Vol.:(0123456789)
Sports Medicine (2022) 52:2283–2295 
https://doi.org/10.1007/s40279-022-01680-5
ORIGINAL RESEARCH ARTICLE
Decoupling of Internal and External Workload During a Marathon: 
An Analysis of Durability in 82,303 Recreational Runners
Barry Smyth1 · Ed Maunder2 · Samuel Meyler3 · Ben Hunter3 · Daniel Muniz‑Pumares3 
Accepted: 27 March 2022 / Published online: 5 May 2022 
© The Author(s) 2022
Abstract
Aim This study characterised the decoupling of internal-to-external workload in marathon running and investigated whether 
decoupling magnitude and onset could improve predictions of marathon performance.
Methods The decoupling of internal-to-external workload was calculated in 82,303 marathon runners (13,125 female). Inter-
nal workload was determined as a percentage of maximum heart rate, and external workload as speed relative to estimated 
critical speed (CS). Decoupling magnitude (i.e., decoupling in the 35–40 km segment relative to the 5–10 km segment) 
was classified as low (< 1.1), moderate (≥ 1.1 but < 1.2) or high (≥ 1.2). Decoupling onset was calculated when decoupling 
exceeded 1.025.
Results The overall internal-to-external workload decoupling experienced was 1.16 ± 0.22, first detected 25.2 ± 9.9 km 
into marathon running. The low decoupling group (34.5% of runners) completed the marathon at a faster relative speed 
(88 ± 6% CS), had better marathon performance (217.3 ± 33.1 min), and first experienced decoupling later in the marathon 
(33.4 ± 9.0 km) compared to those in the moderate (32.7% of runners, 86 ± 6% CS, 224.9 ± 31.7 min, and 22.6 ± 7.7 km), 
and high decoupling groups (32.8% runners, 82 ± 7% CS, 238.5 ± 30.7 min, and 19.1 ± 6.8 km; all p < 0.01). Compared to 
females, males’ decoupling magnitude was greater (1.17 ± 0.22 vs. 1.12 ± 0.16; p < 0.01) and occurred earlier (25.0 ± 9.8 
vs. 26.3 ± 10.6 km; p < 0.01). Marathon performance was associated with the magnitude and onset of decoupling, and when 
included in marathon performance models utilising CS and the curvature constant, prediction error was reduced from 6.45 
to 5.16%.
Conclusion Durability characteristics, assessed as internal-to-external workload ratio, show considerable inter-individual 
variability, and both its magnitude and onset are associated with marathon performance.
 * Barry Smyth 
 
barry.smyth@ucd.ie
 
Daniel Muniz-Pumares 
 
d.muniz@herts.ac.uk
1 
Insight Centre for Data Analytics, School of Computer 
Science, University College Dublin, Dublin, Ireland
2 
Sports Performance Research Institute New Zealand, 
Auckland University Technology, Auckland, New Zealand
3 
School of Life and Medical Sciences, University 
of Hertfordshire, Hatfield AL10 9AB, UK
2284
 
B. Smyth et al.
Key Points 
The decoupling of internal-to-external workload ratio 
can be used to quantify the ‘durability’ of endurance 
athletes during long-duration exercise. We used the 
decoupling of internal (i.e., heart rate) and external 
(i.e., grade-adjusted speed) workloads, expressed as a 
ratio indexed to the 5–10 km segment, to quantify the 
‘durability’ of > 80,000 marathon runners. Specifically, 
we assessed the relationship between the magnitude and 
onset of this decoupling with marathon performance.
There was a large inter-individual variation in the magni-
tude and onset of decoupling. However, when classified 
as low, moderate and high decoupling, athletes experi-
encing low decoupling had better marathon performance. 
Moreover, models of marathon performance were 
improved when both magnitude and onset decoupling are 
included.
The data presented herein suggest that the decoupling of 
internal-to-external workload ratio should be taken into 
consideration during long-duration exercise, as it can 
contribute to explain marathon performance.
1 Introduction
Marathon running has been the subject of considerable inter-
est in recent years, and it is generally accepted that multiple 
factors can affect its performance [1–4]. For example, mod-
els explaining marathon performance have typically consid-
ered three physiological traits: the maximum oxygen uptake 
( ̇VO2 max ), oxygen cost of movement (i.e., running economy), 
and the fraction of ̇VO2 max that can be maintained for the 
duration of the marathon [2, 5, 6]. Combined, these physi-
ological traits result in a ‘performance metabolic rate’, the 
highest oxidative metabolic rate that can be sustained for the 
marathon. Critical speed (CS) is the physiological thresh-
old delineating the heavy- and severe-intensity domains, and 
therefore defines the point at which the maximal metabolic 
steady-state (MMSS) can be attained, and exercise can be 
supported mainly from oxidative metabolism [7–10]. It is 
worth noting that several other terms or approaches have 
been suggested to correspond with, or permit the approxi-
mation of, the MMSS including ventilatory or respiratory 
thresholds, or thresholds derived from blood lactate concen-
tration, such as the maximal lactate steady state [8]. Indeed, 
criticism of the CS model has been levelled as the concord-
ance of estimates with the MMSS can be dependent on the 
methodology used [11, 12]. Since CS (and its analogous 
critical power) demarcates the boundary between heavy and 
severe exercise domains [8, 13, 14], and thus represents a 
marker of the MMSS, it follows that CS shows a strong asso-
ciation with endurance performance—including marathon 
performance [15, 16].
An interesting finding from studies investigating the abil-
ity of CS to predict marathon performance [15, 16] was that 
faster athletes appear to complete the marathon at higher 
speeds relative to their CS than slower athletes. Thus, elite 
marathon runners with an average finishing time of ~ 2 h and 
5 min could complete the marathon at ~ 96% of their CS. 
However, well-trained athletes with an average time of ~ 2 h 
and 30 min completed the marathon at ~ 93% CS, whereas 
recreational athletes with an average marathon time of ~ 4 h 
managed to complete the marathon at ~ 79% CS. A plausible 
explanation of this apparently linear decrease in marathon 
speed, relative to CS, with increasing marathon times is that 
physiological attributes crucial in marathon performance, 
reflected as the CS, represent the maximum ability of a fully 
rested athlete, but such physiological attributes deteriorate 
during prolonged exercise, such as a marathon. Clark et al. 
[17, 18] recently reported that critical power, the cycling 
equivalent of CS, decreased by ~ 10–15% following 2 h of 
heavy exercise. Therefore, if a similar decrease in CS also 
occurs with prolonged running, it is plausible that mara-
thon runners who start the marathon at speeds close to but 
fractionally below their CS transition into severe intensity 
exercise (above CS) during a marathon, even if the speed 
is maintained constant throughout the race. It is plausible 
that better athletes may be able to preserve physiological 
traits, and thus maintain speeds closer to CS. Indeed, it has 
recently been suggested that durability, defined as dete-
rioration in physiological characteristics over time during 
prolonged exercise [19], should be taken into consideration 
during physiological and performance profiling.
