

Citation: Benjamin, D.; Odof, S.;
Abbès, B.; Fourchet, F.; Christiaen, B.;
Taïar, R. Shock Response Spectrum
Analysis of Fatigued Runners.
Sensors 2022, 22, 2350. https://
doi.org/10.3390/s22062350
Academic Editor: Dragan Indjin
Received: 18 February 2022
Accepted: 16 March 2022
Published: 18 March 2022
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sensors
Article
Shock Response Spectrum Analysis of Fatigued Runners
Daniel Benjamin 1,2
, Serge Odof 3, Boussad Abbès 2
, François Fourchet 4,5,6, Benoit Christiaen 1
and Redha Taïar 2,*
1
Podiatry Medicine Department, Centre Luxembourg, 75005 Paris, France;
d.benjamin@centre-luxembourg.com (D.B.); b.christiaen@centre-luxembourg.com (B.C.)
2
MATériaux et Ingénierie Mécanique (MATIM), Université de Reims Champagne Ardenne,
51100 Reims, France; boussad.abbes@univ-reims.fr
3
École Nationale Supérieure D’ingénieurs de Reims (ESIREIMS), Université de Reims Champagne Ardenne,
51100 Reims, France; serge.odof@univ-reims.fr
4
Physiotherapy Department, Hospital La Tour, 1217 Meyrin, Switzerland; francois.fourchet@gmail.com
5
French Society of Sports Physical Therapist (SFMKS Lab), 93380 Pierreﬁte sur Seine, France
6
Inter-University Laboratory of Human Movement Biology (LIBM), Savoie Mont-Blanc University,
73000 Chambery, France
*
Correspondence: redha.taiar@univ-reims.fr
Abstract: The purpose of this study was to determine the effect of fatigue on impact shock wave
attenuation and assess how human biomechanics relate to shock attenuation during running. In
this paper, we propose a new methodology for the analysis of shock events occurring during the
proposed experimental procedure. Our approach is based on the Shock Response Spectrum (SRS),
which is a frequency-based function that is used to indicate the magnitude of vibration due to a shock
or a transient event. Five high level CrossFit athletes who ran at least three times per week and who
were free from musculoskeletal injury volunteered to take part in this study. Two Micromachined
Microelectromechanical Systems (MEMS) accelerometers (RunScribe®, San Francisco, CA, USA) were
used for this experiment. The two RunScribe pods were mounted on top of the foot in the shoelaces.
All ﬁve athletes performed three maximum intensity runs: the 1st run was performed after a brief
warmup with no prior exercise, then the 2nd and the 3rd run were performed in a fatigued state. Prior
to the 2nd and the 3rd run, the athletes were asked to perform at maximum intensity for two minutes
on an Assault AirBike to tire them. For all ﬁve athletes, there was a direct correlation between fatigue
and an increase in the aggressiveness of the SRS. We noticed that for all ﬁve athletes for the 3rd run
the average SRS peaks were signiﬁcantly higher than for the 1st run and 2nd run (p < 0.01) at the
same natural frequency of the athlete. This conﬁrms our hypothesis that fatigue causes a decrease in
the shock attenuation capacity of the musculoskeletal system thus potentially involving a higher risk
of overuse injury.
Keywords: Shock Response Spectrum; fatigue; injuries; gait analysis; Micromachined Microelec-
tromechanical Systems (MEMS) accelerometer
1. Introduction
Running is the exercise of choice for millions of people all over the world and across
the age spectrum. One of the main reasons for its popularity stems from its simplicity.
However, running also carries the risk of increased musculoskeletal injuries and there is a
need to understand the etiology of injury in order to efﬁciently prevent it [1]. One of the
important functions of the human musculoskeletal system is to attenuate and dissipate
shock waves initiated with foot ground contact [2]. Those shock waves are initiated by
most types of motion, such as walking and running. The demarcation between walking
and running occurs when periods of double support during the stance phase of the gait
cycle (both feet are simultaneously in contact with the ground) give way to two periods
of double ﬂoat at the beginning and the end of the swing phase of gait (neither foot is
Sensors 2022, 22, 2350. https://doi.org/10.3390/s22062350
https://www.mdpi.com/journal/sensors
Sensors 2022, 22, 2350
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touching the ground) [3]. Generally, as speed increases further, initial contact changes from
being on the hindfoot to the forefoot.
Running involves repeated single-leg impacts between the foot and the surface. Such
impacts are characterized by a transient peak in the ground reaction force (impact force),
rapid deceleration of the lower extremity (impact shock), and the initiation of a wave of
acceleration and deceleration (impact shock wave) that is propagated through the body [4].
The impact shock wave experienced by the body due to landings must be attenuated
by several structures and mechanisms in the body including bone, synovial ﬂuids, carti-
lage, soft tissues, joint kinematics and muscular activity. Passively, shock attenuation is
achieved by soft tissues and bone. Actively, shock attenuation is achieved through eccentric
muscle action [5]. This active mechanism is thought to be far more signiﬁcant than the
passive mechanism in attenuating shock. Since muscles are thought to play a primary role
in energy and shock absorption during landing, it has been hypothesized that reduced
muscular function, through fatigue, decreases the shock absorbing capacity of the body
and subsequently can lead to an increased chance of injury [6]. Fatigue has been deﬁned as
any reduction in the force generating capacity of the total neuromuscular system regardless
of the force required in any given situation [7].
The loads produced by repeated impacts have been linked to degenerative joint
diseases and athletic overuse injuries including, for example, stress fractures, shin splints,
osteoarthritis and lower back pain. Although the exact mechanisms of impact related injury
are relatively unknown and controversial evidence linking impact, fatigue and injuries are
well documented [8–11].
In this paper, we propose a new methodology for the analysis of shock events occurring
during the proposed experimental procedure. Our approach is based on the Shock Response
Spectrum (SRS) [12], which is a frequency-based function that is used to indicate the
magnitude of vibration due to a shock or a transient event [13]. The main aim is to analyze
the ability of the human musculoskeletal system to attenuate the mechanical stresses
resulting from the fatigue effect by Shock Responses Spectrum (SRS) of the foot strike–
generated shock waves during running. Most previous studies focused on shocks/impacts,
ground force reaction, or spectral or vertical impact load rate. Using SRS as a measurement
in running gait analysis has never been studied as of today. This innovative approach
could pave the way to a whole new way of assessing a runner’s gait pattern using smart
connected shoes.
The purpose of this study was to determine the effect of fatigue on impact shock
wave attenuation and assess how human biomechanics relate to shock attenuation during
running. It was hypothesized that fatigue would cause a decrease in the shock attenua-
tion capacity of the musculoskeletal system, thus potentially involving a higher risk of
overuse injury.
2. Materials and Methods
2.1. Procedures
Five high level CrossFit athletes (four males, one female) who ran at least three times
per week and who were free from musculoskeletal injury volunteered to take part in this
study. The athletes had a mean age of 26.4 (±3.9) years, stature 182.3 (±5.7) cm, and body
mass 81.7 (±8.5) kg, respectively. The athletes usually performed 10 km to 15 km runs
twice a week and one sprint interval training of various lengths and intensities. The study
was conducted in accordance with the Helsinki Declaration on human experimentation
stated in compliance with the 1964 Helsinki Declaration and its later amendments. Every
participant provided written consent after information was given on the aim, protocol,
and methodology of the study. The original study was approved by the Medical and
Ethical Board of the Centre Luxembourg (protocol code LUX_2021_0308_CLAB and date of
approval of 3 August 2021). Two Micromachined Microelectromechanical Systems (MEMS)
accelerometers (RunScribe®) were used for this experiment. The two RunScribe pods were
mounted on top of the foot in the shoelaces (Figure 1).
Sensors 2022, 22, 2350
3 of 11
Sensors 2022, 22, x FOR PEER REVIEW 
3 of 11 
 
