Citation: van Rassel, C.R.; Ajayi,
O.O.; Sales, K.M.; Grifﬁths, J.K.;
Fletcher, J.R.; Edwards, W.B.;
MacInnis, M.J. Is Running Power a
Useful Metric? Quantifying Training
Intensity and Aerobic Fitness Using
Stryd Running Power Near the
Maximal Lactate Steady State. Sensors
2023, 23, 8729. https://doi.org/
10.3390/s23218729
Academic Editors: Manuel E.
Hernandez, Yih-Kuen Jan, Chi-Wen
Lung and Ben-Yi Liau
Received: 27 September 2023
Revised: 20 October 2023
Accepted: 23 October 2023
Published: 26 October 2023
Copyright:
© 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed
under
the
terms
and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sensors
Article
Is Running Power a Useful Metric? Quantifying Training
Intensity and Aerobic Fitness Using Stryd Running Power Near
the Maximal Lactate Steady State
Cody R. van Rassel 1
, Oluwatimilehin O. Ajayi 1, Kate M. Sales 1, James K. Grifﬁths 1, Jared R. Fletcher 2
,
W. Brent Edwards 1 and Martin J. MacInnis 1,*
1
Faculty of Kinesiology, University of Calgary, Calgary, AB T2N 1N4, Canada; crvanras@ucalgary.ca (C.R.v.R.)
2
Department of Health and Physical Education, Mount Royal University, Calgary, AB T3E 6K6, Canada
*
Correspondence: martin.macinnis@ucalgary.ca
Abstract: We sought to determine the utility of Stryd, a commercially available inertial measure-
ment unit, to quantify running intensity and aerobic ﬁtness. Fifteen (eight male, seven female)
runners (age = 30.2 [4.3] years;
·
VO2max = 54.5 [6.5] mL·kg−1·min−1) performed moderate- and
heavy-intensity step transitions, an incremental exercise test, and constant-speed running trials to
establish the maximal lactate steady state (MLSS). Stryd running power stability, sensitivity, and
reliability were evaluated near the MLSS. Stryd running power was also compared to running speed,
·
VO2, and metabolic power measures to estimate running mechanical efﬁciency (EFF) and to deter-
mine the efﬁcacy of using Stryd to delineate exercise intensities, quantify aerobic ﬁtness, and estimate
running economy (RE). Stryd running power was strongly associated with
·
VO2 (R2 = 0.84; p < 0.001)
and running speed at the MLSS (R2 = 0.91; p < 0.001). Stryd running power measures were strongly
correlated with RE at the MLSS when combined with metabolic data (R2 = 0.79; p < 0.001) but not in
isolation from the metabolic data (R2 = 0.08; p = 0.313). Measures of running EFF near the MLSS were
not different across intensities (~21%; p > 0.05). In conclusion, although Stryd could not quantify
RE in isolation, it provided a stable, sensitive, and reliable metric that can estimate aerobic ﬁtness,
delineate exercise intensities, and approximate the metabolic requirements of running near the MLSS.
Keywords: wearable technology; running economy; critical intensity; human performance; inertial
measurement unit; treadmill
1. Introduction
A consensus regarding an approach to evaluate mechanical running power output
(PO) is lacking, resulting in a range of PO values for a given running speed, depending on
the method [1,2]. During level running, the working muscles transfer energy to produce
and absorb the forces needed to move body segments. As a result, there is no dissipative
load external to the body that can be measured to quantify mechanical PO. Instead, running
mechanical PO measurements may be derived from “external” or “internal” work per-
spectives by evaluating the centre of mass (CoM) or the body segments, respectively [1–3].
Such approaches require sophisticated laboratory assessments of joint kinetics and/or kine-
matics based on ground reaction force and motion-capture data. Several methodological
challenges also limit the utility of running mechanical PO to approximate the metabolic
work rate [1,3], and, in contrast to cycling, where there is a strong relationship between
mechanical and metabolic PO [4,5], many factors complicate the relationship between me-
chanical and metabolic PO when running [6–8]. Nevertheless, a wearable running device
that can quantify and monitor training intensity, analogous to a cycling power meter [9,10],
would be useful to guide training and maximize running performance.
Sensors 2023, 23, 8729. https://doi.org/10.3390/s23218729
https://www.mdpi.com/journal/sensors
Sensors 2023, 23, 8729
2 of 19
Several consumer technologies providing a running power metric have been devel-
oped [11,12]. These technologies derive a measurement of mechanical PO using estimates
of ground reaction forces, CoM velocity, and/or vertical displacement from global position-
ing system (GPS) and/or inertial measurement unit (IMU) sensor data [11–13]. Previously,
the Stryd running power device (a portable IMU), has provided the closest relationship
with
·
VO2 when compared to other available commercial devices [11]. Possibly by gen-
erating a running power metric based on estimates of horizontal velocity and vertical
displacement using acceleration data, it is purported that Stryd power can be used as a
proxy for metabolic PO, despite changes in external conditions such as air resistance or
gradient [13]. Thus, Stryd running power can theoretically quantify training intensity
in a manner analogous to cycling mechanical PO and could be superior to conventional
measurement approaches using running speed. Despite evidence of repeatability [11],
reliability [14,15], stability during prolonged running [16], and strong linear correlations
with running speed [17,18], limited research has investigated the Stryd running metric
at stable metabolic work rates relative to exercising thresholds. Thus, to determine the
utility of Stryd power to indicate relative exercise intensity and assess running ﬁtness and
performance, the relationship between Stryd mechanical power and metabolic power needs
to be established using an exercise intensity domain training approach (i.e., evaluating
running power metrics during steady-state exercise relative to the gas exchange threshold
(GET) and maximal metabolic steady state (MMSS)).
Prior to determining whether Stryd running power can monitor training, like cycling
power output, in uncontrolled environments (e.g., variable inclines, wind speeds, and
surfaces), the primary purpose of the present study was to evaluate the Stryd power metric
in a controlled environment (i.e., in situ). Using an exercise intensity domain approach,
we assessed the stability, sensitivity, and reliability of Stryd at stable metabolic work rates
to (i) determine the efﬁcacy of Stryd running power as a training intensity and running
performance metric, (ii) explore the relationship between running power and running
economy (RE), (iii) estimate mechanical efﬁciency during constant-speed treadmill running,
and (iv) contrast steady-state measurements with measurements derived from incremental
exercise. We hypothesized that Stryd running power would be repeatable across two visits,
stable during a 30-min run, and sensitive to running speeds near the maximal lactate steady
state (MLSS)—a proxy measure of the MMSS. In addition, we hypothesized that Stryd
power would be strongly associated with running speed,
·
VO2, and RE measurements,
thereby providing a tool to guide exercise training and assess running ﬁtness.
2. Materials and Methods
2.1. Participants
Fifteen (8 male; 7 female) recreationally active or trained/developmental runners [19]
(mean [SD]; age = 30.2 [4.3] years; body mass = 68.8 [8.2] kg; height = 173.2 [8.4] cm;
·
VO2max, 54.5 [6.5] mL·kg−1·min−1) were recruited using convenience sampling. Partic-
ipants were included if they were healthy, uninjured, and between 18 and 45 years of
age, with recent 10-km performances of ≤50 min and ≤55 min for males and females,
respectively. Within the 3 months prior to testing, runners reported exercising an average
of 3.5 [1.4] days per week, running an average of 27.7 [17.1] km each week, and having
10-km best performance times of 44.6 [6.5] min. Written informed consent was provided by
the runners to participate in the experimental procedures, which were approved by the
University of Calgary Conjoint Health Research Ethics Board (REB20-0111) and conducted
in accordance with the declaration of Helsinki, except for pre-trial registration. Participants
had the option to cease participation at any time during the experimental procedures. Prior
to test administration, runners completed the physical activity readiness questionnaire
(PAR-Q+) to identify contraindications to exercise testing and to ensure that participants
were free of medical conditions and injuries that could interfere with metabolic and car-
Sensors 2023, 23, 8729
3 of 19
diorespiratory exercise responses. All runners provided their own lightweight running
shoes and wore the same shoes for all testing sessions.
2.2. Experimental Design
Runners visited the laboratory for ﬁve to six exercise testing sessions, with a minimum
of 48 h between visits. The exercise sessions included: (1) a “Step-Ramp-Step” (SRS) exercise
test to determine maximal exercising parameters [20]; (2) a series of 3–4 constant-speed
bouts to determine the MLSS; and (3) a repeated trial at the MLSS running speed. Runners
were asked to refrain from smoking, eating, or consuming caffeine within 2 h prior to their
testing sessions. Runners did not engage in strenuous exercise on the same day as the
testing sessions. A manuscript validating the SRS approach to identify the running speed
and Stryd running power associated with the MLSS has been published [20]; however,
despite the overlap in experimental procedures, the results presented herein are distinct.
2.3. Exercise Protocols
2.3.1. Step-Ramp-Step (SRS) Protocol
As described in detail in our previous study [20], runners performed an SRS exercise
protocol during their ﬁrst testing visit to establish their maximal exercising values and
estimate the running speed associated with the MLSS. This SRS protocol was modiﬁed for
treadmill running from a cycle ergometer-based method [21]. Of relevance to the present
study, the SRS protocol involved a moderate-intensity step-transition (MOD; 6 min at
1.9 m·s−1, 6 min at 2.4 m·s−1, and 6 min at 1.9 m·s−1); an incremental treadmill running
test (an initial speed of 1.9 m·s−1, increasing by ~0.2 m·s−1 (i.e., 0.5 mph) per min, until
volitional exhaustion); and a heavy-intensity step transition (HVY; 4 min of treadmill
running at 1.9 m·s−1, followed by 12 min of treadmill running at a speed associated with
the heavy-intensity exercise domain). The incremental treadmill test immediately preceded
the MOD step, but the participants recovered passively for 30 min between the incremental
test and the HVY step. The SRS protocol facilitated the identiﬁcation of the MLSS in
2–3 constant-speed trials [20].