The aims of this study, therefore, were to (i) character-
ise the decoupling of internal-to-external workload during 
a marathon in a large cohort of recreational runners; and 
(ii) investigate whether the magnitude and time of onset 
of the decoupling could predict marathon performance, 
and whether taking into consideration the decoupling 
improved predictions derived from CS alone. Further-
more, given recent reports highlighting the differences in 
fatigability between males and females [20], which may 
contribute to the observed sex differences in endurance 
performance [20, 21], we report and compare decoupling 
traits for male and female athletes separately. We hypoth-
esised that marathon runners with faster finishing times 
would exhibit reduced decoupling of internal-to-external 
workload ratio compared to runners with slower finishing 
times. Specifically, we hypothesise that athletes exhib-
iting low decoupling and/or late onset in decoupling of 
2285
Internal and External Workload Decoupling During Marathon Running
internal-to-external workload ratio will be able to per-
form closer to their CS. Therefore, we hypothesised that 
by combining CS with estimations of the magnitude of the 
decoupling of internal-to-external workload ratio, models 
of marathon performance would be improved. Finally, we 
hypothesised that the magnitude of decoupling would be 
lower in female athletes compared to that observed in their 
male counterparts.
2  Methods
2.1  Dataset
A large dataset of recreational runners was made available 
to the authors by the running platform  Strava® (Strava, 
Inc., San Francisco, CA, USA) under limited research 
license. The dataset contained anonymised data and, there-
fore, the ethics boards of all institutions (Auckland Univer-
sity of Technology, University College Dublin, and Uni-
versity of Hertfordshire) deemed the study exempt from 
ethical approval. Athletes uploaded the data from training 
sessions, collected through smartphones or other devices 
(e.g., running pods), into the running platform. The dataset 
consisted of time, location, distance, and elevation data 
sampled at 100 m intervals. In addition, heart rate (HR) 
was available from all training sessions. HR data was pro-
cessed in a similar way to running data, and thus aver-
aged at 100 m intervals. The characteristics of the dataset 
used in the current study are provided in Table 1. There 
were 82,303 runners (~ 16% female) included in this study, 
for whom training data were available for the ~ 4 months 
preceding a marathon. For all athletes, the dataset con-
tained at least one marathon race. In an attempt to identify 
genuine marathons, we identified sessions that matched a 
marathon distance (i.e., 42.2 km), but also contained mul-
tiple runners starting at the same time and location. This 
approach provided a series of candidate marathon races 
that were manually identified, so that genuine marathon 
races were differentiated from ‘practice’ marathons.
2.2  Critical Speed and D′ Determination
Critical speed and D′, the curvature constant of the speed-
duration relationship that represents running capacity above 
CS, were estimated from raw training data, as previously 
described [15]. In brief, raw data from all training ses-
sions for each athlete were first converted to grade-adjusted 
speed. This approach accounts for changes in elevation, for 
instance when running uphill or downhill, and is described 
in more detail elsewhere [15, 22]. The fastest grade-adjusted 
speed observed in any training session for each athlete was 
recorded for a range of distances (400, 800, 1500, 3000, 
and 5000 m), and then used to construct the distance-time 
relationship according to a linear model of distance and time 
[23]. For each athlete, the slope of this line was considered 
CS, and the intercept of the line the curvature constant, D′ 
[23].
2.3  Durability and Decoupling
Each marathon was divided into eight 5-km segments plus 
the final 2 km of the race, and the decoupling of internal-
to-external workload ratio was calculated for each segment. 
The internal workload was determined as a percentage of 
maximum HR  (HRmax). The  HRmax for the cohort was given 
as 178 ± 18 beats per min (bpm) and 187 ± 8 bpm using an 
age-predicted calculation [24] and the highest HR recorded 
in any training session, respectively. Therefore,  HRmax was 
defined as the highest HR recorded in any training session for 
each runner. The external workload was determined as the 
speed, relative to CS, during the recorded marathon. The first 
(0–5 km) and last (40–42.2 km) segments of the race were 
excluded to avoid possible artefacts caused by sudden changes 
in pace in the first and last few kms of the race, respectively. 
The decoupling observed in the last 5 km segment of the race 
(35–40 km) was used to determine the overall magnitude of 
the decoupling experienced by each athlete, and expressed 
relative to the 5–10 km segment. Thus, a decoupling of 1.15 
indicates that internal-to-external ratio (ratio between %HRmax 
and %CS) was 15% greater in the 35–40 km segment com-
pared to that observed in the 5–10 km segment of the race. To 
Table 1  Descriptive statistics of 
the dataset
F female runners, M male runners, All all runners
F
M
All
Athletes (n)
13,125
69,178
82,303
Age (y)
37 ± 8
40 ± 26
39 ± 24
Finish time (min)
245.2 ± 29.6
223.3 ± 32.5
226.8 ± 33.1
Training sessions (n)
72 ± 33
70 ± 34
70 ± 34
Weeks (n)
18.2 ± 2.6
18.2 ± 2.5
18.2 ± 2.5
Training frequency (sessions·wk−1)
3.9 ± 1.6
3.8 ± 1.7
3.8 ± 1.7
Training volume (km·wk−1)
40.9 ± 15.74
43.0 ± 17.9
42.7 ± 17.6
2286
 
B. Smyth et al.
estimate the onset of decoupling, the race segment from which 
decoupling remained consistently (i.e., for the remaining of the 
race) above 1.025 was calculated for each athlete, focusing on 
the race segments from 10 to 40 km. We converted this race 
segment into an estimated distance by calculating the mid-
point of the segment. Thus, if a decoupling > 1.025 was first 
detected in the 20–25 km segment of the marathon and sus-
tained to the 35–40 km segment, then the onset was assumed 
to be at 22.5 km. The distance at which decoupling was first 
observed was converted to time of onset using average running 
speed. If a decoupling > 1.025 was not detected at all for a run-
ner, the onset was assumed to be their either 42.2 km or their 
finish-time, as appropriate, to represent a runner completing 
the marathon without decoupling.
