1. 1
Effects of Fatigue on
Complexity during
Bipedal Locomotion
Arroyo, G., Chew, P., and Funai, P., Seattle University Center for the Study
of Sports and Exercise,2015.
─
Abstract
Variability in human mechanics has traditionally been associated with a source of noise
and chaos (Glass and Mackey, 1998). Nevertheless, as new research has risen, new models
have suggested that variability within a system is far more than noise or random error and an
optimal state of variability, or complexity, exists (Stergiou, Harbourne, & Cavanaugh, 2006).
Under this new model, it has been proposed that movement complexity can be affected by a
number of factors, such as fatigue. The aim of this experiment was to investigate the impact
exercise-induced fatigue has on running kinematics of collegiate runners as fatigue has been
proposed to hinder human performance and increase the risk of injury. The changes in segment
accelerations (SA) for the thighs, shank, feet, and pelvis were used to compare the complexity
of two collegiate distance runners before and after fatigue. Motion analysis techniques were
used to track SA. Multivariate multiscale entropy (MMSE) was utilized as a nonlinear tool to
analyze the fluctuations of the SA. At the conclusion of our the study, there was no difference
between the SA in post and pre fatigue present, suggesting that a revision of the protocol and
further research is needed to reveal any new insights in the world of movement complexity. The
ultimate goal of the experiment was to provide insight on the implications fatigue has on running
kinematics in order to determine if deviating from optimal variability increases the risk for injury.
Key Words Locomotion, complexity, fatigue
Introduction

2. 2
Variability in Linear and Nonlinear Statistics
In the world of human performance, the movement of an individual or individuals is
never exactly the same as the the one that follows. Despite talent or mastery, there is always a
degree of variation in human motion. Movements end at a certain point spatially and temporally,
but the path of the movement tends to vary and deviates from the target (Newell and Slifkin,
1998). Variability within a repetitive task has been seen as irrelevant error, random events, and
noise, and has been commonly assessed by linear tools such as means and standard
deviations in the past (Newell and Slifkin, 1998). To assess variability, linear assessments have
relied on analysis of distributions of variables compiled from repetitive movements, standard
deviation being the primary statistical tool (Newell and Slifkin, 1998). Traditionally, the amount
of variability, as measured by standard deviation of a particular movement, has been assumed
to be a direct indicator of the amount of noise in the underlying “perceptual-motor process”
(Newell and Slifkin, 1998). For example, as stated by the generalized Motor Program Theory,
the error produced by the inability to determine the needed parameters for utilizing the
underlying motor program results in the variability that we see in the system (Schmidt and Lee,
2005). Other theories associate this variability to the failure of the system to perform, instability,
and motor redundancy (Schmidt and Lee, 2005). One assumption behind this claims that the
frequency distribution of the samples follows normal distribution and any observation that
deviates from that is considered a random error (Newell and Slifkin, 1998). However, further
characterization of this behavior has moved from just collapsing the data into means and
standard deviations and shifted its focus to the patterns of variability over time that tend to be
lost under standardization in order to capture the dynamic structure of variability (Newell and
Slifkin, 1998). It is with a nonlinear statistical approach that movement variability has been
analyzed to explore beyond the reach of linear tools.
Compared to conventional statistics used to understand the parameters of variability
(mean, standard deviation, coefficient of variation, etc.), nonlinear tools (sample entropy,
approximate entropy, etc.) have shown to provide more useful information within the variation in
movement patterns (Richman and Moorman, 2000). The following points explain why non linear
tools are appropriate when analyzing movement variability data (Stergiou et. al., 2006):
1. Kinematic data is often averaged to produce a ‘mean’ picture of the subject’s movement
pattern. When studies average or standardize this data, the temporal patterns of the
data are lost (variation is lost)
2. Linear tools to study variability assume that the observations are random and
independent but research shows that such variations have a deterministic nature, they
cannot be random or independent.
3. Traditional linear tools provide different answers when compared with nonlinear tools
regarding stability and complexity of a movement pattern
4. The number of human movement patterns and motor control feedback loops movement
are similar to other physiological life rhythms such as heart rate.
Stergiou, Harbourne, and Cavanaugh (2006) indicate why a nonlinear approach is a
more appropriate method when tackling movement variability. In studies that use nonlinear
approaches to analyze kinematics of human movement, sample entropy has been a primary
method to analyze variance in systems, among other types, in order to quantify the regularity of
time series on a single scale and evaluate repetitive patterns (Richman and Moorman, 2000).
Analysis of Various Entropies
Like mentioned before, sample entropy is one way to process data to gain a better
understanding of variance in a system, but it is not the only type of entropy. Other entropies that

