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This is to certify that the

thesis entitled

SYMMETRY 0F GROUND REACTION

DATA IN NON-PATHOLOGICAL GAIT
presented by

David G. Snow

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MS Biomechanics

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SYMMETRY OF GROUND REACTION
DATA IN NON-PATHOLOGICAL GAIT

By
David G. Snow

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Biomechanics

1990

ABSTRACT

SYMMETRY OF GROUND REACTION
DATA IN NON-PATHOLOGICAL GAIT

By
David G. Snow

While observing human locomotion, it becomes clear to the observer
that a variety of gait patterns exist. Given this variety of patterns and the
associated difficulties in defining norms, attention in pathological gait is often
focused on its asymmetries. This study explored the amount of symmetry
that was present in ground reaction data of non-pathological subjects. Sixteen
functionally non-pathological subjects were evaluated for their symmetry
under walking and running conditions, while barefoot and in shoes. The
analytical methods included comparisons of ground reaction forces, torques
and the path of the resultant vector intercept with the platform surface.
Relative symmetry was found in the vertical and anterior-posterior ground
reaction forces, while symmetry of a lesser degree was observed in the shape
characteristics of the torque data. However, the medial-lateral ground
reaction forces, the intercept paths and the ground reaction torque
magnitudes appeared to contribute to gait asymmetrically, although

displaying symmetrical characteristics.

iii

dedicated to

The Al Bransdorfer Family

ACKNOWLEDGMENTS

Special thanks to:

Brooks Shoe Company for their financial support of this work and of
my graduate studies

Dr. R. W. Soutas-Little for serving as my advisor

Dr. D. Ulibarri, Dr. R. Hubbard, and Dr. A. Jacobs for serving on my

committee

Bob Wells for his assistance in data collection

My fellow students for their help in data collection and analysis

iv

TABLE OF CONTENTS

List of Tables

List of Figures

Introduction
Survey of Literature
Experimental Methods
Set-Up
Subjects
Protocol
Analytical Methods
Quantitative Analysis
Comparative Analysis
Results
Ground Reaction Forces
Barefoot walking
Shoed walking
Running data
Resultant Vector Intercept Paths

Resultant Vector Force Plots

vii

viii

11

14

30

33

36

42

vi

Resultant Vector Torque Plots
Summary
Discussion

Conclusions

Appendix 1. Subject Information

Bibliography

45

45

52

55

59

6O

IO.
11.
12.
13.

LIST OF TABLES

Subject contribution to data collection

Subject contribution to bilateral comparison

Vertical ground reaction force magnitude data of
barefoot walking

Additional ground reaction force data of barefoot
walking

Vertical ground reaction force magnitude data of
shoed walking

Additional ground reaction force data of shoed walking

Vertical ground reaction force magnitude data of the
running conditions

Additional ground reaction force data of the running
conditions

Symmetric characteristics of barefoot walking

Symmetric characteristics of shoed walking

Symmetric characteristics of the running conditions

Observed symmetry in the ground reaction data of walking

Observed symmetry in the ground reaction data of running

vii

26

27

29

31
32

34

35
49
50
51
56
57

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LIST OF FIGURES

. Experimental set-up

Force platform with indicated sign conventions

Ground reaction force graphs of running

Ground reaction force graphs of walking

Resultant vector intercept path of a left shoed walk

Resultant vector force plot of a right shoed run

Resultant vector force plot of a left barefoot walk

Resultant vector torque plot of a left shoed run

Resultant vector torque plot of a left shoed walk

Ground reaction torque sign convention

Between-trial variability of resultant vector intercept paths
Resultant vector intercept paths of barefoot walking
Resultant vector intercept paths of shoed walking

Resultant vector intercept paths of shoed running

Resultant vector intercept paths of barefoot running
Between-trial variability of resultant vector force plots
Bilateral comparison of resultant vector force plots of running
Bilateral comparison of resultant vector force plots of walking
Between-trial variability of resultant vector torque plots

Bilateral comparison of resultant vector torque plots

viii

15
16
18
20
21

23
24
36
37
38
39
4O
43

46
47
48

INTRODUCTION

In the Fall of 1988, the Department of Biomechanics in the College of
Osteopathic Medicine at Michigan State University evaluated a number of
subjects suffering from scoliosis. Due to the nature of the condition, it
seemed natural to approach the analysis from the standpoint of ground
reaction asymmetries. However, there was a need to know the amount of
symmetry that was present in non- pathological gait, so that abnormalities
could be identified.

It was apparent that a level of bilateral symmetry exists in the human
body based on the level of anatomical symmetry and the observed symmetry
of ambulation. However, it could be argued that most individuals have a
preferred leg for actions such as kicking, which would indicate the presence of
functional asymmetry. Published research supports both of these arguments
(Chhibber & Singh, 1970; Singh, 1970; Hamill, Bates 8: Knutzen, 1984), but due
to recent advancements in the area of force platform data analysis, there was
an opportunity for additional studies.

A majority of the research performed in ground reaction symmetry has
focused on the ground reaction forces (Hamill, Bates 6: Knutzen, 1984;
Munro, Miller & Fuglevand, 1987). From this work, it was evident that
symmetry was to be expected in the vertical and anterior-posterior forces.
Even though a large amount of information may be obtained through the
analysis of ground reaction data, these forces do not completely describe the
complex interaction between the foot and ground. Additional understanding
is obtained in the analysis of the ground reaction torque magnitudes and their

associated wrench axes.

2

This study was designed to evaluate the levels of ground reaction
symmetry produced by functionally non-pathological human gait. This
analysis included comparison of resultant force and torque vectors, as well as
their positions and the paths of the intercepts with the platform surface. The
results of this study will be used for comparison with data from the scoliosis

subject analysis and will be available for future subject and patient analyses.

SURVEY OF LITERATURE

The history of the force platform included contributions by many
researchers. The intent here was to present a brief history of literature
pertaining to this study by reviewing several appropriate examples of gait
analysis studies that utilized the force platform and other studies pertaining
to bilateral symmetry.

The collection of position data in the analysis of human locomotion
had become quite advanced by 1930. In a paper published at that time by Fenn
(1930), motion was recorded on film at 120 Hz and used to evaluate velocities
and accelerations of the body segments. Fenn's primary interest was the work
done in running and he desired a more direct method of measurement.
Several sparsely documented studies performed prior to Fenn's work
encouraged him to build an instrument to measure the anterior-posterior
distributed forces of the foot on the running surface. Fenn's study included
16 plots that nearly approximate anterior-posterior plots produced in modern
studies using force platforms.

