Kramer, Rosa Du Randt, Mark Watson, Robert W. Pettitt.
Writing – review & editing: Rosa Du Randt, Mark Watson.
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Oxygen uptake kinetics and speed-time correlates of modified 3-minute all-out shuttle running in soccer players.
Kramer, Mark,Du Randt, Rosa,Watson, Mark,Pettitt, Robert W