 
(MEMS) accelerometers (RunScribe®) were used for this experiment. The two RunScribe 
pods were mounted on top of the foot in the shoelaces (Figure 1). 
 
Figure 1. MEMS accelerometers placement. 
The RunScribe pods encompass 9-Axis Motion Tracking which combines a 3-axis gy-
roscope, 3-axis accelerometer, and 3-axis compass in the same device together with an 
onboard Digital Motion Processor. This enables us also to measure at a 500 Hz sampling 
rate: Efficiency (Stride Rate, Contact Time, Flight Ratio), Motion (Footstrike Type, Prona-
tion, Pronation Velocity), Shock (Impact Gs, Braking Gs), Symmetry and Power. 
After a warmup, participants were asked to perform a first 800 m run at maximum 
intensity. Right after the first run, they jumped on an Assault AirBike (Rogue, Columbus, 
OH, USA) (Figure 2) where they were asked to perform at maximum intensity for 2 min 
(the power had to stay above 400 Watts for the 2 min). They dismounted the Assault Air-
Bike and they were then asked again to perform a second 800 m run at maximum inten-
sity. The same protocol was then repeated with another 2 min on the Assault AirBike then 
a third run at maximum intensity. The RunScribe pods were turned off during the Assault 
AirBike sessions and were only recording the three 800 m run intervals. 
 