2.3.2. Constant-Speed Treadmill Running—MLSS Determination
Following the initial SRS testing visit, runners completed the constant-speed exercise
sessions during 4 to 5 separate visits to the lab. These visits consisted of 5 min of treadmill
running at 1.9 m·s−1, followed by treadmill running at the predetermined testing speed.
During all constant-speed testing visits, participants were encouraged to run until volitional
exhaustion, up to a maximum duration of 45 min (excluding warm-up). Data collected
beyond 30 min were not used in this study. All runners performed their initial constant-
speed test at the running speed estimated to be the MLSS by the SRS protocol. Depending on
whether the difference between the 10- and 30-min blood lactate concentrations ([BLa]) was
≤1 mmol·L−1 or >1 mmol·L−1, the subsequent visit was performed at a treadmill speed
that was 5% faster or 5% slower, respectively. The MLSS for each runner was identiﬁed
as the highest treadmill speed whereby at least 30 min of exercise was performed and the
difference between the [Bla] at 10 and 30 min was ≤1 mmol·L−1 [22]. All participants
performed constant-speed treadmill running trials at the MLSS, 5% above the MLSS, 5%
below the MLSS, and once more at the MLSS. Data analysis was primarily based on data
collected at the 10- and 30-min (or at task failure if <30 min) time points.
2.4. Equipment and Measurements
2.4.1. Cardiorespiratory Measurements
All exercise sessions were performed on a treadmill (Desmo Pro Evo, Woodway USA
Inc., Waukesha, WI, USA) with an incline set to a 1% gradient [23]. Adjustments to treadmill
speed could be made in 0.1 mph increments (i.e., ~0.04 m·s−1); however, all running speed
data were reported in SI units (i.e., m·s−1). Ventilatory and gas exchange variables were
measured using the Quark CPET metabolic cart (COSMED, Rome, Italy), with a mixing
Sensors 2023, 23, 8729
4 of 19
chamber (COSMED), facemask (7450 Series V2, Hans-Rudolph, Shawnee, KS, USA), 2-way
non-rebreathing valve (Hans-Rudolph), and gas collection hose. The metabolic cart system
was calibrated using a 3 L syringe and gas mixture of known composition (5% CO2, 16% O2,
and N2 for the balance) prior to each testing visit. For the analysis, 10-s average ventilatory
and gas exchange data were used. Heart rates were recorded during all testing sessions
using a Polar H10 chest strap (Polar Electro Oy, Kempele, Finland).
The
·
VO2 associated with a disproportionate increase in the rate of carbon dioxide
production (
·
VCO2) and minute ventilation (
·
VE) relative to the increase in
·
VO2 was used
to identify the GET [24]. The
·
VO2 associated with a second disproportionate increase in
·
VE and a disproportionate increase in
·
VE/
·
VCO2 relative to the increase in
·
VO2 was used
to identify the respiratory compensation point (RCP) [24,25].
·
VO2max was identiﬁed as
the highest 30-s average
·
VO2 achieved during the incremental test. All incremental tests
were considered maximal, based on the observation of a
·
VO2 plateau (deﬁned as a change
in
·
VO2 of less than 150 mL·min−1, despite an increased intensity) or any of the following
criteria: maximum HR within 10 bpm of the age-predicted maximal value, a respiratory
exchange ratio (RER) greater than 1.15, or [Bla] ≥ 8 mmol·L−1 upon test completion.
2.4.2. Blood Lactate Measurements
All [Bla] data were collected using capillary blood drawn from a pinprick of the ﬁnger
and analyzed for [Bla] using the Biosen C-Line (EKF Diagnostics, Cardiff, Wales; n = 7)
or Lactate Plus (Nova Biomedical, Waltham, MA, USA; n = 8) lactate analyzer. Runners
straddled the treadmill (~60–75 s) during [Bla] measurements at 10 and 30 min (or at task
failure if <30 min).
2.4.3. Perceptual Responses
After familiarization with the scale, the rating of perceived exertion (RPE) was mea-
sured every 5 min during constant-speed running, using the Borg RPE scale (6–20) [26].
2.4.4. Running Power—Stryd
Running power measurements were made using the Stryd Summit Running Pod
(Stryd, Boulder, CO, USA). The Stryd pod, which is a lightweight (8.0 g) and unobtrusive
(4.0 cm in length) wearable sensor (Model v.19, ﬁrmware v.2.1.16, software v.4), was afﬁxed
to the runner’s left shoe, approximately equidistant between the runner’s malleoli and the
shoe’s toe. A unique Stryd user proﬁle was created for each runner that included their
respective height and body mass, which was kept constant for all testing sessions. The
iPhone Stryd application (Apple Inc., Cupertino, CA, USA) was used to pair the Stryd
device and collect the Stryd running power data during the testing sessions. Running
power data were sampled at 1 Hz (see Figure 1).
2.5. Data Analysis
2.5.1. Cardiorespiratory, Running Speed, and Stryd Running Power Data
The average
·
VO2 and running power, measured between minutes 4 and 6 of the MOD
step and between minutes 10 and 12 of the HVY step, were calculated from the SRS test.
Maximal aerobic speed (MAS) and maximal aerobic power (MAP) were determined as the
running speed associated with the highest completed 1-min stage during the incremental
test and the average running power during that stage, respectively.
Cardiorespiratory and running power data used for analysis from the constant-speed
MLSS-determination running trials included the 10- and 30-min
·
VO2,
·
VCO2, RER,
·
VE, HR,
and running power measures for running trials 5% below, at, and 5% above MLSS. To
align with the timing of [BLa] measurement (i.e., a short pause in running), mean values
Sensors 2023, 23, 8729
5 of 19
for
·
VO2,
·
VCO2, RER,
·
VE, HR, and Stryd running power were calculated from the 2 min
of data collected prior to the 10-min and the 30-min (or at task failure if <30 min) time
points. Although the MLSS is thought to represent the highest intensity at which energy
provision is supplied exclusively via oxidative metabolism [27], data collected at 5% above
the MLSS were included in the analysis due to the similarly stable
·
VO2 measurements
between the 10- and 30-min values across the three intensities (i.e., differences between
10- and 30-min
·
VO2 measures were ~50 mL·min−1 at intensities of 5% below, at, and 5%
above the MLSS)—with similar ﬁndings previously being reported [28]—and to provide a
more comprehensive dataset for the analyses.
Sensors 2023, 23, x FOR PEER REVIEW 
5 of 20 
 
 
Figure 1. Example of the running power signal during constant-speed treadmill running at diﬀerent 
intensities for one participant. Data are shown for the moderate (MOD; 6 min) and heavy (HVY; 12 
min) intensity steps, and during 30 min of running at 5% below the maximal lactate steady state 
(MLSS), at the MLSS, 5% above the MLSS, and during a repeat trial at the MLSS, preceded by run-
ning power data recorded for 3–4 min at a running speed of 1.9 m·s−1. Running power data were not 
collected during the ﬁrst ~1–2 min of each exercise protocol (i.e., warm-up) to allow for synchroni-
zation with other measurements. Note that the repeat MLSS trial is obscured by the ﬁrst MLSS trial. 
2.5. Data Analysis 
2.5.1. Cardiorespiratory, Running Speed, and Stryd Running Power Data 
The average V̇ O2 and running power, measured between minutes 4 and 6 of the MOD 
step and between minutes 10 and 12 of the HVY step, were calculated from the SRS test. 
Maximal aerobic speed (MAS) and maximal aerobic power (MAP) were determined as the 
running speed associated with the highest completed 1-min stage during the incremental 
test and the average running power during that stage, respectively.  
Cardiorespiratory and running power data used for analysis from the constant-speed 
MLSS-determination running trials included the 10- and 30-min V̇ O2, V̇ CO2, RER, V̇ E, HR, 
and running power measures for running trials 5% below, at, and 5% above MLSS. To 
align with the timing of [BLa] measurement (i.e., a short pause in running), mean values 
for V̇ O2, V̇ CO2, RER, V̇ E, HR, and Stryd running power were calculated from the 2 min of 
data collected prior to the 10-min and the 30-min (or at task failure if <30 min) time points. 
Although the MLSS is thought to represent the highest intensity at which energy provi-
sion is supplied exclusively via oxidative metabolism [27], data collected at 5% above the 
MLSS were included in the analysis due to the similarly stable V̇ O2 measurements be-
tween the 10- and 30-min values across the three intensities (i.e., diﬀerences between 10- 
and 30-min V̇ O2 measures were ~50 mL·min−1 at intensities of 5% below, at, and 5% above 
the MLSS)—with similar ﬁndings previously being reported [28]—and to provide a more 
comprehensive dataset for the analyses. 
2.5.2. Incremental and Constant-Speed V̇ O2–Power and Speed–Power Gains 
A least-squares linear regression was performed to calculate the V̇ O2–power gain 
(i.e., the slope of the regression equation) for each participant during both incremental 
and constant-speed exercise trials, measured separately. This method allowed for the cal-
l
i
f
V̇ O
i
d
d
d d
i
i
i
hi h
i
ld
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0
120
160
200
240
280
320
Time (min)
Stryd Power (W)
MOD
HVY
5% Below MLSS
At MLSS
5% Above MLSS
Repeat at MLSS
Figure 1. Example of the running power signal during constant-speed treadmill running at different
intensities for one participant. Data are shown for the moderate (MOD; 6 min) and heavy (HVY;
12 min) intensity steps, and during 30 min of running at 5% below the maximal lactate steady
state (MLSS), at the MLSS, 5% above the MLSS, and during a repeat trial at the MLSS, preceded by
running power data recorded for 3–4 min at a running speed of 1.9 m·s−1. Running power data
were not collected during the ﬁrst ~1–2 min of each exercise protocol (i.e., warm-up) to allow for
synchronization with other measurements. Note that the repeat MLSS trial is obscured by the ﬁrst
MLSS trial.