3. 3
previous research has used includes correlation entropy, approximate entropy, and multiscale
entropy. With any statistical tool, these types of entropies have limitations. Correlation entropy
was historically not developed to be used for stochastic data like complexity, but to differentiate
between “deterministic systems by rates of information generations” (Ahmed and Mandic,
2011). Therefore, correlation entropy will not be able to analyze complexity since complexity is
random in nature. On the other hand, approximate entropy is similar to correlation entropy, but
aims to be more statistically valid formula for entropy that is widely applicable (Ahmed and
Mandic, 2011). Approximate entropy can be used for noisy, short, real-time series and can
distinguished between correlated, randomly determined data (Ahmed and Mandic, 2011). Due
to approximate entropy being used for short real-time series, this type of entropy will not
provided adequate analysis of our data collected since we are looking at multiple, long durations
of complexity. Furthermore, sample entropy builds off of approximate entropy. Sample entropy
analyzes length of time series that are independent from other factors (Ahmed and Mandic,
2011).
Sample entropy analyzes biological signals whose complexity is of both deterministic
and random in nature (Costa, Peng, Goldberger, and Hausdorff, 2003). Higher entropy values
reflect an increase in randomness of the time series give an insight to physiologic control
mechanism of lower limbs of gait (Costa et. al., 2003). Changes in the regularity of motor
patterns may be related to changes in motor strategies and may thus reveal the effects of
adaptations, pathologies, and motor memory (Bartlett et al., 2007). Although sample entropy is
an unbiased estimator, it is based on a one-step difference (Ahmed and Mandic, 2011). With
sample entropy being based off of a one-step difference, it does not account for features that
are important to analyze when dealing with complexity. Over a range of times scales, sample
entropy neglects feature that relates to the structure and organization of it (Ahmed and Mandic,
2011). For our purposes, we need to be able to analyze multiple time scales instead of a long
time period. With all this in mind, multiscale entropy is closer to fit our purpose as it aims to
analyze the difference between scale and entropy that quantifies the interdependence of them
(Ahmed and Mandic, 2011). The previous acknowledge sample entropy is used to help evaluate
univariate time series looking at multiple temporal scales (Ahmed and Mandic, 2011). Multiscale
sample entropy, unlike other entropies, uses multivariate time series as an individual set by
viewing each variable as independent (Ahmed and Mandic, 2011). By doing so, the applicability
of multiscale sample entropy is limited to having all data being statistically independent or
uncorrelated, which is usually not the case (Ahmed and Mandic, 2011). Therefore, multiscale
entropy is not a helpful tool to use when analyzing complexity, since complexity is dependent.
Moreover, for processing our data collected, multivariate multiscale entropy (MMSE) is
more applicable for processing our data instead of using other variations of entropy. MMSE is
similar to multivariate sample entropy. However, it asses multivariate sample entropy over
various time scales instead of one (Ahmed and Mandic, 2011). From there, MMSE uses a
thorough and unified way to contract the various dimensions such as time lags and amplitude
ranges (Ahmed and Mandic, 2011). For our purposes, acceleration at multiple joints are
analyzed. MMSE has been used for complex dynamical couplings as well as numerous degrees
of synchronization over multiple scales, making MMSE able to analyze multichannel data
(Ahmed and Mandic, 2011). Through the use of MMSE for data processing, it allows us to
understand correlations that may be present over a long duration of a subject’s gait. In order to
analyze MMSE, temporal scales needs to be defined and multivariate sample entropy needs to
be calculated (Ahmed and Mandic, 2011). For full information on how MMSE was calculated
refer to Mosabber Uddin Ahmed and Danilo P. Mandic’s Multivariate multiscale entropy: A tool
for complexity analysis of multichannel data (2011).
From Variability to Complexity

