![Schematic view of heart rate (HR, grey) and DFAa1 (blue) of one 20‐min continuous running bout at vDFAa1‐1 (here: 11.7 km/h); warm‐up at 80% of vDFA1‐1 (here: 9.4 km/h); and passive recovery data included (Kubios HRV Scientific, version 4.1). Data of HR, HR variability (HRV), oxygen consumption (VO2), and respiratory frequency (RF) were continuously recorded, blood lactate concentration [La‐] before (Pre) and at the end (End) of the running bouts.](https://www.researchgate.net/publication/384157008/figure/fig1/AS:11431281288612156@1730782136393/Schematic-view-of-heart-rate-HR-grey-and-DFAa1-blue-of-one-20-min-continuous-running_Q320.jpg)
Access to this full-text is provided by Wiley.
Content available from European Journal of Sport Science
This content is subject to copyright. Terms and conditions apply.
Received: 22 February 2024
-
Revised: 27 June 2024
-
Accepted: 16 July 2024
DOI: 10.1002/ejsc.12175
ORIGINAL PAPER
Correlation properties of heart rate variability for exercise
prescription during prolonged running at constant speeds: A
randomized cross‐over trial
Thomas Gronwald
1,2
|Leonie Horn
3
|Marcelle Schaffarczyk
1
|Olaf Hoos
3
1
Institute of Interdisciplinary Exercise Science
and Sports Medicine, MSH Medical School
Hamburg, Hamburg, Germany
2
G‐Lab, Faculty of Applied Sport Sciences and
Personality, BSP Business and Law School,
Berlin, Germany
3
Center for Sports and Physical Education,
Faculty of Human Sciences, Julius‐
Maximilians‐University Wuerzburg,
Wuerzburg, Germany
Correspondence
Thomas Gronwald, MSH Medical School
Hamburg, Institute of Interdisciplinary
Exercise Science and Sports Medicine, Am
Kaiserkai 1, 20457 Hamburg, Germany.
Email: thomas.gronwald@medicalschool-
hamburg.de
Abstract
The study explores the validity of the nonlinear index alpha 1 of detrended fluc-
tuation analysis (DFAa1) of heart rate (HR) variability for exercise prescription in
prolonged constant load running bouts of different intensities. 21 trained endurance
athletes (9 w and 12 m) performed a ramp test for ventilatory threshold (vVT1 and
vVT2) and DFAa1‐based (vDFAa1‐1 at 0.75 and vDFAa1‐2 at 0.5) running speed
detection as well as two 20‐min running bouts at vDFAa1‐1 and vDFAa1‐2 (20‐
vDFAa1‐1 and 20‐vDFAa1‐2), in which HR, oxygen consumption (VO
2
), respiratory
frequency (RF), DFAa1, and blood lactate concentration [La‐] were assessed. 20‐
vDFAa1‐2 could not be finished by all participants (finisher group (FG), n=15
versus exhaustion group (EG), n=6). Despite similar mean external loads of
vDFAa1‐1 (10.6 �1.9 km/h) and vDFAa1‐2 (13.1 �2.4 km/h) for all participants
compared to vVT1 (10.8 �1.7 km/h) and vVT2 (13.2 �1.9 km/h), considerable
differences were present for 20‐vDFAa1‐2 in EG (15.2 �2.4 km/h). 20‐vDFAa1‐1
and 20‐DFAa1‐2 yielded significant differences in FG for HR (76.2 �5.7 vs.
86.4 �5.9 %HR
PEAK
), VO
2
(62.1 �5.0 vs. 77.5 �8.6 %VO
2PEAK
), RF (40.6 �11.3 vs.
46.1 �9.8 bpm), DFA‐a1 (0.86 �0.23 vs. 0.60 �0.15), and [La‐] (1.41 �0.45 vs.
3.34 �2.24 mmol/L). Regarding alterations during 20‐vDFAa1‐1, all parameters
showed small changes for all participants, while during 20‐vDFAa1‐2 RF and DFAa1
showed substantial alterations in FG (RF: 15.6% and DFAa1: −12.8%) and more
pronounced in EG (RF: 20.1% and DFAa1: −35.9%). DFAa1‐based exercise pre-
scription from incremental testing could be useful for most participants in pro-
longed running bouts, at least in the moderate to heavy intensity domain. In
addition, an individually different increased risk of overloading may occur in the
heavy to severe exercise domains and should be further elucidated in the light of
durability and decoupling assessment.
KEYWORDS
decoupling, DFAa1, endurance sports, HRV, intensity distribution
This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any
medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
© 2024 The Author(s). European Journal of Sport Science published by Wiley‐VCH GmbH on behalf of European College of Sport Science.
Eur J Sport Sci. 2024;24:1539–1551. wileyonlinelibrary.com/journal/ejsc
-
1539
Highlights
�DFAa1‐based exercise prescription from incremental testing shows potential for prolonged
constant load exercise, at least in the moderate to heavy intensity domains for most trained
runners.
�Caution is advised for the heavy to severe exercise domains as individual overload may
occur.
�The relationship of DFAa1 and vDFAa1 seems to be highly individual as well as perspectives
for the durability and decoupling assessment and should be further elucidated during longer
exercise bouts.
1
|
INTRODUCTION
Analyses of the nonlinear characteristics of heart rate (HR) variability
(HRV) show that the short‐term scaling exponent alpha1 of detren-
ded fluctuation analysis (DFAa1) may be a sensitive marker for
assessing global organismic demands during acute endurance exer-
cise (Gronwald, Törpel, et al., 2020; Gronwald & Hoos, 2020). DFAa1
was shown to provide a wide dynamic range encompassing the
moderate, heavy, and severe exercise intensity domains (3‐zone‐
model) during exercise compared to linear metrics of HRV (Rogers &
Gronwald, 2022).
In general, the exponent quantifies the fractal scale and corre-
lation properties of HR time series in cardiac beat‐to‐beat intervals
and represents a rather qualitative marker of the autonomic nervous
system (ANS) regulation, which means that under resting conditions,
DFAa1 values around 1.0 mirror the homeodynamic behavior of
control systems to dynamically self‐organize in between order
(persistence) and disorder (de Godoy, 2016; Goldberger et al., 2002;
Kauffman, 1995). During exercise, DFAa1 shows strongly correlated
patterns (values well above 1.0) at low‐intensity exercise in the
moderate domain, transitions to fractal patterns (value at around and
below 1.0) at moderate to heavy exercise intensities, and drops to
uncorrelated and anticorrelated patterns at the highest intensities
with values around and below 0.5, which indicates a loss of fractal
dynamics and a change toward random and/or anticorrelated
behavior (Hautala et al., 2003). Easily accessible HRV data acquisition
with chest belt sensors allows for laboratory and in‐field use and also
opens up opportunities to provide real‐time feedback on exercise
intensity (Gronwald, Berk, et al., 2021; Rogers & Gronwald, 2022).
Given these properties and based on signal‐theory background,
applying this metric may be used as a biomarker for exercise in-
tensity domain delineation. It has been shown that discrete numerical
values of this biomarker may demarcate the transition from moder-
ate to heavy intensity exercise around the aerobic threshold (DFAa1
of 0.75) and from heavy to severe intensities around the anaerobic
threshold (DFAa1 of 0.5), respectively, corresponding to traditional
threshold markers based on different organismic subsystem mea-
sures, such as blood lactate concentration [La‐] or gas exchange data,
taking into account the potential limitations and deviations on an
individual level (Mateo‐March et al., 2023; Rogers, Giles, Draper,
Hoos, et al., 2021; Rogers, Giles, Draper, Mourot, et al., 2021;
Schaffarczyk et al., 2023; van Hooren, Mennen, et al., 2023). Further,
DFAa1 has been shown to be useful as a marker of acute fatigue in
terms of a systemic perturbation (Rogers, Mourot, et al., 2021;
Schaffarczyk et al., 2022; van Hooren, Bongers, et al., 2023; van
Hooren, Mennen, et al., 2023) or as an internal load measure of fa-
tigue resistance in studies with prolonged exercise (Gronwald
et al., 2018,2019; Gronwald, Rogers, et al., 2021). Therefore,
expanding these findings to future approaches of real‐time moni-
toring of prolonged exercise seems to be promising, as the DFAa1
marker might bear the potential to mirror decoupling mechanisms as
alterations of external‐to‐internal load relationships or “durability”
aspects of endurance performance that were recently described as
“the time of onset and magnitude of deterioration in physiological‐
profiling characteristics over time during prolonged exercise”
(Maunder et al., 2021; Smyth et al., 2022). Jones (2023) recently
introduced this construct in terms of physiological resilience consti-
tuting an independent, fourth dimension of endurance exercise per-
formance in addition to the classical ones of maximal oxygen uptake
(VO
2MAX
), economy or efficiency, and fractional utilization of VO
2MAX
(e.g., Joyner, 1991; Joyner & Coyle, 2008). In that regard, recent
studies show prior moderate‐intensity exercise could decrease po-
wer output at threshold estimates between moderate to heavy ex-
ercise intensities and time trial performance (Gallo et al., 2024;
Hamilton et al., 2024; Stevenson et al., 2024). This alteration of
internal‐to‐external load relationship could be also shown from an
internal load perspective with fixed external load in the moderate
intensity domain according to HR metrics and DFAa1 (Rogers,
Mourot, et al., 2021; van Hooren, Bongers, et al., 2023; van Hooren,
Mennen, et al., 2023). Here, it should be still differentiated between
pre and post comparisons (e.g., Hamilton et al., 2024; Stevenson
et al., 2024) and alterations during continuous prolonged exercise
bouts (e.g., Gronwald et al., 2018; Gronwald, Rogers, et al., 2021;
Maunder et al., 2021; Smyth et al., 2022).
