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Relationship between  
biomechanics and energy cost 
in graded treadmill running
Marcel Lemire 1,3, Robin Faricier 2, Alain Dieterlen 1,3, Frédéric Meyer 4,5* & 
Grégoire P. Millet 4*
The objective of this study was to determine whether the relationships between energy cost of 
running (Cr) and running mechanics during downhill (DR), level (LR) and uphill (UR) running could 
be related to fitness level. Nineteen athletes performed four experimental tests on an instrumented 
treadmill: one maximal incremental test in LR, and three randomized running bouts at constant 
speed (10 km  h−1) in LR, UR and DR (± 10% slope). Gas exchange, heart rate and ground reaction forces 
were collected during steady-state. Subjects were split into two groups using the median Cr for all 
participants. Contact time, duty factor, and positive external work correlated with Cr during UR (all, 
p < 0.05), while none of the mechanical variables correlated with Cr during LR and DR. Mechanical 
differences between the two groups were observed in UR only: contact time and step length were 
higher in the economical than in the non-economical group (both p < 0.031). This study shows that 
longer stance duration during UR contributes to lower energy expenditure and Cr (i.e., running 
economy improvement), which opens the way to optimize specific running training programs.
Although complex physiological and biomechanical factors play important roles in level running (LR), the energy 
cost of running (Cr) appears as one of the three main predictive factors determining  performance1. The Cr rep-
resents the amount of energy required per unit of kilometer at a given submaximal running velocity allowing to 
maintain a physiological steady  state2. Though, the influence of LR Cr on graded running performance remains 
 unclear3–6. It has been reported that LR cost of locomotion is a poor indictor of performance in short distance 
trail  races3,4 but the importance of energy cost on ultramarathon remains  debated5,6. A relationship has been 
observed between the oxygen cost (amount of oxygen consumed per distance unit) in uphill running (UR) and 
LR in elite ultra-trail  runners7. However, additional specific parameters such as knee extensor muscle endurance 
and UR Cr may play a role on inclined running  performance4.
It has been suggested that changes in the running pattern from negative to positive slopes explain the positive 
linear increase in Cr with positive  slope8–11, but not in downhill running (DR), where the relationship between 
the slopes and Cr has an U-shape with the lowest Cr value at approximately − 10 to − 20%  slope9,12. While each 
individual naturally develops their optimal running pattern (i.e., spatiotemporal parameters of stride, running 
gait) according to their personal characteristics in order to lower their  Cr13,14, it is well known that changing this 
self-selected running pattern may alter the  Cr15–18. Therefore, one may suggest that the most economical runners 
efficiently adapt their running mechanics to the slope condition. Though, which biomechanical adaptations are 
associated with a lower Cr remains an open question. According to experimental data, DR involves braking 
muscle actions of the lower limbs and is considered a predominantly eccentric exercise  modality19. In contrast, 
UR predominantly involves concentric propulsive muscle  contractions19. While the physiological adaptations 
to hilly terrain are currently being widely investigated, the main performance determinants for LR, UR and DR 
may differ, with a greater contribution of biomechanical parameters in DR  performance20.
Compared to LR, UR induces a decrease of aerial time and step length, whereas DR increases the aerial time 
and the step length. However, the contact phase is less affected by slope, leading to an increase of step frequency 
during  UR9,10,21,22. Furthermore, the ratio of positive to negative work is another important biomechanical factor 
that may explain the slope-dependent variations in  Cr9,23. The mechanical positive and negative external works 
 (Wext
+ and  Wext
−, respectively) represent the work performed at each step to support the upward and downward 
OPEN
1Faculty of Sport Sciences, University of Strasbourg, Strasbourg, France. 2School of Kinesiology, The University of 
Western Ontario, London, ON, Canada. 3Institut de Recherche en Informatique, Mathématiques, Automatique Et 
Signal, Université de Haute-Alsace, 68070 Mulhouse, France. 4Institute of Sport Sciences, University of Lausanne, 
Lausanne, Switzerland. 5Digital Signal Processing Group, Department of Informatics, University of Oslo, Oslo, 
Norway. *email: fredem@ifi.uio.no; gregoire.millet@unil.ch
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movements of the center of mass of the body (CoM),  respectively24. As the downward movement of the CoM 
decreases with positive slopes,  Wext
− decreases and the  Wext
+ increases, and conversely with negative slopes the 
downward movement increases whereas the upward  decreases24. Since the energy required to perform  Wext
− is 
less than that of  Wext
+ 25, the more positive the slope, the higher the concentric muscle actions for the elevation 
of the CoM, leading to an increase in energy  expenditure8. Conversely, the energy demand in DR is lowered due 
to the increased part of the eccentric muscle activation and the gravity effect, saving  energy8. Nevertheless, the 
direct relationship between running mechanics and Cr in UR or DR is under investigated.