Figure 2. Assault AirBike. 
The Assault AirBike, also known as “the Devil’s tricycle” was used to induce fatigue 
because they procure a unique and extremely challenging effort. It is considered among 
the crossfit community as the most dreaded but most effective tool for HIIT (High Inten-
sity Interval Training) and metabolic conditioning. 
2.2. Shock Response Spectrum Calculation 
Spectral analysis is commonly used to study the structure of composite waveforms, 
such as the impact shock waves. The primary tool of spectral analysis is the Fast Fourier 
Transformation (FFT) that enables us to determine the runner’s natural frequency [14] 
which corresponds to the peak of the Power Spectral Density (Figure 3): 
Figure 1. MEMS accelerometers placement.
The RunScribe pods encompass 9-Axis Motion Tracking which combines a 3-axis
gyroscope, 3-axis accelerometer, and 3-axis compass in the same device together with an
onboard Digital Motion Processor. This enables us also to measure at a 500 Hz sampling
rate: Efﬁciency (Stride Rate, Contact Time, Flight Ratio), Motion (Footstrike Type, Pronation,
Pronation Velocity), Shock (Impact Gs, Braking Gs), Symmetry and Power.
After a warmup, participants were asked to perform a ﬁrst 800 m run at maximum
intensity. Right after the ﬁrst run, they jumped on an Assault AirBike (Rogue, Columbus,
OH, USA) (Figure 2) where they were asked to perform at maximum intensity for 2 min (the
power had to stay above 400 Watts for the 2 min). They dismounted the Assault AirBike
and they were then asked again to perform a second 800 m run at maximum intensity. The
same protocol was then repeated with another 2 min on the Assault AirBike then a third
run at maximum intensity. The RunScribe pods were turned off during the Assault AirBike
sessions and were only recording the three 800 m run intervals.
Sensors 2022, 22, x FOR PEER REVIEW 
3 of 12 
(MEMS) accelerometers (RunScribe®) were used for this experiment. The two RunScribe 
pods were mounted on top of the foot in the shoelaces (Figure 1). 
 
Figure 1. MEMS accelerometers placement. 
The RunScribe pods encompass 9-Axis Motion Tracking which combines a 3-axis gy-
roscope, 3-axis accelerometer, and 3-axis compass in the same device together with an 
onboard Digital Motion Processor. This enables us also to measure at a 500 Hz sampling 
rate: Efficiency (Stride Rate, Contact Time, Flight Ratio), Motion (Footstrike Type, Prona-
tion, Pronation Velocity), Shock (Impact Gs, Braking Gs), Symmetry and Power. 
After a warmup, participants were asked to perform a first 800 m run at maximum 
intensity. Right after the first run, they jumped on an Assault AirBike (Rogue, Columbus, 
OH, USA) (Figure 2) where they were asked to perform at maximum intensity for 2 min 
(the power had to stay above 400 Watts for the 2 min). They dismounted the Assault Air-
Bike and they were then asked again to perform a second 800 m run at maximum inten-
sity. The same protocol was then repeated with another 2 min on the Assault AirBike then 
a third run at maximum intensity. The RunScribe pods were turned off during the Assault 
AirBike sessions and were only recording the three 800 m run intervals. 
 
 
Figure 2. Assault AirBike.
The Assault AirBike, also known as “the Devil’s tricycle” was used to induce fatigue
because they procure a unique and extremely challenging effort. It is considered among
the crossﬁt community as the most dreaded but most effective tool for HIIT (High Intensity
Interval Training) and metabolic conditioning.
2.2. Shock Response Spectrum Calculation
Spectral analysis is commonly used to study the structure of composite waveforms,
such as the impact shock waves. The primary tool of spectral analysis is the Fast Fourier
Sensors 2022, 22, 2350
4 of 11
Transformation (FFT) that enables us to determine the runner’s natural frequency [14]
which corresponds to the peak of the Power Spectral Density (Figure 3):
PSD = 1
N

Z +∞
−∞ a(t)e−j2π f tdt

2
(1)
where N is the number of points of the recording, a(t) is the acceleration modulus, f is the
frequency and t is the time.
Sensors 2022, 22, x FOR PEER REVIEW 
4 of 11 
 
𝑃𝑆𝐷 ൌ 1
𝑁 ቤන
𝑎ሺ𝑡ሻ𝑒ି௝ଶగ௙௧
ାஶ
ିஶ
𝑑𝑡ቤ
ଶ
 
(1) 
where 𝑁 is the number of points of the recording, 𝑎ሺ𝑡ሻ is the acceleration modulus, 𝑓 is 
the frequency and 𝑡 is the time. 
 