However, validation data of DFAa1 during prescribed prolonged
exercise bouts are still scarce and the true significance for exercise
prescription remains to be fully elucidated. In addition, exercise
prescription based on a percentage of maximum HR, oxygen con-
sumption, or various approaches of fixed [La‐] and individual gas
exchange utilization most often lead to an inaccurate and
1540
-
GRONWALD
ET AL.
inconsistent representation of the relationship between external and
internal load during prolonged exercise with large interindividual
variability of the internal load situation (Brownstein et al., 2022;
Fleckenstein et al., 2023; Jamnick et al., 2020; Mann et al., 2013).
Therefore, the aim of the present pilot study was to evaluate the
construct validity of DFAa1 to prescribe and monitor exercise in-
tensity during continuous running bouts at the transition of moderate
to heavy and heavy to severe exercise domains.
2
|
METHODS AND MATERIALS
2.1
|
Participants
21 trained (McKay et al., 2022) endurance athletes (9 w and 12 m;
age: 25.9 �3.6 years, height: 178.4 �9.9 cm, body weight:
70.8 �8.7 kg, body fat: 12.2 �4.4%, peak heart rate – HR
PEAK
:
198.4 �7.9 bpm, and peak oxygen consumption – VO
2PEAK
:
59.0 �8.3 mL/kg/min) voluntarily participated in this study. All
subjects were informed about risks and benefits of the procedures
and signed an informed consent form. The ethics committee of the
MSH Medical School Hamburg (reference no.: MSH‐2022/172)
approved all tests performed in the study. The study was also carried
out in accordance with the principles set forth in the most recent
revision of the Declaration of Helsinki.
2.2
|
Study design
All participants visited the laboratory on three separate days. On the
first day, they were informed about risks and benefits of the study
and were accustomed to treadmill, face mask, and blood lactate
concentration measurement procedures. Body fat percentage (BF%)
was measured using bio‐impedance analysis (InnerScanV). Afterward,
participants completed an incremental running test on a treadmill
(Woodway DESMO Pro XL, Woodway Europe, Weil am Rhein) with
an increment of 1 km/h per minute starting at 7 km/h for women and
8 km/h for men until volitional exhaustion. Prior to the test, athletes
completed a 10‐min warm‐up on the treadmill at the initial test
speed. The running speeds (v) at the first and second ventilatory
threshold (vVT1 and vVT2) and at DFAa1 of 0.75 and 0.5 (vDFAa1‐1
and vDFAa1‐2) were determined during the running test. Afterwards,
two 20‐min continuous running bouts at vDFAa1‐1 and vDFAa1‐2
(20‐vDFAa1‐1, 20‐vDFAa1‐2) were conducted in randomized and
counterbalanced order within one week. Prior to 20‐vDFAa1‐1 and
20‐vDFAa1‐2, all participants warmed‐up on the treadmill at a speed
corresponding to 80% of their vDFAa1‐1 speed for 10 min (see
Figure 1). All tests were conducted at similar times of the day with at
least a 72 h' time‐lag to the next or previous test or intense exercise
session. The participants were instructed to obtain enough sleep the
night before testing (at least 7 h), to refrain from alcohol intake for
24 h, and to have a last light meal 2–3 h before the investigation.
2.3
|
Data measurement
On all three laboratory days, HR and HRV were continuously
measured during all test conditions using Polar H10 (transmitter
sensor as chest belt recording) and V800 (receiver as wrist‐worn
watch) HR devices (Polar Electro Oy, Kempele, Finland; Schaffarc-
zyk et al., 2022). [La‐] was collected from the ear lobe before and at
the end of the continuous running bouts using an enzymatic‐
amperometric method (Biosen C‐line, EKF‐Diagnostics, Eppendorf,
Germany). Further, oxygen consumption (VO
2
in ml/kg/min) and
respiratory frequency (RF in breaths per minute, bpm) were contin-
uously measured during all three exercise sessions using a portable
breath‐by‐breath metabolic cart (Metamax 3B, Cortex Biophysik
GmbH, Leipzig, Germany; van Hooren et al., 2024).
2.4
|
HRV analysis and threshold determination
To analyze RR‐intervals (in ms) and HR (in beats per minute, bpm),
data were exported from the Polar Flow web service (Polar Electro
Oy, Kempele, Finland) and processed in Kubios HRV Scientific
(version 4.1, Biosignal Analysis and Medical Imaging Group,
Department of Physics, University of Kuopio, Kuopio, Finland).
Preprocessing settings were set to the default values, including the
RR detrending method, which was kept at “smoothness priors”
(Lambda =500). The RR‐interval series were then corrected using
the Kubios HRV “automatic correction” method. To calculate
DFAa1, the root mean square (RMS) fluctuations of the integrated
and detrended RR‐intervals were analyzed in observation windows
of different sizes and then further processed as the slope between
the RMS‐fluctuation data in relation to the different window sizes
on a log‐log scale (Peng et al., 1995). Window size was set to
4≤n≤16 beats in the software preferences. Data were also
scanned visually for artefacts (e.g., spikes in RR‐interval series
which were not corrected by the artefact correction algorithm),
marked as “noise” and removed manually by an expert with expe-
rience in HRV data analysis. Datasets with >5% artefacts were
excluded from HRV analysis. The time varying DFAa1 kinetic was
then calculated over a 120 s window width with grid intervals of
5 s for the threshold estimation during incremental testing and
10 s for the alignment with ventilatory data during prolonged ex-
ercise. HRV thresholds were determined based on fixed values of
DFAa1. Linear regression was performed on the subset of data
consisting of the rapid, near straight‐line drop from DFAa1 values
close to 1.0 to approximately 0.5 or below if the values continued
in a non‐deviating fashion. The running speeds where DFAa1
reached either 0.75 (vDFAa1‐1) and 0.5 (vDFAa1‐2) were calcu-
lated based on the regression equation from that linear section
(Rogers, Giles, Draper, Hoos, et al., 2021; Rogers, Giles, Draper,
Mourot, et al., 2021) or based on established multiphasic dose‐
response modeling (Di Veroli et al., 2015), if its goodness‐of‐fit
exceeded the one of standard linear regression.
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1541
2.5
|
Ventilatory threshold determination
To determine VT1, the V‐slope method was used (Beaver
et al., 1986). In case of inconclusive VCO
2
and VO
2
trajectories,
additionally an increase in end tidal O
2
pressure versus time and a
rise in the O
2
equivalent without a simultaneous increase in CO
2
equivalent was used as criteria for VT1. VT2 was defined as the point
of a disproportional rise in minute volume (VE) versus VCO
2
. Addi-
tional criteria were a decrease in end expiratory CO
2
pressure versus
time and an increase in the CO
2
equivalent versus time (Meyer
et al., 2005). VT1 and VT2 were both determined independently by
two researchers. In cases where both researchers did not agree, the
mean value was used for VT1 and VT2 estimation.
2.6
|
Efficiency factor
For the analysis of internal‐to‐external load relationship and a
possible decoupling mechanism, an efficiency factor (EF) was defined.
This internal‐to‐external workload ratio was calculated for the start
and end of the continuous running bouts using the ratio of internal
load indicators (HR, VO
2
, RF, and DFAa1) and running pace (in km/h).
For those participants who exhausted before the end of 20‐vDFAa1‐
2, minutes 4/5 versus the last 2 minutes of exercise were used. The
difference of the EF from the start and end was calculated and
divided by the EF from the start multiplied by 100 to get a per-
centage of alteration (%). Thus, a value of 10% indicates that internal‐
to‐external ratio was 10% greater at the end segment compared to
that observed in the start segment (Maunder et al., 2021; Smyth
et al., 2022).
3
|
STATISTICAL ANALYSES
Statistics were conducted using the SPSS 27.0 (IBM), and Microsoft
Excel (Microsoft Corp, Redmond, USA). Prior to all tests, normality of
distribution was tested using the Shapiro–Wilk testing. To analyze
the effects of the exercise bouts on dependent variables, a two‐way
analysis of variance with repeated measures (ANOVA; intensity x
time) was applied and both the main effects and the interaction
(intensity �time) were reported. In addition, post‐hoc testing and
comparison of different approaches of external load assessment at
estimated exercise intensity thresholds as well as mean differences
between 20‐vDFAa1‐1 and 20‐vDFAa1‐2 were conducted via paired
t‐tests. Additionally, partial η
2
was used to denote main effects and
Hedge's g for the effect size estimation of t‐test results (difference
between mean values divided by corrected standard deviation;
Hedges, 1981), with no effect (d<0.2), small effect size (d<0.5),
moderate effect size (d≥0.5), and large effect size (d>0.8)
(Cohen, 1988). In addition to mean values for the complete contin-
uous running bouts, the values at start and end at minutes 4/5 versus
19/20 were used for comparisons (see Figure 1). Statistical tests
were deemed to be significant at p≤0.05. All results are reported as
means �standard deviation (SD).