The stride kinematic adaptations in graded running may also influence Cr, as debated in  LR13. One study 
has investigated the relationship between running economy and spatiotemporal running parameters within 
specific slope conditions in a homogeneous group of well-trained runners and reported correlations between 
spatiotemporal parameters only in  DR12. The Cr in DR was negatively correlated with both step frequency and 
step length while positively correlated with contact  time12. The step length and frequency, and the vertical stiffness 
were negatively correlated whereas ground contact time was positively correlated with Cr in  DR12. Conversely, 
Lussiana et al.14 showed that minimal shoes reduced contact time and increased aerial phase whatever the slope 
condition (± 8% slope), while Cr was not affected. Taken together these results tend to show that biomechanical 
responses may affect Cr in graded running. However, to the best of our knowledge, no study examined these 
relationships, including ground reaction forces, in a large heterogeneous group.
Moreover, the running pattern appears to be dependent on the fitness level in LR. Lower vertical forces were 
observed during the stance phase in a group of runners with the lowest oxygen consumption for a given speed 
(~ 13 km  h−1)17. The magnitude of peak vertical force determines the work performed by the leg muscles to sup-
port the running motion. During incline running, these peak vertical forces have been shown to increase and 
decrease during DR and UR,  respectively21. Nevertheless, to our knowledge, no previous study has attempted to 
determine whether peak vertical forces are also a factor of Cr in incline running (DR and/or UR).
Identification of key running pattern parameters associated with low Cr may have direct practical applications 
such as developing grade-specific training methods to improve running technique and potentially performance. 
Thus, it appears interesting to investigate whether specific biomechanical responses can distinguish economical 
and less economical runners.
Therefore, the objectives of this study were, first, to determine if there was a relationship between Cr and 
mechanical responses associated with the running pattern; and second, to determine if these biomechanical 
responses were different between two groups of different Cr levels (economical vs. non-economical). Our hypoth-
eses were first that Cr values would correlate with their biomechanical responses; and second that biomechanical 
responses would be different between two groups of different economy levels in each slope condition.
Methods
Participants. 
Nineteen volunteer athletes took part in this study (Table 1) and were informed of the benefits 
and risks of this investigation before giving their written informed consent. They performed between one and 
five session per week of running training but were not trail specialists. The experiment was previously approved 
by our Institutional Review Board (CCER-VD 2015-00006) and complied with the Declaration of Helsinki.
Experimental setup. 
All participants completed (1) a level running (0% slope) incremental test to exhaus-
tion; and (2) three randomized running bouts at constant velocity (10 km  h−1) with different slope conditions, 
LR, UR (+ 10%) and DR (− 10%). The running speed of 10 km  h−1 was selected to ensure that subjects were below 
the second ventilatory threshold in each slope condition. Participants performed all the sessions on a treadmill 
(T-170-FMT, Arsalis, Belgium) at the same time of the day with 1 week of recovery allocated. The subjects were 
instructed to not perform any eccentric and/or strenuous exercises in this time interval.
Maximal incremental level running test. 
The first session was an incremental running test until 
exhaustion. The test began at 8 km  h−1 for 4 min and then the speed increased by 1 km  h−1 every min. During 
each session, V̇O2, carbon dioxide output (V̇CO2), and respiratory exchange ratio (RER) were collected breath-
by-breath through a facemask with an open-circuit metabolic cart with rapid  O2 and  CO2 analyzers (Quark 
Table 1.  Participant characteristics (n = 19). vV̇O2max velocity associated to V̇O2max, VT1 and VT2 V̇O2 at the 
first and the second ventilatory thresholds, respectively, HRmax maximal heart rate.