2.4  Data Analysis
Athletes experiencing a decoupling < 1.1 in the last segment of 
the race were classified as low decoupling, a decoupling ≥ 1.1 
but < 1.2 was considered as moderate, and if the decoupling 
was ≥ 1.2 it was deemed as high decoupling [19]. In order 
to investigate whether decoupling experienced by an athlete 
contributed to explain marathon performance, the correlation 
between key decoupling characteristics (i.e., magnitude and 
the onset of decoupling) and absolute (marathon time) and rel-
ative (marathon speed relative to CS) marathon performance 
was determined. To calculate these correlations, athletes were 
grouped based on their relative performance (in 5% bins, from 
70% CS to 90% CS) and absolute performance (in 30 min bins, 
from 150 to 270 min). Finally, a SciKit learn [Python (Python 
Software Foundation, Wilmington, DA, USA)] implementa-
tion of a gradient boosting regressor [25] was used to predict 
marathon performance based on CS and D′; this regressor was 
configured to use n = 5,000 estimators and a learning rate of 
0.005 [25]. This approach has already been shown to predict 
performance with relative success (~ 7% error, Ref. [15]). 
Therefore, the model was modified to consider CS and D′ as 
well as durability traits, namely the magnitude and onset of 
the decoupling. Mean values between sexes and decoupling 
groups (low vs. moderate, moderate vs. high) were compared 
with a Welch's t-test (which does not assume equal population 
variance), and significance was accepted at p < 0.01. Cohen’s 
d was used as a measure of effect-size, and interpreted as 
very small (0.01), small (0.20), medium (0.50), large (0.80), 
very large (1.20) and huge (2.00) [26]. Results are reported as 
mean ± standard deviation.
3  Results
3.1  Marathon Performance and Critical Speed
The overall marathon performance and decoupling char-
acteristics of the athletes within the dataset are pre-
sented in Table 2. Overall, the marathon was completed 
at 3.17 ± 0.47 m·s−1, and thus marathon time was ~ 3 h 
and 47 min ± 33 min. The CS and D′, estimated from 
raw training data corresponded to 3.72 ± 0.48 m·s−1 and 
196 ± 90 m, respectively, and therefore the average mara-
thon speed corresponded to 85 ± 7% of CS. Male runners 
had ~ 10% superior marathon performance and CS com-
pared to female runners (both p < 0.01), but females were 
able to complete the marathon at speeds closer to their CS 
(87 ± 6 vs. 85 ± 7% CS, respectively; p < 0.01, d = 0.23).
3.2  Internal‑to‑External Workload Decoupling 
During Marathon Running
The average decoupling experienced in the 35–40 km seg-
ment was 1.16 ± 0.22. However, there was considerable 
inter-individual variation. Out of 82,303 runners, 34.5% 
(28,404 runners) exhibited low decoupling (decoupling < 1.1 
in the 35–40 km segment), 32.7% (26,879 runners) moderate 
decoupling (≥ 1.1 but < 1.2), and 32.8% (27,020 runners) 
were classified as high decoupling (≥ 1.2). The time-course 
of decoupling for the low, moderate, and high decoupling 
groups over the course of a marathon is shown in Fig. 1.
The overall magnitude of decoupling was greater 
for males compared to female runners (1.17 ± 0.22 vs. 
1.12 ± 0.16; p < 0.01, d = 0.22). Male runners were relatively 
evenly distributed in the low, moderate and high decoupling 
groups (32.3%, 32.6% and 35.1%, respectively), whereas 
their female counterparts were more frequently classified as 
low and moderate decoupling compared to high decoupling 
(46.1%, 33.2% and 20.7%, respectively).
The onset of decoupling, when runners first exhibited a 
continuous decoupling > 1.025 sustained to the end of the 
marathon, occurred after 25.2 ± 9.9 km. However, there 
were differences for each decoupling group (Table 2), 
whereby the onset of the decoupling occurred later in 
the low decoupling group, compared to the moderate and 
high decoupling groups. The onset of decoupling occurred 
first in male runners, irrespective of the magnitude of 
2287
Internal and External Workload Decoupling During Marathon Running
decoupling experienced (low, moderate or high), as shown 
in Table 2. When the onset of decoupling was expressed 
as time, males also experienced earlier decoupling com-
pared to female runners (147.3 ± 63.6 vs. 125.1 ± 51.6 min, 
respectively; p < 0.01, d = 0.41). This held true for all 
decoupling groups (low, moderate and high decoupling; 
Table 2, Fig. 2).
Table 2  Marathon performance and decoupling characteristics in 83,303 recreational runners
ALL represents all athletes in the dataset, whereas F and M represent data from female and male athletes, respectively. The column ‘F v M’ 
shows whether there was a difference between male and females, where the symbol * depicted a significant difference (p < 0.01) and the corre-
sponding effect size
The subscripts a, b and c indicate whether a significant difference (p < 0.01) was observed between low vs. moderate decoupling, moderate vs. 
high decoupling, and low vs. high decoupling, respectively. Decoupling magnitude represents the internal-to-external workload ratio in the 
35–40 km segment, and is reported in arbitrary units (AUs)
ALL
F
M
M v F
Sig
d
Sig
D
Sig
d
Sig
d
Marathon time (min)
 Low decoupling
217.3 ± 33.1
a
0.23
240.5 ± 29.9
a
0.22
211.1 ± 31.1
a
0.31
*
0.95
 Moderate decoupling
224.9 ± 31.7
b
0.43
246.9 ± 28.9
b
0.21
220.7 ± 30.4
b
0.53
*
0.87
 High decoupling
238.5 ± 30.7
c
0.66
252.9 ± 28.0
c
0.42
236.9 ± 30.6
c
0.84
*
0.53
 All athletes
226.8 ± 33.1
245.2 ± 29.6
223.3 ± 32.5
*
0.68
Marathon speed (m·s−1)
 Low decoupling
3.31 ± 0.50
a
0.26
2.97 ± 0.38
a
0.22
3.40 ± 0.49
1
0.33
*
0.92
 Moderate decoupling
3.19 ± 0.45
b
0.44
2.89 ± 0.36
b
0.21
3.25 ± 0.45
2
0.53
*
0.83
 High decoupling
3.00 ± 0.41
c
0.68
2.82 ± 0.34
c
0.42
3.02 ± 0.41
3
0.85
*
0.51
 All athletes
3.17 ± 0.47
2.91 ± 0.37
3.22 ± 0.48
*
0.67
Critical speed (m·s−1)
 Low decoupling
3.78 ± 0.51
a
0.14
3.39 ± 0.40
1
0.09
3.89 ± 0.48
1
0.23
*
1.10
 Moderate decoupling
3.71 ± 0.47
b
0.11
3.35 ± 0.39
3.78 ± 0.45
2
0.19
*
0.98
 High decoupling
3.67 ± 0.44
c
0.25
3.36 ± 0.38
3
0.08
3.70 ± 0.43
3
0.42
*
0.80
 All athletes
3.72 ± 0.48
3.37 ± 0.39
3.79 ± 0.46
*
0.93
Marathon speed (/CS)
 Low decoupling
0.88 ± 0.06
a
0.25
0.88 ± 0.06
a
0.24