2.5.2. Incremental and Constant-Speed
·
VO2–Power and Speed–Power Gains
A least-squares linear regression was performed to calculate the
·
VO2–power gain
(i.e., the slope of the regression equation) for each participant during both incremental
and constant-speed exercise trials, measured separately. This method allowed for the
calculation of a
·
VO2–power gain mean and standard deviation in which comparisons could
be made between the incremental and constant-speed running tests and to contrast the
measurements with cycling data [29]. The “incremental
·
VO2–power gain” for each runner
was calculated as the slope ((mL·min−1)·W−1) of a least-squares linear regression line
through the incremental exercise
·
VO2–power response, from the onset of a systemic rise
in
·
VO2 until test termination or the onset of a plateau, if detected. The “constant-speed
·
VO2–power gain” for each runner was calculated as the slope ((mL·min−1)·W−1) of a least-
squares linear regression line for the steady-state
·
VO2 and power data from ﬁve constant-
speed intensities: the MOD and HVY steps from the SRS-protocol and the constant-speed
exercise trials 5% below, at, and 5% above the MLSS. Replacing
·
VO2 with running speed,
these same procedures were used to calculate the “incremental speed–power gain” and the
“constant-speed speed–power gain” for each participant.
Sensors 2023, 23, 8729
6 of 19
2.5.3. Metabolic Power, Mechanical Power, and Mechanical Efﬁciency
Running metabolic power, mechanical power, and mechanical efﬁciency measure-
ments were calculated during constant-speed running trials at MOD, HVY, 5% below, at,
and 5% above MLSS. Metabolic power was calculated as a gross energy cost per unit of
body mass and distance travelled (kJ·kg−1·km−1) using
·
VO2 and RER [30]. This calcula-
tion of metabolic power was used to represent the energy cost of running (i.e., RE) at each
respective intensity, providing a reference measure of RE in which all subsequent compar-
isons were made. Metabolic power (i.e., StrydMET) was also calculated by expressing the
energy cost—using
·
VO2 and RER [30]—per unit of absolute Stryd power ((J·s−1)·W−1)
and per unit of relative Stryd power ((kJ·s−1)·(W·kg−1)−1). StrydMET was calculated in
isolation from running speed to provide a metric that characterized the metabolic power
requirements per unit of Stryd running power. The units used to describe StrydMET were
not simpliﬁed in order to distinguish among related terms and to provide units that clearly
described the energy cost of running per unit of absolute and relative Stryd running power.
Mechanical power (i.e., StrydMECH) was calculated in isolation from the
·
VO2 and RER by
expressing Stryd running power (W) in units of J·s−1 and by converting mechanical power
to an absolute energy cost per unit of the distance travelled (kJ·km−1) and a relative energy
cost per unit of distance (kJ·kg−1·km−1). Mechanical efﬁciency (EFF) was calculated as the
ratio between StrydMECH (kJ·kg−1·km−1) and metabolic power (kJ·kg−1·km−1), expressed
as a percentage.
2.6. Statistical Analysis
2.6.1. General
Statistical analyses were performed using the Statistical Package for the Social Sciences
(SPSS, version 26, IBM, Armonk, NY, USA). Linear mixed-effects models were performed us-
ing the nlme package (version 3.1-157) in RStudio (version 4.2.0) (R Core Team (2018)). Data
visualization was performed using Prism (version 9.5.1 for macOS; GraphPad Software,
San Diego, CA, USA). Data are presented as mean [standard deviation (SD)]. Statistical sig-
niﬁcance was set at an α level of <0.05. Where appropriate, Bonferroni post hoc tests were
used. Test-retest reliability was measured using two-way mixed effects, absolute agree-
ment, and single-rater intraclass correlation models wherein reliability was interpreted
as poor (ICC < 0.5), moderate (0.5 ≤ ICC < 0.75), good (0.75 ≤ ICC < 0.9), or excellent
(ICC ≥ 0.9) [31].
2.6.2. Stability, Sensitivity, and Reliability
Multiple two-way repeated-measure ANOVAs were used to assess stability (the main
effect of duration) and sensitivity (the main effect of intensity) of Stryd running power and
the physiological and perceptual responses (i.e.,
·
VO2,
·
VCO2, RER,
·
VE, HR, [BLa], and RPE)
at 10 min and 30 min (or task failure, if <30 min) during constant-speed treadmill running
at 5% below, at, and 5% above the MLSS. For the same variables, the two MLSS trials were
compared using paired Student’s t tests, intraclass correlations, and Bland–Altman analyses
(with 95% limits of agreement) to assess reliability at the 30-min timepoint. Stryd running
power stability was further assessed by evaluating the linear association and agreement
between the 10- and 30-min running power data for the ﬁrst MLSS trial using a Pearson’s
correlation coefﬁcient and Bland–Altman analysis, respectively.
2.6.3. Stryd Running Power—Association with
·
VO2 and Running Speed
Paired Student’s t tests were used to compare the mean
·
VO2–power gains and
·
VO2–speed gains between incremental and constant-speed exercise trials. To determine
the association between Stryd running power and training intensity, linear mixed-effects
models were used to assess the within-individual and between-individual association
Sensors 2023, 23, 8729
7 of 19
between running power and
·
VO2 measurements, and between running power and running
speed during the MOD, HVY, MLSS −5%, MLSS, and MLSS +5% running trials. Models
included ﬁxed-effects models of absolute running power and relative running power while
allowing intercepts as random effects for the participants to account for repeated measure-
ments within individuals [32]. Models were estimated using maximum likelihood, model
selection was assessed using a chi-squared likelihood ratio test, and model ﬁt was assessed
using pseudo-R2 [32]. These analyses were performed for absolute (i.e., W) and relative
measures of power (i.e., W·kg−1). The spread of the participants’ intercepts was compared
using the
·
VO2 and absolute power and the
·
VO2 and relative power relationships and using
the speed and absolute power and speed and relative power relationships, employing the
Pitman–Morgan test for the homogeneity of variance of paired samples.
2.6.4. Stryd Running Power—Running Economy and Efﬁciency
To determine whether Stryd running power provides an indication of RE during
constant-speed treadmill running trials at MLSS, Pearson’s correlation coefﬁcients were
calculated between metabolic power (kJ·kg−1·km−1) and each of the following variables:
absolute StrydMECH (kJ·km−1), relative StrydMECH (kJ·kg−1·km−1), absolute StrydMET
((J·s−1)·W−1), and relative StrydMET ((kJ·s−1)·(W·kg−1)−1). One-way repeated-measures
ANOVAs were used to assess the main effect of running intensity on metabolic power,
StrydMECH, and StrydMET measurements. Using the 30-min timepoint mean (i.e., 28–30 min)
data from the two MLSS trials, the reliability of metabolic power, StrydMECH, and StrydMET
were assessed by paired Student’s t tests, intraclass correlations, and Bland–Altman analy-
ses (with 95% limits of agreement). One-way repeated-measures ANOVAs were also used
to determine whether running intensity affected Stryd-derived assessments of EFF.
2.6.5. Stryd Running Power—Aerobic Fitness
To determine whether Stryd running power provides an indication of an athlete’s
aerobic ﬁtness during constant-speed treadmill running, Pearson’s correlation coefﬁcients
were calculated for the following pairs of variables:
·
VO2 at MLSS and running power at
MLSS, and
·
VO2 at MLSS and running speed at MLSS.
3. Results
3.1. Participants
Table 1 displays the female and male participant characteristics, incremental exercise
testing results, and MLSS testing results. All incremental tests were maximal, and the
duration of the incremental test portion of the SRS protocol was 12.1 [2.0] min. The
measured
·
VO2 during constant-speed running at MOD and HVY was 91.2 [8.0]% and 92.9
[5.6]% of the
·
VO2 at GET and RCP, respectively. All runners completed at least 30 min of
treadmill running at 5% below the MLSS, at the MLSS, and during the repeat trial at the
MLSS; however, seven runners were unable to complete 30 min of running at 5% above
the MLSS.
3.2. Stability, Sensitivity, and Reliability of Stryd Running Power
The 10- and 30-min running power measurements taken during constant-speed run-
ning trials near the MLSS are presented in Figure 2. While the intensity × duration
interaction and the main effect of duration were not statistically signiﬁcant for running
power, there was a signiﬁcant main effect for running intensity, with signiﬁcant differences
between all pairs of intensities (p < 0.001 for all post hoc comparisons; Table 2).
Sensors 2023, 23, 8729
8 of 19
Table 1. Participant characteristics, maximal exercise results, and maximal lactate steady-state (MLSS)
results.
Sex (n)
Weight
(kg)
Maximal Exercising Measurements
MLSS Measurements
·
VO2max
(L·min−1)
MAS
(m·s−1)
MAP
(W)
·
VO2 at
MLSS
(L·min−1)
Speed at
MLSS
(m·s−1)
Power at
MLSS
(W)
Female (7)
65.5 [2.9]
3.37 [0.26]
4.29 [0.44]
280 [19]
2.96 [0.17]
3.29 [0.34]
224 [18]
Male (8)
71.7 [10.4]
4.10 [0.82]
4.54 [0.44]
330 [58]
3.61 [0.58]
3.43 [0.42]
254 [44]
Total (15)
68.8 [8.2]
3.76 [0.71]
4.42 [0.44]
307 [50]
3.30 [0.54]
3.35 [0.37]
240 [37]
·
VO2max, maximal oxygen uptake; MAS, maximal aerobic speed; MAP, maximal aerobic power. Data are reported
as mean [standard deviation].
Sensors 2023, 23, x FOR PEER REVIEW 
9 of 20 
 
 
Figure 2. Running power data near the maximal lactate steady state (MLSS). Panel (A) shows the 
comparison between the 10-min and 30-min mean running power measurements during treadmill 
running near the MLSS. Lines representing individual participants, asterisks (*) indicate statistically 
signiﬁcant diﬀerences between speeds, and error bars represent one standard deviation. Panel (B) 
shows the relationship between 10 min and 30 min of running power from the ﬁrst run at the MLSS, 
and Panel (C) shows the relationship between 30 min of running power from the two separate runs 
at the MLSS. Panels (D,E) show Bland–Altman plots corresponding to the data in Panels B and C, 
respectively. In Panels (B–E), squares represent individual data, solid lines represent y=0, dashed 
lines represent bias, and dotted lines represent 95% limits of agreement. n = 15 for all panels. 