4
|
RESULTS
The analyzed data exhibited a normal distribution. External loads of
vDFAa1‐1 (10.6 �1.9 km/h) and vDFAa1‐2 (13.1 �2.4 km/h) for all
participants were comparable to vVT1 (10.8 �1.7 km/h, p=0.418,
and g=0.13) and vVT2 (13.2 �1.9 km/h, p=0.661, and g=0.07),
FIGURE 1 Schematic view of heart rate (HR, grey) and DFAa1 (blue) of one 20‐min continuous running bout at vDFAa1‐1 (here: 11.7 km/h);
warm‐up at 80% of vDFA1‐1 (here: 9.4 km/h); and passive recovery data included (Kubios HRV Scientific, version 4.1). Data of HR, HR variability
(HRV), oxygen consumption (VO
2
), and respiratory frequency (RF) were continuously recorded, blood lactate concentration [La‐] before (Pre) and
at the end (End) of the running bouts.
1542
-
GRONWALD
ET AL.
but considerable differences between both methods were present for
the comparison of vVT2 versus vDFAa1‐2 in EG (see also descriptive
analysis and differentiation for FG and EG in Table 1). 20‐vDFAa1‐1
was successfully performed by all participants. In this regard, 20‐
vDFAa1‐2 was completed by only 15 participants (finisher group,
FG), while six participants had to stop ahead of time at
11:47 �03:13 min: s due to exhaustion (exhaustion group, EG), as
indicated by [La‐] mean values of 9.98 �2.41 mmol/L (see Table 1).
Due to artefact rates >5% in RR‐interval raw data, two participants
had to be excluded from the analysis of 20‐vDFAa1‐2 (for DFA a1) in
the FG.
ANOVA results indicate a significant main effect for intensity in
comparison of 20‐vDFAa1‐1 and 20‐DFAa1‐2 for all analyzed pa-
rameters in FG. In addition, a significant main effect of time could be
determined in HR, VO
2
, and RF but not for DFAa1. An effect of inter-
action (intensity �time) could only be found for HR (intensity: F=43.3,
p<0.001, η
2
=0.756; time: F=139.9, p<0.001, η
2
=0.909; and
interaction: F=18.2, p=0.001, η
2
=0.565) and VO
2
(intensity: F=34.6,
p<0.001, η
2
=0.712; time: F=25.7, p<0.001, η
2
=0.647; and
interaction: F=15.3, p=0.002, η
2
=0.522), but not for RF (intensity:
F=21.9, p<0.001, η
2
=0.610; time: F=17.5, p=0.001, η
2
=0.556; and
interaction: F=4.3, p=0.056, η
2
=0.236), and DFAa1 (intensity:
F=12.3, p=0.004, η
2
=0.505; time: F=1.1, p=0.320, η
2
=0.082; and
interaction: F=0.4, p=0.526, η
2
=0.034), respectively.
20‐vDFAa1‐1 and 20‐DFAa1‐2 yielded substantial mean differ-
ences in FG for HR (150.4 �10.6 vs. 170.3 �9.8 bpm, p<0.001,
g=1.90; 76.2 �5.7 vs. 86.4 �5.9 %HR
PEAK,
p<0.001, g=1.71), VO
2
(36.7 �5.2 vs. 46.0 �8.7 mL/kg/min, p<0.001, g=1.26; 62.1 �5.0
vs. 77.5 �8.6 %VO
2PEAK
,p<0.001, g=2.13), RF (40.6 �11.3 vs.
46.1 �9.8 bpm, p<0.001, g=0.50), DFA‐a1 (0.86 �0.23 vs.
0.60 �0.15, p=0.004, g= −1.30), and [La‐] at the end of the running
bouts (1.41 �0.45 vs. 3.34 �2.24 mmol/L; p<0.001, g=1.16, see
Figures 2–5, and descriptive analysis and differentiation data for EG
in Tables 1and 2).
In comparison of the start and end of 20‐vDFAa1‐1 in FG HR and
RF increased moderately from 148.4 �11.0 to 153.9 �11.0 bpm
(p<0.001 and g=0.48) and 38.7 �10.7 to 41.3 �11.8 bpm
(p=0.023 and g=0.22), while VO
2
and DFAa1 remained rather
stable with values of 36.6 �5.0 versus 37.1 �5.6 mL/kg/min
(p=0.108 and g=0.09) and 0.86 �0.28 versus 0.84 �0.19
(p=0.666 and g= −0.08), respectively (see Table 3). Regarding the
alteration of the calculated EF, all parameters showed small changes
for FG (HR: 3.7%, VO
2
: 1.3%, RF: 6.0%, and DFAa1: −2.5%). In
addition, EG also showed small alterations of EF <10% for 20‐
vDFAa1‐1 (HF: 4.8%, VO
2
: 1.4%, RF: 7.8%, and DFAa1: −8.3%).
During the 20‐vDFAa1‐2 running bout of FG HR und RF rose
substantially from 166.6 �9.9 to 175.7 �10.5 bpm (p<0.001 and
g=0.87), and 42.0 �11.2 versus 48.4 �9.5 bpm (p=0.002 and
g=0.59); while, VO
2
increased moderately with 44.2 �7.7 versus
46.8 �9.0 mL/kg/min (p<0.001 and g=0.30) and DFA‐a1 remained
rather stable with 0.65 �0.21 versus 0.57 �0.17 (p=0.262 and
g= −0.41) (see Table 3). The calculated EF showed small changes for
HR and VO
2
(HR: 5.4% and VO
2
: 5.6%), while RF and DFAa1 showed
more substantial alterations above 10% (RF: 15.6% and DFAa1:
−12.8%). In addition, in EG, small to moderate alterations of EF
indices during 20‐vDFAa1‐2 were present for HR (2.9%) and VO
2
(6.7%), while changes in RF (20.1%) and DFAa1 (−35.9%) were sub-
stantially more pronounced.
5
|
DISCUSSION
The aim of this pilot study was to evaluate the ability of DFAa1 to
prescribe and monitor exercise intensity during continuous running
at the boundaries of moderate to heavy and heavy to severe exercise
intensities, respectively. Even though it was not the primary goal to
directly compare different approaches of exercise intensity domain
demarcation (see e.g., Galán–Rioja et al., 2020; Kaufmann et al., 2023),
TABLE 1Comparison of peak running speeds (v
PEAK
) and total duration from the incremental test, vDFAa1‐1, vDFAa1‐2, vVT1, vVT2,
and blood lactate concentration [La‐] before (Pre) and at the end (End) of both running bouts for all participants, the finisher group and the
exhaustion group.
All [n=21] FG [n=15] EG [n=6]
v
PEAK
[km/h] 17.5 �1.7 17.5 �1.7 17.6 �1.8
Test duration [min] 10.9 �1.4 10.8 �1.4 11.3 �1.4
vDFAa1‐1 [km/h] (%v
PEAK
) 10.6 �1.9 (60.2 �8.0) 10.0 �1.5 (57.4 �5.9) 12.0 �2.5 (67.4 �8.4)
vVT1 [km/h] (%v
PEAK
) 10.8 �1.7 (61.7 �6.8) 10.6 �1.8 (60.4 �7.3) 11.5 �1.4 (65.0 �4.3)
vDFAa1‐2 [km/h] (%v
PEAK
) 13.1 �2.4 (74.5 �10.0) 12.3 �1.9 (69.9 �6.8) 15.2 �2.4 (85.8 �7.6)
vVT2 [km/h] (%v
PEAK
) 13.2 �1.9 (75.5 �6.3) 13.1 �2.0 (74.8 �7.0) 13.6 �1.5 (77.2 �3.8)
[La‐] Pre 20‐vDFAa1‐1 [mmol/L] 0.95 �0.29 0.92 �0.27 1.01 �0.37
[La‐] End 20‐vDFAa1‐1 [mmol/L] 1.56 �0.59 1.41 �0.45 1.94 �0.78
[La‐] Pre 20‐vDFAa1‐2 [mmol/L] 1.08 �0.22 1.09 �0.24 1.07 �0.15
[La‐] End 20‐vDFAa1‐2 [mmol/L] 5.24 �3.79 3.34 �2.24 9.98 �2.41
Note: FG: group of 15 participants who finished both prolonged exercise tests; EG: group of 6 participants who did not finish 20‐vDFAa1‐2.