0.88 ± 0.07
a
0.25
*
0.04
 Moderate decoupling
0.86 ± 0.06
b
0.59
0.86 ± 0.06
b
0.36
0.86 ± 0.06
b
0.61
*
0.07
 High decoupling
0.82 ± 0.07
c
0.84
0.84 ± 0.06
c
0.60
0.82 ± 0.07
c
0.85
*
0.34
 All athletes
0.85 ± 0.07
0.87 ± 0.06
0.85 ± 0.07
*
0.23
Decoupling magnitude (AU)
 Low decoupling
1.01 ± 0.18
a
1.00
1.02 ± 0.12
1
1.33
1.01 ± 0.2
1
0.95
 Moderate decoupling
1.15 ± 0.03
b
1.07
1.14 ± 0.03
2
1.67
1.15 ± 0.03
2
1.03
*
0.11
 High decoupling
1.33 ± 0.24
c
1.49
1.31 ± 0.16
3
2.18
1.33 ± 0.24
3
1.42
*
0.07
 All athletes
1.16 ± 0.22
1.12 ± 0.16
1.17 ± 0.22
*
0.22
Decoupling onset (km)
 Low decoupling
33.4 ± 9.0
a
1.32
32.9 ± 9.8
1
1.26
33.6 ± 8.7
a
1.35
*
0.25
 Moderate decoupling
22.6 ± 7.3
b
0.49
21.7 ± 7.6
2
0.34
22.8 ± 7.2
b
0.52
*
0.15
 High decoupling
19.1 ± 6.8
c
1.79
19.1 ± 7.3
3
1.01
19.2 ± 6.7
c
1.86
 All athletes
25.2 ± 9.9
26.3 ± 10.6
25.0 ± 9.8
*
0.13
Decoupling onset (min)
 Low decoupling
170.1 ± 53.8
a
1.15
185.1 ± 61.1
1
1.16
166.1 ± 50.9
a
1.14
*
0.36
 Moderate decoupling
115.2 ± 40.7
b
0.43
121.0 ± 45.8
2
0.35
114.1 ± 39.6
b
0.43
*
0.17
 High decoupling
98.4 ± 37.2
c
1.54
105.3 ± 42.4
3
1.43
97.6 ± 36.5
c
1.56
*
0.21
 All athletes
128.6 ± 54.3
147.3 ± 63.6
125.1 ± 51.6
*
0.41
2288
 
B. Smyth et al.
3.3  Internal‑to‑External Workload Decoupling 
and Marathon Performance
Both relative marathon performance (marathon speed 
relative to CS) and absolute marathon performance (mar-
athon finish time) exhibited a strong association with the 
magnitude of the decoupling. Athletes exhibiting lower 
decoupling magnitude completed the marathon at a higher 
percentage of CS (p < 0.01, R2 = − 0.97) and faster mara-
thon time (p < 0.01, R2 = 0.99, Fig. 3). Similarly, a strong 
association was observed between the onset of decoupling 
and marathon performance (Fig. 3), whereby athletes who 
experienced decoupling early during the marathon were 
able to complete the marathon at a higher fraction of their 
CS (p < 0.01, R2 = 0.92), and had faster marathon times 
(p < 0.01, R2 = − 0.99, Fig. 3a, b).
3.4  Prediction of Marathon Performance
Marathon performance was predicted with 6.45% error using 
a model that included CS and D′. Incidentally, marathon 
predictions based exclusively on CS presented with 6.62% 
error. However, including either the magnitude of the decou-
pling in the 35–40 km segment or the decoupling onset time 
reduced this error to 5.85% and 5.90%, respectively, which 
corresponds to relative improvements of 9.3% or 8.5%, 
respectively (see Fig. 4). When both magnitude and time of 
onset are included (alongside CS and D′), prediction error 
falls to 5.16%, which represents an overall improvement 
of 20.00% compared to the model using CS and D′ only. 
Overall, the prediction error was lower for female athletes 
(p < 0.01), irrespective of the model used (Fig. 5).
4  Discussion
The primary aim of the present study was to explore the 
durability characteristics of a large, heterogenous group of 
recreational runners by calculating the decoupling of inter-
nal-to-external workload ratio during marathon running. 
In addition, we investigated whether the overall magnitude 
and onset of decoupling experienced by runners contributed 
to marathon performance, and whether these results were 
different in male and female runners. The main findings 
Fig. 1  Time-course of the 
decoupling of internal-to-
external workload for athletes 
with low, moderate, and high 
decoupling. Low, moderate and 
high decoupling was defined as 
athletes with a decoupling < 1.1, 
between 1.1 and 1.2, and > 1.2 
in the 35–40 km segments. 
Decoupling is expressed relative 
to the 5–10 km segment of the 
marathon
Fig. 2  Estimated onset of decoupling during a marathon and decoupling type (low, moderate and high), for male (M) and female (F) runners. 
The filled circles in the high decoupling indicate a male—female difference (p < 0.01)
2289
Internal and External Workload Decoupling During Marathon Running
were that athletes experienced a ~ 1.16 (~ 16%) decou-
pling between HR and speed in marathon running, which 
started after 25.2 ± 9.9 km. However, there was large inter-
individual variability, and runners could be classified into 
low, moderate and high decoupling groups. We found that 
runners in the low decoupling group completed the race at 
a higher percentage of their CS, with a faster overall time, 
and had a later onset of decoupling. Moreover, whilst CS 
and D′ were able to predict marathon performance, a model 
that incorporates durability characteristics (i.e., magnitude 
and onset of the decoupling) reduced the prediction error 
by 20%. Female runners exhibited a better durability pro-
file, as the decoupling exhibited lower magnitude and later 
onset than that observed in male runners. These findings 
suggest that durability characteristics, such as its magnitude 
and onset, should be taking into consideration in marathon 
running because both parameters were associated with mar-
athon performance. Moreover, the results from this study 
indicate that female runners experience less decoupling than 
their male counterparts.
Fig. 3  The onset (distance and time) and the magnitude of the decou-
pling of internal-to-external workload ratio relative to marathon per-
formance, where marathon performance is calculated: a relative CS, 
and b in absolute units (min). Estimated onset of the decoupling of 
internal-to-external workload relative to marathon performance, 
where marathon performance is calculated: c relative CS, and d in 
absolute units (min). Filled markers indicate a significant difference 
between male and female runners (p < 0.01) and a solid line between 
two makers indicates a statistically significant difference between 
consecutive pace bins (p < 0.01)
2290
 
B. Smyth et al.
4.1  Inter‑Individual Variation in Decoupling 
Characteristics
The large sample of recreational marathon runners ana-
lysed in the current study experienced internal-to-external 
workload decoupling of ~ 1.16, which indicates that the ratio 
between internal workload (HR) and external workload 
(grade-adjusted speed, relative to CS) increased by ~ 16% 
throughout a marathon. However, there was considerable 
inter-individual variability in the magnitude of decoupling. 