4. 4
As we have discussed, variability is a feature of biological processes present in daily
living, heart rate being a common example (Stergiou et. al., 2006). Variability is internal in
biological systems and can be easily measured. There is a distinctive amount of variability
within the mechanics of human movement as variation exists in tasks of human performance
that require consecutive repetitions over a given time (Preatoni, Ferrario, Dona, Hamill, &
Rodano, 2010). With that said, a growing number of new studies have began to introduce
variability through a different scope. New theories have established that variability has a
deterministic origin (Miller, Stergiou, and Kurz, 2006; Dingwell and Cusumano, 2000; Dingwell
and Kang, 2007). It has been suggested that variability is not random nor independent and the
body possesses the ability to to adapt to stressful conditions using “motor memory” (Stergiou
and Decker, 2011). Let us take trail running for example since running is the focus of our study.
When running on technical trails, one must attempt to obtain proper footing and have wide-
ranging excursions of the center of pressure and mass at the support surface and wide
movements of body segments as one tries to get through the terrain (Harbourne & Stergiou,
2009). This type of movement displays large amounts of variability as the literature supports in
terms of kinematics and center of pressure and mass movement (Harbourne & Stergiou, 2009).
A runner might need to modify his gait by adjusting initial contact, foot/heel strike, and even
adjust upper body behavior (Harbourne,& Stergiou, 2009). It is this type of behavior that is
defined as complexity, despite its high variability (Harbourne & Stergiou, 2009). Complexity is
developed by fine-tuned adjustments, with specific and well-practiced yet flexible strategies to
complete the task at hand (Harbourne, & Stergiou, 2009).
Stergiou, Harbourne, & Cavanaugh (2006) refer to this concept of complexity based on
a new theoretical model describing complexity as an optimal state of motor movement in
association with motor learning. They suggest that optimal variability of a system reflects the
adaptability of the system. The way that this model has brought a new insight to the area of
movement complexity by displaying the relationship between chaotic temporal variations and
the concept of the predictability (Figure 1):
Figure 1: Illustration of theoretical model proposed (Stergiou, Harbourne, & Cavanaugh, 2006)
The model exhibits an inverted U-shape relationship in terms of the presence of chaotic
temporal variations in the steady state output of a healthy biological system with the concept of
predictability (Figure 1). Practically at this optimal state of movement variability the biological
system is in a healthy state and is characterized by exhibiting chaotic temporal variations in the
steady state output (i.e., the uppermost point along the inverted U-shaped function), attaining
high values only in the intermediate region between excessive order (i.e., maximum