Figure 3. SRS vs. PSD running analysis. 
Power Spectral Density (PSD) provides a convenient method for separating different 
frequency components in the impact shock wave, such as acceleration moments due to 
impact shock [15]. 
In this paper, we propose a new methodology for the analysis of shock events occur-
ring during the proposed experimental procedure. Our approach is based on the Shock 
Response Spectrum (SRS), which is a frequency-based function that is used to indicate the 
magnitude of vibration due to a shock or a transient event. The following procedure, con-
sisting of several steps, is adopted in the present study: 
• 
Step 1: 
The acceleration modulus 𝑎ሺ𝑡ሻ is extracted from the recording. Figure 4 illustrates 
the acceleration modulus results for one CrossFit athlete. 
 
Figure 4. Acceleration modulus 𝑎ሺ𝑡ሻ for one CrossFit athlete. 
• 
Step 2: 
The power spectral density (PSD) given in Equation (1) is then calculated using a Fast 
Fourier Transform (FFT). This calculation allows us to determine the fundamental fre-
quency of the runner 𝑓଴ corresponding to the position of the largest peak of the PSD. The 
inverse of this frequency gives the time period of the runner’s step as: 𝑇 ൌ 1/𝑓଴. The pro-
posed algorithm extracts automatically the “first” step from the entire signal, and thus 
defines the “pattern” of the runner as shown in Figure 5. 
Figure 3. SRS vs. PSD running analysis.
Power Spectral Density (PSD) provides a convenient method for separating different
frequency components in the impact shock wave, such as acceleration moments due to
impact shock [15].
In this paper, we propose a new methodology for the analysis of shock events occurring
during the proposed experimental procedure. Our approach is based on the Shock Response
Spectrum (SRS), which is a frequency-based function that is used to indicate the magnitude
of vibration due to a shock or a transient event. The following procedure, consisting of
several steps, is adopted in the present study:
•
Step 1:
The acceleration modulus a(t) is extracted from the recording. Figure 4 illustrates the
acceleration modulus results for one CrossFit athlete.
Sensors 2022, 22, x FOR PEER REVIEW 
4 of 11 
 
𝑃𝑆𝐷 ൌ 1
𝑁 ቤන
𝑎ሺ𝑡ሻ𝑒ି௝ଶగ௙௧
ାஶ
ିஶ
𝑑𝑡ቤ
ଶ
 
(1) 
where 𝑁 is the number of points of the recording, 𝑎ሺ𝑡ሻ is the acceleration modulus, 𝑓 is 
the frequency and 𝑡 is the time. 
 
Figure 3. SRS vs. PSD running analysis. 
Power Spectral Density (PSD) provides a convenient method for separating different 
frequency components in the impact shock wave, such as acceleration moments due to 
impact shock [15]. 
In this paper, we propose a new methodology for the analysis of shock events occur-
ring during the proposed experimental procedure. Our approach is based on the Shock 
Response Spectrum (SRS), which is a frequency-based function that is used to indicate the 
magnitude of vibration due to a shock or a transient event. The following procedure, con-
sisting of several steps, is adopted in the present study: 
• 
Step 1: 
The acceleration modulus 𝑎ሺ𝑡ሻ is extracted from the recording. Figure 4 illustrates 
the acceleration modulus results for one CrossFit athlete. 
 
Figure 4. Acceleration modulus 𝑎ሺ𝑡ሻ for one CrossFit athlete. 
• 
Step 2: 
The power spectral density (PSD) given in Equation (1) is then calculated using a Fast 
Fourier Transform (FFT). This calculation allows us to determine the fundamental fre-
quency of the runner 𝑓଴ corresponding to the position of the largest peak of the PSD. The 
inverse of this frequency gives the time period of the runner’s step as: 𝑇 ൌ 1/𝑓଴. The pro-
posed algorithm extracts automatically the “first” step from the entire signal, and thus 
defines the “pattern” of the runner as shown in Figure 5. 
Figure 4. Acceleration modulus a(t) for one CrossFit athlete.
•
Step 2:
The power spectral density (PSD) given in Equation (1) is then calculated using a
Fast Fourier Transform (FFT). This calculation allows us to determine the fundamental
frequency of the runner f0 corresponding to the position of the largest peak of the PSD.
The inverse of this frequency gives the time period of the runner’s step as: T = 1/ f0. The
proposed algorithm extracts automatically the “ﬁrst” step from the entire signal, and thus
deﬁnes the “pattern” of the runner as shown in Figure 5.
Sensors 2022, 22, 2350
5 of 11
Sensors 2022, 22, x FOR PEER REVIEW 
5 of 11 
 
