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Parametric Study for Clinical Evaluation
of Postural Stability

presented by

Kathleen Mary Hillmer

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MSU loAn Affirmative AotloNEquol Opportunity lnotiMion

 

PARAMETRIC STUDY FOR CLINICAL EVALUATION
OF POSTURAL STABILITY

By

Kathleen Mary Hillmer

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Material Science and Mechanics

1993

ABSTRACT

PARAMETRIC STUDY FOR CLINICAL EVALUATION
OF POSTURAL STABILITY

By
Kathleen Mary Hillmer

Balance evaluation parameters were identified which were
sensitive to postural instabilities, characterized the subj ects' postural
responses and served as useful quantitative measures for comparing
subjects. Force platform data were collected for normative subjects and
one patient during quiet stance in various conditions. Comparisons
were conducted between the subject and norms for the following time
domain parameters: radial average displacement, radial velocity,
ground reaction torque; and the frequency domain parameters: Xcop
power, Ycop power, radial power, radial velocity power and ground
reaction torque power. Peak frequency and amplitude were used as
characteristic measures in the frequency domain. A definition of
sensitivity for balance parameters was proposed. Based on this
definition, radial average displacement was less sensitive than velocity
and ground reaction torque. In the frequency domain, the parameters
considered contained valuable information about stability and the type
of control strategies used for maintenance of balance. The patient peak

frequency was larger than norm for all but one condition.

ACKNOWLEDGMENTS

I take this opportunity to show my appreciation to the following people

whose contributions made the completion of the thesis possible:

To my major professor, Dr. Robert Soutas-Little, for his faith,
encouragement, and constant teaching throughout my years at BEL.

A special thank you to Yasin Dhaher for being so helpful and sharing
his expertise in control systems and dynamic modeling, and for many

hours of helpful guidance.

To Brock, Chang, Dave, Jim, Kimberly, Tammy, Patricia, and LeAnn
who were not only coworkers to me, but also friends and a source of
laughter, moral support and encouragement when times got tough.

Each one of you has helped me in a special way.

To my fiancé Brian and my loving family. Your belief in me along with
constant motivation to achieve my goals and fulfill my dreams helped
give me the confidence I needed to complete this endeavor. I will

always love you and appreciate your faith in me.

TABLE OF CONTENTS

Page
LIST OF TABLES ..................................................................... v
LIST OF FIGURES ................................................................... vi
Chapter
I. INTRODUCTION .............................................................. 1
II. LITERATURE REVIEW .................................................. 4
2. 1 Visual/Vestibular and Proprioceptive Input .......... 5
2.2 Postural Steadiness ................................................. 6
2.3 Postural Stability ..................................................... 19
2.4 Postural Control System Models ........................... 25
2.5 Clinical Applications ............................................... 30
III. EXPERIMENTAL METHODS ........................................ 35
3.1. E uipment ............................................................. 35
3.2. Su jects ................................................................. 37
3.3. Experimental Preparation .................................... 37
3.4. Testing Procedure ................................................. 38
N. ANALYTICAL METHODS .............................................. 41
4.1. Calculation of COP ............................................... 41
4.2. Time Domain Analysis ......................................... 44
4.3. Frequency Domain Analysis ................................ 46
V. RESULTS AND DISCUSSION .......................................... 48
VI. CONCLUSIONS ................................................................ 73
APPENDIX
A. Balance and Stability Questionnaire ...................... 76
B. Mathematical Development of Gain vs.
Frequenc Ratio Expression ................................... 81
C. Spectral 'stribution Plots for Norm
and Patient ............................................................... 84
BIBLIOGRAPHY ...................................................................... 96

iv

LIST OF TABLES

Page
1. Comparison between reported and experimental norms ............ 54
2. Patient Values versus Norm ........................................................ 70

a. Characteristic Frequency Comparison
b. Characteristic Amplitude Comparison

3. Patient Percentage Above Norm ................................................... 7 1
a. Characteristic Frequency Comparison