5. 5
predictability) and excessive disorder (i.e., no predictability) (Stergiou et. al., 2006). This reflects
the adaptability of the system and it deterministic structure and states that any deviation from
this optimal state brings noise and unpredictability or rigidness and predictability leading to a
lack of health within the system. A decline in the health of the system does not only hinder the
ability to reproduce the necessary movements needed to undertake the task, but it makes the
system vulnerable to possible failure (Stergiou et. al., 2006).
Effects of Fatigue on Complexity and Risk of Injury
Complexity during locomotion is a critical aspect of human movement as it is involved in
interacting with the environmental, distributing workload on tissue, and possessing flexibility to
adapt to new stressors (Glass and Mackey, 1998). Complexity relies on the organization of the
system and on its ability to sustain normal function during a given repetitive task. With that said,
a number factors, such as fatigue, have the potential to disrupt the organization of the system
and hinder desired performance (Enoka and Stuart, 1992). Fatigue has an overwhelming
influence on the system as it can alter neuromuscular function centrally and peripherally and it is
a sign of decrement in aspects of movement performance (Enoka and Stuart, 1992). Its impact
ranges from alterations of the pattern of muscle activity and force fluctuations to postural tremor
and altered dynamics of limb motion (Gandevia, 2001). With that said, a decline in the ability to
maintain optimal performance and the organization of the system, as that caused by fatigue,
impacts the complexity of the system, and as a result, its health, putting in a place where the
individual is more susceptible to injuries (Stergiou and Decker, 2011). It is the aim of this study
to look at how fatigue causes changes in complexity and how the effects on the health in the
system could be linked to injury.
The Problem and Understanding the Gap
As previously mentioned, research is still limited on what it means for a system to have
“optimal” complexity and what it means for the biological system in terms of health and
performance. Current gaps in research are specifically related to the effects of fatigue, its
relation to injury, and how fatigue changes complexity in a pre and post fatigue state (Davids
and Newell, 2006). Determining whether fatigue occurs in the system as a whole or in the lower
extremity muscles is a gap that still needs more research. As to what is becoming fatigued could
be a failure of the system as a whole, or the lower extremity muscles becoming fatigued and
unable to keep up with the demands of the exercise. In addition, what is causing changes in
variability is still in need of research. Moreover, the statistical methods used to analyze this type
of data have not always been used to study complexity in previous studies. We hope to close
that gap by utilizing nonlinear tools to analyze running kinematics and provide useful data on
how the system’s complexity is affected by fatigue during locomotion.
Purpose and Hypothesis
The purpose of this study is to investigate the effects of exercise-induced fatigue on
complexity of the lower extremities during locomotion. We hypothesize that there will be a
decrease in complexity in the lower extremities kinematics as fatigue reduces the ability for the
system to sustain baseline mechanics.

6. 6
Operational Definitions
Complexity, will be defined as the complex index derived from the SA values using
MMSE. In our study, complexity is defined as the complexity index derived from the acceleration
of the hips, knees, ankles, and pelvis. With fatigue acting as our explanatory variable, this will
be defined as the inability of our subjects to maintain a set pace on the treadmill.
Limitations and Delimitations
Complexity is present in multiple biological processes in humans, but is yet to be fully
understood. Movement complexity has been studied, for spinal movement for example, but not
many studies have observed changes in complexity as a result of fatigue. This study has a
number of limitations. Errors associated with kinematic measurements were acknowledged.
Errors could come from calibration or electromagnetic interference. Despite the fact that the
treadmill is a means of collecting data during locomotion, there is a distinctive difference
between treadmill and overground running. The recovery process after fatigue onset is
considered a limitation in all fatigue experiments. On top of this, one needs to acknowledge the
delimitations present in this study. First, the subjects were selected using a convenience
sampling method and only included two individuals from a collegiate team with similar
experience and training regimen. Subjects were free from any muscular injury and were just
coming back from a period of time off from training as they concluded their cross country
season two weeks prior to the experiment. The tests were done in the Human Performance Lab
at Seattle University. No record of diet or recent training was done for the subjects prior to the
tests.
Methods
Sample Population
The population of interest for the study is competitive long distance runners
from Seattle University’s Track and Cross Country Team. A convenience sampling
method was used to obtain participants. The sample (n=2) is composed of two male
collegiate athletes (18士1 years old, weight of 66.9士4.4 kg, best 5k pace per mile
of 5:00士0:10 and 5士1 years of experience). Each participant just recently finished
competing during the Fall season. Both participants will perform the same test using
85% and 100% of PR 5K pace, which was reported by the subjects.
Instrumentation
A lab-setting steady pace test on treadmill utilizing fifteen units of Xsens BIOMECH
Inertial Measurement Units (IMUs) for live motion capturing. Xsens IMUs and software are
reliable and accurate human measurement instruments that are becoming “increasingly popular
for the biomechanical analysis of human movement” (Brodie, Walmsley, Page, 2008). Previous
research has reported “highly accurate results” with a maximum orientation error of 0.5 degrees
(Brodie et. al., 2008). For our purposes, we used MVN to track in-time 3D animation of our
subjects as well as graph movement of each trackers. Through MVN, we are able to analyze