Elftman (1938) built what is known as the first force platform. This
device recorded three orthogonal forces acting on the body. In the
introduction of the apparatus, Elftman suggested its importance in deriving
torque and acceleration data and also noted that the platform could be used to
evaluate the center of gravity in stationary subjects. In subsequent work,
Elftman (1939) used the platform data in combination with cinematographic
data to evaluate the center of pressure and joint moments.

The question of symmetry in normal human locomotion was first

addressed in anatomical and functional terms. In a study by Chhibber (1970),

3

4

a significant bilateral difference was found in the weight of cadaveric legs and
certain leg muscles. This work was followed by a study by Singh (1970), in
which the function of subject's left and right legs in activities including
walking, maximum force, kicking and lifting were compared. He concluded
that functional asymmetry existed in the lower limbs.

Along with the increasing popularity of walking and running as sport
and recreation in the 1970's and 1980's, came ground reaction force studies of
athletes (Bates, Osternig, & Sawhill, 1983; Payne, 1978; Payne, 1983). By this
time, the force platform had been enhanced by the use of strain gauges,
advances in material science, and the increased usage of the computer. These
force platform studies were intended to gain understanding of the forces
involved in locomotion and therefore increase the level of performance and
reduce injury. For the most part these studies assumed symmetry or chose
not to address it. However, in a study on distance runners, Cavanagh and
Lafortune (1980) stated: "A further limitation of the present study is that only
the right foot was studied and there is no reason to expect symmetry between
right and left sides." (p. 403).

Symmetry in terms of ground reaction forces was analyzed by Hamill,
Bates, and Knutzen (1984). Their study involved shoed subjects in
walking and running situations. These researchers found statistically
significant symmetry in each of the components of the resultant force vector.
This work also addressed the existence of a preferred limb as defined by Singh
(1970) and found no significant difference between the ground reaction forces
of the dominant and non-dominant legs.

In 1987, Munro, Miller, and Fuglevand (1987) focused on speed
dependent variables in the ground reaction forces of running subjects. The
study included bilateral data that supported symmetry of the vertical and
anterior-posterior forces, but pointed out asymmetries in the medial-lateral
forces. Although this result presents a contradiction to the findings of Hamill
et a1. (1984), both of these studies pointed out that the differences in

5

medial-lateral data are differences in a small quantity relative to the forces
produced in the vertical and anterior-posterior directions.

The description of quantities derived from the force platform data were
clarified by Shimba (1984). By applying dynamic principles to the problem,
Shimba estimated the position of the center of gravity, defined angular
momentum, and used the screw axis to define the center of pressure. The
center of pressure definition as defined by Shimba (1984) was revised by
Soutas-Little (1987) who took into consideration a force platform reference
center that was below the platform surface. Soutas-Little's unique definition
was used in the present study and will be accurately referred to as the

resultant vector intercept (RVI).

EXPERIMENTAL METHODS

5:1an

The testing area consisted of a 17 meter runway with a rubber tile
surface. An AMTI model OR6-3 force platform was mounted flush with the
surface at half the length of the runway. A Sony CCD—V8 video camera
positioned on a tripod was aimed perpendicular to the path of motion across
the force platform so that its recorded image would include full subject

motion involved in the strides on and off the platform. (Figure I.)

 

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Figure 1. Experimental set-up

6

7

Strips of tape were placed on the runway surface at 20 cm intervals
perpendicular to the line of motion throughout the camera view (200 cm
before and after the platform). A sweep timer and a board with trial
information were also included in the video image but not interfering with
the view of the subject.

Ground reaction forces and moments were collected by the force
platform at a sampling frequency of 1000 Hz. The sign conventions for the
force platform are shown in Figure 2. The six signals sent from the force
platform were wired through a 12 bit in-house A to D converter to an IBM
9000 computer for storage and eventual transfer to the Prime Computer in
the Case Center for Computer-Aided Engineering and Manufacturing located
in the College of Engineering at Michigan State University.

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Subjects

Sixteen subjects ranging in age from 18 to 50 years included nine males
and seven females. Subjects were chosen that were free from injuries and
conditions that would reasonably affect their performances at the time of
testing and included practiced runners as well as those who did not run
regularly. These subjects were selected to represent a functional norm of

human gait.

Protocol
After arriving at the Michigan State University Center for the Study of

Human Performance and given an explanation of the study's protocol, each
subject was asked to sign an informed consent waver. Each subject was then
weighed and measured for stature. Each subject's gender, age, and
participation in running and walking activities were also recorded (see
Appendix 1). This was followed by a practice period and warm-up. Since no
attempt was made to compare results between subjects, each subject brought
his/ her own running shoes and the pace of each set of trials was determined
by the comfort of the subject.

The testing included bilateral data collection under four conditions:
walking barefoot, walking shoed, running barefoot, and running shoed.
Twelve of the subjects performed under all four conditions while the other
four subjects did not complete one or more of the conditions due to a variety
of reasons including subject discomfort, inappropriate shoes, and data loss
(see Table 1). The order of condition completion was determined randomly
as was the choice of starting with the left or right trials for each condition.

When each subject was ready to begin testing, they were asked to walk
or run at a comfortable pace. A trial was deemed successful if: 1) the
foot-strike was entirely on the force platform, 2) the subject felt it was a
comfortable stride, and 3) the trial was not discarded by the discretion of one

or more experienced observers as an unusual series of strides. Trials

9

discarded by the observers were commonly due to the subject looking down
through the stride and making unnatural stride length adjustments in order
to strike the force platform. A change in cadence would reveal a change in
trial velocity or stride length and would also indicate an inappropriate trial.
In most cases the subjects were close enough to the center of the platform that
observation from the camera's position was sufficient for identifying a contact
that was partially off of the platform. In cases where there were any questions
of whether the contact was completely on the force platform, the trial was

rejected.