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1543
our data indicate that external loads of vDFAa1‐1 and vDFAa1‐2 were
comparable to vVT1 for all participants and to vVT2 for most of the
participants (FG), respectively. In addition, the overall comparison of
mean values from 20‐vDFAa1‐1 and 20‐vDFAa1‐2 yielded a clear
distinction between the two exercise intensities in all physiological
parameters and indicate a reasonable demarcation of a 3‐zone‐model
of intensity distribution for moderate, heavy, and severe exercise do-
mains (Jamnick et al., 2020; Haugen et al., 2022). Therefore, as already
suggested based on signal‐theory and findings from prior studies using
incremental exercise tests (Gronwald, Törpel, et al., 2020; Gronwald &
Hoos, 2020; Rogers & Gronwald, 2022; Sempere‐Ruiz et al., 2024),
exercise prescription using running speeds at DFAa1 values of 0.75 and
0.5 (vDFAa1‐1, vDFAa1‐2) separate reasonable intensity domains for
prolonged constant exercise bouts for most participants. In our
approach, these different domains do not directly rely on metabolic
markers but rather are based on the complex changes in autonomic
modulation due to parasympathetic withdrawal, sympathetic activa-
tion, altered nonneural factors, and the potential loss of interaction
between the two branches of the ANS with increased exercise intensity
(Persson, 1996; White & Raven, 2014). However, substantial interin-
dividual fluctuations in internal load occur for both prolonged running
bouts that are related to general problems of exercise prescription for
prolonged exercise when intensity zone markers are derived from in-
cremental exercise tests (Iannetta, de Almeida Azevedo, et al., 2019,
2020; Jamnick et al., 2020; Zuccarelli et al., 2018). Further, our data
also support the notion that the magnitude and practical relevance of
FIGURE 2 Comparison of heart rate (%HR
PEAK
, mean, and SD) kinetics during 20‐vDFAa1‐1 and 20‐vDFAa1‐2 of the finisher group.
FIGURE 3 Comparison of oxygen consumption (%VO
2PEAK
, mean, and SD) kinetics during 20‐vDFAa1‐1 and 20‐vDFAa1‐2 of the finisher
group.
1544
-
GRONWALD
ET AL.
these interindividual differences depend on the addressed intensity
domain, as substantial and practically relevant differences were mainly
found in vDFAa1‐2, and these differences lead to premature exhaus-
tion in the high intensity running bout for more than 25% of the par-
ticipants (EG, n=6).
5.1
|
Prolonged constant load exercise prescription
from incremental testing
Prolonged constant load exercises derived from external load pre-
scriptions of incremental tests bear the general problem that the
physiological response may vary considerably between individuals
both at the beginning and throughout the constant load exercise (e.g.,
Iannetta, de Almeida Azevedo, et al., 2019; Jamnick et al., 2020). This
could be seen in all our metabolic and cardiorespiratory markers,
including DFAa1, which was used for prescription of vDFAa1‐1
(DFAa1 =0.75) and vDFAa1‐2 (DFAa1 =0.5). In addition, recent
findings even indicate an unclear assignment of an intensity domain
during constant load exercise of prolonged duration when using the
highly individual acute responses of %HR
PEAK
as a benchmark (Ian-
netta, de Almeida Azevedo, et al., 2019). In that regard, for prolonged
exercise prescription, it must be considered that laboratory testing
with incremental design (step and ramp) needs to account for specific
response kinetics of the corresponding physiological markers, and
the magnitude of the interindividual variability depends on the
interaction of the used biomarker, its response kinetics, and the in-
cremental exercise protocol (Zuccarelli et al., 2018; Iannetta,
FIGURE 4 Comparison of respiratory frequency (RF, mean, and SD) kinetics during 20‐vDFAa1‐1 and 20‐vDFAa1‐2 of the finisher group.
FIGURE 5 Comparison of DFAa1 (mean and SD) kinetics during 20‐vDFAa1‐1 and 20‐vDFAa1‐2 of the finisher group.
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1545
Murias, & Keir, 2019). External load prescription assumes that
physiological responses are rather static (Jamnick et al., 2020;
Maunder et al., 2021) and neglect the influence of internal and
external factors leading to heterogeneity in exercise tolerance and
physiological responses over time (e.g., personal or environmental
factors, Gronwald, Törpel, et al., 2020; Meyler et al., 2023). The large
variation of internal load responses in our data seem to be also
present when prescriptions based on fixed submaximal threshold
approaches (e.g., [La‐]) or individual submaximal threshold ap-
proaches are made (e.g., GET) (Fleckenstein et al., 2023; Brownstein
et al., 2022). In addition, pre‐exhaustion due to incremental testing
may also lead to an altered internal‐to‐external load relationship at
an intensity domain transition compared to the beginning of pro-
longed exercise (with or without standardized warm‐up procedures)
revealing the need to address exercise duration as an important in-
dependent prescription factor (Hofmann & Tschakert, 2017; Tscha-
kert et al., 2022). This also applies to other external load indicators
such as movement frequency (e.g., cadence in cycling exercise; Ben-
eke & Leithäuser, 2017; Gronwald et al., 2018). In this regard, recent
findings from DFA of HRV during running show that repeated in-
cremental running tests shift the agreement between gas exchange
thresholds and DFAa1‐derived boundaries for intensity demarcation,
leading to the assumption of fatigue‐related inter‐and intraindividual
physiological perturbations depicted in DFAa1 kinetics (van Hooren,
Bongers, et al., 2023; van Hooren, Mennen, et al., 2023). Therefore, it
seems reasonable to address these issues using an internal‐load‐
based approach of exercise prescription for prolonged constant
load exercise to consider the individual and daily responses to a
prescribed external load accounting for personal and environmental
influences on the most prominent underlying trend in HR data, the
cardiovascular drift (Ekelund, 1967). Recently, a HR‐based exercise
intensity control approach using a HR clamp that kept HR constant
over time by adjusting speed/power (Zuccarelli et al., 2018; Li
et al., 2023) showed substantial differences for standard HRV metrics
during exercise when compared to constant load exercise with cor-
responding HR drifts (Brockmann & Hunt, 2023; Hernando
et al., 2018; Hunt & Saengsuwan, 2018). However, in this context,
further questions need to be clarified about suitability of different
subsystem parameters of internal load and an “optimal” and feasible
real‐time monitoring approach for the control of exercise intensity
(e.g., HR drift and the potential underestimation of rating of perceived
exertion (RPE); Cartón–Llorente et al., 2022). Here, a dimensionless,
global, and systemic internal load indicator, such as DFAa1 (in addition
to RPE as an easily accessible subjective marker), could provide the
potential for further investigation in prolonged exercise regimes
(Gronwald, Berk, et al., 2021; Rogers & Gronwald, 2022). However, it
seems mandatory to evaluate mid‐and long‐term training outcomes
when controlling exercise intensity based on internal load markers, as
this may lead to significant and interindividual varying reduction in
exercise and training stimuli (Zuccarelli et al., 2018).
5.2
|
Intensity domain dependency for prolonged
exercise prescription
Besides the already discussed general problems of exercise pre-
scription for prolonged constant load exercise from incremental
testing, our data also points toward an intensity specific aspect of
these issues that needs to be further addressed. On the one hand, our
data show that the intensity prescription for 20‐vDFAa1‐1 elicits a
[La‐] below 2 mmoL/L, and magnitudes of %HR
PEAK
and %VO
2PEAK
for FG and EG (Tables 1–3) that clearly mirror medium to upper
levels of a moderate intensity domain in established 3‐zone‐models
(Jamnick et al., 2020; Haugen et al., 2022). Besides the mean
values the interindividual differences in %HR
PEAK
and %VO
2PEAK
are
in line with the magnitudes shown in a recent study based on [La‐]‐
derived LT prescription (Fleckenstein et al., 2023). In addition, when
considering recently proposed ratios for the assessment of internal‐
to‐external load relationships and decoupling mechanisms (Maunder
et al., 2021; Smyth et al., 2022) in terms of EF of HR, VO
2
, RF, and
DFAa1 in relation to running speed, a comparison of start and end of
the running bouts lead to rather small alterations of EF <10% in all
TABLE 2Summary of all physiological mean data (�standard deviation) from 20‐vDFAa1‐1 and 20‐vDFAa1‐2 for the finisher group and
the exhaustion group.
FG [n=15, n=13 for DFAa1 in 20‐
vDFAa1‐2] EG [n=6]
20‐vDFAa1‐1
20‐
vDFAa1‐2 Statistics 20‐vDFAa1‐1
20‐
vDFAa1‐2
HR [bpm]
(%HR
PEAK
)
150.4 �10.6
(76.2 �5.7)
170.3 �9.8
(86.4 �5.9)
p<0.001,
g=1.90
165.1 �10.5
(82.3 �5.3)
189.3 �5.5
(94.3 �2.1)
VO
2
[ml/kg/min]
(%VO
2PEAK
)
36.7 �5.2
(62.1 �5.0)
46.0 �8.7
(77.5 �8.6)
p<0.001,
g=1.26
41.5 �7.2
(71.7 �10.7)
53.9 �7.3
(92.9 �2.2)
RF [bpm] 40.6 �11.3 46.1 �9.8 p<0.001,
g=0.50
40.6 �6.8 51.1 �3.4
DFAa1 0.86 �0.23 0.60 �0.15 p=0.004,
g= −1.30
0.76 �0.27 0.48 �0.17
Note:T‐test statistics and effect sizes are stated for the comparison of 20‐vDFAa1‐1 versus vDFAa1‐2 in FG. FG: group of 15 participants who finished
both prolonged exercise tests; EG: group of 6 participants who did not finish 20‐vDFAa1‐2.