 
 
Figure 5. Pattern of one CrossFit athlete. 
• 
Step 3: 
We then carry out the cross-correlation 𝐶𝐶ሺ𝜏ሻ between the runner’s pattern and the 
recording’s duration 𝑎ሺ𝑡ሻ: 
𝐶𝐶ሺ𝜏ሻ ൌ න
𝑎ሺ𝑡ሻ𝑝𝑎𝑡𝑡𝑒𝑟𝑛ሺ𝑡 ൅ 𝜏ሻ𝑑𝑡
ାஶ
ିஶ
 
(2) 
We observe that at each step, the convolution is maximum. For each maximum value 
of 𝐶𝐶ሺ𝜏ሻ we calculate the SRS of each step and of the entire signal as explained in the next 
step. 
• 
Step 4: 
The calculation of the SRS is based on the acceleration time history. It applies an ac-
celeration time history as a common base excitation ሺ𝑦ሷሻ to an array of single-degree-of-
freedom (SDOF) systems composed of spring ሺ𝑘௜ሻ, mass ሺ𝑚௜ሻ and damper ሺ𝑑௜ሻ, as de-
picted in Figure 6. 
 
Figure 6. SRS model. 
𝑥ሷ௜ is the absolute response of each system to the input 𝑦ሷ. This can be determined by 
applying Newton’s law to a free-body diagram of an individual system, as shown in Fig-
ure 7. 
 
Figure 7. Free-body diagram of an individual system. 
The force balance yields the following governing differential equation of motion: 
𝑚𝑥ሷ ൅ 𝑑𝑥ሶ ൅ 𝑘𝑥 ൌ 𝑑𝑦ሶ ൅ 𝑘𝑦 
(3) 
Figure 5. Pattern of one CrossFit athlete.
•
Step 3:
We then carry out the cross-correlation CC(τ) between the runner’s pattern and the
recording’s duration a(t):
CC(τ) =
Z +∞
−∞ a(t)pattern(t + τ)dt
(2)
We observe that at each step, the convolution is maximum. For each maximum value of
CC(τ) we calculate the SRS of each step and of the entire signal as explained in the next step.
•
Step 4:
The calculation of the SRS is based on the acceleration time history. It applies an
acceleration time history as a common base excitation
Sensors 2022, 22, 2350
6 of 11
By deﬁning the relative displacement z = x − y, Equation (3) can be rewritten as:
..z + 2ξω
.z + ω2z = −
..y
(4)
where ω0 = k
m is the natural frequency in radians per second and ξ =
d
(2ω0m) is the
damping ratio. Moreover, ξ is usually represented by the ampliﬁcation factor Q =
1
(2ξ).
Since the base excitation
..y is an arbitrary function of time, Equation (4) does not
have a closed-form solution. To calculate the SRS of each step and of the entire signal, we
have used the algorithm for the calculation of the SRS proposed in [13]. SRS enables us to
determine the maximum acceleration a system will undergo when one knows the natural
frequency f0 and the quality factor Q for each possible natural frequency. In this study,
a relative damping of 5% was used, resulting in Q = 10. SRS can also be calculated for
the entire duration of a recording. We then observed the peaks at the fundamental and
harmonic frequencies of the recorded signal [16]. In this context, SRS combines both the
notion of transfer function and response to transient regimes.
Intra comparison of the SRS offers a lot more ﬁnesse to the analysis since the frequency
is also taken into account. The aggressiveness of a running step is not only due to the value
of the maximum acceleration but also to the general shape of the movement, only the SRS
allows this to be taken into account in the analysis.
Figure 8 gives the general workﬂow for SRS determination.
Sensors 2022, 22, x FOR PEER REVIEW 
6 of 11 
 