Table 1. Subject contribution to data collection

Sub'kzct Condition
Walk Barefoot Wflk Shoed Run Barefoot Run Shoed

05

X
X

07

10
12
I3
14
15
16
17
18
19
20
21

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key: x subject-conditions performed at the sight of data collection

10

The subjects completed a condition when they had performed three
successful trials for both left and right legs. Bates et a1. (1983) recommended
that eight trials should be collected in order to establish valid measurement
parameters. However, given the reproducibility of past ground reaction force
data, it was decided that three trials provided sufficient data for comparison.
Practice time was included between the different conditions and between
trials if the subject felt it was necessary.

After completion of the data collection, the ground reaction force data
were graphed on the IBM 9000 and then all of the ground reaction data were
transferred to the Prime Computer for imaging and quantitative analysis.
The spatial images were displayed on a Tektronix 4105 Color Monitor, and
printed by a Tektronix 4696 Ink Jet Printer. The video tape was copied onto
3/ 4 inch tape for viewing on a Sony VO-5600 Videocassette Recorder.

ANALYTICAL METHODS

Before the examination of bilateral symmetry, trial reproducibility had
to be verified. Trial reproducibility was of particular importance in this study
since data for the left and right sides were not collected simultaneously and
some practice may have separated the bilateral trials.

The first step in this verification process was the initial screening of
trials at the site of data collection. As described in the experimental methods,
the trials discarded at this point were either considered unnatural or were
strides in which the foot was not completely on the force platform. The data
saved were then subjected to the analysis described in the following section.
The purpose of this quantitative analysis was to exclude the incomparable
trials that remained to this point.

Q I'II' 51'

In this screening of trials, several quantities were measured and
compared to the other trials within the condition. These quantities were:
stride duration, the subject's average velocity, the integral of the
anterior-posterior force for braking and propulsion (impulse), and stride
length before and after platform contact.

The video images of the two available strides in each trial were timed
with a stopwatch in order to verify consistent trial velocity. This method
produced an accuracy of approximately 10.3 m/ sec in the running trials and
$0.2 m/ sec in the walking trials. Although crude, the method was sufficient
for identifying the unusually fast or slow trials. Hamill, Bates, Knutzen and

Sawhill (1983) observed variations in magnitude of ground reaction forces of

11

12

individuals tested at various speeds, therefore it was important that the
bilateral trials used for comparison were of comparable velocities.

The trials that were of incomparable speed were then excluded from
the study. A trial in a running condition with a velocity deviating more than
0.6 m/ sec from the average velocity of a subject condition was discarded. A
similar procedure was followed for the walking trials using a $0.4 m/ sec
tolerance as a cutoff. Hamill et al. (1983) reported changes in ground reaction
force descriptors at velocity changes slightly smaller than the tolerances used
in the present study. However, the accuracy of the present measuring device
limited the tightening of these tolerances.

Integration of the anterior-posterior force curve yielded values of total
braking and propulsive impulse. A stride of constant velocity would ideally
have a braking impulse equal to the propulsive impulse. Some variation in
these values was attributed to the normal trial variation, the effect of air
resistance on the body in motion (Cavanagh & Lafortune, 1980), and the
possibility of non-pathological bilateral asymmetry in the subjects. Strides in
which acceleration or deceleration could not be attributed to normal variation
were indicative of an unnatural stride and were therefore considered
inappropriate for trial comparisons. From past data collection and analyses, it
was determined that a braking impulse of less than 40% or greater than 60%
of the total impulse was an indication of this type of unnatural motion, and
these trials were discarded. However, even in these extreme cases of
anterior-posterior impulse imbalance, bilateral asymmetry was considered as
an explanation. This comparison was done by examining unilateral data for
consistency, and by comparing bilateral data for a reversed pattern. For
example, a subject that produced a relatively large braking impulse with the
right leg would also produce a correspondingly large propulsion with the left
leg in order to maintain a constant gait velocity. It should be noted that none
of the subjects exhibited this level of bilateral asymmetry in anterior-posterior

impulse.

13

Stride lengths were measured to a degree of accuracy (:3 cm) using the
video tape record of the study. This measurement was performed by
comparing the position of the subject's heel to the strips of tape on the testing
surface. The stride length onto the platform for trials of the same unilateral
condition were compared. Similar comparisons were made with the stride
lengths off the platform. Bilateral variation explained by asymmetry would
result in bilateral consistencies and the same type of bilateral reversal
mentioned with respect to the anterior-posterior impulse. For example,
bilateral asymmetry would be demonstrated by a subject who consistently
stepped onto the platform with a short right leg stride, and who would also
step off of the platform with a comparable short stride in the left leg trials.
However, this type of asymmetry was not observed for any of the subjects.

Several strides that had been discarded at the sight of data collection
were saved on the video tape and these stride lengths were measured. Of
these trials, those that had been discarded due to an unnatural stride typically
had strides that measured 7 to 20 cm longer than the average stride of that
subject-condition. Taking into account the degree of accuracy of the data
collection record, a trial that had been saved but had a stride length of :t10 cm
from the average trial of the same subject condition was assumed to be
inappropriate for comparison and was discarded.

It is important to note that although the process was focused on three
distinct areas (velocity, anterior-posterior curve integration, and stride
length), the discarded "unnatural" trials would be expected to reflect
inconsistencies in more than one area. In fact, these inconsistencies tended to
be the case and served to support the decision to discard.

After this screening process was completed, the subject conditions that
had at least one "good" trial for each leg were then subjected to bilateral
comparisons. Where more than one trial was available, between trial
variations were also analyzed. The comparative analysis to follow includes

both quantitative and qualitative analysis of this data.

14

C l' l l .

The three orthogonal ground reaction forces measured by the force
platform were the vertical, the anterior-posterior (A-P), and the medial-lateral
(M-L) components of the resultant force vector. Bilateral examples of the
ground reaction force (GRF) component graphs are presented in Figures 3 and
4.

The GRF curves of bilateral trials of a running shoed subject-condition
is shown in Figure 3. The smaller initial loading seen in the vertical curve
corresponds to the subject's heel-strike. In the barefoot conditions this
loading was subjected to less attenuation and therefore resembles a "spike".
The maximum loading of the vertical curve can be seen through mid-stance
and typically reached a magnitude of between 200 and 300 percent of the
subject's body weight.

The shape of the anterior-posterior GRF curves was typically similar to
an inverted sine curve with some degeneration in the area of heel-strike.
Around mid-stance this curve typically changed sign at a point which was
referred to as the AP Curve Crossover.