5% Below
MLSS
5% Above
Repeat MLSS
0
150
200
250
300
350
Speed
Running Power (W)



10-min
30-min
175
225
275
325
175
225
275
325
10-min Running Power (W)
30-min Running Power (W)
Y = 1.01 * X − 1.57
R2 = 1.00; P < 0.001
150
200
250
300
350
-5.0
-2.5
0.0
2.5
5.0
Mean of 10-min and 30-min
Running Power at MLSS (W)
30-min - 10-min 
Running Power at MLSS (%)
LOA: −1.4 to 1.3%
Bias: 0.1% 
175
225
275
325
175
225
275
325
First MLSS Trial
Running Power (W)
Repeat MLSS Trial
Running Power (W)
Y = 1.00 * X + 0.32
R2 = 0.99; P < 0.001
B
D
C
E
A
150
200
250
300
350
-5.0
-2.5
0.0
2.5
5.0
Mean of First and Repeat Trial
Running Power at MLSS (W)
First - Repeat MLSS Trial 
Running Power  (%)
LOA: −3.4 to 2.6%
Bias: -0.4% 
Figure 2. Running power data near the maximal lactate steady state (MLSS). Panel (A) shows the compar-
ison between the 10-min and 30-min mean running power measurements during treadmill running near
the MLSS. Lines representing individual participants, asterisks (*) indicate statistically significant differ-
ences between speeds, and error bars represent one standard deviation. Panel (B) shows the relationship
Sensors 2023, 23, 8729
9 of 19
between 10 min and 30 min of running power from the ﬁrst run at the MLSS, and Panel (C) shows
the relationship between 30 min of running power from the two separate runs at the MLSS. Panels
(D,E) show Bland–Altman plots corresponding to the data in Panels (B) and (C), respectively. In
Panels (B–E), squares represent individual data, solid lines represent y=0, dashed lines represent bias,
and dotted lines represent 95% limits of agreement. n = 15 for all panels.
Table 2.
·
VO2 and running power responses to exercise near the maximal lactate steady state (MLSS).
5% below MLSS
At MLSS
5% above MLSS
ANOVA
(DxI, D, I) b
10 min
30 min
10 min
30 min
10 min
30 min a
·
VO2
(L·min−1)
3.12 [0.55] ¶
3.16 [0.56] *,¶
3.26 [0.54] †
3.30 [0.54] *,†
3.41 [0.55] †,¶
3.46 [0.57] *,†,¶
0.202, 0.001,
<0.001
Running
Power (W)
231 [35] ¶
230 [35] ¶
239 [36] †
240 [37] †
250 [38] †,¶
250 [38] †,¶
0.334, 0.528,
<0.001
DxI, duration by intensity interaction; D, duration; I, intensity;
·
VO2, oxygen uptake. a Or the ﬁnal 2 min if task
failure was < 30 min. b p-values are provided for these statistical tests. The * denotes a signiﬁcant difference from
the 10-min timepoint at the same intensity (p < 0.05); the † denotes a signiﬁcant difference from 5% below the
MLSS (p < 0.05); the ¶ denotes a signiﬁcant difference from the MLSS (p < 0.05). n = 15 for all variables. Data are
reported as mean [standard deviation].
The 10- and 30-min running power measurements during the repeat constant-speed
running trial at MLSS are reported in Table 3. There was excellent reliability and low bias
between the running power measured at two time points within one run at the MLSS and
across two runs at the MLSS, without differences between repeated trials at the MLSS
(Figure 2; Table 3).
Table 3. Reliability of
·
VO2 and running power responses and metabolic and mechanical power
measurements to exercise at the maximal lactate steady state (MLSS).
At MLSS (Repeat) a
Reliability of Repeated Runs at MLSS (30-min)
10 min
30 min
t Test b
Bias
LOA
ICC
·
VO2 (L·min−1)
3.25 [0.54]
3.26 [0.52]
0.177
0.04
−0.18 to 0.27
0.99 (0.96 to 1.00)
Running Power (W)
240 [37]
241 [37]
0.322
−1
−8 to 6
1.00 (0.99 to 1.00)
Metabolic Power (kJ·kg−1·km−1)
-
4.99 [0.29]
0.249
0.06
−0.30 to 0.42
0.91 (0.74 to 0.97)
StrydMECH (kJ·km−1)
-
71.9 [9.5]
0.324
−0.28
−2.32 to 1.77
1.00 (0.99 to 1.00)
StrydMECH (kJ·kg−1·km−1)
-
1.04 [0.03]
0.331
0
−0.04 to 0.03
0.94 (0.82 to 0.98)
StrydMET((J·s−1)·W−1)
-
4.78 [0.30]
0.153
0.07
−0.29 to 0.44
0.91 (0.73 to 0.97)
StrydMET ((kJ·s−1)·(W·kg−1)−1)
-
0.33 [0.04]
0.121
0.01
−0.02 to 0.03
0.98 (0.93 to 0.99)
LOA, limits of agreement; ICC, intraclass correlation. a See Tables 2 and 4 for data from the ﬁrst MLSS trial. Note
that metabolic and mechanical power measures are based on the 30-min time point only. b p-values are provided
for these statistical tests. Data are reported as mean [standard deviation].
Table 4. Mean metabolic and mechanical power measures during the moderate-intensity step
(MOD) and during constant-speed running 5% below, at, and 5% above the maximal lactate steady
state (MLSS).
6-min
30-min
ANOVA
(p-Value)
MOD
5% below MLSS
At MLSS
5% above MLSS
Metabolic Power (kJ·kg−1·km−1)
4.31 [0.36] *,†,¶
5.05 [0.35]
5.05 [0.36]
5.07 [0.30]
<0.001
StrydMECH (kJ·km−1)
73.8 [9.8] *,†,¶
72.3 [9.6] *,¶
71.7 [9.5]
71.1 [9.0]
<0.001
StrydMECH (kJ·kg−1·km−1)
1.07 [0.03] *,†,¶
1.05 [0.03] ¶
1.04 [0.03]
1.03 [0.03]
<0.001
StrydMET ((J·s−1)·W−1)
4.02 [0.29] *,†,¶
4.82 [0.40]
4.86 [0.34]
4.91 [0.32]
<0.001
StrydMET ((kJ·s−1)·(W·kg−1)−1)
0.28 [0.04] *,†,¶
0.33 [0.05]
0.33 [0.05]
0.34 [0.05]
<0.001
Data are based on the moderate-intensity step (MOD) from the “Step-Ramp-Step” protocol or the 30-min timepoint
of the indicated trial. * Denotes a signiﬁcant difference between the denoted intensity compared to MLSS (p < 0.05).
† Denotes a signiﬁcant difference between the denoted intensity compared to 5% below MLSS (p < 0.05). ¶ Denotes
a signiﬁcant difference between the denoted intensity compared to 5% above MLSS (p < 0.05). Data are reported
as mean [standard deviation]. n = 15 for all variables.
Sensors 2023, 23, 8729
10 of 19
3.3. Physiological and Perceptual Responses
The duration × intensity interaction was not signiﬁcant for
·
VO2; however, there was a
main effect of intensity, with signiﬁcant differences across the three running speeds and
a main effect of duration, demonstrating 30-min values greater than the 10-min values
(p < 0.05 for all post hoc comparisons; Table 2). The
·
VO2 values measured at two time
points within one run at the MLSS had excellent reliability and low bias across two runs at
the MLSS, without differences between repeated trials at the MLSS (Table 3).
Descriptive data and statistical results for
·
VCO2, RER,
·
VE, HR, [BLa], and RPE mea-
sured at two time points (10-min and 30-min) for three speeds near the MLSS are reported
in the Supplementary Materials (Table S1).
3.4. Stryd Running Power—Association with
·
VO2 and Running Speed
The incremental and constant-speed
·
VO2–power gains and speed–power gains are
reported in Table 5. From the constant-speed running trials, the linear mixed-effects models
revealed a strong, positive relationship between absolute running power and
·
VO2 and
between relative power and
·
VO2 (Table 6; Figure 3). There was signiﬁcant variance between
participant intercepts for both models that differed between models (Table 6; Figure 3),
providing evidence that the relationship between absolute power and
·
VO2 was stronger
and less variable between the participants than the relationship between relative power
and
·
VO2.
Table 5. The
·
VO2–power gain and speed–power gain calculated from the incremental exercise test
and constant-speed running trials.
Variable
Test
p-Value
Incremental
Constant-Speed
Absolute
·
VO2–power gain ((mL·min−1)·W−1)
11.6 [1.5]
19.8 [3.5]
<0.001
Relative
·
VO2–power gain ((mL·min−1)·(W·kg−1) −1)
810.9 [148.9]
1364.2 [298.7]
<0.001
Absolute speed–power gain ((m·s−1)·W−1)
0.015 [0.002]
0.015 [0.002]
0.365
Relative speed–power gain ((m·s−1)·(W·kg−1) −1)
1.05 [0.08]
1.03 [0.07]
0.333
Data are reported as mean [standard deviation]. N = 15 for all variables.
Table 6. The within-individual and between-individual association between running power and
·
VO2
measurements and between running power and running speed during the MOD, HVY, maximal
lactate steady state (MLSS) −5%, MLSS, and MLSS +5% running trials.
Variable
b
[95% CI]
Statistics
SD
[95% CI]
χ2 Statistics
Pitman–Morgan
Test
Absolute running
power and
·
VO2
18.2 [17.1, 19.3]
t(59) = 32.7; p < 0.001;
R2 = 0.97
196.9
[130.7, 296.8]
χ2(4) = −494.8;
p < 0.001
t(13) = −3.08;
p = 0.009
Relative running
power and
·
VO2
1246.3
[1150.2, 1342.4]
t(59) = 25.6; p < 0.001;
R2 = 0.95
414.0
[285.9, 599.6]
χ2(4) = 92.3;
p < 0.001
Absolute running
power and speed
0.015 [0.014, 0.015]
t(59) = 37.9; p < 0.001;
R2 = 0.97
0.414
[0.288, 0.596]
χ2(4) = 125.8;
p < 0.001
t(13) = 15.72;
p = 0.002
Relative running
power and speed
1.01 [0.96, 1.06]
t(59) = 42.7; p < 0.001;
R2 = 0.97
0.063
[0.039, 0.104]
χ2 (4) = 12.7;
p < 0.001
b denotes the calculated slope from the linear mixed-effects model. The units of the slope are (mL·min−1)·W−1
and (mL·min−1)·W−1 for absolute and relative running power and
·
VO2, respectively, and (m·s−1)·W−1 and
(m·s−1)·(W·kg−1)−1 for absolute and relative running power and speed, respectively. SD denotes the standard
deviation, which is presented in units of mL·min−1 and m·s−1 for
·
VO2 and speed variables, respectively.