1546
-
GRONWALD
ET AL.
parameters in both FG and EG. These values of a small HR drift
without a slow component in VO
2
support the notion of a DFAa1‐
derived separation of the moderate and heavy intensity domain.
On the other hand, for 20‐vDFAa1‐2 derived from DFAa1 values
of 0.5 during incremental testing, [La‐]‐values of approx. 3.5 mmol/l
as well as %HR
PEAK
and %VO
2PEAK
in FG (n=15) can be matched
within the lower to medium range of the heavy intensity domain,
while the corresponding values for EG (n=6) that could not sustain
the 20‐min exercise duration clearly exceed the boundary toward the
severe intensity domain (Jamnick et al., 2020; Haugen et al., 2022).
Further, 20‐vDFAa1‐2 lead to substantial alterations of EF with a
magnitude of >10% for RF and DFAa1 in FG and >20% for EG, which
shows the potential of these two internal load parameters regarding
further decoupling analysis of internal‐to‐external relationship. In
this context, RF was recently mentioned as a promising internal load
marker in exercise physiology and offers new possibilities for wear-
able analyses in research and practical settings (Nicolo et al., 2017;
Nicolo & Sacchetti, 2023).
The probable overestimation of running velocity in the subsam-
ple of EG is further in line with previous studies that already dis-
cussed potential overestimations for a relevant number of
participants using the present approach of nonlinear HRV analysis to
delineate the heavy from the severe intensity domain (Rogers, Giles,
Draper, Mourot, et al., 2021; Mateo‐March et al., 2023). One factor
might be that (linear) HRV metrics are both intensity and time
dependent and may reach close to minimum values with low signal‐
to‐noise ratio rapidly (Brockmann & Hunt, 2023). However, to what
extent this is true for nonlinear measures, such as DFAa1, needs to
be further elucidated in, for example, HR clamp exercise. Further, as
stated before (Gronwald & Hoos, 2020; Kaufmann et al., 2023;
Rogers & Gronwald, 2022), despite the need for comparison with
established intensity domain threshold concepts, it should be kept in
mind that the present approach is based on the theoretical frame-
work of a self‐organized dynamic regulation of the central autonomic
network (CAN, Benarroch, 1993) that is reflected in the correlation
properties of HR dynamics. Therefore, it is rather complementary to
and does not necessarily coincide with classical metabolic threshold
concepts based on metabolic and/or respiratory biomarkers. As
mentioned above, the definition of intensity domain boundaries
might involve different approaches based on performance indicators
of external load (e.g., critical speed or power, CS, and CP), subsystem
indicators of internal load such as [La‐] (e.g., lactate threshold and
maximal lactate steady state) and/or gas exchange data (e.g., gas
exchange threshold, GET), that interact with their corresponding
different testing protocols. This may produce inconsistent results
leading to substantially different delineations of the boundaries in a
3‐zone‐model of intensity zones and is reflected in the still ongoing
debate about gold standard approaches to delineate moderate from
heavy, and especially heavy from severe intensity domains (Chicharro
et al., 1997; Galán‐Rioja et al., 2020; Hopker et al., 2011; Iannetta, de
Almeida Azevedo, et al., 2019; Jamnick et al., 2018; Pallarés
et al., 2016; Poole et al., 2021). Therefore, misleading comparisons
between protocols as well as undesired training outcomes in athletes
attempting to emulate a proposed method are also present when
other approaches are used, and this seems to be most problematic
for the boundary of heavy to severe exercise intensity (Galán‐Rioja
TABLE 3Summary of all physiological mean data (�standard deviation) from the start and end of 20‐vDFAa1‐1 and 20‐vDFAa1‐2 for
the finisher group and the exhaustion group.
20‐vDFAa1‐1 20‐vDFAa1‐2
Start End Statistics Start End Statistics
FG [n=15, n=13 for DFAa1 in 20‐vDFAa1‐2]
HR [bpm]
(%HR
PEAK
)
148.4 �11.0
(75.2 �6.0)
153.9 �11.0
(78.0 �5.8)
p<0.001,
g=0.48
166.6 �9.9
(84.5 �6.1)
175.7 �10.5
(89.1 �6.2)
p<0.001,
g=0.87
VO
2
[ml/kg/min]
(%VO
2PEAK
)
36.6 �5.0
(61.9 �5.1)
37.1 �5.6
(62.7 �5.7)
p=0.108,
g=0.09
44.2 �7.7
(74.5 �7.3)
46.8 �9.0
(78.9 �9.2)
p<0.001,
g=0.30
RF [bpm] 38.7 �10.7 41.3 �11.8 p=0.023,
g=0.22
42.0 �11.2 48.4 �9.5 p=0.002,
g=0.59
DFAa1 0.86 �0.28 0.84 �0.19 p=0.666,
g= −0.08
0.65 �0.21 0.57 �0.17 p=0.262,
g= −0.41
EG [n=6]
HR [bpm]
(%HR
PEAK
)
161.8 �10.1
(80.7 �4.7)
169.7 �11.2
(84.6 �5.9)
‐188.5 �4.7
(94.0 �2.7)
194.3 �5.9
(96.8 �2.5)
‐
VO
2
[ml/kg/min]
(%VO
2PEAK
)
41.2 �6.4
(71.1 �8.4)
41.8 �7.4
(72.3 �12.3)
‐51.9 �6.8
(89.4 �2.4)
55.5 �8.3
(95.4 �2.0)
‐
RF [bpm] 38.8 �7.6 42.0 �7.3 ‐46.3 �5.4 55.7 �3.2 ‐
DFAa1 0.81 �0.36 0.62 �0.26 ‐0.55 �0.25 0.34 �0.13 ‐
Note:T‐test statistics and effect sizes are stated for the comparison of “Start” versus “End” in 20‐vDFAa1‐1 and vDFAa1‐2 in FG. FG: group of 15
participants who finished both prolonged exercise tests; EG: group of 6 participants who did not finish 20‐vDFAa1‐2.
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1547
et al., 2020; Iannetta, de Almeida Azevedo, et al., 2019; Jamnick
et al., 2018; Poole et al., 2021).
Taken together based on the present results and the available
data of previous studies using DFAa1 as an complementary exercise
prescriptor (Mateo‐March et al., 2023; Rogers, Giles, Draper, Hoos,
et al., 2021; Rogers, Giles, Draper, Mourot, et al., 2021; Schaffarczyk
et al., 2023; van Hooren, Mennen, et al., 2023), it must be noted that
for some individuals the present approach does not lead to an
adequate specification of exercise intensity at the boundary of the
heavy to severe exercise domain. Therefore, further investigations
should be dedicated to the considerable differences of DFAa1‐
derived threshold determination for 20‐vDFAa1‐2 in EG, leading to
overestimation of running velocity in this subsample. Here, for
example, the influence of individuality in time and intensity depen-
dent changes in the scaling behavior of DFA (Molkkari et al., 2020;
Kanniainen et al., 2023) as well as the model fitting and the model
type (e.g., linear, polynomial, and sigmoidal) of DFAa1‐derived
threshold determination could be subject to further investigations.
In prior studies, we observed inappropriate suppression of correla-
tion properties of HR time series in some individuals losing dynamic
range of DFAa1 despite good ECG waveform and little artefact (van
Hooren, Mennen, et al., 2023). In addition, future studies should
enlighten the relevance of standardization of methodological aspects
(e.g., quality of data acquisition, preprocessing, and artifact correction
methods depending on the type/mode of exercise and/or laboratory
vs. field conditions) on DFAa1‐derived exercise prescription and
evaluate more thoroughly the significance of primary internal (e.g.,
breathing) and external influencing factors (e.g., environmental
conditions).
6
|
LIMITATIONS
The prolonged exercise bouts were too short to provide evidence
whether our approach of DFAa1‐derived exercise prescription may
be useful for typical duration of running training (e.g., 30–60 min), as
these longer durations may further complicate potential “decoupling
mechanisms”. However, our data as well as findings from prior
studies at least indicated that the magnitude of duration‐related
influences and the potential for fatigue resistance assessment dur-
ing prolonged exercise regimes could be further evaluated using a
DFAa1 approach (Gronwald et al., 2018,2019; Gronwald, Berk,
et al., 2021). Longer exercise bouts are also needed to increase
sensitivity for the evaluated EF. In addition, since external load was
maintained constantly for the prolonged exercise bouts, the analysis
of internal‐to‐external load relationship and decoupling mechanism
would be more appropriate to use within the application in‐field
conditions and/or self‐paced scenarios. Whether other theoreti-
cally appealing approaches using ratios of individually designed
external‐to‐internal load markers, such as, maximal or submaximal
external load markers like CP or CS in combination with DFAa1
and/or %HR recovery or %HR
MAX
might be helpful also remains an
open question.