 
By defining the relative displacement 𝑧 ൌ 𝑥 െ 𝑦, Equation (3) can be rewritten as: 
𝑧ሷ ൅ 2𝜉𝜔𝑧ሶ ൅ 𝜔ଶ𝑧 ൌ െ𝑦ሷ 
(4) 
where 𝜔଴ ൌ 𝑘 𝑚
ൗ  is the natural frequency in radians per second and 𝜉 ൌ 𝑑 ሺ2𝜔଴𝑚ሻ
ൗ
 is the 
damping ratio. Moreover, 𝜉  is usually represented by the amplification factor 𝑄 ൌ
1 ሺ2𝜉ሻ
ൗ
. 
Since the base excitation 𝑦ሷ is an arbitrary function of time, Equation (4) does not 
have a closed-form solution. To calculate the SRS of each step and of the entire signal, we 
have used the algorithm for the calculation of the SRS proposed in [13]. SRS enables us to 
determine the maximum acceleration a system will undergo when one knows the natural 
frequency 𝑓଴ and the quality factor 𝑄 for each possible natural frequency. In this study, 
a relative damping of 5% was used, resulting in 𝑄 ൌ 10. SRS can also be calculated for the 
entire duration of a recording. We then observed the peaks at the fundamental and har-
monic frequencies of the recorded signal [16]. In this context, SRS combines both the no-
tion of transfer function and response to transient regimes. 
Intra comparison of the SRS offers a lot more finesse to the analysis since the fre-
quency is also taken into account. The aggressiveness of a running step is not only due to 
the value of the maximum acceleration but also to the general shape of the movement, 
only the SRS allows this to be taken into account in the analysis. 
Figure 8 gives the general workflow for SRS determination. 
 
Figure 8. Workflow for SRS determination. 
3. Results 
A goal of the present study was to analyze the effect of fatigue through SRS on the 
ability of the human musculoskeletal system to attenuate foot strike–generated shock 
waves. The results of this study suggest that, for the analysis of impact shock during run-
ning, the different components of the acceleration signal can be distinguished in the fre-
quency domain by means of spectral analysis as shown in Figure 9. 
Figure 8. Workﬂow for SRS determination.
3. Results
A goal of the present study was to analyze the effect of fatigue through SRS on the
ability of the human musculoskeletal system to attenuate foot strike–generated shock
waves. The results of this study suggest that, for the analysis of impact shock during
running, the different components of the acceleration signal can be distinguished in the
frequency domain by means of spectral analysis as shown in Figure 9.
The main advantage of spectral analysis over time-domain analysis of the impact shock
wave is the ability to separate spectral peaks from the rest of the data. Since the motion,
impact, and resonant components of the acceleration signal have different fundamental
frequencies: they produce peaks at different points in the power spectrum [12].
Sensors 2022, 22, 2350
7 of 11
Sensors 2022, 22, x FOR PEER REVIEW 
7 of 11 
 
 
 
Figure 9. Example of SRS results for one CrossFit athlete extracted for three runs on both feet. 
The main advantage of spectral analysis over time-domain analysis of the impact 
shock wave is the ability to separate spectral peaks from the rest of the data. Since the 
motion, impact, and resonant components of the acceleration signal have different funda-
mental frequencies: they produce peaks at different points in the power spectrum [12]. 
The hypothesis is that fatigue hampers the ability of the human musculoskeletal sys-
tem to protect itself from overloading due to foot strike–generated shock waves, loss of 
protection may manifest as an increased shock wave amplitude. For all five athletes, there 
was a direct correlation between fatigue and an increase in the aggressiveness of the SRS 
as shown in Figure 10. We noticed that for all five athletes for the 3rd run the average SRS 
peak was significantly higher than for the 1st run and 2nd run (p < 0.01) at the same natural 
frequency of the athlete. This confirms our hypothesis that fatigue causes a decrease in the 
shock attenuation capacity of the musculoskeletal system thus potentially involving a 
higher risk of overuse injury. 
 