7. 7
segment kinematics. Figure 2 shows the location of all IMUs. We used use full body tracking to
help ensure the reception and quality of our data, but will only focus on the lower body as seen
in Figure 3 for a total of 7 trackers measuring lower body kinematics. Before placing all IMUs on
subject, several measurements are required for Xsens program. The measurements include
body height, foot size, arm span, ankle height, hip height, hip width, knee height, and shoulder
width. These measurements were recorded.
Figure 2: Full body Xsens trackers and stagnant calibration (anterior sagittal, and poster view)
Figure 3: Illustration of lower limb trackers (Seel, Raisch, and Schauer, 2014)
Calibration Test
Two calibration tests were done during pre fatigue and post fatigue phases on the
treadmill. The calibration tests consisted of a stagnant stance standing shoulder width apart
posture (Figure 2) and a palm calibration. The calibration tests took no more than 2 minutes to
complete both tests.
Warm-Up and Testing Protocol

8. 8
Each participant self-selected a pace in which they were most comfortable with for a light
5 minute jog on the treadmill. Once participant warmed up, testing initiated utilizing participant’s
85% PR 5K pace for 2 minutes. The participants then went straight into the fatigue protocol
phase. The 100% PR 5K pace time was used to get the runners to reach fatigue. The subjects
should reach the point of exhaustion between 7-15 minutes. Once subjects reached fatigue, the
subjected stepped off the treadmill and had a 2-3 minute rest phase used to calibrate the
Xsense system. After this, the subjects returned to the treadmill and speed was reduced back
down to 85% of PR 5K pace for 2 minutes.
Data Collection and Analysis
Data collection will take place on an indoor treadmill looking at lower body kinematics
using the Xsens BIOMECH IMUs and software. Accelerometry-based systems have been
suggested to be valid and reliable tools to quantify kinematic data (Kavanagh and Menz, 2007).
With the use of fifteen IMUs, the sampling update rates will run at 60Hz. Data collection will
occur during two minutes pre and post fatigue at 85% of the participants 5k pace. MMSE was
used to analyze the pre and post fatigue data and complexity index for each stage were
compared for each subject, as MMSE and complexity indexes are valid and reliable tools to
analyze complexity in this context (Ahmed and Mandic, 2011).
Results
Stage Left Foot
(CI)
Right Foot
(CI)
Left Shank
(CI)
Right
Shank (CI)
Left Thigh
(CI)
Right Thigh
(CI)
Pelvis (CI)
Pre
Fatigue
10.224 10.862 10.897 11.710 8.708 9.139 9.307
Post
Fatigue
10.459 10.835 10.773 11.685 9.068 9.250 9.799
Table 1: Complexity Index of each lower limbs for subject A

9. 9
Graph 1: Lower body complexity index for subject A pre and post fatigue
Stage Left Foot
(CI)
Right Foot
(CI)
Left Shank
(CI)
Right
Shank (CI)
Left Thigh
(CI)
Right
Thigh (CI)
Pelvis (CI)
Pre
Fatigue
11.672 12.630 10.008 11.601 8.902 8.686 7.448
Post
Fatigue
11.380 12.454 9.859 11.241 8.660 8.432 7.256
Table 2: Complexity Index of each lower limbs for subject B
Graph 2: Lower body complexity index for subject B pre and post fatigue
Discussion
We set out to quantify complexity of the lower extremities in response to fatigue,
hypothesizing that our subjects’ complexity would decrease following complete exhaustion.
However, as Table 1 and 2 show, the complex index (CI) for both subjects remained unchanged
for the left and right feet, shanks, thighs, and pelvis. The CI data does not show distinctive
change in complexity between pre and post fatigue for either of our participants and, therefore,
cannot provide any evidence for the potential impact of fatigue on complexity during locomotion.
There might have been discrepancies that skewed the results of this study. A major possible
cause could have been that the fatigue protocol was not intense enough to fully fatigue our
experienced runners. Towards the end of the fatigue protocol, the subjects displayed self-
reported reaching a level of exhaustion via RPE rating and verbal warnings, indicating that they
could no longer hold their 100% 5k pace (Tables 3.3 and 4.3). Nevertheless, the subjects
seemed to have recovered down to a lower RPE level as shown in Table 3.3 and Table 4.3 after
the calibration phase close to the conclusion of the test. We speculate that since the subjects
are fairly aerobically trained athletes, the time they had during calibration towards the end was
too much recovery time, leading them to recover quicker than desired. With that in mind, it is
possible that by the time the recording of the post fatigue phase occurred, they were no longer
fatigued as we intended them to be. Since the subjects were less fatigued than expected, we