Sensors 2023, 23, 8729
11 of 19
 
Variable 
p-Value 
Incremental 
Constant-Speed 
Absolute V̇ O2–power gain ((mL·min−1)·W−1) 
11.6 [1.5] 
19.8 [3.5] 
<0.001 
Relative V̇ O2–power gain ((mL·min−1)·(W·kg−1) −1) 
810.9 [148.9] 
1364.2 [298.7] 
<0.001 
Absolute speed–power gain ((m·s−1)·W−1) 
0.015 [0.002] 
0.015 [0.002] 
0.365 
Relative speed–power gain ((m·s−1)·(W·kg−1) −1) 
1.05 [0.08] 
1.03 [0.07] 
0.333 
Data are reported as mean [standard deviation]. N = 15 for all variables. 
 
Figure 3. Relationships between absolute and relative running power, running speed, and oxygen 
uptake (V̇ O2). Panels (A,B) show the relationships between absolute running power and V̇ O2 and 
between absolute running power and running speed for each participant during the moderate 
(MOD) and heavy (HVY) intensity steps and constant-speed trials near the maximal lactate steady 
state (MLSS). Panels (C,D) show the relationships between relative running power and V̇ O2 and 
between relative running power and running speed for each participant at each running intensity, 
respectively. Each color represents a single participants set of trials. N = 15 for all panels. 
3.5. Stryd Running Power—Association with Running Economy 
Based on the constant-speed running trials at MOD and near the MLSS, there were 
signiﬁcant eﬀects of intensity on metabolic power, StrydMECH, and StrydMET measurements 
(Table 6). The metabolic power and StrydMET measurements were signiﬁcantly lower at 
MOD compared to measurements 5% below, at, and 5% above the MLSS (p < 0.001 for all 
pairwise comparisons; Table 6). In contrast, the StrydMECH measurements were signiﬁ-
cantly higher at MOD compared to the three higher intensities (p < 0.001 for all compari-
sons; Table 6). All variables had excellent reliability for the repeated trials at the MLSS, 
without signiﬁcant diﬀerences between trials at the MLSS (Table 3). 
 
 
150
200
250
300
1000
2000
3000
4000
5000
Running Power (W)
V̇ O2 (mL·min−1)
2.0
2.5
3.0
3.5
4.0
4.5
1000
2000
3000
4000
5000
Running Power (W·kg−1)
V̇ O2 (mL·min−1)
150
200
250
300
2.0
2.5
3.0
3.5
4.0
4.5
Running Power (W)
Speed (m·s−1)
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5
Running Power (W·kg−1)
Speed (m·s−1)
C
D
A
B
Figure 3. Relationships between absolute and relative running power, running speed, and oxygen
uptake (
·
VO2). Panels (A,B) show the relationships between absolute running power and
·
VO2 and
between absolute running power and running speed for each participant during the moderate (MOD)
and heavy (HVY) intensity steps and constant-speed trials near the maximal lactate steady state
(MLSS). Panels (C,D) show the relationships between relative running power and
·
VO2 and between
relative running power and running speed for each participant at each running intensity, respectively.
Each color represents a single participant’s set of trials. N = 15 for all panels.
Results were similar when speed was used in place of
·
VO2; however, the difference in
model intercept variances was in the opposite direction, with a stronger and less variable
relationship between relative power and speed compared to absolute power and speed
(Table 6; Figure 3).
3.5. Stryd Running Power—Association with Running Economy
Based on the constant-speed running trials at MOD and near the MLSS, there were
signiﬁcant effects of intensity on metabolic power, StrydMECH, and StrydMET measurements
(Table 6). The metabolic power and StrydMET measurements were signiﬁcantly lower at
MOD compared to measurements 5% below, at, and 5% above the MLSS (p < 0.001 for all
pairwise comparisons; Table 6). In contrast, the StrydMECH measurements were signiﬁcantly
higher at MOD compared to the three higher intensities (p < 0.001 for all comparisons;
Table 6). All variables had excellent reliability for the repeated trials at the MLSS, without
signiﬁcant differences between trials at the MLSS (Table 3).
Figure 4 depicts the relationships between metabolic power (kJ·kg−1·km−1) and
absolute StrydMECH (kJ·km−1), relative StrydMECH (kJ·kg−1·km−1), absolute StrydMET
((J·s−1)·W−1), and relative StrydMET ((kJ·s−1)·(W·kg−1)−1) at the MLSS. Metabolic power
(kJ·kg−1·km−1) was not signiﬁcantly correlated with absolute StrydMECH (kJ·km−1) or
relative StrydMECH (kJ·kg−1·km−1); however, strong positive and moderately positive
correlations were detected between metabolic power (kJ·kg−1·km−1) and absolute StrydMET
(J·s−1)·W−1) and relative StrydMET ((kJ·s−1)·(W·kg−1)−1), respectively (Figure 4). The
results for other intensities were similar.
Sensors 2023, 23, 8729
12 of 19
 
lute StrydMECH (kJ km ), relative StrydMECH (kJ kg
km ), absolute StrydMET ((J s ) W ), 
and relative StrydMET ((kJ·s−1)·(W·kg−1)−1) at the MLSS. Metabolic power (kJ·kg−1·km−1) was 
not signiﬁcantly correlated with absolute StrydMECH (kJ·km−1) or relative StrydMECH 
(kJ·kg−1·km−1); however, strong positive and moderately positive correlations were de-
tected between metabolic power (kJ·kg−1·km−1) and absolute StrydMET (J·s−1)·W−1) and rela-
tive StrydMET ((kJ·s−1)·(W·kg−1)−1), respectively (Figure 4). The results for other intensities 
were similar. 
 
Figure 4. Relationships between metabolic power and absolute StrydMECH (A), relative StrydMECH (B), 
absolute StrydMET (C), and relative StrydMET (D) during constant-speed running trials performed at 
the maximal lactate steady state (MLSS). Circles represent individual data. n = 15 for all panels. 
4.0
4.5
5.0
5.5
6.0
45.0
60.0
75.0
90.0
Metabolic Power (kJ·kg−1·km−1)
StrydMECH (kJ·km−1)
y = 7.5x + 33.9
R2 = 0.079
p = 0.313
4.0
4.5
5.0
5.5
6.0
0.9
1.0
1.1
1.2
Metabolic Power (kJ·kg−1·km−1)
StrydMECH (kJ·kg−1·km−1)
y = 0.024x + 0.92
R2 = 0.066
p = 0.356
4.0
4.5
5.0
5.5
6.0
4.0
4.5
5.0
5.5
6.0
Metabolic Power (kJ·kg−1·km−1)
StrydMET ((J·s−1)·W−1)
y = 0.83x + 0.64
R2 = 0.791
p < 0.001
4.0
4.5
5.0
5.5
6.0
0.3
0.3
0.4
0.4
0.5
0.5
Metabolic Power (kJ·kg−1·km−1)
StrydMET ((kJ·s−1)·(W·kg−1)−1)
y = 0.084x − 0.091
R2 = 0.373
p = 0.016
A
B
C
D
Figure 4. Relationships between metabolic power and absolute StrydMECH (A), relative StrydMECH
(B), absolute StrydMET (C), and relative StrydMET (D) during constant-speed running trials performed
at the maximal lactate steady state (MLSS). Circles represent individual data. n = 15 for all panels.
3.6. Stryd Running Power—Estimates of Mechanical Running Efﬁciency
There was a statistically signiﬁcant main effect of running speed for EFF (p < 0.001;
Figure 5). Pairwise comparisons revealed that EFF was signiﬁcantly higher at MOD (25.0
[1.8]%) compared to HVY (21.3 [1.2]%), 5% below MLSS (20.9 [1.7]%), MLSS (20.7 [1.4]%),
and 5% above MLSS (20.4 [1.4]%) (p < 0.001 for these pairwise comparisons). No other
signiﬁcant differences were detected between the EFF measurements.
Sensors 2023, 23, x FOR PEER REVIEW 
13 of 20 
 
3.6. Stryd Running Power—Estimates of Mechanical Running Eﬃciency 
There was a statistically signiﬁcant main eﬀect of running speed for EFF (p < 0.001; 
Figure 5). Pairwise comparisons revealed that EFF was signiﬁcantly higher at MOD (25.0 
[1.8]%) compared to HVY (21.3 [1.2]%), 5% below MLSS (20.9 [1.7]%), MLSS (20.7 [1.4]%), 
and 5% above MLSS (20.4 [1.4]%) (p < 0.001 for these pairwise comparisons). No other 
signiﬁcant diﬀerences were detected between the EFF measurements. 
 
Figure 5. Average running mechanical eﬃciency (EFF) measurements during the moderate- (MOD) 
and heavy-intensity (HVY) steps, and during constant-speed trials near the maximal lactate steady 
state (MLSS). The asterisks (*) indicate statistically signiﬁcant diﬀerences between intensities. Error 
bars represent one standard deviation. Circles represent individual data. n = 15. 
3.7. Stryd Running Power—Association with Aerobic Fitness  
Absolute running power at the MLSS was strongly correlated with absolute V̇ O2 at 
the MLSS, moderately correlated with relative V̇ O2 and absolute running speed at the 
MLSS, and not correlated with relative running speed at the MLSS (Table 1; Figure 6). 
Relative running power at the MLSS was not correlated with absolute V̇ O2 at the MLSS, 
but it was strongly correlated with relative V̇ O2 and absolute running speed at the MLSS 
and moderately correlated with relative running speed at the MLSS (Table 1; Figure 6). 