Figure 10. Average SRS peaks for every athlete. 
102 G 
86 G 
74 G 
Figure 9. Example of SRS results for one CrossFit athlete extracted for three runs on both feet.
The hypothesis is that fatigue hampers the ability of the human musculoskeletal
system to protect itself from overloading due to foot strike–generated shock waves, loss of
protection may manifest as an increased shock wave amplitude. For all ﬁve athletes, there
was a direct correlation between fatigue and an increase in the aggressiveness of the SRS as
shown in Figure 10. We noticed that for all ﬁve athletes for the 3rd run the average SRS
peak was signiﬁcantly higher than for the 1st run and 2nd run (p < 0.01) at the same natural
frequency of the athlete. This conﬁrms our hypothesis that fatigue causes a decrease in
the shock attenuation capacity of the musculoskeletal system thus potentially involving a
higher risk of overuse injury.
Sensors 2022, 22, x FOR PEER REVIEW 
7 of 11 
 
 
 
Figure 9. Example of SRS results for one CrossFit athlete extracted for three runs on both feet. 
The main advantage of spectral analysis over time-domain analysis of the impact 
shock wave is the ability to separate spectral peaks from the rest of the data. Since the 
motion, impact, and resonant components of the acceleration signal have different funda-
mental frequencies: they produce peaks at different points in the power spectrum [12]. 
The hypothesis is that fatigue hampers the ability of the human musculoskeletal sys-
tem to protect itself from overloading due to foot strike–generated shock waves, loss of 
protection may manifest as an increased shock wave amplitude. For all five athletes, there 
was a direct correlation between fatigue and an increase in the aggressiveness of the SRS 
as shown in Figure 10. We noticed that for all five athletes for the 3rd run the average SRS 
peak was significantly higher than for the 1st run and 2nd run (p < 0.01) at the same natural 
frequency of the athlete. This confirms our hypothesis that fatigue causes a decrease in the 
shock attenuation capacity of the musculoskeletal system thus potentially involving a 
higher risk of overuse injury. 
 