b. Characteristic Amplitude Comparison

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LIST OF FIGURES

Page

Force platform coordinate system and dimensions ................ 36
Foot placement protocol ........................................................... 40
Vertical torque method ............................................................ 42
Parallel torque method ............................................................ 43
Xcop versus Ycop for: (a) FTEC, (b) TDEO ........................... 5O
Torque for: (a) FTEC, (b) TDEO ............................................ 51
Balance summary chart for patient ........................................ 56
Spring-mass-damper 1-DOF model ........................................ 58
Gain versus frequency ratio plot for 1-DOF model ................ 59
Inverted double pendulum 2-DOF model ................................ 61
Double inverted flywheel, 2-DOF torsional model .................. 62
Norm spectral distribution for FAEO ..................................... 66
Norm spectral distribution for FAEC ..................................... 67
Patient spectral distribution for FAEO .................................. 68
Patient spectral distribution for FAEC .................................. 69
Norm spectral distribution for FTEO ..................................... 84
Norm spectral distribution for FTEC ..................................... 85
Norm spectral distribution for TDEO ..................................... 86
Norm spectral distribution for TDEC ..................................... 87
Norm spectral distribution for RLEO ..................................... 88

21.
22.
23.
24.
25.
26.
27.

Norm spectral distribution for LLEO ..................................... 89

Patient spectral distribution for FTEO .................................. 90
Patient spectral distribution for FTEC .................................. 91
Patient spectral distribution for TDEO .................................. 92
Patient spectral distribution for TDEC .................................. 93
Patient spectral distribution for RLEO .................................. 94
Patient spectral distribution for LLEO .................................. 95

CHAPTER I
INTRODUCTION

Postural balance, the body's ability to remain upright, is an
essential aspect of everyday life. Often taken for granted, the complex
and efficient system that maintains balance also makes possible the
successful completion of daily activities such as standing, walking,
running, squatting, etc. Without an adequate postural control system
the central nervous system (CNS) would not be able to assess
movements of the body, or of the surroundings, and perform the
necessary muscle response to prevent falling. Thus, if a deficiency in
any aspect of the postural control system develops, it is necessary to
have a reliable and efficient way to assess balance and decide on
appropriate treatments. Development of such an evaluation technique
requires knowledge of the working mechanisms of the postural control
system.

Postural balance, with assistance from the musculoskeletal
system, is controlled by three different mechanisms: the visual,
vestibular, and proprioceptive systems. The loss of input from one or
more of these systems requires the postural control system to depend
on the available input to maintain balance. Although each system has
a specialized control of balance, there does exist some overlap in
function between them.

Nerve impulses sent to the CNS regarding head position and
movement strongly influence the muscle activity involved in
maintaining balance. The visual system utilizes surrounding objects as

a reference frame to establish a known vertical and provides
1

2

information about the orientation of the head with respect to gravity.
However, the body is also equipped with other mechanisms to sense
head position.

The inner ear, in addition to its role in hearing, provides
information about the positioning and movement of the head. This
information is then utilized to determine what movements may be
necessary to maintain balance. Signals sent from the inner ear are also
involved in controlling extrinsic eye muscles so that the eye may remain
fixed on one object despite movements of the head. Specialized receptor
cells which are responsible for this are located within the utricle,
saccule, and the ampulae of the semicircular ducts and make up the
vestibular apparatus. This system also uses mechanisms within the
inner ear to sense both linear and angular accelerations.

In addition to the importance of knowing head position with
respect to gravity, it is also essential to know how the whole body is
positioned. The proprioceptive system uses receptors in the tissues and
joints and pressure receptors in the feet in conjunction with velocity
and position sensitive muscle spindles to provide information to the
balance system about body orientation and posture. Receptors within
the neck provide information about the head relative to the rest of the
body. This information is needed since the vestibular system senses
head position only. Knowledge of where the head is with respect to the
rest of the body will aid in the determination of whether body
equilibrium is in a threatening position, as in the case where the whole
body is tilted and on one foot but the neck is straight, or when
equilibrium is not threatened as when the body is upright and only the
head is tilted. Input from each of these systems is used by the central

3

nervous system to signal the necessary muscle response to maintain

balance.

With this complicated and integrated system, what happens
when one portion of the system does not provide the necessary
information and the body is unable to adapt? What can be done to
evaluate such problems and determine treatment? As early as 1851,
physicians began to take note of patients' observed balance difficulties
and investigate the origin of such problems. Studies were begun to
obtain an in depth understanding of how balance is controlled and how
specific diseases or injuries may impair the ability to maintain balance.