Age (years)
34
 ± 
10
Height (cm)
175
 ± 
10
Body mass (kg)
68.5
 ± 
12.2
BMI (kg  m−2)
22.2
 ± 
2.3
vV̇O2max (km  h−1)
17.3
 ± 
2.3
V̇O2max  (mlO2  kg−1  min−1)
58.3
 ± 
7.7
VT1  (mlO2  kg−1  min−1)
40.8
 ± 
4.9
VT2  (mlO2  kg−1  min−1)
54.0
 ± 
7.3
HRmax (bpm)
179
 ± 
12
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CPET, Cosmed, Rome, Italy) in order to calculate the Cr. Heart rate (HR) was continuously measured (Polar 
Electro, Kempele, Finland). The highest V̇O2 value over 30 s during the maximal incremental test represented 
the V̇O2max. The speed associated with V̇O2max (vV̇O2max) was determined as the speed of the step that elicited 
V̇O2max
26. The first ventilatory threshold was determined as a breakpoint in the plot of V̇CO2 as a function of 
V̇O2. At that point, the ventilatory equivalent for  O2 (V̇E/V̇O2) increases without an increase in ventilatory equiv-
alent for  CO2 (V̇E/V̇CO2)27. The second ventilatory threshold was located between the first ventilatory threshold 
and V̇O2max, when V̇E/V̇CO2 starts to increase while V̇E/V̇O2 continues to  rise28. These thresholds were blind 
assessed by two accustomed experimenters. The average value was kept, and in case of a difference above 30 s, a 
third experimenter was involved, and the average of the two closest values was used. The rate of perceived exer-
tion was obtained by using a designed  scale29 to assess the exercise intensity about 30 s after the end of the test. 
During the second session, after a short warm-up participant performed three randomized constant velocity 
running bout of 4 min. As for the maximal incremental test, V̇O2, V̇CO2 and RER continuously recorded. Before 
each session, the  O2 and  CO2 analyzers were calibrated according to the manufacturer’s instructions.
Metabolic power during constant velocity bouts in level, uphill, and downhill running. 
Mean 
Cr values were recorded between 3:15 and 3:45 (min:s) of each running bout. The Cr was computed as  following12:
where Cr is expressed in J  kg−1  m−1, ΔV̇O2 for the difference between oxygen consumption at steady-state and 
oxygen consumption at baseline in  mlO2  kg−1  min−1 30, v corresponded to the velocity of the trial (10 km  h−1), and 
E(O2) for  O2 energy equivalent determined with RER. As the V̇O2 response is slope-dependent in  running31, for 
each slope condition (i.e., LR, UR and DR), the subjects were arbitrarily divided into two groups (i.e., economi-
cal vs. non-economical) based on the absolute Cr median value (2.42, 3.83, and 6.09 J  kg−1  m−1 for DR, LR, and 
UR, respectively), to obtain equal proportion of runners within each  group17.
Biomechanical data collection and processing. 
An instrumented treadmill equipped with a three-
dimensional force platform sampling 1000 Hz was used in this study. To reduce the noise inherent to the tread-
mill’s vibrations, we first applied, a second order stop-band Butterworth filter with edge frequencies set at 25 and 
65 Hz, on the vertical ground reaction force signal. The filter configuration was chosen empirically to obtain 
a satisfactory reduction of the oscillations observed during flight phases while minimizing its widening effect 
during ground contact time. Further data analysis was conducted using MATLAB software version R2021a 
(MathWorks Inc., Natick, MA, USA). The instants of initial contact and terminal contact were identified using 
a threshold of 7% of bodyweight on the filtered vertical ground reaction force  signal32, and ~ 80 steps were ana-
lyzed for each condition. The contact time (in ms) is the time between initial and terminal contacts of the same 
leg, the aerial time (in ms) is the time between the terminal contact of one leg and the initial contact of the oppo-
site leg. Duty factor (expressed in %) was computed as the ratio between the contact time and the stride time (i.e., 
contact time + aerial time). The step frequency (in Hz) is the reciprocal of the time required for one step (time 
between two consecutive initial contacts). The step length (m) is the quotient of the treadmill belt speed divided 
by step frequency. Peak vertical ground reaction force (GRF) was computed over the entire stance phase. The 
 Wext was determined using the method proposed by Saibene and  Minetti33 and is defined as the sum of potential, 
and horizontal and vertical kinetic works associated with the displacement of the CoM. The  Wext
− and  Wext
+ 
represent the work done due to decelerate and accelerate, respectively, the body’s CoM with respect to the envi-
ronment. The percentage of negative work is the ratio between the  Wext
− and the total external work. These data 
were continuously recorded during 30 s between 3:15 and 3:45 (min:s) of each constant velocity running bouts.