7
|
CONCLUSION
For most participants, DFAa1 shows great potential as a dimen-
sionless and systemic index for internal load‐based exercise pre-
scription with a clear demarcation perspective for a 3‐zone training
intensity distribution model. However, for some individuals, the
present approach does not lead to an adequate separation of exer-
cise intensities, especially not for the heavy to severe exercise do-
mains. Therefore, further investigations are recommended to account
for interindividual differences and to better understand the rela-
tionship of DFAa1 and vDFAa1 and its relevance for the time evo-
lution of fatigue during prolonged constant load exercise. In this
regard, the potential for internal load‐based real‐time monitoring and
intraindividual internal‐to‐external load analysis as a regular biolog-
ical calibration procedure accounting for personal and environmental
factors might be strengthened by further exercise specific method-
ological refinements of DFA. In addition, future studies should
elucidate possible decoupling mechanisms of DFAa1 and other in-
ternal load measures in relation to external load (and other influ-
encing factors, e.g., exercise mode, environmental conditions, and
pre‐exhaustion) during even longer exercise bouts that correspond to
typical exercise durations of real‐world running training (>30 min).
AUTHOR CONTRIBUTIONS
Olaf Hoos and Thomas Gronwald designed the research. Leonie Horn
and Olaf Hoos conducted the experiments and data processing.
Thomas Gronwald and Olaf Hoos conducted data analysis and
interpretation. Thomas Gronwald drafted the raw manuscript. All
authors provided critical comments on the manuscript, read, and
approved the final version of the manuscript.
ACKNOWLEDGMENTS
The authors would like to thank all participants for their time for
taking part in this study. The authors would also like to thank
Sebastian Kaufmann, Moritz Wagenhaeuser, and Lukas Berberich for
their help in data acquisition. None of the authors received funding
for this work from any organization other than salary support for the
authors from their respective institutions.
Open Access funding enabled and organized by Projekt DEAL.
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no conflicts of interest.
DATA AVAILABILITY STATEMENT
Data are available from the corresponding author on reasonable
request.
ORCID
Thomas Gronwald
https://orcid.org/0000-0001-5610-6013
REFERENCES
Beaver, W. L., K. Wasserman, and B. J. Whipp. 1986. “A New Method for
Detecting Anaerobic Threshold by Gas Exchange.” Journal of Applied
1548
-
GRONWALD
ET AL.
Physiology 60(6): 2020–7. https://doi.org/10.1152/jappl.1986.60.6.
2020.
Benarroch, Eduardo E. 1993. “The Central Autonomic Network: Func-
tional Organization, Dysfunction, and Perspecti‐Ve.” Mayo Clinic
Proceedings 68(10): 988–1001. https://doi.org/10.1016/s0025‐6196
(12)62272‐1.
Beneke, Ralph, and Renate M. Leithäuser. 2017. “Maximal Lactate Steady
State's Dependence on Cycling Cadence.” International Journal of
Sports Physiology and Performance 12(3): 304–9. https://doi.org/10.
1123/ijspp.2015‐0573.
Brockmann, Lars, and Kenneth J. Hunt. 2023. “Heart Rate Variability
Changes with Respect to Time and Exercise Intensity During Heart‐
Rate‐Controlled Steady‐State Treadmill Running.” Scientific Reports
13(1): 8515. https://doi.org/10.1038/s41598‐023‐35717‐0.
Brownstein, Callum G., Frederic Sabater Pastor, José Mira, Juan M.
Murias, and Guillaume Y. Millet. 2022. “Power Output Manipulation
from Below to Above the Gas Exchange Threshold Results in
Exacerbated Performance Fatigability.” Medicine & Science in Sports &
Exercise 54(11): 1947–60. https://doi.org/10.1249/mss.000000
0000002976.
Cartón‐Llorente, Antonio, Luis E. Roche‐Seruendo, Elena Mainer‐Pardos,
Hadi Nobari, Alberto Rubio‐Peirotén, Diego Jaén‐Carrillo, and Felipe
García‐Pinillos. 2022. “Acute Effects of a 60‐min Time Trial on
Power‐Related Parame‐Ters in Trained Endurance Runners.” BMC
Sports Science, Medicine & Rehabilitation 14(1): 142. https://doi.org/
10.1186/s13102‐022‐00538‐7.
Chicharro, J. L., M. Pérez, A. F. Vaquero, A. Lucía, and J. C. Legido. 1997.
“Lactic Threshold vs Ventilatory Threshold During a Ramp Test on a
Cycle Ergometer.” The Journal of Sports Medicine and Physical Fitness
37(2): 117–21.
Cohen, J. 1988. Statistical Power Analysis for the Behavioural Sciences.
Hillsdale, MI, USA: Erlbaum.
Di Veroli, Giovanni Y., Chiara Fornari, Ian Goldlust, Graham Mills,
Siang Boon Koh, Jo L. Bramhall, Frances M. Richards, and Duncan I.
Jodrell. 2015. “An Automated Fitting Procedure and Software for
Dose‐Response Curves with Multiphasic Features.” Scientific Reports
5(1): 14701. https://doi.org/10.1038/srep14701.
Ekelund, L. G. 1967. “Circulatory and Respiratory Adaptation During
Prolonged Exercise of Moderate Intensity in the Sitting Position.”
Acta Physiologica Scandinavica 69(4): 327–40. https://doi.org/10.
1111/j.1748‐1716.1967.tb03529.x.
Fernandes de Godoy, Moacir. 2016. “Nonlinear Analysis of Heart Rate
Variability: A Comprehensive Review.” Journal of Cardiology: Therapy
3: 528–33. https://doi.org/10.17554/j.issn.2309‐6861.2016.03.
101‐4.
Fleckenstein, Daniel, Jannik Seelhöfer, Nico Walter, and Olaf Ueberschär.
2023. “From Incremental Test to Continuous Running at Fixed
Lactate Thresholds: Individual Responses on %VO2max, %HRmax,
Lactate Accumulation, and RPE.” Sports (Basel). 11(10): 198. https://
doi.org/10.3390/sports11100198.
Galán‐Rioja, Miguel Ángel, Fernando González‐Mohíno, David C. Poole,
and José M. ª. González‐Ravé. 2020. “Relative Proximity of Critical
Power and Metabolic/Ventilatory Thresholds: Systematic Review
and Meta‐Analysis.” Sports Medicine 50(10): 1771–83. https://doi.
org/10.1007/s40279‐020‐01314‐8.
Gallo, Gabriele, Emanuela Luisa Faelli, Piero Ruggeri, Luca Filipas, Roberto
Codella, Daniel J. Plews, and Ed Maunder. 2024. “Power Output at
the Moderate‐To‐Heavy Intensity Transition Decreases in a Non‐
linear Fashion During Prolonged Exercise.” European Journal of
Applied Physiology: Advance online publication. https://doi.org/10.
1007/s00421‐024‐05440‐3.
Goldberger, Ary L., Luis A. N. Amaral, Jeffrey M. Hausdorff, Plamen Ch
Ivanov, C. K. Peng, and H. Eugene Stanley. 2002. “Fractal Dynamics
in Physiology: Alterations with Disease and Aging.” PNAS
99(suppl_1): 2466–72. https://doi.org/10.1073/pnas.012579499.
Gronwald, Thomas, Sander Berk, Marco Altini, Laurent Mourot, Olaf
Hoos, and Bruce Rogers. 2021. “Real‐Time Estimation of Aerobic
Threshold and Exercise Intensity Distribution Using Fractal Corre-
lation Properties of Heart Rate Variability: A Single‐Case Field
Application in a Former Olympic Triathlete.” Frontiers in Sports and
Active Living 3: 668812. https://doi.org/10.3389/fspor.2021.668812.
Gronwald, Thomas, and Olaf Hoos. 2020. “Correlation Properties of Heart
Rate Variability During Endurance Exercise: A Systematic Review.”
Annals of Noninvasive Electrocardiology 25(1): e12697. https://doi.org/
10.1111/anec.12697.
Gronwald, Thomas, Olaf Hoos, and Kuno Hottenrott. 2019. “Effects of
Acute Normobaric Hypoxia on Non‐linear Dynamics of Cardiac
Autonomic Activity during Constant Workload Cycling Exercise.”
Frontiers in Physiology 10: 999. https://doi.org/10.3389/fphys.2019.
00999.
Gronwald, Thomas, Sebastian Ludyga, Olaf Hoos, and Kuno Hottenrott.
2018. “Non‐linear Dynamics of Cardiac Autonomic Activity During
Cycling Exercise with Varied Cadence.” Human Movement Science 60:
225–33. https://doi.org/10.1016/j.humov.2018.06.013.