Fig. 4  Error associated with predictions of marathon performance 
derived from a CS and D’ only, b CS and D’ plus the magnitude of 
the decoupling, and c CS and D’ plus the decoupling degree and time 
to decoupling onset. The error is calculated as the mean absolute dif-
ference between the predicted finish-time and the actual finish-time 
as a fraction of actual finish-time for each finish-time group and the 
dotted lines show the mean error for male and females for all finish-
times. In (a) a filled marker indicates a difference between the corre-
sponding male and female means (p < 0.01), and a solid line between 
two makers indicates a difference between relative pace segments 
(p < 0.01). The overall R2 value for each finish-time is also shown
Fig. 5  Overall performance of different models based exclusively on CS and D′, as well as parameters related to the decoupling of the internal-
to-external workload ratio
2291
Internal and External Workload Decoupling During Marathon Running
Athletes were classified, based on the magnitude of the 
decoupling observed in the last 5 km segment of the mara-
thon, as low, moderate and high decoupling, as previously 
suggested [19]. Despite this being an arbitrary classification, 
we found a remarkably even distribution, and each of the 
three decoupling groups contained ~ 33% of athletes in the 
sample. Such inter-individual variability in the magnitude of 
decoupling supports consideration of durability in physio-
logical profiling and performance modelling, as resilience to 
exercise-induced shifts in intensity domain transitions may 
contribute to performance capabilities in the latter stages of 
prolonged events [17–19].
Prolonged exercise, such as marathon running, neces-
sitates a physiological steady state, and thus is typically 
performed at intensities close to, but below, CS [15, 16]. 
Exercise at intensities that exceed CS (or its cycling analo-
gous, critical power) results in an inexorable increase in the 
concentration of muscle metabolites, such as hydrogen ions 
and inorganic phosphate, until an intolerable threshold is 
reached coinciding with the depletion of D′ and the attain-
ment of ̇VO2 max , which, ultimately, results in task failure 
soon afterwards [9, 27, 28]. Alternatively, exercise may 
be continued after the depletion of D′, but the intensity of 
exercise must remain below CS [29]. Previous studies have 
demonstrated that the power profile [30], CS [17, 18] and 
endurance performance [31] decrease with prolonged, sub-
maximal exercise. Combined, the results from these studies 
and the data presented herein suggest that it is inappropriate 
to rely exclusively on physiological traits determined in fully 
rested state athletes to predict endurance performance. It is 
unlikely that such characteristics, determined at rest, remain 
constant during prolonged exercise, or that they deteriorate 
at a constant rate. Instead, athletes appear to exhibit different 
abilities to preserve their physiological abilities during pro-
longed exercise. Thus, monitoring the durability of athletes 
(e.g., by monitoring the decoupling of internal-to-external 
workload) should be taken into consideration in physiologi-
cal profiling, when prescribing prolonged exercise or aiming 
to predict endurance (e.g., marathon) performance.
4.2  Decoupling Characteristics and Marathon 
Performance
Previous studies have shown that CS is a strong predictor of 
marathon performance, with elite marathon runners’ best 
performances completed at 96% CS [16], and faster rec-
reational marathon runners also completing marathons at 
speeds close to (> 90%), but below, CS [15]. In the present 
study, athletes in the low decoupling group were able sus-
tain a higher fraction of their CS throughout the marathon, 
which also occurred later in the marathon. The results from 
the present study demonstrate that marathon runners who 
exhibited superior durability (i.e., had low decoupling) were 
also able to run closer to their CS, and also able to complete 
the marathon faster.
The onset of decoupling was estimated to occur when 
a decoupling of at least 1.025 was first detected. This is, 
again, an arbitrary threshold representing a 2.5% increase 
in internal-to-external workload ratio. However, we found 
that this approach of detecting the onset of decoupling 
was also associated with marathon performance (Fig. 3). 
Athletes exhibiting low decoupling were able to complete 
a further ~ 14 km of the marathon without signs of physi-
ological deterioration (Table 2). Moreover, when the onset 
of decoupling was expressed as time, overall results indicate 
that decoupling is first observed ~ 128 min into the race (see 
Table 2). Clark et al. [17] reported that a decrease in critical 
power was observed following 2 h of cycling at moderate 
intensities, but not after 80 min. In the present study, how-
ever, the onset of decoupling was detected ~ 80 min later 
in the low decoupling groups compared to the low decou-
pling group (~ 105 vs. 185 min, see Table 2). Overall, this 
study shows that both magnitude of decoupling and onset of 
decoupling, expressed as distance covered or time elapsed 
before it was first detected, were associated with marathon 
performance.
Critical speed denotes the highest sustainable oxidative 
metabolic rate, and thus is strongly associated with endur-
ance performance. Indeed, previous studies have shown that 
marathon performance can be predicted with ~ 7% error 
using models derived from CS [15]. Similarly, in the pre-
sent study marathon performance was predicted with 6.45% 
error using a model that included CS and D′. The addition 
of durability traits to this model, namely its magnitude and 
onset, reduced the prediction error to 5.16%, a 20% improve-
ment in accuracy. Therefore, the data presented in the cur-
rent study support that models aiming to predict marathon 
performance, and more generally models of endurance per-
formance, should take into consideration the durability of 
physiological traits.
4.3  Mechanisms Underpinning Decoupling
There are several factors that can explain the decoupling 
of internal-to-external workload decoupling. The mecha-
nisms explaining the inter-individual variability in durabil-
ity characteristics may be related to skeletal muscle fibre 
type characteristics given type I fibres are more resilient to 
exercise-induced loss of mechanical efficiency [32]. There-
fore, the muscle metabolic cost of producing a given running 
speed may be better maintained during marathon running 
in athletes with a greater proportion of type I fibres, and 
therefore reduced decoupling between internal and exter-
nal work as the race progresses. Similarly, the availability 
of proteins involved in management of cellular stress, such 
as the heat shock proteins [33], may promote durability 
2292
 
B. Smyth et al.
characteristics by improving the capacity to manage the cel-
lular stress generated during prolonged exercise [34]. Dura-
bility characteristics may also be related to mitochondrial 
protein content, as a larger mitochondrial pool may spread 
the oxidative burden of demanding exercise and therefore 
reduce mitochondrial damage at the level of the individual 
mitochondrion during prolonged exercise. These physiologi-
cal mechanisms remain speculative and warrant attention 
from laboratory-based investigations of the determinants of 
durability characteristics.