Statistical analysis. 
Jamovi statistical software (Jamovi 1.6.23, Sydney; Australia) was used for all statisti-
cal analyses. All variables were examined for normality using a Shapiro–Wilk. A repeated measures ANOVA 
was performed to compare the effect of the slope’s condition on the Cr and the biomechanical data, after using 
Mauchly’s test to assess sphericity. Bonferroni’s correction was applied on the alpha level to account for repeated 
univariate testing. When significant effects were observed, Bonferroni’s post-hoc tests were used to localize the 
significant differences. For each condition of slope, scale intercept and Pearson’s product–moment correlation 
coefficients (r) were used to assess the intensity of the relations between Cr and the selected biomechanical vari-
ables, with Bonferroni’s multiplicity  correction33. A one-way ANOVA was used to compare the biomechanical 
responses on the treadmill between efficiency groups. For all these analyses, data are expressed as mean ± SD and 
a p value inferior to 0.05 was considered statistically significant.
Ethics approval. 
This study was performed in line with the principles of the Declaration of Helsinki. 
Approval was granted by the Ethics Committee by our Institutional Review Board (CCER-VD 2015-00006).
Consent to participate. 
Informed consent was obtained from all individual participants included in the 
study.
Results
Cost of locomotion and biomechanics. 
Values of Cr and biomechanical parameters in the different 
slope conditions are presented in Table 2. The contact time was negatively correlated with the Cr in UR only 
(r = − 0.54; p = 0.017; Fig. 1). For both UR and LR only, the aerial time was positively correlated (r = 0.54 and 
r = 0.57, respectively; both p ≤ 0.018; Fig. 1), while the duty factor was negatively correlated with the Cr (r = − 0.50 
Cr = V·O2/(v × 1000) × 60 × E(O2)
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and r = − 0.57, respectively; both p ≤ 0.029; Fig. 1). The relative peak force was correlated with the Cr in LR and 
UR only (r = 0.50 and r = 0.56, respectively; both p ≤ 0.031) but not in DR. Regarding mechanical work param-
eters, the Cr correlated to  Wext
+ in UR (r = 0.49; p = 0.035), but none of the mechanical work parameters corre-
lates with Cr in DR and UR. In addition, Cr was significantly positively correlated between each slope condition: 
DR-LR (r = − 0.57; p = 0.011), DR-UR (r = − 0.53; p = 0.020), and LR-UR (r = − 0.72; p < 0.001).
Economical and non-economical runners. 
All running pattern parameters were similar between eco-
nomical and non-economical groups in both DR and LR (Table 3). The contact time, step length, and mass-
specific peak vertical GRF (Fig. 2A, B, D) were higher while the step frequency (Fig. 2C) was lower in the eco-
nomical than in the non-economical group in UR (all p < 0.031). However, aerial time, GRF, or mechanical work 
values were not different between the two groups in UR (all p > 0.05).
Discussion
This study provides new insights into biomechanical factors according to the level of metabolic economy of 
runners on different running slopes. The main findings of the present study are that (1) aerial time, peak verti-
cal ground reaction force, positive mechanical work, and duty factor were associated with Cr during LR and 
UR; while contact time correlated only with Cr during UR; (2) no relationship was observed between Cr and 
biomechanical responses during DR; and (3) most economical runners tend to have specific running pattern 
adaptations (i.e., longer contact time and greater step length as well as a lower step frequency) during UR only. 
These results partially support the hypothesis since specific running pattern responses were characterized by a 
lower metabolic cost of running on flat or positive slopes but not on negative slope.