Figure 10. Average SRS peaks for every athlete. 
102 G 
86 G 
74 G 
Figure 10. Average SRS peaks for every athlete.
When fatigue begins, we could hypothesize that athletes will slow down as a protective
means. The result could be moving away from the state of fatigue, in which case the
acceleration data could have not increased. It was not the case in our study.
Previous studies have shown that the loading rate of the lower limb is directly and
highly correlated with running speed, and the vertical impact force increased with increas-
ing running velocity [17].
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Muscle activation lowers the bending stress on bone and attenuates the peak dynamic
loads that can damage musculoskeletal tissues. Previous studies have suggested that the
fatigued muscles cannot support “optimal” running and they also suggested that fatigue of
the runner may lead to modiﬁcation of landing phase mechanics. It was also found that the
transfer of mechanical energy between the eccentric and concentric phases is drastically
reduced during muscle fatigue. Such changes may be involved in the development of
injuries [18–20].
4. Discussion
According to the results presented in this study, for the acceleration data to increase,
fatigue should be present. We may conclude that the musculoskeletal system becomes less
capable of handling foot strike–induced shock waves when the muscles are signiﬁcantly
fatigued. One of the most common running overuse injuries are bone stress fractures
(SF) [21,22]. In bones, microcracks are normally present and are thought to be fatigue-related
cracks because their numbers increase following repetitive loading. Bone remodeling serves
to repair fatigue microcracks. When a bone is loaded repeatedly, resulting in repetitive or
cyclic strain, the subsequent accumulation of microdamage is believed to be the threshold
of a pathological continuum that is clinically manifested as stress reactions and SF (29).
Ultimately, if the activity is not ceased and the bone is not able to self-repair, a complete bone
fracture might ensue. Notably, with increasing strain or greater strain rates, the number
of loading cycles a bone–29 can withstand before a fatigue failure occurs is reduced [23].
Stress fractures are the clinical manifestation of the accumulation of fatigue damage in
bones [24–26]. Although the effect of running and its mechanical strain in bone tissues is
well documented, the evidence for SF etiology is less conclusive [24,27–30]. Nevertheless,
several researchers reported clear relationships between bone stress related injuries and
fatigue. For instance, it is known that the tensile strains on the tensile side of a bending
bone are dampened by the contraction of adjacent muscles, aiming at protecting the bone
from stress related injury [29–34]. It may then be hypothesized that muscles also play
the role of shock absorbers and that consequently, muscle fatigue might decrease their
absorption properties, resulting in a more aggressive loading rate or loading peak at the
bones as fatigue increases [31–33].
The obtained results showed that acceleration amplitude steadily increased with the
fatigue group and that there was a clear association between fatigue and shock waves (as
revealed by the SRS). We may then conﬁrm the conclusions of the aforementioned studies,
that the human musculoskeletal system becomes less capable of single leg strike–induced
shock waves absorption when the muscles are signiﬁcantly fatigued. This condition may
promote the development of injuries and the present results have a signiﬁcant implication
regarding the etiology of running injuries. Therefore, several recommendations may be
effective towards runners’ community or coaches in order to reduce this stress related
injury risk, notably as proposed by the multifactorial model of Brukner and Khan [35].
First, it may be advantageous to ensure that the majority of training and exercise
is performed to avoid severe fatigue and in line with the load management theory. For
instance, external parameters must be considered, such as progressive increment of training
loads [36], training surfaces or footwear adaptations [35]. Understanding the inﬂuence of
SRS on fatigue and on the magnitude of dynamic loading on the human musculoskeletal
system will allow the development of proper training procedures and may participate in
the reduction of damages to the musculoskeletal tissues.
Secondly and directly in accordance with the present research purpose, lower limb
muscles resistance to fatigue is a major component of stress related injury prevention in run-
ners. The present outcomes are in line with former ﬁndings reporting that fatigue-related
imbalance between the plantar ﬂexors and dorsiﬂexors may compromise the protective
action of these muscles on the lower leg bony structures [29]. Here, it is plausible that
deteriorated properties of the calf muscles due to fatigue may affect the role of these soft
tissues to protect the bone from stress injury risk.
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Finally, injuries in running are also often provoked by fatigue and improper technique,
which are both reﬂected in the runner’s kinematics [18,37,38]. A gait retraining approach
has been proposed by several researchers through a modest increase in step rate or a transi-
tion from rearfoot to forefoot strike and was considered as effective notably at reducing
impact forces and vertical load rate and then at preventing running-related bone stress
injuries [37,39].
An individualized approach is nevertheless of high interest and most likely available
nowadays. Indeed, state-of-the-art research on kinematics in sports uses optical motion
capture systems that are inaccessible to most athletes. With the recent development of
Micromachined Microelectromechanical Systems (MEMS), inertial sensors have become
widely used in the research of wearable running gait analysis [40] due to several factors,
such as being easy-to-use and low-cost. Considering the fact that each individual has a
unique way of running, inertial sensors can be applied to the problem of gait recognition
where assessed gait can be interpreted as a biometric signature. Thus, inertial sensor-based
gait recognition has a great potential to play an important role in many health-related
applications. In this work, we demonstrated the potential of wearable technology for the
assessment of kinematic parameters using the example of running. We concluded that wear-
able technology opens possibilities for technique improvement and injury risk reduction to
a wide spectrum of athletes. Since inertial sensors are included in smart devices that are
nowadays present at every step, inertial sensor-based gait recognition has become a very
attractive and emerging ﬁeld of research that will provide many interesting discoveries.
Although the small sample size is indeed a limitation to applying our ﬁndings to the
general population, this study is a qualitative and prospective research study exploring a
novel and unknown topic. Using SRS as a measurement in running gait analysis has never
been studied as of today, leaving us with very little data similar to our study design to be
able to calculate a traditional sample size. However, these results still provide valuable
information regarding the use of SRS as a biomechanical risk factor in runners. Larger
studies on this topic will further advance our understanding of injury risk in runners. It is
acknowledged that the relatively low subject numbers used in this study limit the drawing
of deﬁnitive conclusions, this is particularly true if the study ﬁndings conﬂict with those
of previous investigations. The results of our research were in accordance with previous
studies and our hypothesis. In the future, a study on a larger group of athletes will be
carried out to conﬁrm our previous ﬁndings. It is also planned to carry out the same
type of studies on high level runners and compare results. Our obvious hypothesis is that
elite runners will have a unique ability to dampen the SRS and/or sustain a much higher
SRS threshold.
Author Contributions: Conceptualization, D.B., S.O., B.A. and R.T.; methodology D.B., S.O., B.A.
and R.T.; software, S.O. and B.A.; validation, S.O., B.A., F.F. and R.T.; formal analysis, S.O. and B.A.;
investigation, D.B., B.C. and R.T.; resources, D.B. and B.C.; data curation, D.B. and R.T.; writing
original draft preparation, D.B.; writing review and editing, R.T. and B.A.; visualization, B.C. and
F.F.; supervision, R.T.; project administration, R.T. and D.B. All authors have read and agreed to the
published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: The study was conducted according to the guidelines of
the Declaration of Helsinki and approved by the Ethical Review Board of the University of Reims
Champagne-Ardenne and the medical board of the Centre Luxembourg.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to ethical reasons.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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Shock Response Spectrum Analysis of Fatigued Runners.
Benjamin, Daniel,Odof, Serge,Abbès, Boussad,Fourchet, François,Christiaen, Benoit,Taïar, Redha