10. 10
will have to develop a more appropriate fatigue protocol for the subjects or decide to focus on
less trained athletes that will not return to a recovered state during the re-calibration time.
Obstacles
When conducting the test we faced a couple of obstacles. One included the
electromagnetic interference caused by the treadmill. The longer the subject ran on the
treadmill, the greater the interference was when tracking runner’s performance. We believe the
treadmill has an electromagnetic field that contributes to the noise of Xsens trackers, but it is
unclear to how much noise is contributed. If we were able to repeat the research, we would like
to be able to have all testing done on a treadmill with lower magnetic field, use something to
help block the electromagnetic field, or perform all tests on a track. Additionally, we
acknowledge that each participant’s own diet and activity level may contribute to our findings.
We purposely did not include hydration, nutrition and exercise in our study, but know these may
be a factor in their respective performance.
Conclusion
At the conclusion of the study, we were unable to support our hypothesis as no
difference was found in the complexity of each runner between the pre and post fatigue
protocols (Graph 1 and 2). Further research would be needed with a larger sample size or
modified fatigue protocol to derive better results. Another direction to this study might involve
recreational runners to get a better understanding of how complexity relates to running in a
fatigued state. With this data, more knowledge about performance and injury prevention could
be gained in order to help athletes push their limits while still being able to avoid injury.

11. 11
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Appendix
Age 18 years old
Years of Competitive Experience 4 years
Height 178.7 cm
Weight 71.2 kg
PR 5K Pace 5 minutes 10 seconds
Table 3.1: Subject A Information
Percent of PR 5K
Pace
Speed (kph) Duration of Run Distance Ran
85% pace (pre-
fatigue)
15.9 kph 2 minutes 47
seconds
0.74 km
100% pace 18.7 kph 11 minutes 2
seconds
3.43 km
85% (post-fatigue) 15.9 kph 2 minutes 57
seconds
0.86 km
Table 3.2: Subject A Data Measured
Duration of Test Percent of PR 5K Pace RPE Rating
1-3 minutes 85% pace 2
4 minutes 100% pace 4
5 minutes 100% pace 4
6 minutes 100% pace 5
7 minutes 100% pace 5
8 minutes 100% pace 6
9 minutes 100% pace 6
10 minutes 100% pace 7
11 minutes 100% pace 7
11 minutes 30 seconds 100% pace 8

14. 14
12 minutes 100% pace 8
13 minutes 100% pace 9
14 minutes 100% pace 10 (no longer can keep pace)
15-17 minutes recallibration NA
18-20 minutes 85% pace 4
Table 3.3: Subject A RPE During Testing
Age 19 years old
Years of Competitive Experience 6 years
Height 170 cm
Weight 62.5 kg
PR 5K Pace 4 minutes 50 seconds
Table 4.1: Subject B Information
Percent of PR 5K
Pace
Speed (kph) Duration of Run Distance Ran
85% pace (pre-
fatigue)
17 kph 2 minutes 0.57 km
100% pace 21 kph 8 minutes 2.8 km
85% (post-fatigue) 17 kph 2 minutes 0.57 km
Table 4.2: Subject B Data Measured
Duration of Fatigue Percent of PR 5K Pace RPE Rating
1 minutes 100% pace 4
2 minutes 100% pace 6
3 minutes 100% pace 7
4 minutes 100% pace 8
5 minutes 100% pace 9
6 minutes 100% pace 9

15. 15
7 minutes 100% pace 10
7-9 minutes Recallibration NA
9-11 minutes 85% pace 3
Table 4.3: Subject B RPE During Testing