During UR, Cr positively correlated with several running pattern parameters such as  Wext
+, aerial time, and 
mass specific GRF, and negatively correlated with contact time and duty factor. These correlations demonstrate 
that UR is related to specific running pattern parameters and highlight that the running pattern may influence 
Cr, especially during UR. Our results revealed that Cr,  Wext
−,  Wext
+, duty factor, and step frequency were lower; 
whereas areal time, step length (in absolute and relative to the height), GRF (expressed in both absolute and rela-
tive values), and the percentage of the  Wext
− were higher during LR than during UR, which is rather consistent 
with the  literature23. Furthermore, as already observed on similar  slopes8,9,34, the running economy was reduced 
when running on the positive slope.
Most of the mechanical work performed comes from positive external mechanical work during UR (~ 69% of 
 Wext was provided by  Wext
+ and only ~ 31% by  Wext
−; Table 2). Comparable distribution on equivalent slope and 
speed was  reported9. These results confirm that UR is primarily a concentric muscle contraction that is energy-
consuming25. Indeed, the  Wext
+ represents the amount of mechanical energy spent during the pushing phase to 
elevate and move forward the  CoM24.
It has been highlighted that the increase in  Wext
+ was caused by the elevation of CoM related to the upward 
movement of the body during  UR24. The external work is the product of vertical displacement of the CoM and 
the step frequency. It was observed that lower vertical displacements of the CoM and/or a higher step frequency 
in LR were associated with better running  economy35. Therefore, one could potentially expect a similar relation-
ship during UR. However, no correlation was observed between step frequency and Cr, possibly because runners 
choose their own optimal step frequency and step length, whatever the slope  level16, close to their minimal  Cr36. 
Nevertheless, other spatiotemporal parameters such as the contact time and aerial time were correlated with Cr 
during UR. Contact time was negatively correlated to the Cr, meaning that a longer contact was associated with 
Table 2.  Cost of locomotion and biomechanical parameters in downhill, level and uphill running (n = 19). 
GRF peak ground reaction force. a p < 0.05 versus downhill running. b p < 0.05 versus level running.
Downhill running
Level running
Uphill running
F-STATISTICS
Energy cost of running
 Energy cost (J  kg−1  m−1)
2.56 ± 0.51
3.87 ± 0.43a
6.21 ± 0.51ab
674
Running kinematics and GRF
 Contact time (s)
0.28 ± 0.03
0.29 ± 0.03
0.29 ± 0.03
3.73
 Aerial time (s)
0.09 ± 0.03
0.08 ± 0.02a
0.07 ± 0.02ab
25.9
 Duty factor (%)
74.9 ± 7.6
78.1 ± 5.8a
81.5 ± 5.2ab
22.6
 Step frequency (Hz)
2.66 ± 0.10
2.71 ± 0.12
2.81 ± 0.11ab
26.6
 Step length (m)
1.05 ± 0.04
1.03 ± 0.05
0.99 ± 0.04ab
26.2
 Relative step length (% of height)
60.0 ± 3.8
58.8 ± 3.8
56.7 ± 3.3ab
25.1
 Peak vertical GRF (kN)
1.41 ± 0.20
1.35 ± 0.19a
1.29 ± 0.18ab
21.8
 Mass-specific vertical GRF (N  kg−1)
20.8 ± 2.1
19.8 ± 1.5a
19.0 ± 1.2ab
22.1
Mechanical work
 External work (J  kg1)
3.06 ± 0.44
2.75 ± 0.29a
2.76 ± 0.19a
17.5
 Positive external work (J  kg−1)
1.07 ± 0.23
1.42 ± 0.15a
1.91 ± 0.11ab
367
 Negative external work (J  kg−1)
− 1.99 ± 0.22
− 1.34 ± 0.14a
− 0.85 ± 0.09ab
737
 Percentage negative external work (%)
65.3 ± 2.3
48.5 ± 0.2a
30.8 ± 1.1ab
2270
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a better running economy. This result is in agreement with the observation made by Vernillo et al.37 after an 
ultramarathon event (330 km with 24,000 m elevation gain). The UR Cr (4 min at 6 km  h−1 and + 15% incline) 
was negatively correlated with contact time, duty factor, and as well as rate of force application (characterized 
by inverse contact time:  tc
−1). For instance, shorter contact time reduces the time allowed to generate force into 
the ground and increases the rate at which the muscle fibers  shorten38,39, so more fast muscle fibers or muscle 
mass should be required for a given applied  force37,38. The step frequency depends on the interrelationship 
Figure 1.  Relationships between the cost of locomotion and contact time (A), aerial time (B), duty factor (C), 
mass-specific peak vertical ground reaction force (D), and positive external mechanical work (E) in different 
slope conditions (DR downhill running—unfiled circles, LR level running—filled diamonds, UR uphill 
running—*p < 0.05).