Early evaluations were based solely on observations and
comparison of patients with normative subjects performing various
tasks. However, with today's advancements in technology, a variety of
measurement parameters have been developed, and controversy exists
concerning which measures should be used as well as how to interpret
them. Some researchers have used external perturbations such as force
platform movements to induce a state of imbalance. Others have tried
to measure a persons natural sway by having the patient stand in
various positions on a force platform. The controversy between which
method is more accurate and which measurements should be taken
emphasizes the need for more research and consistency in this area of
biomechanics. The purpose of this thesis is to explore differences
between normal and balance impaired individuals, determine the most
informative and reliable means of measuring postural steadiness and

develop a feasible testing protocol for use in a clinical setting.

CHAPTER II
LITERATURE REVIEW

For many years, researchers and physicians have been searching
for an effective means of assessing postural balance and stability.
Surprisingly, methods first used in 185 1 by Romberg are still in use
today in conjunction with many new ones. Romberg conducted
subjective assessments of patients' balance through observation of sway
and standing ability. At that time, comparison to "normal" stance was
the only means of measuring sway. Thus, the physician relied purely
on observation. Romberg used this method of sway observation and
expanded upon it by conducting balance evaluations of patients
standing with both eyes open and closed. He observed a dramatic
increase in postural sway with eyes closed for patients with disease
impaired proprioception [23, 113]. Later, this method of balance
assessment became standard procedure and was known as the
"Romberg Test". This was the beginning of research on postural
balance and sparked a great deal of interest in the specific mechanisms
of the postural control system of the body.

Since the advancements in balance evaluations by Romberg,
many devices and techniques have been developed. These vary from
standing on one foot to the use of moving walls and force platforms.
However, knowledge of the postural control system is essential before
the development of an effective evaluation protocol may begin.
Research shows that balance is maintained through the evaluation of

afferent information from several inputs, and investigations have been

 

5

conducted to identify the specific roles played by each input and how
each one contributes to the maintenance of balance [12, 21, 55, 88].

2.1 Visual, Vestibular, and Proprioceptive Inputs

Maintenance of postural balance requires three types of input:
visual, vestibular, and proprioceptive. Although there is some overlap,
Nashner noted in 1970 that the three sensory control loops are each
specialized to work within a specific domain of amplitudes and
frequencies, indicating this in not a totally redundant system [16, 21].
As will be discussed in section 2.2, the comparison of sway power
spectra from patients and normals and the separate determination of
the efficiency of the three control loops over a range of frequencies for
each type of input is useful in the identification of problem areas and
work has been done to define each system's role in postural control.

Proprioceptive Input - The proprioceptive system includes
receptors in the tissues of joints, connective tissue, muscles, and
cutaneous tissues with elements such as the pressure receptors of the
feet and the velocity and position sensitive muscle spindles [50]. These
sensors send information to the CNS regarding the location and
orientation of each part of the body with respect to a reference frame.
Results of experiments investigating afferent input from proprioceptive
receptors show that spindle afferents have their working range above 1
Hz. Pressure, joint, and skin receptors are more important in the low
frequency range [21].

Visual Input - Vision also plays an important role in the
postural control system. Along with the vestibular system, it helps to

maintain the head and body's orientation with respect to gravity [50].

 

6

Results from experiments with visual perturbations indicated that
visual stabilization of posture operates mainly in the low frequency
range at and below 0.1 Hz [16, 21].

Vestibular Input - The vestibular system is essential for
maintaining head orientation in space with respect to gravity [50]. This
system consists of both angular (semicircular canals) and linear
(utricular otoliths) acceleration sensors [87]. The working range of the
vestibular system has been investigated by many researchers. Nashner
[87] predicted the semicircular canals best sense the rate of sway above
0. 1 Hz while the otoliths sense sway below this frequency [21].

DeWit [14] investigated postural steadiness in normals, subjects
without vestibular function, subjects with weak proprioception but
normal vestibular input, and persons with abnormal labyrinth function,
such as Menier-Syndrome. The results revealed two types of
oscillations: one originating from the proprioceptive muscular system
and the other from the vestibular system. The oscillation from the
proprioceptive system was characterized by high frequency and small
amplitudes. While the vestibular driven oscillation displayed large

amplitudes and low frequency.