MOD
HVY
Below
MLSS Above
0
10
20
30
Condition
Mechanical Efficiency (%)
*
Figure 5. Average running mechanical efﬁciency (EFF) measurements during the moderate- (MOD)
and heavy-intensity (HVY) steps, and during constant-speed trials near the maximal lactate steady
state (MLSS). The asterisks (*) indicate statistically signiﬁcant differences between intensities. Error
bars represent one standard deviation. Circles represent individual data. n = 15.
3.7. Stryd Running Power—Association with Aerobic Fitness
Absolute running power at the MLSS was strongly correlated with absolute
·
VO2 at the
MLSS, moderately correlated with relative
·
VO2 and absolute running speed at the MLSS,
and not correlated with relative running speed at the MLSS (Table 1; Figure 6). Relative
Sensors 2023, 23, 8729
13 of 19
running power at the MLSS was not correlated with absolute
·
VO2 at the MLSS, but it
was strongly correlated with relative
·
VO2 and absolute running speed at the MLSS and
moderately correlated with relative running speed at the MLSS (Table 1; Figure 6).
Sensors 2023, 23, x FOR PEER REVIEW 
14 of 20 
 
 
Figure 6. Relationships between absolute and relative running power, running speed, and oxygen 
uptake (V̇ O2) at the maximal lactate steady state (MLSS). Panels (A–D) show the relationship be-
tween V̇ O2 at the MLSS and running power at the MLSS in absolute and relative units. Panels (E–H) 
show the relationship between running speed at the MLSS and running power at the MLSS in abso-
lute and relative units. Individual data are plotted, along with the regression lines. n = 15 for all 
panels. 
4. Discussion 
The results from this investigation support the use of Stryd in research and applied 
settings. The Stryd running power metric was stable during 30-min constant-speed 
2.5
3.0
3.5
4.0
4.5
150
200
250
300
350
V̇ O2 at MLSS (L·min−1)
MLSS Power (W)
y = 61.7x + 35.8
R2 = 0.841
p < 0.001
40
45
50
55
60
150
200
250
300
350
V̇ O2 at MLSS (mL·kg−1·min−1)
MLSS Power (W)
y = 3.9x + 50.9
R2 = 0.280
p = 0.042
2.5
3.0
3.5
4.0
4.5
150
200
250
300
350
Speed at MLSS (m·s−1)
MLSS Power (W)
y = 51.6x + 66.3
R2 = 0.283
p = 0.041
0.03
0.04
0.05
0.06
0.07
150
200
250
300
350
Speed at MLSS (m·s−1·kg−1)
MLSS Power (W)
y = −596x + 269
R2 = 0.018
p = 0.638
2.5
3.0
3.5
4.0
4.5
2.5
3.0
3.5
4.0
4.5
V̇ O2 at MLSS (L·min−1)
MLSS Power (W·kg−1)
y = 0.28x + 2.57
R2 = 0.211
p = 0.085
40
45
50
55
60
2.5
3.0
3.5
4.0
4.5
V̇ O2 at MLSS (mL·kg−1·min−1)
MLSS Power (W·kg−1)
y = 0.052x + 1.00
R2 = 0.604
p < 0.001
2.5
3.0
3.5
4.0
4.5
2.5
3.0
3.5
4.0
4.5
Speed at MLSS (m·s−1)
MLSS Power (W·kg−1)
y = 0.83x + 0.71
R2 = 0.905
p < 0.001
0.03
0.04
0.05
0.06
0.07
2.5
3.0
3.5
4.0
4.5
Speed at MLSS (m·s−1·kg−1)
MLSS Power (W·kg−1)
y = 27.8x + 2.1
R2 = 0.478
p = 0.004
A
B
C
D
E
F
G
H
Figure 6. Relationships between absolute and relative running power, running speed, and oxygen
uptake (
·
VO2) at the maximal lactate steady state (MLSS). Panels (A–D) show the relationship between
·
VO2 at the MLSS and running power at the MLSS in absolute and relative units. Panels (E–H) show
the relationship between running speed at the MLSS and running power at the MLSS in absolute and
relative units. Individual data are plotted, along with the regression lines. n = 15 for all panels.
Sensors 2023, 23, 8729
14 of 19
4. Discussion
The results from this investigation support the use of Stryd in research and applied
settings. The Stryd running power metric was stable during 30-min constant-speed running
trials, repeatable across trials at the MLSS, and sensitive enough to differentiate between
trials performed at running speeds of 5% below, at, and 5% above the MLSS threshold.
Running power was strongly correlated with running speed and
·
VO2 during constant-
speed exercise relative to the GET and MLSS, supporting its use as a training intensity
metric. Furthermore, running power measurements at the MLSS were strongly associated
with both the
·
VO2 and running speed at the MLSS. Although metabolic power was strongly
associated with absolute StrydMET, it appears that Stryd power cannot provide an indication
of RE in isolation from metabolic data, as the associations between metabolic power and
StrydMECH were weak. Despite this ﬁnding, the mechanical running efﬁciency derived
using Stryd (i.e., EFF) remained consistent and proportional at various exercise intensities
near the MLSS threshold.
4.1. Stability, Sensitivity, and Reliability
Mean running power measurements were similar across the 10- and 30-min timepoints
during constant-speed running trials at 5% below, at, and 5% above the MLSS. Along
with a strong correlation, zero bias, and narrow LOA between time points, these ﬁndings
indicate that the Stryd signal remained stable during constant-speed treadmill running.
Running power across two runs at the MLSS was also strongly correlated, with a near-
zero bias and narrow LOA, indicating the excellent day-to-day reliability of the metric.
Furthermore, the Stryd power metric was able to distinguish between exercise intensities
near the MLSS. In agreement with our results, previous investigations also reported that
Stryd running power was stable during constant-speed running [33], repeatable [11], and
sensitive between conditions [34]; however, our investigation is the ﬁrst to evaluate these
running power parameters near the MLSS, an important threshold for training programs
and ﬁtness assessment [35,36]. In support of the Stryd running power metric results, besides
a signiﬁcantly lower RPE measurement during the second compared to the ﬁrst MLSS trial
(i.e., 0.8 units on the Borg 6–20 scale), which may indicate increased comfort during testing,
the
·
VO2 (Table 2) and other physiological and perceptual responses to running near the
MLSS were also stable, sensitive, and reliable (Table S1).
4.2. Stryd Running Power and Exercise Intensity
The strong associations observed between running power,
·
VO2, and speed support
the use of Stryd running power to guide exercise training relative to the exercise intensity
domains. Of note, the relationship between Stryd running power and
·
VO2, considered
at the group level, was stronger when running power was expressed in absolute units,
whereas the relationship between Stryd running power and speed, at the group level, was
stronger when running power was expressed in relative units. In practice, our results
suggest that absolute Stryd power may be best used as a metric to approximate the rate of
absolute oxygen consumption, while relative running power may be best used to indicate
running speed—at least during treadmill running. Due to the varying methodological ap-
proaches used to establish
·
VO2–power relationships in previous research [11,17,18,37–39],
it is difﬁcult to make comparisons across studies.
A major strength of the current investigation is that exercise intensity domains were
delineated and the
·
VO2 was subsequently evaluated during appropriate durations of
constant-speed running before examining the relationship between
·
VO2 and running
power. Exercise in the heavy-intensity domain can result in a slow
·
VO2 component that
delays the attainment of a steady
·
VO2 measure by ~10–15 min or longer [40]. Thus, without
Sensors 2023, 23, 8729
15 of 19
appropriately delineating the exercise intensity domain, it is difﬁcult to discern whether
a given absolute work rate or stage duration will produce steady-state exercising condi-
tions. The inﬂuence that intensity domain and
·
VO2 kinetic responses have on subsequent
·
VO2–power relationships can be highlighted by the substantial difference between the
incremental (i.e., 11.6 [1.5] (mL·min−1)·W−1) and constant-speed
·
VO2–power gains (i.e.,
19.8 [3.5] (mL·min−1)·W−1). Of interest, this
·
VO2–power gain from incremental tread-
mill running, measured using Stryd running power, is similar to previously observed
·
VO2–power gain measured during 15 W·min−1 incremental cycling protocols (i.e., 11.3
[1.2] (mL·min−1)·W−1) [29].
4.3. Stryd Running Power and Running Fitness
Runners with greater MLSS running powers displayed greater
·
VO2 and running
speeds at the MLSS (Figure 6). As the
·
VO2 and running speed associated with the MLSS
are strong predictors of running performance [41,42], at least in samples with broad aerobic
ﬁtness ranges, it appears that the Stryd running power metric can be used to indicate ﬁtness
in a similar manner to that used for cycling PO from constant-intensity exercise [43,44];
however, in contrast to cycling, where the cycling speed at any given PO is primarily
dictated by surface area and aerodynamics [45], body mass has a more substantial inﬂuence
on the relationship between Stryd running power and running speed. Thus, while absolute
Stryd running power may be used to estimate ﬁtness in terms of absolute
·
VO2 at the MLSS,
in order to evaluate ﬁtness from a speed perspective, it is best to interpret Stryd running
power relative to body mass or to only interpret the speed–power relationship relative to the
individual. Previous investigations have also reported strong associations between Stryd
assessments of critical power (CP) and ﬁtness metrics such as the RCP and
·
VO2max [38,46],
providing further support for the utility of Stryd to quantify running ﬁtness.
4.4. Stryd Running Power, Running Economy, and Mechanical Efﬁciency
Although strong associations were observed between absolute running power and
·
VO2 during constant-speed treadmill running conditions, there was a degree of variabil-
ity between the measured
·
VO2 for a given absolute running power (Figure 3). A large
proportion of this variance may be explained by the range of StrydMET requirements for a
speciﬁc metabolic power between runners (Figure 4). Indeed, runners with greater absolute
StrydMET measurements also exhibited greater metabolic power measures during each
constant-speed running intensity test (i.e., MOD and near to the MLSS). Although this
ﬁnding may suggest that Stryd can be used as an indication of RE, the strong relationship
between running power and running speed likely explains this ﬁnding. Accordingly, when
examining the relationship between metabolic power and StrydMECH (i.e., determining
whether the Stryd running power metric can be used in isolation from energy expenditure
to approximate the RE), there is no indication that StrydMECH is related to RE (i.e., metabolic
power), suggesting that this approach cannot distinguish between more and less economi-
cal runners. Previous investigations have similarly concluded that Stryd running power
metrics may be insufﬁcient for detecting differences in RE between trained runners [46,47]
or detecting worsened RE (i.e., increased
·
VO2 at a given running speed) after purposefully
altering running biomechanics [37].