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Table 3.  Comparison of the cost of locomotion and biomechanical responses for economical versus non-
economical runners in the three slope conditions (n = 19). GRF peak ground reaction force. Significant values 
are in [bold].
Downhill running
Level running
Uphill running
Economical N = 9
Non-economical 
N = 10
p
Economical N = 9
Non-economical 
N = 10
p
Economical N = 9
Non-economical 
N = 10
p
Energy cost of running
 Energy cost of run-
ning (J  kg−1  m−1)
2.15 ± 0.20
2.93 ± 0.42
 < .001
3.52 ± 0.18
4.20 ± 0.32
 < .001
5.82 ± 0.27
6.55 ± 0.42
 < .001
Running kinematics and GRF
 Contact time (s)
0.28 ± 0.03
0.29 ± 0.03
0.697
0.30 ± 0.04
0.28 ± 0.02
0.199
0.30 ± 0.02
0.28 ± 0.02
0.013
 Aerial time (s)
0.10 ± 0.03
0.09 ± 0.02
0.621
0.07 ± 0.02
0.09 ± 0.02
0.063
0.06 ± 0.01
0.07 ± 0.02
0.130
 Duty factor (%)
74.1 ± 8.9
75.7 ± 6.5
0.654
80.5 ± 5.8
76.0 ± 5.3
0.093
83.7 ± 4.1
79.5 ± 5.5
0.080
 Step frequency (Hz)
2.65 ± 0.09
2.66 ± 0.12
0.900
2.71 ± 0.16
2.70 ± 0.09
0.864
2.75 ± 0.10
2.86 ± 0.10
0.026
 Step length (m)
1.05 ± 0.04
1.05 ± 0.05
0.932
1.03 ± 0.06
1.03 ± 0.03
0.947
1.01 ± 0.04
0.97 ± 0.03
0.038
 Relative step length 
(% of height)
60.1 ± 2.4
59.8 ± 4.8
0.871
58.3 ± 3.3
59.3 ± 4.4
0.560
56.5 ± 3.5
56.8 ± 3.2
0.854
 Peak vertical GRF 
(kN)
1.43 ± 0.14
1.39 ± 0.2
0.619
1.36 ± 0.16
1.34 ± 0.22
0.875
1.34 ± 0.14
1.25 ± 0.2
0.252
 Mass-specific verti-
cal GRF (N  kg−1)
21.1 ± 2.5
20.5 ± 1.7
0.573
19.2 ± 1.5
20.4 ± 1.4
0.102
18.5 ± 0.9
19.5 ± 1.3
0.075
Mechanical work
 External work 
(J  kg−1)
3.13 ± 0.47
3.00 ± 0.43
0.537
2.69 ± 0.23
2.81 ± 0.34
0.368
2.71 ± 0.14
2.80 ± 0.23
0.317
 Positive external 
work (J  kg−1)
1.11 ± 0.25
1.04 ± 0.22
0.502
1.38 ± 0.12
1.45 ± 0.18
0.363
1.87 ± 0.08
1.93 ± 0.13
0.255
 Negative external 
work (J  kg−1)
− 2.02 ± 0.23
− 1.97 ± 0.21
− 1.30 ± 0.11
− 1.36 ± 0.17
0.375
− 0.84 ± 0.06
− 0.87 ± 0.11
0.468
 Percentage negative 
external work (%)
64.9 ± 2.5
65.7 ± 2.1
0.448
48.5 ± 0.2
48.5 ± 0.2
0.652
30.8 ± 0.8
30.8 ± 1.3
0.996
Figure 2.  Contact time (A), step length (B), step frequency (C) and mass-specific ground reaction force (D) in 
economical (white box-plots) and non-economical runners (gray box-plots) during uphill running.