The reproducibility and symmetry of the vertical and anterior-posterior
ground reaction force histories were examined in terms of several quantities
that were previously determined as descriptors of these plots (Bates, Osternig,
Sawhill, 8: Hamill, 1983). The descriptors used in the present study were: the
magnitude of the maximum vertical GRF load, the vertical impulse, the
average vertical GRF, the A-P curve crossover, the duration of the stride, and
the magnitude of the GRF at heel-strike.

The small relative magnitudes, irregular shapes, and inconsistent signs
of the medial-lateral GRF curves did not indicate the use of quantitative
analyses for detecting consistency or bilateral symmetry. Instead, these graphs
were compared qualitatively with the intent of observing possible unilateral
and bilateral trends in shape, magnitude, and sign. Although inconsistent

with the force platform conventions illustrated in Figure 2, the medial GRF

Percent of Subject Body Weight

 

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Figure 3. Ground reaction force graphs of running

Percent of Subject Body Weight

16

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Percent of Stance

Figure 4. Ground reaction force graphs of walking

17

was chosen arbitrarily as the positive value in Figures 3 and 4 for ease in
bilateral comparison.

The GRF curves of bilateral trials of a walking shoed subject-condition
are seen in Figure 4. The vertical curve typically displayed two areas of
loading that reached magnitudes of between 100 and 140 percent of the
subject's body weight. In barefoot trials, these loadings were preceded by a
heel-strike spike that was absent in all of the shoed trials. The
anterior-posterior curve of Figure 4 was similar in shape to the A-P curve of
the running trials. The small initial propulsive loading seen in this curve
was found in several of the subjects, and was assumed to be due to a backward
motion of the subject's foot as it contacted the platform at heel-strike.

The descriptors used to analyze these curves were the same as those
used for the data on running, taking into account the lack of heel-strike
loading in the trials of the shoed walking condition and the additional value
for the second vertical loading seen in all of the walking trials. Again, the
medial-lateral GRF curves were analyzed qualitatively.

In addition to the GRF components, the force platform collects three
components of ground reaction torque which define a resultant torque vector.
As described by Shimba (1984) and Soutas-Little (1987), the resultant torque
vector can be separated into parallel and perpendicular components to the
resultant force vector. The resultant force vector with its associated parallel
torque component is called a wrench axis. The intercept of this wrench axis
with the platform surface is uniquely defined by the magnitude and direction
of the torque component perpendicular to the wrench axis.

The resultant vector intercept (RVI) path is the collective loci of the
millisecond wrench axis intercepts with the platform surface. An example of
a RVI path is presented in Figure 5. The small bulb at the low end of the plot
illustrates the slight medial-lateral variation of the intercepts which was
typically associated with the intercept dwell of the heel-strike in walking
trials. The smooth, even length of the plot was produced by the relatively

18

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19

consistent flow of the stride. Finally, the scattering intercepts about the area
of toe-off can be explained by shoe slippage and was a common characteristic
of such plots.

Five characteristics were chosen to describe the level of symmetry
present in the RVI plots. These characteristics were: the length of the path,
the medial-lateral shifts of the path, the magnitude of these shifts, the shape
of the path at heel-strike, and the shape of the path at toe-off. Although these
characteristics did not describe the paths completely, they did provide a good
indication of the symmetries and asymmetries present.

When the resultant force vectors were combined with the RVI plots,
the result was a resultant vector force (RVF) plot as seen in Figures 6 and 7.
In addition to combining the GRF and RVI path information, these plots
more clearly illustrated areas of vector dwell. To facilitate this visualization,
sampling rates of three or four milliseconds for trials of running and six to
eight milliseconds for trials of walking were used to adjust vector density.
The plots appeared to be spatial representations of the vertical GRF graphs
due to the contribution of this relatively large vertical component. The sharp
heel-strike vectors characteristic of a trial in a barefoot condition is illustrated
in Figure 7. The scale factor for the vector length in these plots was held
constant for the trials within a condition and each plot was oriented to
produce a lateral view so that direct comparisons could be made. The
symmetry of the vector density in the RVF plots was analyzed in terms of a
qualitative presence or absence of this symmetric characteristic in the first and
second halves of the plot length.

The resultant vector torque (RVT) plots share position, direction, and
rates of position change with the RVF plots. In the case of the RVT plots,
however, the vector lengths represent the magnitude and sign of the
resultant torque. Examples of RVT plots for both trials of running (Figure 8)
and walking (Figure 9) follow. A positive vector (extending outward from

the top of the platform image) is defined as the torque produced by the

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24

platform's resistance to potential lateral rotation of either foot. In other
words, a positive vector represents a medial ground reaction torque (see
Figure 10). This definition was not consistent bilaterally with the sign
conventions provided in Figure 2, but was done in the interest of bilateral
comparison. The scale factors were held constant for each condition so that

bilateral comparisons could be made.

subject' 3 left leg
Ca- — potential lateral rotation of the left leg
force platform
I' --—>
TT— medial pound reaction torque

 

1’/

Figure 10. Ground reaction torque sign convention

RESULTS

Of the original 330 trials saved at the time of data collection, 74 were
inappropriate for use in bilateral comparisons due to one or more of the
verification steps taken in the quantitative analysis. The loss of these trials
led to the exclusion of 11 subject conditions due to a lack of bilateral data (see
Table 2). The remaining data included 44 subject conditions (15 running and
29 walking) and 240 "good" trials (of a possible 264 trials in these conditions).
The results in the following sections reflected the bilateral comparisons of the
data from these trials.

Whom

The descriptors used to evaluate the level of symmetry in the ground
reaction forces (GRF) were: the magnitude of the peak load(s), the vertical
impulse, the average vertical force, the point of crossover of the
anterior-posterior force curve, the duration of the stride, and the magnitude
of the heel-strike force. It should be noted that heel-strike spikes were not
present in the graphs of the walking shoed trials, and that double spikes were
observed in the graphs of seven of the walking barefoot subject- conditions

and three of the running barefoot subject-conditions.