Our Stryd-derived measures of mechanical efﬁciency (~21–25%) are lower than pre-
vious estimates of “apparent” running mechanical efﬁciency during level running (e.g.,
~50–70%) [6,7,39] but are similar to estimates of gross cycling efﬁciency (e.g., ~20–25%) [4].
Furthermore, in comparison with the up to ~20% difference in previously reported esti-
mates of running efﬁciency measurements at various running speeds [6,7,39], the Stryd
estimates of running mechanical efﬁciency for level running during MOD and heavy-
Sensors 2023, 23, 8729
16 of 19
intensity running were relatively small (i.e., ~4%). Consequently, our results indicate that
Stryd-based measures of mechanical running efﬁciency remain relatively stable at various
submaximal intensities and that the metabolic requirement per unit of Stryd running power
and the metabolic requirement per unit of cycling PO are similar.
Despite certain limitations related to the accurate detection of changing RE [37,47] and
the quantiﬁcation of running mechanical PO [39], our data suggest that foot-worn running
power metrics can still be used to monitor training and quantify running performance.
Although these ﬁndings do question the ability of Stryd running power to accurately
represent the running mechanical PO, we suggest that a wearable running power device
need not evaluate running power in a manner that is true to the deﬁnition of mechanical PO
to be useful. Indeed, as the relationship between metabolic demand and measurements of
running mechanical PO may vary with running speed, incline, and surface [6–8], a running
training tool that provides a consistent and seemingly equivalent evaluation of metabolic
demand may be more useful than one that evaluates external work rate, particularly for
such applied uses.
4.5. Experimental Considerations
Several limitations warrant discussion. Firstly, as all testing was performed on a
treadmill with a ﬁxed incline (1%), it remains unknown whether our ﬁndings can be
extended to outdoor running conditions under variable running gradients, surfaces, or
air resistances. With varying inclines, Stryd has shown evidence of repeatability [11] and
strong correlations with
·
VO2 [11,18,39], but the inﬂuence of variable running gradients and
surfaces on metabolic cost requires further investigation. Secondly, it remains unknown
whether Stryd power can adjust for changes in air resistance, such as changes in wind
speed. For example, changes in air resistance (e.g., wind, drafting, or drag) impact the
cycling
·
VO2–speed relationship [45] without inﬂuencing the
·
VO2–PO relationship. As
Stryd seemingly derives its estimate of running power by quantifying positive changes in
vertical displacement and horizontal velocities, whether it can account for the increases in
mechanical PO required to overcome greater air resistance is unclear [13]. Despite evidence
that Stryd may detect changes in wind speed [48] and has introduced a metric, “Air power”,
to adjust running power based on changes in air resistance from increasing or decreasing
wind speeds and/or running speeds [49], it remains unknown whether the Stryd power
metric–
·
VO2 relationship is linear in uncontrolled environments.
5. Conclusions
A wide variety of internal and external load-monitoring methods have been used
in endurance sports, such as running speed and pace, RPE, [BLa], HR, step count, step
frequency, and distance [50]; however, none of these variables provide a continuous, instan-
taneous, and reliable method to measure training intensity, and imprecise measurements of
training stress may negatively affect performance and elevate injury risk. With evidence
of stability, reliability, and sensitivity, our study suggests that Stryd’s foot-worn wearable
device can be used to monitor training intensity and quantify aerobic ﬁtness. While the
impact of variable running gradients, surfaces, and air resistance on the Stryd running
power metric still needs to be assessed, our results support the use of Styrd running power
to delineate exercise intensity domains, guide training intensity, and assess aerobic ﬁtness
during level treadmill running.
Supplementary Materials: The following supporting information can be downloaded at: https://
www.mdpi.com/article/10.3390/s23218729/s1, Table S1: Mean physiological and perceptual responses
to exercise near the maximal lactate steady state (MLSS), and indices of reliability between two runs at
the MLSS.
Sensors 2023, 23, 8729
17 of 19
Author Contributions: Conceptualization: C.R.v.R. and M.J.M.; data curation: C.R.v.R. and M.J.M.;
formal analysis: C.R.v.R., J.K.G. and M.J.M.; funding acquisition: M.J.M.; investigation: C.R.v.R., O.O.A.
and K.M.S.; methodology: all authors; project administration: C.R.v.R. and M.J.M.; resources: M.J.M.;
software: M.J.M.; supervision: M.J.M.; validation: C.R.v.R., O.O.A., K.M.S. and M.J.M.; visualization:
C.R.v.R., J.K.G. and M.J.M.; writing—original draft: C.R.v.R. and M.J.M.; writing—reviewing and editing:
all authors. All authors have read and agreed to the published version of the manuscript.
Funding: This work was supported by an operating grant from the Natural Sciences and Engineering
Research Council of Canada (NSERC; grant number RGPIN-2018-06424) and start-up funding from
the Faculty of Kinesiology (University of Calgary) received by M.J.M. C.V.R. was funded by NSERC,
the NSERC CREATE Wearable Technology and Collaboration (We-TRAC) Training Program, an Al-
berta Innovates Graduate Student Scholarship for Data-Enabled Innovation, and an Alberta Graduate
Excellence Scholarship. OOA was also funded by NSERC and the NSERC CREATE We-TRAC. The
authors would like to acknowledge the contributions of all participants, students, faculty, and staff,
who assisted and made this investigation possible.
Institutional Review Board Statement: The study was conducted in accordance with the Declaration
of Helsinki, except for pre-registration of the trial, and was approved by the University of Calgary
Conjoint Health Research Ethics Board (REB20-0111, approved 29 July 2020).
Informed Consent Statement: Informed consent was obtained from all participants involved in
the study.
Data Availability Statement: Individual data are shown where possible; however, other data are
available from the corresponding author upon reasonable request.
Conﬂicts of Interest: M.J.M. has received several foot pods from Stryd for research purposes; how-
ever, that equipment was not used in this study. Stryd had no involvement in the conduct, analysis,
or reporting of this study, and M.J.M. has no professional relationship with Stryd. All authors declare
no competing interests. The funders of this study (NSERC, University of Calgary) had no role in
the design of the study; in the collection, analyses, or interpretation of data; in the writing of the
manuscript; or in the decision to publish the results.
References
1.
Williams, K.R.; Cavanagh, P.R. A model for the calculation of mechanical power during distance running. J. Biomech. 1983,
16, 115–128. [CrossRef] [PubMed]
2.
Arampatzis, A.; Knicker, A.; Metzler, V.; Bruggemann, G.P. Mechanical power in running: A comparison of different approaches.
J. Biomech. 2000, 33, 457–463. [CrossRef] [PubMed]
3.
Willems, P.A.; Cavagna, G.A.; Heglund, N.C. External, internal and total work in human locomotion. J. Exp. Biol. 1995, 198,
379–393. [CrossRef] [PubMed]
4.
Ettema, G.; Loras, H.W. Efﬁciency in cycling: A review. Eur. J. Appl. Physiol. 2009, 106, 1–14. [CrossRef]
5.
Keir, D.A.; Paterson, D.H.; Kowalchuk, J.M.; Murias, J.M. Using ramp-incremental
·
VO2 responses for constant-intensity exercise
selection. Appl. Physiol. Nutr. Metab. 2018, 43, 882–892. [CrossRef]
6.
Rasica, L.; Porcelli, S.; Minetti, A.; Pavei, G. Biomechanical and metabolic aspects of backward (and forward) running on uphill
gradients: Another clue towards an almost inelastic rebound. Eur. J. Appl. Physiol. 2020, 120, 2507–2515. [CrossRef]
7.
Monte, A.; Maganaris, C.; Baltzopoulos, V.; Zamparo, P. The inﬂuence of Achilles tendon mechanical behaviour on “apparent”
efﬁciency during running at different speeds. Eur. J. Appl. Physiol. 2020, 120, 2495–2505. [CrossRef]
8.
Lejeune, T.M.; Willems, P.A.; Heglund, N.C. Mechanics and energetics of human locomotion on sand. J. Exp. Biol. 1998,
201, 2071–2080. [CrossRef]
9.
Jamnick, N.A.; By, S.; Pettitt, C.D.; Pettitt, R.W. Comparison of the YMCA and a custom submaximal exercise test for determining
·
VO2max. Med. Sci. Sports Exerc. 2016, 48, 254–259. [CrossRef]
10.
Passﬁeld, L.; Hopker, J.G.; Jobson, S.; Friel, D.; Zabala, M. Knowledge is power: Issues of measuring training and performance in
cycling. J. Sports Sci. 2017, 35, 1426–1434. [CrossRef]
11.
Cerezuela-Espejo, V.; Hernández-Belmonte, A.; Courel-Ibáñez, J.; Conesa-Ros, E.; Mora-Rodríguez, R.; Pallarés, J.G. Are we
ready to measure running power? Repeatability and concurrent validity of ﬁve commercial technologies. Eur. J. Sport. Sci. 2021,
21, 341–350. [CrossRef]
12.
Jaen-Carrillo, D.; Roche-Seruendo, L.E.; Carton-Llorente, A.; Ramirez-Campillo, R.; Garcia-Pinillos, F. Mechanical power in
endurance running: A scoping review on sensors for power output estimation during running. Sensors 2020, 20, 6482. [CrossRef]
[PubMed]
Sensors 2023, 23, 8729
18 of 19
13.
Stryd, T. How to Lead the Pack: Running Power Meters & Quality Data. 2022. Available online: https://blog.stryd.com/2017/1
2/07/how-to-lead-the-pack-running-power-meters-quality-data/ (accessed on 11 January 2022).
14.