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between contact time and step length. Thus, for a given step frequency, increasing the aerial time will shorten 
the contact time and lead to Cr deterioration, since the metabolic cost of force generation increases as the con-
tact time  shortens38. In addition, as it exists an inverse relationship between the step frequency and the vertical 
oscillation of CoM in  running35, Furthermore, reducing aerial time and vertical displacement (which will occur 
together) are the result of less external positive work (resulting in a reduced vertical velocity at takeoff) during 
UR. However, an excessive increase of the stride frequency during running to reduce mechanical work could 
be disadvantageous as it causes a Cr  raise16. The negative correlation observed between Cr and the duty factor 
might underline the importance of optimizing energy transfer (from metabolic to mechanics) to reduce energy 
demands in UR. Altogether, increasing the stance phase and decreasing the aerial time may be an appropriate 
strategy for improving running economy during UR. As such, patterns of locomotion may play a decisive role 
in lowering the cost of locomotion by walking compared to running on a steep positive  slope40. Indeed, walking 
pattern is characterized by a longer contact time, a higher duty factor, and a lower stride frequency associated 
with reduced muscle activation compared to the running pattern on a 30°  slope41.
The present data showed a relationship between the Cr and GRF. Normalized GRF to body weight was 
positively correlated with Cr during UR. Since GRF is the result of the forces produced by all the muscles in the 
vertical direction during the stance phase, an excessive GRF value in this orientation is a waste of energy. Thus, 
minimizing the vertical GRF seems to be more economical during UR. Increasing step frequency could lower 
the vertical GRF and might be a useful strategy in UR. Therefore, the adoption of strategies to reduce vertical 
GRF forces should be incorporated in training programs in order to improve running economy during UR as 
well as during LR. However, such adjustments must be individually adapted.
In the present study, we confirm that negative slope has a significant effect on the running pattern and 
decreases Cr compared to  LR42. Total mechanical work,  Wext
−, proportion of  Wext
−, aerial time, and GRF 
(expressed in absolute and mass-specific values), increased in DR while the  Wext
+ decreased, in agreement with 
the  literature9,23,24,43. However, conversely to UR, downhill Cr was not correlated with any mechanical aspects, 
suggesting that, at least for the present velocity and slope, there was not a more economical running pattern 
during DR. These results are not in agreement with previous  results12 which reported a significant correlation 
between Cr and several spatiotemporal parameters such as step length, step frequency, and contact time during 
DR (− 15%). According to these later results, it was suggested that the ability to store and restitute elastic energy 
had an important role in DR  Cr12. The difference observed in the literature may come from differences in the 
experimental design and the fitness level of the participants. As observed by Minetti et al.9 more than half (~ 65%) 
of the total external work is provided by  Wext
−. The latter represents the work done during the braking phase of 
the stance phase. During this phase, the knee extensor muscles forcibly lengthen (i.e., eccentric muscle action) 
under the potential effect of gravity to limit the drop-down of the CoM. From an energetical point of view, this 
eccentric muscle’s action requires less energy than a concentric muscle  contraction25, and part of the potential 
energy from the vertical oscillation of the CoM is either dissipated as wasted heat (mostly) or stored in the mus-
cle–tendon units during the braking phase prior its restitution during the pushing phase. The stretch–shorten-
ing cycle is mainly involved during  DR16,44 and is known to be less energy consuming than purely concentric 
 actions45, saving energy and reducing the Cr as  well45. For moderate negative slopes (~ 15%), the elastic energy 
stored in the muscle–tendon units can supply almost all the energy demand for the push  phase44. However, no 
correlation was observed between  Wext
− and the Cr.
Runners have their own running style based on ability and experience which implies that a similar Cr from 
one individual to another can be associated with different biomechanical parameters. Indeed, there was only a 
relatively small influence of each of the parameters measured on CR, even when the relationship was significant 
(Fig. 1). Therefore, we have to be cautious when suggesting potential gait modifications for performance enhance-
ment. Changing one parameter of the running pattern can alter the overall mechanics and potentially the running 
 economy46. For example, ± 15% changes in preferred step frequency increased Cr by ~ 20% in  DR16. Running in 
negative slopes is demanding for the body, as greater braking force must be applied on the ground to maintain 
a constant speed, which can generate muscle  damage47. Furthermore, since force absorption is less energetically 
demanding, runners may neglect their running mechanics. A more protective running pattern is privileged by 
runners based on their experience in  DR9. Running on negative slopes where the fear of falling is higher could 
also exacerbate emotional aspect, when compared to LR and UR. During treadmill running, irrespective of the 
slope, it is well-known that the mechanics is different than during overground running: the influence of the 
motion belt that affects both potential and kinetic works remains difficult to be accurately  assessed48. Therefore, 
we have to be cautious for translating the present findings to field running.