Barefoot walking

The vertical ground reaction force descriptors of the barefoot walking
trials are presented in Table 3. In general, the heel-strike magnitudes
represent the largest between-trial deviations and the largest bilateral

differences seen in these descriptors. The differences between these unilateral

25

26

Table 2. Subject contribution to bilateral comparison

 

 

 

Subject Condition
WallBarefoot Walk Shgg Run Barefmt Run Shoed
05 incl incl incl incl
06 incl incl - --
07 incl incl - -
08 incl incl incl incl
09 incl incl excl excl
10 incl incl excl excl
12 incl - -- -
13 incl - excl --
14 excl incl excl incl
15 incl incl incl incl
16 incl incl incl excl
17 incl incl excl incl
18 incl incl excl incl
19 incl incl incl incl
20 incl incl excl incl
21 incl incl incl incl
key: incl trials were included in comparison

excl trials were excluded from comparison

— trial conditions not collected

27

Table 3. Vertical ground reaction force magnitude data of barefoot walking

ub' t Heel- trik Loadin

05"
06
07
08
09
10
12"
13
15
16
17*
18"
19*
20"
21*

Subject First Loading

05"
06
07
08
09
10
12*
13
15
16
17"
18"
19*
20*
21*

(percent of subject body weight)

.“

57.3 (1.15)
65.3 (12.50)
43.0 (5.20)
69.0 (7.07)
71.7 (4.73)
68.7 (5.51)
81.3 (7.51)
75.0 (6.24)
66.0 (4.36)
88.7 (8.08)
80.3 (12.74)
150.0 (11.36)
61.3 (2.08)
66.0 (3.46)
74.5 (6.36)

1' ' .P
56.7 (3.51)
68.7 (11.72)
47.0 ( - )
65.0 (10.58)
73.0 (7.94)
80.7 (8.08)
103.7 (5.51)
86.7 (10.02)
75.3 (4.16)
92.0 (8.19)
64.5 (2.12)
149.7 (16.50)
76.0 (1.41)
65.3 (10.21)
83.0 (9.54)
average

t'1fl0.

0.6
3.4
4.0
4.0
1.3
12.0
22.4
11.7
9.3
3.3
15.8
0.3
14.7
0.7
8.5

7’“
1.1
5.2
9.3
6.2
1 .8

17.5
27.6
15.6
14.1
3.7
24.5
0.2
24.0
1.1
1_1-_4
10.9 %

Average Vertical Force

(percent of subject body weight)
' .I. m.onif ‘7

53.4 (0.32)
64.0 (0.70)
53.2 (0.61)
51.9 (0.42)
67.9 (0.81)
62.6 (0.91)
67.0 (0.60)
60.3 (0.72)
65.8 (0.25)
49.4 (0.62)
57.4 (2.65)
51.0 (0.76)
48.5 (0.36)
63.2 (0.10)
67.5 (1.34)

53.4 (0.90)
65.1 (0.55)
53.7 (0.61)
50.0 (0.31)
62.8 (0.86)
63.7 (0.64)
68.7 (0.82)
64.0 (0.67)
65.4 (0.85)
50.3 (0.49)
54.5 (0.07)
53.0 (0.61)
48.4 (0.14)
63.8 (1.39)
67.8 (0.10)

0.0
1.1
0.5
1.9
5.1
1.1
1.7
3.7
0.4
0.9
2.9
2.0
0.1
0.6
0.3

Second Loading

(percent of subject body weight)
1 it .D. ri h

 

2.9
0.3
1.2
2.4

15.1
1.6
5.6

10.2
5.0
4.3
4.6
3.6
5.9
4.3
4._1

(percent of subject body weight)
1m (5.0.) right (SD) mean dif %
117.3 (1.15) 114.0 ( - ) 3.3
116.0 (7.21) 116.3 (2.08) 0.3
107.0 (1.00) 108.3 (1.53) 1.3
134.5 (0.71) 131.3 (3.79) 3.2
129.3 (6.81) 112.3 (4.04) 17.0
127.7 (6.43) 125.7 (1.15) 2.0
114.3 (2.89) 120.7 (5.86) 6.4
127.3 (2.89) 140.3 (3.79) 13.0
120.7 (4.16) 126.7 (2.52) 6.0
111.3 (3.06) 106.7 (6.03) 4.6
132.3 (5.86) 126.5 (0.71) 5.8
121.3 (5.03) 125.7 (2.08) 4.4
113.3 (4.04) 120.0 ( - ) 6.7
107.7 (3.79) 103.3 (5.77) 4.4
122.5 (2.12) 117.7 (1.15) 4.8
average

I-

I"

4.7 %

108.3 (5.13) 106.0 (2.65) 2.3
124.3 (5.13) 130.3 (5.51) 6.0
110.7 (2.08) 111.3 (2.08) 0.6
122.0 ( - )120.3 (1.15) 1.7
128.3 (2.08) 118.7 (3.21) 9.6
121.0 (1.00) 120.3 (3.06) 0.7
112.0 (2.00) 117.7 (4.16) 5.7
121.7 (1.53) 129.7 (2.52) 8.0
124.3 (1.53) 128.0 (2.65) 3.7
120.0 (2.00) 120.7 (2.52) 0.7
116.3 (2.31) 111.5 (2.12) 4.8
122.0 (1.00) 122.3 (1.15) 0.3
109.7 (5.03) 113.5 (3.54) 3.8
107.7 (3.79) 107.0 (4.36) 0.7
119.5 (2.12) 121.7 (2.52) 2.2

subject displayed double heel-strike spikes bilaterally
standard deviation values were omitted when only one trial was available unilaterally

0.0
1.7
0.9
3.8
8.1
1.8
2.5
6.1
0.6
1.8
5.3
3.9
0.2
0.9
aa
2.5 %

..mnif%

2.2
4.8
0.5
1.4
8.1
0.6
5.1
6.6
3.0
0.6
4.3
0.2
3.5
0.7
L8
2.9 %

*" the deviation between the means is presented as a percent of the smaller unilateral value

28

mean values were as much as 27 percent of the heel-strike magnitude. Seven
of the subjects displayed a double heel-strike loading bilaterally, however, this
characteristic was not unique to a single group within the study. This group
of double heel-strikers represented males and females, runners and
non-runners, and an age range from 18 to 48 years. In addition, the presence
of this characteristic did not predict a general level of symmetry in any of the
descriptors, therefore, the double heel-strike spikes were considered to be a
difference based solely on the individual.

The bilateral difference seen in the first loading was considerably
smaller than that seen in the heel-strike, and although one of these values
was 15 percent of the force magnitude, the average bilateral difference was on
the order of only five percent. The data of the second loading and the average
vertical force were slightly closer bilaterally. In each case the largest difference
was eight percent and the average difference was three percent of each
quantity.