Gronwald, Thomas, Bruce Rogers, and Olaf Hoos. 2020. “Fractal Corre-
lation Properties of Heart Rate Variability: A New Biomarker for
Intensity Distribution in Endurance Exercise and Training Prescrip-
tion?” Frontiers in Physiology 11: 550572. https://doi.org/10.3389/
fphys.2020.550572.
Gronwald, Thomas, Bruce Rogers, Laura Hottenrott, Olaf Hoos, and Kuno
Hottenrott. 2021. “Correlation Properties of Heart Rate Variability
During a Marathon Race in Recreational Runners: Potential
Biomarker of Complex Regulation During Endurance Exercise.”
Journal of Sports Science and Medicine 20(4): 557–63. https://doi.org/
10.52082/jssm.2021.557.
Gronwald, Thomas, Alexander Törpel, Fabian Herold, and Henning Budde.
2020. “Perspective of Dose and Response for Individualized Physical
Exercise and Training Prescription.” Journal of Functional Morphology
and Kinesiology 5(3): 48. https://doi.org/10.3390/jfmk5030048.
Hamilton, Kate, Andrew E. Kilding, Daniel J. Plews, Mathew J. Mildenhall,
Mark Waldron, Thanchanok Charoensap, Tobias H. Cox, Matthew J.
Brick, Warren B. Leigh, and Ed Maunder. 2024. “Durability of the
Moderate‐To‐Heavy‐Intensity Transition Is Related to the Effects of
Prolonged Exercise on Severe‐Intensity Performance.” European
Journal of Applied Physiology: Advance online publication. https://doi.
org/10.1007/s00421‐024‐05459‐6.
Haugen, Thomas, Øyvind Sandbakk, Stephen Seiler, and Espen Tønnessen.
2022. “The Training Characteristics of World‐Class Distance Run-
ners: An Integration of Scientific Literature and Results‐Proven
Practice.” Sports Medicine ‐Open 8(1): 46. https://doi.org/10.1186/
s40798‐022‐00438‐7.
Hautala, Arto J., Timo H. Mäkikallio, Tapio Seppänen, Heikki V. Huikuri,
and Mikko P. Tulppo. 2003. “Short‐term Correlation Properties of R‐
R Interval Dynamics at Different Exercise Intensity Levels.” Clinical
Physiology and Functional Imaging 23(4): 215–23. https://doi.org/10.
1046/j.1475‐097x.2003.00499.x.
Hedges, Larry V. 1981. “Distribution Theory for Glass’s Estimator of Ef-
fect Size and Related Estimators.” Journal of Educational Statistics
6(2): 107–28. https://doi.org/10.3102/10769986006002107.
Hernando, David, Alberto Hernando, Jose A. Casajús, Pablo Laguna, Nuria
Garatachea, and Raquel Bailón. 2018. “Methodological Framework
for Heart Rate Variability Analysis During Exercise: Application to
Running and Cycling Stress Testing.” Medical, & Biological Engineer-
ing & Computing 56(5): 781–94. https://doi.org/10.1007/s11517‐
017‐1724‐9.
Hofmann, Peter, and Gerhard Tschakert. 2017. “Intensity‐and Duration‐
Based Options to Regulate Endurance Training.” Frontiers in Physi-
ology 8: 337. https://doi.org/10.3389/fphys.2017.00337.
Hopker, J. G., S. A. Jobson, and J. J. Pandit. 2011. “Controversies in the
Physiological Basis of the 'Anaerobic Threshold' and Their
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1549
Implications for Clinical Cardiopulmonary Exercise Testing.” Anaes-
thesia 66(2): 111–23. https://doi.org/10.1111/j.1365‐2044.2010.
06604.x.
Hunt, Kenneth J., and Jittima Saengsuwan. 2018. “Changes in Heart Rate
Variability with Respect to Exercise Intensity and Time During
Treadmill Running.” BioMedical Engineering Online 17(1): 128. https://
doi.org/10.1186/s12938‐018‐0561‐x.
Iannetta, Danilo, Rafael de Almeida Azevedo, Daniel A. Keir, and Juan M.
Murias. 2019. “Establishing the V
o2 VSersus Constant‐Work‐Rate
Relationship from Ramp‐Incremental Exercise: Simple Strategies
for an Unsolved Problem.” Journal of Applied Physiology 127(6):
1519–27. https://doi.org/10.1152/japplphysiol.00508.2019.
Iannetta, Danilo, Erin Calaine Inglis, Anmol T. Mattu, Federico Y. Fontana,
Silvia Pogliaghi, Daniel A. Keir, and Juan M. Murias. 2020. “A Critical
Evaluation of Current Methods for Exercise Prescription in Women
and Men.” Medicine & Science in Sports & Exercise 52(2): 466–73.
https://doi.org/10.1249/mss.0000000000002147.
Iannetta, Danilo, Juan M. Murias, and Daniel A. Keir. 2019. “A Simple
Method to Quantify the V˙O2 Mean Response Time of Ramp‐
Incremental Exercise.” Medicine & Science in Sports & Exercise 51(5):
1080–6. https://doi.org/10.1249/mss.0000000000001880.
Jamnick, Nicholas A., Javier Botella, David B. Pyne, and David J. Bishop.
2018. “Manipulating Graded Exercise Test Variables Affects the
Validity of the Lactate Threshold and VO2peak.” PLoS One 13(7):
e0199794. https://doi.org/10.1371/journal.pone.0199794.
Jamnick, Nicholas A., Robert W. Pettitt, Cesare Granata, David B. Pyne,
and David J. Bishop. 2020. “An Examination and Critique of Current
Methods to Determine Exercise Intensity.” Sports Medicine 50(10):
1729–56. https://doi.org/10.1007/s40279‐020‐01322‐8.
Jones, Andrew M. 2023. “The Fourth Dimension: Physiological Resilience
as an Independent Determinant of Endurance Exercise Perfor-
mance.” The Journal of Physiology: Advance online publication.
https://doi.org/10.1113/JP284205.
Joyner, M. J. 1991. “Modeling: Optimal Marathon Performance on the
Basis of Physiological Factors.” Journal of Applied Physiology 70(2):
683–7. https://doi.org/10.1152/jappl.1991.70.2.683.
Joyner, Michael J., and Edward F. Coyle. 2008. “Endurance Exercise
Performance: The Physiology of Champions.” The Journal of physi-
ology 586(1): 35–44. https://doi.org/10.1113/jphysiol.2007.143834.
Kanniainen, Matias, Teemu Pukkila, Joonas Kuisma, Matti Molkkari,
Kimmo Lajunen, and Esa Räsänen. 2023. “Estimation of Physiological
Exercise Thresholds Based on Dynamical Correlation Properties of
Heart Rate Variability.” Frontiers in Physiology 14: 1299104. https://
doi.org/10.3389/fphys.2023.1299104.
Kauffman, S. A. 1995. At Home in the Universe: The Search for Laws of Self‐
Organization and Complexity. Oxford, UK: Oxford University Press.
Kaufmann, Sebastian, Thomas Gronwald, Fabian Herold, and Olaf Hoos.
2023. “Heart Rate Variability‐Derived Thresholds for Exercise In-
tensity Prescription in Endurance Sports: A Systematic Review of
Interrelations and Agreement with Different Ventilatory and Blood
Lactate Thresholds.” Sports Medicine ‐Open 9(1): 59. https://doi.org/
10.1186/s40798‐023‐00607‐2.
Li, Siu Nam, Peter Peeling, Brendan R. Scott, Jeremiah J. Peiffer, Alex
Shaykevich, and Olivier Girard. 2023. “Automatic Heart Rate Clamp:
A Practical Tool to Control Internal and External Training Loads
during Aerobic Exercise.” Frontiers in Physiology 14: 1170105.
https://doi.org/10.3389/fphys.2023.1170105.
Mann, Theresa, Robert Patrick Lamberts, and Michael Ian Lambert. 2013.
“Methods of Prescribing Relative Exercise Intensity: Physiological
and Practical Considerations.” Sports Medicine 43(7): 613–25.
https://doi.org/10.1007/s40279‐013‐0045‐x.
Mateo‐March, Manuel, Manuel Moya‐Ramón, Alejandro Javaloyes,
Cristóbal Sánchez‐Muñoz, and Vicente J. Clemente‐Suárez. 2023.
“Validity of Detrended Fluctuation Analysis of Heart Rate Variability
to Determine Intensity Thresholds in Elite Cyclists.” European Journal
of Sport Science 23(4): 580–7. https://doi.org/10.1080/17461391.
2022.2047228.
Maunder, Ed, Stephen Seiler, Mathew J. Mildenhall, Andrew E. Kilding,
and Daniel J. Plews. 2021. “The Importance of 'Durability' in the
Physiological Profiling of Endurance Athletes.” Sports Medicine 51(8):
1619–28. https://doi.org/10.1007/s40279‐021‐01459‐0.
McKay, Alannah K. A., Trent Stellingwerff, Ella S. Smith, David T. Martin,
Iñigo Mujika, Vicky L. Goosey‐Tolfrey, Jeremy Sheppard, and
Louise M. Burke. 2022. “Defining Training and Performance Caliber:
A Participant Classification Framework.” International Journal of
Sports Physiology and Performance 17(2): 317–31. https://doi.org/10.