Further to purely physiological mechanisms, it could be 
postulated that runners with greater durability are able to 
preserve a more economical pattern of running through-
out the marathon. The greatest sustainable running speed 
is strongly mediated by running economy (e.g., references 
[1, 5]). However, the  O2 cost of running has been shown 
to increase concomitantly over increased distances [35]. 
Elevated levels of markers of muscular fatigue and skeletal 
muscle damage can interfere with contractile mechanisms 
through inhibitory effects on α-motoneurons by activating 
fatigue-sensitive afferent fibres [36]. Consequently, dur-
ing periods of prolonged running the force output during 
the push off phase has been shown to be reduced. Indeed, 
running induced fatigue has been shown to alter kinemat-
ics [37], kinetics [38], as well as stride dynamics [39, 40]. 
Resultant compensatory alterations in gait pattern to main-
tain running speed may result in an upward drift in ̇VO2 , and 
an increase in internal workload at a given running speed. 
However, compensatory movement patterns observed along-
side and increase in ̇VO2 have been shown to be highly vari-
able between runners [41]. Furthermore, it is important to 
acknowledge the extent of muscular fatigue will be depend-
ent on the intensity domain in which exercise is performed. 
Therefore, further investigations are warranted to elucidate 
whether diminished running economy is a cause or a conse-
quence of durability characteristics.
Decoupling was quantified as the internal-to-external 
ratio [19], and therefore decoupling could represent an 
increase in internal workload (i.e., HR), decrease in exter-
nal workload (i.e., speed), or both. In the current dataset, 
speed fell following the onset of decoupling by 11.3%, whilst 
the HR remained constant throughout the marathon, and 
only increased by 1.6% (or ~ 2 bpm) since decoupling was 
first detected. These data suggest that during a marathon, a 
‘mirror image’ of the slow component was present, whereby 
workload has to be decreased in order to maintain a constant 
̇VO2 [42] or HR [43] during prolonged, submaximal exer-
cise. Therefore, factors typically associated with the slow 
component (e.g., mainly metabolic requirements of fatiguing 
muscle fibres and additional recruitment of motor units with 
lower efficiency, see [44] for a review) may also have con-
tributed to the observed decoupling of internal-to-external 
workload ratio.
4.4  Female Runners Exhibit Less Decoupling
The results of the present study demonstrate that females 
displayed a lower magnitude and later onset of decoupling 
than males (Fig. 2, Table 1). Moreover, there were over 
twice as many female athletes classified as low decoupling 
than high decoupling. Previous studies have shown that 
physiological thresholds that demarcate the exercise inten-
sity domains are typically positioned at a higher percentage 
of ̇VO2 max in females [45]. The data from the current study 
indicate that, in addition, female runners can also preserve 
their physiological characteristics better than males, as 
demonstrated by the low decoupling. Females demonstrate 
a greater proportional area of type I fibres, greater capillary-
to-fibre ratio, greater volumes and densities of mitochon-
dria, superior rates of oxidative enzyme activity [46, 47], 
have greater reliance on fat metabolism than males [48], and 
may thus be better protected from glycogen depletion. As a 
result, females may preserve muscular contractile function 
through better maintenance of glycogen [49], and propensity 
for greater proportion of fatigue resistance of type I fibres 
[46, 47]. Combined, whilst males will typically demonstrate 
a higher CS and better overall marathon performance, these 
factors may help explain why females were able to complete 
the marathon at a greater percentage of CS than males and 
did so whilst experiencing less decoupling.
4.5  Limitations and Future Research Directions
For this study, we relied on a large dataset of recreational 
runners. Using such a large dataset allowed the explora-
tion of decoupling characteristics during the marathon, and 
offers an insight as to whether the internal-to-external work-
load experienced during prolonged exercise contributes to 
explain marathon performance. However, when utilising this 
approach to use raw training data to calculate CS, it was not 
possible to verify if participants have performed a maxi-
mal effort, for example, checking whether ̇VO2 max has been 
attained during constant work rate trials [19]. Nonetheless, 
it is worth noting that this approach has previously been 
used to estimate CS with a low standard error of estimate 
(~ 8%) and to successfully predict marathon performance 
[15]. Data was used for ~ 4 months prior to a marathon event, 
and so it is likely that some activities included in the data 
set corresponded to maximal efforts through shorter races 
(e.g., 5 km) or higher intensity training sessions. Moreover, 
it has been demonstrated that extraction of data from training 
results in a high level of agreement with laboratory-based 
testing when estimating critical power, with low prediction 
errors (< 5%) [50]. Future research may wish to identify 
means of verifying maximal efforts to improve CS estimates 
from training data. It is also worth noting that the CS is 
an estimation of the upper boundary of the heavy intensity 
2293
Internal and External Workload Decoupling During Marathon Running
domain, and it was not possible to verify whether this rep-
resented the MMSS in the current study. It has been sug-
gested that the CS may overestimate the MMSS relative to 
other methods and is highly dependent on the protocol used 
[11, 12]. However, the CS has been shown to closely repre-
sent the MMSS [14], and is widely regarded as an accurate 
tool to estimate of the heavy-severe domain transition [8, 
13]. Furthermore, other methods used to approximate the 
heavy-severe boundary, for example, ventilatory thresholds, 
maximal lactate steady state, etc., were not permissible using 
the current approach.
To quantify internal workload, we used HR data, and it 
should be acknowledged that HR is likely to exhibit some-
what different kinetics to that of ̇VO2 during prolonged exer-
cise [43, 51]. Moreover, prolonged exercise can result in 
fluid loss due to excessive sweating and inadequate fluid 
replacement, particularly in hot environments. This imposes 
an additional cardiac strain, which results in a cardiovascu-
lar drift (i.e., increased HR, with concomitant reductions 
in ̇VO2 max [52]). Environmental conditions were not taken 
into consideration for the current analysis, but it is plausi-
ble that the decoupling of internal-to-external workload is 
increased in hot environments. Moreover, males and females 
may not be equally affected by exercise-induced dehydra-
tion [53]. A question that remains unanswered and warrants 
further investigation is whether durability traits are sensitive 
to training adaptations. We would also encourage further 
research to investigate whether training characteristics, such 
as training volume, intensity, or the distribution of training 
load, can influence durability. Nonetheless, the findings from 
the current study would suggest that training may be able to 
reduce the decoupling of the internal-to-external workload 
ratio.