Three additional descriptors of the ground reaction data for barefoot
walking are seen in Table 4. The vertical impulse varied on the average at
about three percent of the total impulse magnitudes with a range of difference
extending to 14 percent for one of the subjects. The stride duration values
would be expected to be reproducible given that trials with extremely different
trial velocities had been excluded from this portion of the analysis and that a
strong relationship has been observed between these two trial characteristics
(Munro et al., 1987). The largest bilateral difference in stride duration was
only six percent of the total stance time. The average bilateral difference seen
in both the stride duration and anterior-posterior crossover was two percent
of their respective quantities.

Obvious trends supporting symmetry, or lack of symmetry, of the
groups within the subjects of this study are not illustrated in this study. For
example, Subject #09 displayed the largest bilateral variations in a majority of

the descriptors. However, the differences seen in Subject #09 (50 years old,

29

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30

male non-runner) are not comparable to either Subject #06 (49 years) or
Subject #07 (50 years), nor are they comparable to the other male non-runners
(Subjects #13 and #20). The male runners (Subjects #05, #08, #10, #12, #15,
and #21) displayed a wide range of bilateral differences including the
complete range of differences seen in the heel-strike magnitudes. This same
range of bilateral differences was produced by the female non-runners
(Subjects #06, #07, #16, #17, #18, and #19) in the stride duration descriptor.

Shoed walking

The data of the shoed walking trials were similar to the results of the
barefoot trials, even to the extent that Subject #09 displayed the largest degree
of bilateral asymmetry in most of the descriptors. However, there was a slight
decrease in the average bilateral difference for four of the six descriptors. The
force data for these trials is presented in Table 5. The differences between the
unilateral means of the two maximum loads each represented an average
difference of four percent of the load magnitude. The average bilateral
differences between the unilateral average vertical force data were on the
order of two percent of this quantity.

Table 6 contains the remaining descriptors of the shoed walking trials.
In each of these descriptors the average bilateral difference was one to two
percent of the descriptor quantity. The data of the walking shoed condition
did not illustrate any group trends, however, individual trends became
apparent. For example, several of the subjects (#05, #06, #07, #10, #15, and
#21) displayed close symmetry in all of the descriptors.

The medial-lateral GRF curves for each subject in the walking
conditions displayed levels of symmetry consistent with the graphs in Figure
4. The trials tended to display a lateral GRF of as much as 10 percent of the
subject's body weight through the first 10 to 20 percent of stance followed by a
medial GRF of up to 15 percent of the subject's body weight through toe—off.

However, the seemingly natural variability and asymmetry of this

31

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33

characteristic, in combination with the small relative magnitude of the force,
often produced an asymmetric change of sign (see the right M-L GRF of
Figure 4).

Running data

The force magnitude descriptors of the ground reaction data for running
are shown in Table 7. Again, the heel-strike values displayed the greatest
degree of unilateral and bilateral variation. The average subject in the
barefoot trials displayed a bilateral variation of 12 percent of the total
heel-strike force with a maximum of 30 percent. In the shoed condition, this
same variation was 14 percent with four subjects having produced differences
on the order of 20 to 25 percent. An average of the subjects common to both
of these conditions produces a more appropriate comparison between the two
conditions; 12 percent for the barefoot trials and seven percent for the shoed
trials.

The maximum vertical loading and the average vertical loading, for
each the barefoot and shoed conditions, all revealed an average bilateral
variation of four percent of the descriptor magnitude. Analysis of only the
subjects common to both conditions also produced bilateral variation of four
percent in the maximum and average vertical loading. The additional
descriptors of the subject-conditions for running will be found in Table 8.

The consistent individual differences between descriptors become less
apparent in the running conditions. However, the between-trial variance of
the descriptors has increased noticeably in a majority of the sets of trials.

The medial-lateral GRF curves of the trials in the running conditions
displayed magnitudes consistent with the trials of walking and with the
curves of Figure 3 (zero to 20 percent of the subject's body weight). Symmetry
of the curve signs and between-subject trends in the shape of the curves were
not observed. However, the curves were generally reproducible in a given

unilateral subject-condition.

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Typical between-trial variability of the RVI paths is presented in Figure

11. The superimposed shoe outline on the image illustrates the scale of the
platform, but, since actual stance position data was not recorded, this shoe
outline will not be included in the remaining plots. The direction of motion
in all of the RVI plots of this study is toward the top of the page.
As stated in the Analytical Methods, the following descriptors were used

to assess the level of symmetry present in the RW plots;

the length of the path,

the medial-lateral shifts of the path,

the magnitude of these shifts,

. the shape of the path at heel-strike, and

the shape of the path at toe—off.
Examples of these characteristics are illustrated for each of the conditions in
Figures 12 through 15. In these plots, perfect symmetry would be indicated by

a path demonstrating the mirror-image of its bilateral plot.

 

 

 

 

 

 

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Figure 11. Between-trial variability of resultant vector intercept paths

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Figure 13. Resultant vector intercept paths of shoed walking

a)

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Figure 14. Resultant vector intercept paths of shoed running

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Figure 15. Resultant vector intercept paths of barefoot running

41

Figures 12 through 15 serve as examples of the presence or absence of
the symmetric characteristics of these plots. A compilation of the symmetric
characteristics for each subject is presented along with the results of the RVF
and RVT data in Tables 9 through 11 at the end of the Results section.

The path in Figure 12a (Subject #12) was symmetric in terms of each of
the descriptors with the exception of slightly larger medial-lateral shifts in the
path of the left foot. The paths of Figure 12b (Subject #05) were not similar in
shape to the paths of Subject #12, but the levels of symmetry were similar.
Again in 12b, the medial-lateral shift of the left path was slightly larger than
that of the right path including a lateral shift at toe-off. Figure 12c (Subject
#06) displays asymmetry in each descriptor with the exception of the
symmetric length of the two paths.

Examples of the RVI paths of shoed walking will be found in Figure 13.
The first set, 13a (Subject #05), illustrated paths that were close to being mirror
images of each other. The lower end of the paths in 13b (Subject #21)
displayed symmetry in the presence of the medial-lateral shifts, however,
these shifts were not symmetric in magnitude. The same level of symmetry
was present in the paths of 13c (Subject #20) with a slightly increased level of
the symmetry at toe-off.