2.2 Postural Steadiness and Measurement Parameters

Since the introduction of the Romberg test in 1851, evaluations of
postural balance have been a routine part of neurological exams. Early
studies were primarily based on measurement of static equilibrium
during quiet standing. This method of evaluation was termed postural
steadiness to avoid confusion with postural stability which consists of

responses to perturbations or dynamic movements [98]. Evaluations of

7

steadiness are often conducted to investigate possible sensory
impairments by quantifying the amount of postural sway, under the
assumption that increased postural sway is associated with increased
effort to maintain balance. Simple external disturbances, such as
closing of the eyes or assuming an atypical stance, are often applied to
decrease the amount of sensory input. However, no disturbances such
as force platform movements are applied. Postural sway may be

characterized in terms of the following [7 O]:

1. Ground reaction forces

2. Displacement of the center of pressure (COP)

3. Displacement of the body's center of gravity (CG)
4. Motion of body segments or joints

5. EMG activity in various muscle groups

Unlike early evaluations, such as the Romberg test, which were based
purely on observation, the use of modern technology provides these

measures of sway which are quantitative and offer greater accuracy.

1. Ground Reaction Forces - Balance is a state of equilibrium
where there is no net external force on the body. Therefore, it seems
logical to focus on external forces to better understand postural balance
and locate problem areas. As the subject stands, forces are exerted onto
the floor due mainly to the body weight. In equilibrium, an equal and
opposite reaction force is applied to the feet by the floor producing a
zero net external force. The three components of these reaction forces
consist of two in the plane of the floor and one in the vertical direction.
The resultant of these reaction components is known as the resultant

ground reaction force.

Various studies have been conducted to investigate the forces
involved in maintenance of balance [67]. Early experiments used
electric scales to measure vertical reaction forces and weight shifting
during stance with eyes open and eyes closed [39, 7 9]. Thomas and
Whitney (1949) employed electric scales to study the NP movements
during normal standing in men [39]. A similar method was also used
by Henriksson, et al [39] where two electric scales using strain gauges
measured the difference in voltage between the two scales and
displayed the difference in pressure exerted by the right and the left
foot. However, more commonly used measures today are ground
reaction forces obtained through the use of force platforms. Originally
the signals were recorded on strip recorders and quantified manually.
Thus, ground reaction forces were measured in either the
anterior/posterior (MP), the medial/lateral (M/L), or the vertical
directions. Now, force platforms are used to measure 3 orthogonal
ground reaction forces and moments about those axes. Some
researchers have used commercially available force platforms while
others have constructed their own. Specifications for building a vertical
force platform to be used as a clinical tool have been presented in the
literature [6].

Although some studies have used two adjacent force platforms
[98] or scales to measure weight distribution and shifting, most studies
are conducted with both feet on only one force platform. Stribley, et al
[113] used a force platform to measure ground reaction forces and
calculated for the last 50 seconds of a 75 second trial the average of the
integrated force signal, which he termed the "steadiness score". The

subjects were evaluated in various stances with both eyes open and

9

closed. By steadiness score comparison, results were obtained which
indicated no significant difference between men and women or between
one-legged stance on the dominant or non-dominant side.

Measurement of the ground reaction forces not only provides
information about the loads applied to the body, but it also allows
evaluation of the type of balance strategy used based on the sway
patterns the subject exhibits. Woolley, et al [134] measured mean A/P
shear force andinterpreted them as measures of hip sway. In a similar
analogy, Barin [4] measured peak to peak horizontal force and
normalized by 111.25 N (a theoretical maximum). This measure was
used to determine whether hip or ankle strategy was mostly used. A
100% corresponded to complete hip strategy while a 0% corresponded to
complete ankle strategy. Balance strategies will be discussed in more
detail in section 2.3 on postural stability.

2. Displacement of the Center of Pressure of the Foot - To
gain additional information on how the ground reaction forces interact
with the feet in maintenance of balance, various attempts have been
made at studying the distribution of pressure, defined as force per unit
area, on the surface of the foot. Elftman [26] in 1934 expanded on
others' past attempts to study the pressure on the feet when walking.
He designed a device to record the momentary distribution of pressure
over the whole foot during normal gait. Subjects walked across a
rubber mat which had pyramidal projections which pressed against a
heavy glass plate. The area of contact of the pyramid with the glass
increased in proportion to the pressure exerted by the foot. Data were

recorded from below the glass plate with a 72 Hz. moving picture

 

10

camera. This technique provided valuable information about weight
transference and pressure distribution, however, more quantitative
measures were necessary for clinical applications.