5  Conclusions
The internal-to-external ratio during a marathon was ~ 1.16, 
which represents a 16% increase in internal-to-exter-
nal ratio over the course of the marathon, and was first 
detected ~ 25 km into the marathon. However, there was a 
large inter-individual variation in both the absolute mag-
nitude of the decoupling and its onset. Importantly, both 
decoupling magnitude and onset were associated with 
performance, and the inclusion of these durability traits 
increased the precision of models of marathon performance 
by ~ 20% compared to those relying exclusively on CS and 
D′. Females had, overall, a better durability profile, as they 
exhibited lower decoupling in internal-to-external ratio. The 
data presented herein, therefore, suggest that appreciation of 
inter-individual differences in athlete durability may help 
improve understanding of an individual athlete’s perfor-
mance capabilities in marathon running.
Declarations 
Funding Open Access funding provided by the IReL Consortium. The 
authors received no other funding for this work.
Conflicts of interest Authors BS, EM, SM, BH and DM-P declare that 
they have no conflicting interests.
Availability of data The data supporting the findings of the current 
study are provided by  Strava® under a limited research license. The data 
are thus not publicly available. Requests to access these data should 
be directed to  Strava®.
Code availability The code used to analyse the data is available upon 
reasonable request to Prof. Barry Smyth (barry.smyth@ucd.ie).
Ethics approval The ethics boards of Auckland University of Technol-
ogy, University College Dublin, and University of Hertfordshire waived 
the requirement for ethical approval for the current study.
Consent An anonymised dataset from  Strava® users was provided to 
the authors under a limited research license. No new data were gener-
ated.
Authors’ contributions BS, EM, SM, BH and DM-P designed the 
study. BS analysed the data and constructed the figures. BS, EM, SM, 
BH and DM-P interpretated the results, prepared and edited the manu-
script, and approved the final version of the manuscript.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long 
as you give appropriate credit to the original author(s) and the source, 
provide a link to the Creative Commons licence, and indicate if changes 
were made. The images or other third party material in this article are 
included in the article's Creative Commons licence, unless indicated 
otherwise in a credit line to the material. If material is not included in 
the article's Creative Commons licence and your intended use is not 
permitted by statutory regulation or exceeds the permitted use, you will 
need to obtain permission directly from the copyright holder. To view a 
copy of this licence, visithttp:// creat iveco mmons. org/ licen ses/ by/4. 0/.
References
 1. Joyner MJ, Hunter SK, Lucia A, Jones AM. Physiology and fast 
marathons. J Appl Physiol. 2020;128:1065–8.
 2. Jones AM, Kirby BS, Clark IE, Rice HM, Fulkerson E, Wylie 
LJ, et al. Physiological demands of running at 2-hour marathon 
race pace. J Appl Physiol. 2021;130:369–79.
 3. Hoogkamer W, Kram R, Arellano CJ. How biomechanical 
improvements in running economy could break the 2-hour 
marathon barrier. Sport Med. 2017;47:1739–50.
 4. Santos-Concejero J, González-Mohíno F, González-Ravé 
JM, Perrey S, Dewolf AH, Yates BA, et al. Commentaries on 
viewpoint: physiology and fast marathons. J Appl Physiol. 
2020;128:1069–85.
2294
 
B. Smyth et al.
 5. Joyner MJ. Modeling: optimal marathon performance on the 
basis of physiological factors. J Appl Physiol. 1991;70:683–7.
 6. Van Der Zwaard S, Van Der Laarse WJ, Weide G, Bloemers 
FW, Hofmijster MJ, Levels K, et al. Critical determinants 
of combined sprint and endurance performance: an integra-
tive analysis from muscle fiber to the human body. FASEB J. 
2018;32:2110–23.
 7. Burnley M, Jones AM. Power–duration relationship: Physiology, 
fatigue, and the limits of human performance. Eur J Sport Sci. 
2018;18:1–12.
 8. Jones AM, Burnley M, Black MI, Poole DC, Vanhatalo A. The 
maximal metabolic steady state: redefining the ‘gold standard.’ 
Physiol Rep. 2019;7:14098.
 9. Nixon RJ, Kranen SH, Vanhatalo A, Jones AM. Steady-state ̇ V 
O 2 above MLSS: evidence that critical speed better represents 
maximal metabolic steady state in well-trained runners. Eur J 
Appl Physiol. 2021;121:3133–44.
 10. Poole DC, Burnley M, Vanhatalo A, Rossiter HB, Jones AM. 
Critical power: an important fatigue threshold in exercise physiol-
ogy. Med Sci Sports Exerc. 2016;48:2320.
 11. Iannetta D, Ingram CP, Keir DA, Murias JM. Methodologi-
cal reconciliation of CP and MLSS and their agreement with 
the maximal metabolic steady state. Med Sci Sports Exerc. 
2022;54:622–32.
 12. Gorostiaga EM, Sánchez-Medina L, Garcia-Tabar I. Over 55 
years of critical power: Fact or artifact? Scand J Med Sci Sports. 
2022;32:116–24.
 13. Galán-Rioja MÁ, González-Mohíno F, Poole DC, González-Ravé 
JM. Relative proximity of critical power and metabolic/ventila-
tory thresholds: systematic review and meta-analysis. Sports Med. 
2020;50(10):1771–83.
 14. Nixon RJ, Kranen SH, Vanhatalo A, Jones AM. 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(11):3133–44.
 15. Smyth B, Muniz-Pumares D. Calculation of critical speed from 
raw training data in recreational marathon runners. Med Sci Sports 
Exerc. 2020;52:2637–45.
 16. Jones AM, Vanhatalo A. The ‘Critical Power’ concept: Applications 
to sports performance with a focus on intermittent high-intensity 
exercise. Sport Med. 2017;47:65–78.
 17. Clark IE, Vanhatalo A, Bailey SJ, Wylie LJ, Kirby BS, Wilkins BW, 
et al. Effects of two hours of heavy-intensity exercise on the power-
duration relationship. Med Sci Sports Exerc. 2018;50:1658–68.
 18. Clark IE, Vanhatalo A, Thompson C, Joseph C, Black MI, Blackwell 
JR, et al. Dynamics of the power-duration relationship during pro-
longed endurance exercise and influence of carbohydrate ingestion. 
J Appl Physiol. 2019;127:726–36.
 19. Maunder E, Seiler S, Mildenhall MJ, Kilding AE, et al. The impor-
tance of “durability” in the physiological profiling of endurance 
athletes. Sport Med. 2021;51:1–10.
 20. Ansdell P, Thomas K, Hicks KM, Hunter SK, Howatson G, 
Goodall S. Physiological sex differences affect the integrative 
response to exercise: acute and chronic implications. Exp Physiol. 
2020;105:2007–21.
 21. Hunter SK. Sex differences in fatigability of dynamic contractions. 
Exp Physiol. 2016;101:250–5.
 22. Minetti AE, Moia C, Roi GS, Susta D, Ferretti G. Energy cost of 
walking and running at extreme uphill and downhill slopes. J Appl 
Physiol. 2002;93:1039–46.