1123/ijspp.2021‐0451.
Meyer, T., A. Lucía, C. P. Earnest, and W. Kindermann. 2005. “A Con-
ceptual Framework for Performance Diagnosis and Training Pre-
scription from Submaximal Gas Exchange Parameters‐‐Theory and
Application.” International Journal of Sports Medicine 26(Suppl 1):
S38–48. https://doi.org/10.1055/s‐2004‐830514.
Meyler, Samuel, Lindsay Bottoms, David Wellsted, and Daniel Muniz‐
Pumares. 2023. “Variability in Exercise Tolerance and Physiological
Responses to Exercise Prescribed Relative to Physiological Thresh-
olds and to Maximum Oxygen Uptake.” Experimental Physiology
108(4): 581–94. https://doi.org/10.1113/ep090878.
Molkkari, Matti, Giorgio Angelotti, Thorsten Emig, and Esa Räsänen. 2020.
“Dynamical Heart Beat Correlations during Running.” Scientific Re-
ports 10(1): 13627. https://doi.org/10.1038/s41598‐020‐70358‐7.
Nicolò, Andrea, Carlo Massaroni, and Louis Passfield. 2017. “Respiratory
Frequency During Exercise: The Neglected Physio‐Logical Measure.”
Frontiers in Physiology 8: 922. https://doi.org/10.3389/fphys.2017.
00922.
Nicolò, Andrea, and Massimo Sacchetti. 2023. “Differential Control of
Respiratory Frequency and Tidal Volume during Exer‐Cise.” Euro-
pean Journal of Applied Physiology 123(2): 215–42. https://doi.org/10.
1007/s00421‐022‐05077‐0.
Pallarés, Jesús G., Ricardo Morán‐Navarro, Juan Fernando Ortega,
Valentín Emilio Fernández‐Elías, and Ricardo Mora‐Rodriguez. 2016.
“Validity and Reliability of Ventilatory and Blood Lactate Thresholds
in Well‐Trained Cyclists.” PLoS One 11(9): e0163389. https://doi.org/
10.1371/journal.pone.0163389.
Peng, C. K., Shlomo Havlin, H. Eugene Stanley, and Ary L. Goldberger.
1995. “Quantification of Scaling Exponents and Crossover Phe-
nomena in Nonstationary Heartbeat Time Series.” Chaos 5(1): 82–7.
https://doi.org/10.1063/1.166141.
Persson, P. B. 1996. “Modulation of Cardiovascular Control Mechanisms
and Their Interaction.” Physiological Reviews 76(1): 193–244. https://
doi.org/10.1152/physrev.1996.76.1.193.
Poole, David C., Harry B. Rossiter, George A. Brooks, and L. Bruce
Gladden. 2021. “The Anaerobic Threshold: 50þYears of Contro-
versy.” The Journal of Physiology 599(3): 737–67. https://doi.org/10.
1113/jp279963.
Rogers, Bruce, David Giles, Nick Draper, Laurent Mourot, and Thomas
Gronwald. 2021. “Detection of the Anaerobic Threshold in Endur-
ance Sports: Validation of a New Method Using Correlation Prop-
erties of Heart Rate Variability.” Journal of Functional Morphology and
Kinesiology 6(2): 38. https://doi.org/10.3390/jfmk6020038.
Rogers, Bruce, David Giles, Nick Draper, Olaf Hoos, and Thomas Gron-
wald. 2021. “A New Detection Method Defining the Aerobic
Threshold for Endurance Exercise and Training Prescription Based
on Fractal Correlation Properties of Heart Rate Variability.” Frontiers
in Physiology 11: 596567. https://doi.org/10.3389/fphys.2020.
596567.
Rogers, Bruce, and Thomas Gronwald. 2022. “Fractal Correlation Prop-
erties of Heart Rate Variability as a Biomarker for Intensity Distri-
bution and Training Prescription in Endurance Exercise: An Update.”
Frontiers in Physiology 13: 879071. https://doi.org/10.3389/fphys.
2022.879071.
1550
-
GRONWALD
ET AL.
Rogers, Bruce, Laurent Mourot, Gregory Doucende, and Thomas Gronwald.
2021. “Fractal Correlation Properties of Heart Rate Variability as a
Biomarker of Endurance Exercise Fatigue in Ultramarathon Runners.”
Physiological Reports 9(14): e14956. https://doi.org/10.14814/phy2.
14956.
Schaffarczyk, Marcelle, Bruce Rogers, Rüdiger Reer, and Thomas Gron-
wald. 2022. “Fractal Correlation Properties of HRV as a Noninvasive
Biomarker to Assess the Physiological Status of Triathletes During
Simulated Warm‐Up Sessions at Low Exercise Intensity: A Pilot
Study.” BMC Sports Science, Medicine & Rehabilitation 14(1): 203.
https://doi.org/10.1186/s13102‐022‐00596‐x.
Schaffarczyk, Marcelle, Bruce Rogers, Rüdiger Reer, and Thomas Gron-
wald. 2022. “Validity of the Polar H10 Sensor for Heart Rate Vari-
ability Analysis During Resting State and Incremental Exercise in
Recreational Men and Women.” Sensors 22(17): 6536. https://doi.
org/10.3390/s22176536.
Schaffarczyk, Marcelle, Bruce Rogers, Rüdiger Reer, and Thomas Gronwald.
2023. “Validation of a Non‐linear Index of Heart Rate Variability to
Determine Aerobic and Anaerobic Thresholds During Incremental
Cycling Exercise in Women.” European Journal of Applied Physiology
123(2): 299–309. https://doi.org/10.1007/s00421‐022‐05050‐x.
Sempere‐Ruiz, Noemí, José Manuel Sarabia, Sabina Baladzhaeva, and
Manuel Moya‐Ramón. 2024. “Reliability and Validity of a Non‐linear
Index of Heart Rate Variability to Determine Intensity Thresholds.”
Frontiers in Physiology 15: 1329360. https://doi.org/10.3389/fphys.
2024.1329360.
Smyth, Barry, Ed Maunder, Samuel Meyler, Ben Hunter, and Daniel
Muniz‐Pumares. 2022. “Decoupling of Internal and External Work-
load During a Marathon: An Analysis of Durability in 82,303 Rec-
reational Runners.” Sports Medicine 52(9): 2283–95. https://doi.org/
10.1007/s40279‐022‐01680‐5.
Stevenson, Julian D., Andrew E. Kilding, Daniel J. Plews, and Ed Maunder.
2024. “Prolonged Exercise Shifts Ventilatory Para‐Meters at the
Moderate‐To‐Heavy Intensity Transition.” European Journal of
Applied Physiology 124(1): 309–15. https://doi.org/10.1007/s00421‐
023‐05285‐2.
Tschakert, Gerhard, Tanja Handl, Lena Weiner, Philipp Birnbaumer,
Alexander Mueller, Werner Groeschl, and Peter Hofmann. 2022.
“Exercise Duration: Independent Effects on Acute Physiologic Re-
sponses and the Need for an Individualized Prescription.” Physio-
logical Reports 10(3): e15168. https://doi.org/10.14814/phy2.
15168.
Van Hooren, Bas, Bart C. Bongers, Bruce Rogers, and Thomas Gronwald.
2023. “The Between‐Day Reliability of Correlation Properties of
Heart Rate Variability during Running.” Applied Psychophysiology and
Biofeedback 48(4): 453–60. https://doi.org/10.1007/s10484‐023‐
09599‐x.
Van Hooren, Bas, Bram Mennen, Thomas Gronwald, Bart C. Bongers, and
Bruce Rogers. 2023. “Correlation Properties of Heart Rate Vari-
ability to Assess the First Ventilatory Threshold and Fatigue in
Runners.” Journal of Sports Sciences: 1–10: Advance online publica-
tion. https://doi.org/10.1080/02640414.2023.2277034.
Van Hooren, Bas, Tjeu Souren, and Bart C. Bongers. 2024. “Accuracy of
Respiratory Gas Variables, Substrate, and Energy Use from 15 CPET
Systems during Simulated and Human Exercise.” Scandinavian Jour-
nal of Medicine & Science in Sports 34(1): e14490. https://doi.org/10.
1111/sms.14490.
White, Daniel W., and Peter B. Raven. 2014. “Autonomic Neural Control
of Heart Rate during Dynamic Exercise: Revisi‐Ted.” The Journal of
Physiology 592(12): 2491–500. https://doi.org/10.1113/jphysiol.
2014.271858.
Zuccarelli, Lucrezia, Simone Porcelli, Letizia Rasica, Mauro Marzorati, and
Bruno Grassi. 2018. “Comparison between Slow Components of HR
and V˙O2 Kinetics: Functional Significance.” Medicine & Science in
Sports & Exercise 50(8): 1649–57. https://doi.org/10.1249/mss.
0000000000001612.
EUROPEAN JOURNAL OF SPORT SCIENCE
-
1551