García-Pinillos, F.; Roche-Seruendo, L.E.; Marcén-Cinca, N.; Marco-Contreras, L.A.; Latorre-Román, P.A. Absolute reliability and
concurrent validity of the Stryd system for the assessment of running stride kinematics at different velocities. J. Strength. Cond.
Res. 2021, 35, 78–84. [CrossRef] [PubMed]
15.
Navalta, J.W.; Montes, J.; Bodell, N.G.; Aguilar, C.D.; Radzak, K.; Manning, J.W.; DeBeliso, M. Reliability of trail walking and
running tasks using the Stryd power meter. Int. J. Sports Med. 2019, 40, 498–502. [CrossRef] [PubMed]
16.
Cartón-Llorente, A.; Roche-Seruendo, L.E.; Mainer-Pardos, E.; Nobari, H.; Rubio-Peirotén, A.; Jaén-Carrillo, D.; García-Pinillos, F.
Acute effects of a 60-min time trial on power-related parameters in trained endurance runners. BMC Sports Sci. Med. Rehabil.
2022, 14, 142. [CrossRef] [PubMed]
17.
García-Pinillos, F.; Latorre-Román, P.Á.; Roche-Seruendo, L.E.; García-Ramos, A. Prediction of power output at different running
velocities through the two-point method with the Stryd™ power meter. Gait Posture 2019, 68, 238–243. [CrossRef]
18.
Taboga, P.; Giovanelli, N.; Spinazze, E.; Cuzzolin, F.; Fedele, G.; Zanuso, S.; Lazzer, S. Running power: Lab based vs. portable
devices measurements and its relationship with aerobic power. Eur. J. Sport. Sci. 2022, 22, 1555–1568. [CrossRef]
19.
McKay, A.K.A.; Stellingwerff, T.; Smith, E.S.; Martin, D.T.; Mujika, I.; Goosey-Tolfrey, V.L.; Sheppard, J.; Burke, L.M. Deﬁning
training and performance caliber: A participant classiﬁcation framework. Int. J. Sports Physiol. Perform. 2022, 17, 317–331.
[CrossRef]
20.
Van Rassel, C.R.; Ajayi, O.O.; Sales, K.M.; Azevedo, R.A.; Murias, J.M.; MacInnis, M.J. A “Step-Ramp-Step” protocol to identify
running speed and power associated with the maximal metabolic steady state. Med. Sci. Sports Exerc. 2022, 55, 534–547. [CrossRef]
21.
Iannetta, D.; Inglis, E.C.; Pogliaghi, S.; Murias, J.M.; Keir, D.A. A “Step-Ramp-Step” protocol to identify the maximal metabolic
steady state. Med. Sci. Sports Exerc. 2020, 52, 2011–2019. [CrossRef]
22.
Beneke, R.; von Duvillard, S.P. Determination of maximal lactate steady state response in selected sports events. Med. Sci. Sports
Exerc. 1996, 28, 241–246. [CrossRef] [PubMed]
23.
Jones, A.M.; Doust, J.H. A 1% treadmill grade most accurately reﬂects the energetic cost of outdoor running. J. Sports Sci. 1996,
14, 321–327. [CrossRef] [PubMed]
24.
Beaver, W.L.; Wasserman, K.; Whipp, B.J. A new method for detecting anaerobic threshold by gas exchange. J. Appl. Physiol. 1986,
60, 2020–2027. [CrossRef] [PubMed]
25.
Whipp, B.J.; Davis, J.A.; Wasserman, K. Ventilatory control of the ‘isocapnic buffering’ region in rapidly-incremental exercise.
Respir. Physiol. 1989, 76, 357–367. [CrossRef] [PubMed]
26.
Borg, G.A. Psychophysical bases of perceived exertion. Med. Sci. Sports Exerc. 1982, 14, 377–381. [CrossRef]
27.
Billat, V.L.; Sirvent, P.; Py, G.; Koralsztein, J.-P.; Mercier, J. The concept of maximal lactate steady state: A bridge between
biochemistry, physiology and sport science. Sports Med. 2003, 33, 407–426. [CrossRef]
28.
Nixon, R.J.; Kranen, S.H.; Vanhatalo, A.; Jones, A.M. Steady-state
·
VO2 above MLSS: Evidence that critical speed better represents
maximal metabolic steady state in well-trained runners. Eur. J. Appl. Physiol. 2021, 121, 3133–3144. [CrossRef]
29.
Wilcox, S.L.; Broxterman, R.M.; Barstow, T.J. Constructing quasi-linear
·
VO2 responses from nonlinear parameters. J. Appl. Physiol.
2016, 120, 121–129. [CrossRef]
30.
Peronnet, F.; Massicotte, D. Table of nonprotein respiratory quotient: An update. Can. J. Sport. Sci. 1991, 16, 23–29.
31.
Koo, T.K.; Li, M.Y. A guideline of selecting and reporting intraclass correlation coefﬁcients for reliability research. J. Chiropr. Med.
2016, 15, 155–163. [CrossRef]
32.
Hoffman, L. Longitudinal Analysis: Modeling within-Person Fluctuation and Change; Routledge: Abingdon, UK, 2015.
33.
García-Pinillos, F.; Soto-Hermoso, V.M.; Latorre-Román, P.Á.; Párraga-Montilla, J.A.; Roche-Seruendo, L.E. How does power
during running change when measured at different time intervals? Int. J. Sports Med. 2019, 40, 609–613. [CrossRef] [PubMed]
34.
Cerezuela-Espejo, V.; Hernandez-Belmonte, A.; Courel-Ibanez, J.; Conesa-Ros, E.; Martinez-Cava, A.; Pallares, J.G. Running
power meters and theoretical models based on laws of physics: Effects of environments and running conditions. Physiol. Behav.
2020, 223, 112972. [CrossRef] [PubMed]
35.
Iannetta, D.; Inglis, E.C.; Fullerton, C.; Passﬁeld, L.; Murias, J.M. Metabolic and performance-related consequences of exercising
at and slightly above MLSS. Scand. J. Med. Sci. Sports 2018, 28, 2481–2493. [CrossRef] [PubMed]
36.
Iannetta, D.; Inglis, E.C.; Mattu, A.T.; Fontana, F.Y.; Pogliaghi, S.; Keir, D.A.; Murias, J.M. A Critical Evaluation of Current Methods
for Exercise Prescription in Women and Men. Med. Sci. Sports Exerc. 2020, 52, 466–473. [CrossRef]
37.
Baumgartner, T.; Held, S.; Klatt, S.; Donath, L. Limitations of foot-worn sensors for assessing running power. Sensors 2021,
21, 4952. [CrossRef] [PubMed]
38.
Ruiz-Alias, S.A.; Olaya-Cuartero, J.; Nancupil-Andrade, A.A.; Garcia-Pinillos, F. 9/3-Minute Running Critical Power Test:
Mechanical Threshold Location With Respect to Ventilatory Thresholds and Maximum Oxygen Uptake. Int. J. Sports Physiol.
Perform. 2022, 17, 1111–1118. [CrossRef]
39.
Imbach, F.; Candau, R.; Chailan, R.; Perrey, S. Validity of the Stryd power meter in measuring running parameters at submaximal
speeds. Sports 2020, 8, 103. [CrossRef]
40.
Poole, D.C.; Jones, A.M. Oxygen uptake kinetics. Compr. Physiol. 2012, 2, 933–996. [CrossRef]
41.
Bassett, D.R., Jr.; Howley, E.T. Limiting factors for maximum oxygen uptake and determinants of endurance performance. Med.
Sci. Sports Exerc. 2000, 32, 70–84. [CrossRef]
Sensors 2023, 23, 8729
19 of 19
42.
Jones, A.M.; Doust, J.H. The validity of the lactate minimum test for determination of the maximal lactate steady state. Med. Sci.
Sports Exerc. 1998, 30, 1304–1313. [CrossRef]
43.
Hawley, J.A.; Noakes, T.D. Peak power output predicts maximal oxygen uptake and performance time in trained cyclists. Eur. J.
Appl. Physiol. Occup. Physiol. 1992, 65, 79–83. [CrossRef] [PubMed]
44.
Smith, J.; Dangelmaier, B.; Hill, D. Critical power is related to cycling time trial performance. Int. J. Sports Med. 1999, 20, 374–378.
[CrossRef] [PubMed]
45.
Faria, E.W.; Parker, D.L.; Faria, I.E. The science of cycling: Factors affecting performance—Part 2. Sports Med. 2005, 35, 313–337.
[CrossRef] [PubMed]
46.
Dearing, C.G.; Paton, C.D. Is Stryd critical power a meaningful parameter for runners? Biol. Sport 2022, 40, 657–664. [CrossRef]
47.
Austin, C.L.; Hokanson, J.F.; McGinnis, P.M.; Patrick, S. The relationship between running power and running economy in
well-trained distance runners. Sports 2018, 6, 142. [CrossRef]
48.
Bello, M.L.; Anglin, D.A.; Gillen, Z.M.; Smith, J.W. The use of wearable technology to quantify power and muscle load differences
during running against varying wind resistances. Int. J. Kines. Sports Sci. 2022, 10, 11–15. [CrossRef]
49.
Stryd, T. New Power-Based Metric Reveals the Wind So You Can Benefit from Its Effects. 2019. Available online: https://blog.stryd.
com/2019/08/16/introducing-air-power/ (accessed on 29 March 2023).
50.
Bourdon, P.C.; Cardinale, M.; Murray, A.; Gastin, P.; Kellmann, M.; Varley, M.C.; Gabbett, T.J.; Coutts, A.J.; Burgess, D.J.; Gregson,
W.; et al. Monitoring Athlete Training Loads: Consensus Statement. Int. J. Sports Physiol. Perform. 2017, 12, S2161–S2170.
[CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.

Is Running Power a Useful Metric? Quantifying Training Intensity and Aerobic Fitness Using Stryd Running Power Near the Maximal Lactate Steady State.
van Rassel, Cody R,Ajayi, Oluwatimilehin O,Sales, Kate M,Griffiths, James K,Fletcher, Jared R,Edwards, W Brent,MacInnis, Martin J