Various levels of symmetry in barefoot running data are displayed in
Figure 14. In 14a (Subject #21), asymmetry was produced in the magnitude of
the medial-lateral shifts at heel-strike and through the length of the path.
The length of the second set of paths (Subject #19) displayed reasonable
symmetry, however, the intercept positions at heel-strike and toe-off display
asymmetry. The paths of 14c (Subject #08) were asymmetric in each of the
descriptors with the exception of the symmetry in their length.

Examples of three sets of resultant vector intercept paths produced by
subjects running with shoes are illustrated in Figure 15. The paths of 15a
(Subject #17) were symmetric with respect to every descriptor with the

exception of the lateral deviation of the right path at toe-off. Symmetry in 15b

42

(Subject #15) was seen only in the length and presence of the medial-lateral
shifts of the paths. The last set of paths, 15c (Subject #08), illustrated
asymmetry in each of the descriptors.

Wm

Typical between-trial variability seen in the resultant vector force (RVF)
plots are shown in Figure 16. The large differences between the heel-strike
spikes in the plots can be explained by vector spacing and therefore may not
indicate between-trial dissimilarities. The reproducibility and symmetry of
the heel-strike GRF magnitudes was more clearly illustrated by the GRF
graphs.

Bilateral examples of RVF plots for each of the conditions are presented
in Figures 17 and 18. The designation of the presence or absence of
"symmetry" in these Figures serves as a guide to the relatively subtle
asymmetries that existed in these plots. The analysis of these plots
concentrated on the symmetry of vector dwell areas in each half of the length
of the path. The results of this analysis for each of the subjects will be found
at the end of this section in Tables 9 through 11.

The bilateral resultant vector force plots of a barefoot running condition
are seen in Figure 17a (Subject #19). Asymmetry of the vector density in the
second half of the length of the path are illustrated in this set of points. A
slightly higher level of symmetry was illustrated in 17b (Subject #20). The
level of symmetry of the RVF data for walking was generally higher than that
seen in the data for running. A high degree of asymmetry relative to the
other data for the walking conditions was displayed in Figure 18a Subject#05).
The plots of 18b (Subject #19) display a slightly higher level of symmetry in
the data of a shoed walk.

43

    

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45

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Variability between the unilateral resultant vector torque (RVT) plots
was typically more evident than the variability seen in the RVF plots. An
example of this RVT plot variability is illustrated in Figure 19. The symmetry
of these plots was determined by the presence or absence of common vector
sign and vector magnitude characteristics in each half of stance. A
compilation of these characteristics for each subject is presented in Tables 9
through 11 at the end of this section.

Examples of these characteristics in trial sets for both a walk and a run
were provided in Figure 20. In the first set of plots, Subject #08 displayed
symmetry of vector sign, however, the torque vector magnitudes produced
were asymmetrically larger throughout a majority of the first half of the left
leg plot. The trials seen in Figure 20b (Subject #17) were produced by a shoed
run. The plots illustrated asymmetry through the first half of stance, and
symmetry through to toe-off.

Summary
The results of the RVI path, the RVF plot, and RVT plot analyses for the

barefoot walking subject-conditions are presented in Table 9. Symmetry of
these descriptors was indicated in each subject-condition that displayed the
characteristic both unilaterally and bilaterally. Similarly, the results of the
analyses of the shoed walking condition and the running conditions are
presented in Tables 10 and 11 respectively. Tables 9 through 11 provide an
overview of the symmetry present in the bilateral data of this study.

 

   

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47

 

Figure 19. Between-trial variability of resultant vector torque plots

 

Figure 20. Bilateral comparison of resultant vector torque plots

49

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DISCUSSION

Although statistical strength would have accompanied a larger number
of condition trials (Bates et al., 1983), and subject group trends may have been
observed using a larger number of subjects, the present data were sufficient to
gain a basic understanding of the symmetry present in the ground reaction
data of non- pathological gait.

The data from the walking conditions indicated that the vertical and
anterior- posterior ground reaction forces are generally symmetrical
characteristics of gait. Other characteristics displaying symmetric qualities
include: the medial-lateral ground reaction forces, the sign of the vectors in
the resultant torque plots, the length of the resultant vector intercept paths,
the rate of change of the resultant vector along the path, and the presence of
the medial-lateral shifts of the path. The specific characteristics of the
resultant vector intercept paths and the resultant vector torque plots were
relatively asymmetric in these trials. In general, the barefoot condition
seemed to decrease the level of symmetry of the descriptors slightly when
compared to the shoed trials of both walking and running.

The data from the running conditions were slightly less symmetric
than that for the walking conditions in a majority of the characteristics. The
exceptions to this were the relative asymmetry of the medial-lateral ground
reaction force curves and the asymmetry of the vector signs in the resultant
torque plots through the second half of stance in the running conditions. The
limited data in the barefoot condition made comparisons between this

condition and that of the shoed trials difficult. However, the results indicated

52

53

that barefootedness seemed to decrease the level of symmetry in the ground
reaction data.

The level of symmetry present in a gait descriptor seemed to be
dependent on the relative magnitude of the quantity, the reproducibility of
the quantity, and the value's overall contribution to locomotion. For
example, the vertical ground reaction forces were large in relation to the
other ground reaction forces, were relatively reproducible, and played a major
role in the performance of gait. And, as noted, the vertical ground reaction
force histories were also relatively symmetric in shape. At the other extreme,
the specific shape characteristics of the resultant vector intercept paths are
relatively small positional changes that are poorly reproduced trial-to-trial,
and are a relatively asymmetric characteristic.

Another variable that seems to have affected the level of symmetry in
this study was the comfort of the subject in a certain condition. A majority of
the subjects made mention of discomfort while performing under the
barefoot running condition, which certainly contributed to the relative
asymmetry of the condition. If the number of failed attempts at platform
contact in the data collection, and the number of subject- conditions that were
rejected through the quantitative analysis was any indication of level of
discomfort, then discomfort decreased the level of symmetry in ground
reaction data. The shoed walking condition involved the fewest number of
trial attempts and was saved through the quantitative analysis in every case.
This pattern continued through the barefoot walking condition, the shoed
running condition, with the barefoot running condition being the most
difficult data to collect and the most frequently discarded in the quantitative
analysis.