The present study compared the metabolic and biomechanical responses of economical and non-economical 
runners at different slopes. Individual Cr values in the three slope conditions were used to split participants into 
two groups. We showed that the most economical runners remained the same ones, independently of the slope 
(i.e., in DR, LR or UR). This result is rather consistent with the literature: Willis et al.7 reported a strong cor-
relation between Cr measured in LR and in UR (12% slope) in a group of elite ultra-trail runners (6 males and 
5 females), while Balducci et al.49 found no correlation between LR and UR (12.5 or 25% slope) in trained trail 
 runners49. Moreover, in the present study, there were differences in biomechanical responses between the two 
groups, but only in UR economical runners had longer contact time and step length compared to less economical 
runners, while their step frequency was smaller. Ultimately, the longer duration of the stance phase may allow 
runners to optimize the direction of propulsive force and the time allowed to apply force to the  ground50. Indeed, 
mass-specific GRF tends to be lower in the economical runners than in the non-economical group (p = 0.070; 
Table 3), suggesting that lower mass-specific GRF in UR may allow to reduce the metabolic cost of running. A 
lower vertical force during the stance phase was observed for the group of runners who had the lowest oxygen 
consumption for a given speed (~ 13 km  h−1) on flat  terrain17.
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No difference for all the biomechanical variables was observed in DR and LR between the groups of economi-
cal and non-economical runners, i.e., with different Cr. This result is rather in line with the  literature13,14, and 
may be partly explained by the heterogeneity of the population in the present study. Less experienced runners 
tend to have a greater stride to stride variability than experienced  runners51. The Cr may be influenced by many 
other factors, such as anthropometry, flexibility, and joint kinematics but also by physiological differences (e.g., 
metabolic efficiency) or equipment (e.g., running shoes)18. Runners naturally chose their optimal running pat-
tern themselves to minimize their  Cr13. Each one having its own specificity, the number of mechanical combina-
tions is likely very important. Nevertheless, even if two groups use different running strategies, there were no 
significant differences in  Cr13,14.
Conclusions
The present study reported that Cr was related to few key running pattern parameters (i.e., contact time, aerial 
time, mass specific GRF and positive mechanical external work) mainly in UR, but not in DR. Moreover, all run-
ning pattern parameters were similar between economical and non-economical runners in DR and LR, but not 
in UR. Interestingly, the contact time and the step length were longer, whereas the step frequency was lower in 
the group of economical runners compared to the group of non-economical runners in UR. These results provide 
interesting insights concerning an optimal running pattern to reduce the cost of locomotion, and consequently 
improve performance during graded running. In practice, it may be preferable to reduce step frequency, or even 
to shift to walking, on a positive slope to increase step length and slow down the knee extension during the pro-
pulsive phase. On steep slopes, poles could facilitate this  mechanism52. Overall, the present study emphasizes 
that the mechanics of LR and UR are fundamentally different. Future investigations are needed to deepen the 
knowledge with a heterogeneous population (trained or untrained runners) to improve the training protocols 
of mountain or trail runners.
Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on 
reasonable request.
Received: 13 October 2022; Accepted: 6 July 2023
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Acknowledgements
The authors thank the subjects for their enthusiastic participation in the present study.
Author contributions
G.P.M. and F.M. participated in the design of the study and contributed to data collection, M.L., A.D. and R.F. 
contributed to the data reduction/analysis; All authors contributed to the manuscript writing. All authors have 
read and approved the final version of the manuscript and agree with the order of presentation of the authors.
Funding
The authors did not receive support from any organization for the submitted work.
Competing interests 
The authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to F.M. or G.P.M.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and 
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© The Author(s) 2023

Relationship between biomechanics and energy cost in graded treadmill running.
Lemire, Marcel,Faricier, Robin,Dieterlen, Alain,Meyer, Frédéric,Millet, Grégoire P