 23. Muniz-Pumares D, Karsten B, Triska C, Glaister M. Methodological 
approaches and related challenges associated with the determination 
of critical power and W’. J Strength Cond Res. 2019;33:584–96.
 24. Inbar O, Oren A, Scheinowitz M, Rotstein A, Dlin R, Casaburi R. 
Normal cardiopulmonary responses during incremental exercise in 
20-to 70-yr-old men. Med Sci Sports Exerc. 1994;26:538–46.
 25. Friedman JH. Greedy function approximation: a gradient boosting 
machine. Ann Stat. 2001;29:1189–232.
 26. Sawilowsky SS. New effect size rules of thumb. J Mod Appl Stat 
Methods. 2009;8:597–9.
 27. Black MI, Jones AM, Blackwell JR, Bailey SJ, Wylie LJ, McDonagh 
STJ, et al. Muscle metabolic and neuromuscular determinants of 
fatigue during cycling in different exercise intensity domains. J Appl 
Physiol. 2017;122:446–59.
 28. Jones AM, Wilkerson DP, DiMenna F, Fulford J, Poole DC. Mus-
cle metabolic responses to exercise above and below the “critical 
power” assessed using 31P-MRS. Am J Physiol Regul Integr Comp 
Physiol. 2008;294:585–93.
 29. Coats EM, Rossiter HB, Day JR, Miura A, Fukuba Y, Whipp BJ. 
Intensity-dependent tolerance to exercise after attaining V̇O2max in 
humans. J Appl Physiol. 2003;95:483–90.
 30. Van Erp T, Sanders D, Lamberts RP. Maintaining power output with 
accumulating levels of work done is a key determinant for success 
in professional cycling. Med Sci Sports Exerc. 2021;53:1903–10.
 31. Noordhof DA. Performance-determining variables in long-dis-
tance events : should they be determined from a rested state or 
after prolonged submaximal exercise? Int J Sport Physiol Perform. 
2020;16:647–54.
 32. Barclay CJ. Mechanical efficiency and fatigue of fast and slow mus-
cles of the mouse. J Physiol. 1996;497:781–94.
 33. Henstridge DC, Febbraio MA, Hargreaves M, Henstridge DC. Heat 
shock proteins and exercise adaptations. Our knowledge thus far and 
the road still ahead. J Appl Physiol. 2016;120:683–91.
 34. Krüger K, Reichel T, Zeilinger C. Role of heat shock proteins 70/90 
in exercise physiology and exercise immunology and their diagnostic 
potential in sports. J Appl Physiol. 2019;126:916–27.
 35. Brueckner JC, Atchou G, Capelli C, Duvallet A, Barrault D, Jous-
selin E, et al. The energy cost of running increases with the distance 
covered. Eur J Appl Physiol Occup Physiol. 1991;62:385–9.
 36. Millet GY, Lepers R. Alterations of neuromuscular function after 
prolonged running, cycling and skiing exercises. Sport Med. 
2012;34:105–16.
 37. Dierks TA, Davis IS, Hamill J. The effects of running in an exerted 
state on lower extremity kinematics and joint timing. J Biomech. 
2010;43:2993–8.
 38. Girard O, Millet GP, Slawinski J, Racinais S, Micallef JP. Changes 
in running mechanics and spring-mass behaviour during a 5-km time 
trial. Int J Sports Med. 2013;34:832–40.
 39. Meardon SA, Hamill J, Derrick TR. Running injury and stride time 
variability over a prolonged run. Gait Posture. 2011;33:36–40.
 40. Mo S, Chow DHK. Stride-to-stride variability and complexity 
between novice and experienced runners during a prolonged run at 
anaerobic threshold speed. Gait Posture. 2018;64:7–11.
 41. Hunter I, Smith GA. Preferred and optimal stride frequency, stiffness 
and economy: changes with fatigue during a 1-h high-intensity run. 
Eur J Appl Physiol. 2007;100:653–61.
 42. Grassi B, Rossiter HB, Zoladz JA. Skeletal muscle fatigue and 
decreased efficiency: two sides of the same coin? Exerc Sport Sci 
Rev. 2015;43:75–83.
 43. Zuccarelli L, Porcelli S, Rasica L, Marzorati M, Grassi B. Compari-
son between slow components of HR and VO2 kinetics: functional 
significance. Med Sci Sports Exerc. 2018;50:1649–57.
 44. Jones AM, Grassi B, Christensen PM, Krustrup P, Bangsbo J, Poole 
DC. Slow component of V̇O2 kinetics: Mechanistic bases and practi-
cal applications. Med Sci Sports Exerc. 2011;43:2046–62.
 45. Ansdell P, Brownstein CG, Škarabot J, Hicks KM, Howatson G, 
Thomas K, et al. Sex differences in fatigability and recovery relative 
to the intensity–duration relationship. J Physiol. 2019;597:5577–95.
 46. Haizlip KM, Harrison BC, Leinwand LA. Sex-based differences 
in skeletal muscle kinetics and fiber-type composition. Physiology. 
2015;30:30–9.
2295
Internal and External Workload Decoupling During Marathon Running
 47. Simoneau JA, Bouchard C. Human variation in skeletal muscle fiber-
type proportion and enzyme activities. Am J Physiol Endocrinol 
Metab. 1989;257:567–72.
 48. Maunder E, Plews DJ, Kilding AE. Contextualising maximal fat 
oxidation during exercise: determinants and normative values. Front 
Physiol. 2018;9:599.
 49. Ørtenblad N, Westerblad H, Nielsen J. Muscle glycogen stores and 
fatigue. J Physiol. 2013;591(18):4405–13.
 50. Karsten B, Jobson SA, Hopker J, Jimenez A, Beedie C. High agree-
ment between laboratory and field estimates of critical power in 
cycling. Int J Sports Med. 2014;35(04):298–303.
 51. Wingo JE, Stone T, Ng J. Cardiovascular drift and maximal oxy-
gen uptake during running and cycling in the heat. Med Sci Sports 
Exerc. 2020;52:1924–32.
 52. Wingo JE, Lafrenz AJ, Ganio MS, Edwards GL, Cureton KJ. Car-
diovascular drift is related to reduced maximal oxygen uptake during 
heat stress. Med Sci Sports Exerc. 2005;37:248–55.
 53. Wickham KA, Mccarthy DG, Spriet LL, Cheung SS. Sex differences 
in the physiological responses to exercise-induced dehydration: con-
sequences and mechanisms. J Appl Physiol. 2021;131:504–10.

Decoupling of Internal and External Workload During a Marathon: An Analysis of Durability in 82,303 Recreational Runners.
Smyth, Barry,Maunder, Ed,Meyler, Samuel,Hunter, Ben,Muniz-Pumares, Daniel