The quantitative analysis of the ground reaction force data has been
well established (Bates, Osternig, Sawhill, & Hamill, 1983; Hamill, Bates, &
Knutzen, 1984; Munro, Miller, 8: Fuglevand, 1987). However, in the present
study a qualitative method has been developed with which the spatial

54

resultant vector plots can be evaluated for bilateral symmetry. It is hoped that
this method of analysis will provide an affective and convenient tool for

future clinical and research works.

CONCLUSIONS

The observed symmetric characteristics of both walking and running
will be found in Tables 12 and 13 respectively. Varying levels of symmetry
appear in the various descriptors with generally higher levels of symmetry
present in the data of the walking conditions when compared to the data of
the running conditions. In both the data for walking and running,
barefootedness seemed to produce a lower level of symmetry when compared
to the data of the subjects wearing shoes. However, this comparison was
difficult within the conditions of barefoot running due to a small number of
contributing subjects.

Each subject's ability to perform a gait condition comfortably seemed to
affect the symmetry present in the ground reaction data. The results of the
present study indicated that the subjects felt comfortable walking in shoes,
which produced relatively symmetric data. The converse was seen in the
barefoot running condition which caused discomfort in a majority of the
subjects and also resulted in relatively asymmetric data. Although this may
seem to be a casual observation, it supported a more important observation
with regard to symmetry. These results indicated that symmetry increases as
the experience and practice of a particular gait increases comfort. This would
support the idea that perfect symmetry in gait is the ideal and more efficient
method of locomotion, and that experience tends to bring the performance
closer to that ideal level of symmetry.

The subjects of this study were chosen to represent a wide variety of
functionally non-pathological subject groups. Although the subjects in this

study allowed general observations to be made concerning ground reaction

55

Table 12. Observed symmetry in the ground reaction data of walking

Ground Reaction Forces
vertical maximum loading
average vertical force
vertical impulse

anterior-posterior crossover

Resultant Vector Intercth Paths
path length

medial-lateral path shifts

heel-strike and toe-off

Resultant Vector Force Plots
rate of change of the vector

position

Resultant Vector Torque Plots
vector sign

vector magnitude

3 to 5 percent bilateral difference
1 to 3 percent bilateral difference
2 to 4 percent bilateral difference
2 percent bilateral difference

close symmetry

symmetric in presence and position
in a majority of the cases, but
rarely symmetric in magnitude

symmetric in appearance in

approximately half of the cases

symmetric in a majority of the cases

symmetric in a majority of the cases
asymmetric in a majority of the

C3585

57

Table 13. Observed symmetry in the ground reaction data of running

Ground Reaction Forces
heel-strike forces
vertical maximum loading
average vertical force
vertical impulse

anterior-posterior crossover

Resultant Vector Intercept Paths

path length
medial-lateral path shifts

heel-s trike

toe-off

Resultant Vector Force Plots

rate of change of the vector
position

Resultant Vector Torque Plots

vector sign

vector magnitude

12 to 14 percent bilateral difference
3 to 5 percent bilateral difference

4 percent bilateral difference

2 to 3 percent bilateral difference

2 percent bilateral difference

5

close symmetry
symmetric in presence and position
in approximately half of the
cases, but rarely symmetric in
magnitude
rarely symmetric in appearance
symmetric in less than half of the cases

symmetric in a half of the cases in
the first half of stance, and in a
majority of the cases through
the second half

symmetric in a majority of the cases
through the first half of stance,
but rarely symmetric through
the second half

rarely symmetric

58

data symmetry, the study was limited in its ability to make comparisons
between subject groups due to a small number of subjects in any given
category. In order to make these comparisons, a future study should
concentrate on two specific groups performing under a specific gait condition.
Additionally, the number of trials collected unilaterally should exceed three
in order to more fully examine the characteristics of the resultant torque

magnitudes and the positions of the wrench axes.

APPENDIX

59

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BIBLIOGRAPHY

Bates, B. T., Osternig, L. R., and Sawhill, I. A., and Hamill, I. "Identification of
critical variables describing ground reaction forces during running",

Biomechanics VIII-B. 1983. pp. 635-640.

Bates, B. T., Osternig, L. R., and Sawhill, J. A., "An assessment of subject
variability, subject-shoe interaction, and the evaluation of running shoes
using ground reaction force data", I. Bigmghanig. Vol. 16, No. 3, 1983,
pp. 181-191.

Cavanagh, P. R., and Lafortune, M. A., "Ground reaction forces in distance
running", I. Biomechanics. Vol. 13, 1980, pp. 397-406.

Chhibber, S. R. and Singh, I., "Asymmetry in muscle weight and one—sided
dominance in the human lower limbs", |. Anat. 106-3, 1970, pp. 553-556.

Elftman, H., "The measurement of the external force in walking", Science.
Vol. 88, No. 2276, 1938, pp. 152-153.

Elftman, H., "Forces and energy changes in the leg during walking", Am. I.
Physiol. 125, 1939, pp. 339-356.

Fenn, W. 0., "Work against gravity and work due to velocity changes in
running", Am. I. Physiol. 93, 1930, pp. 433-462.

Hamill, 1., Bates, B. T., Knutzen, K. M., and Sawhill, J. A., "Variations in
ground reaction force parameters at different running speeds", Human

Movement E'ence. 2, 1983, pp. 47-56.

Hamill, ]., Bates, B. T., and Knutzen, K. M., "Ground reaction force symmetry
during walking and running", Research Quarterly for Exercise and Smrt.
Vol. 55, No. 3, 1984, pp. 289-293.

Munro, C. F., Miller, D. I., and Fuglevand, A. 1., "Ground reaction forces in

running: a reexamination", |. Biomechanics Vol. 20, No. 2, 1987,
pp. 147-155.

60

61

Payne, A. H., "A comparison of the ground reaction forces in race walking
with those in normal walking and running", Biomech_anics VI-A. 1978,
pp. 293-302.

Payne, A. H., "Foot to ground contact forces of elite runners", Biomechanics
VIII-B. 1983, pp. 746-753.

Shimba, T., "An estimation of center of gravity from force platform data",
|. Biomechanig. Vol. 17, No. 1, 1984, pp. 53-60.

Singh, 1., "Functional asymmetry in the lower limbs", Acta. Anat. 77, 1970,
pp. 131-138.

Soutas-Little, R W., "Center of pressure plots for clinical uses", Biomechanics
of normal and prosthetic gait. BED-Vol. 4 DSC-Vol. 7, ASME, 1987,
pp. 69-75.

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