The development of force platforms provided the necessary
technology and accuracy for development of new sway parameters to
describe the interaction between the ground reaction forces and the
foot. The most popular sway parameter, termed the center of pressure
(COP), was defined as the point of application of the resultant ground
reaction force. The COP may be defined according to two different
philosophies: one with a vertical ground reaction torque and the other
with the torque parallel to the resultant force [10, 108, 109, 110]. The
more preferred method is the one with a vertical torque which is more
conceivably possible. Although the parallel resultant force and torque
method is mathematically correct, it is difficult to accept an analysis
technique which says a person is creating an inconceivable torque by
applying forces out of the plane of the force platform.

Research has shown that the COP estimates the movements of
the CG which must remain above the support base to prevent falling
[100, 111, 118]. Thus, when the COP is used, the entire activity of the
postural control system is studied by observing how well the subject can
maintain the COP within the foot support base. The COP is the most
commonly used measurement of postural steadiness today with various
parameters classified into two categories, time or frequency domain.

Time-Domain Measurements - The majority of COP
measurements used in postural evaluations today fall under this
category. Most commonly studied is the time trace of the COP.

However, many different variations are also used. Goldie, Bach and

 

ll

Evans [3 1] tabulated the force platform measures used to evaluate
steadiness from 1972 to 1989. Among the many variations of
evaluating the COP are: the mean COP position [37 , 72, 81], average
displacement from the mean COP [31, 56, 81, 90, 97, 98, 118, 134], RMS
distance from the mean COP [97 , 98], the mean velocity of the COP [63,
64, 97 , 98, 134], the total excursion (or distance traveled) of the COP
[13, 27, 31, 72, 81, 90, 98, 103, 104], the peak-to-peak range [98], the
range of the COP (the maximum distance between any two points on
the path) [38, 97 , 104], and fractal dimension [97, 98]. Fractal
dimension relates the number of points on the COP path with planar
diameter and the total excursions of the COP. The displacement from
the mean COP is sometimes expressed in polar coordinates as an
average radial displacement [62, 81]. Soutas-Little, et al [109]
investigated further parameters of postural steadiness and preferred
the use of COP speed and ground reaction torque due to their
sensitivity and easy comparison between conditions and subjects.

In addition to these, some area measures are also used [98]. Area
of the COP path can be calculated as an enclosed area [98],
circumscribed area, area based on mean distance [54, 63, 64] and 95%
confidence ellipse area [37 , 97]. In addition, some researchers have
used enclosed area as a percentage of base-of-support area [3, 38, 40].
This parameter normalizes the data allowing comparison between
conditions with different base-of-support areas and between different
subjects.

Hasan, Robin and Shiavi [37] carried this idea even further by
having subjects deliberately sway from the ankle a maximum amount
in all directions, without stepping or falling, to obtain the individual's

 

12

maximum COP which he calls the "functional base of support". This
area is somewhat smaller than the base of support (defined by the area
beneath and between the feet) because the intrinsic foot muscles
prevent full body weight bearing by the toes or the back of the heel.
The functional base of support was then used to normalize, instead of
enclosed area of the feet. Riach and Starkes also measured a patient's
maximum sway while maintaining postural stability in the NP and
MIL directions which they termed "stability limits" [137].

Bagchee, and Bhattacharya [3] devised a method of
superimposing a subjects foot prints and GOP excursions to evaluate
one's risk of falls. This method was also used by Riach and Starkes
[137] Since the COP must remain within the stability boundary, the
area outlined by the feet, those whose COP trace was near the edge of
the boundary were at a greater risk of fall and may have decreased
postural stability. The results were presented as a possible means of
identifying decreased postural stability due to chemical exposure and
neurological diseases. I

Posturography is the evaluation of sway during upright stance.
In posturography, two complementary recording methods are often
used. The first, termed a stabilogram (STG), consists of the time series
of the center of pressure movements in the NP and WL directions.
While the second method is termed a statokinesigram (SKG), or "spot
stabilogram", and is the total excursion of a subject during a time
interval [14, 16, 23, 36, 40, 51, 52, 54, 62, 64, 113, 115]. Terekhov [117]
analyzed stabilograms by measuring duration of one oscillation, mean
amplitude of oscillation and maximum amplitude of oscillation.
Kapteyn and deWit [52] and Kapteyn [54] used SKG results such as

13

area and placement of the excursion within the base of support along
with STG frequency analysis in posturography evaluations.

J can [48] conducted an experiment to evaluate the sensitivity of
the COP measurements during quiet stance and found that the COP
displacements were affected by both respiration and eye condition.

The eyes closed to eyes open ratio is often used as in the case of
the Romberg Quotient, an index assigned according to how well a
patient stands with feet together and eyes closed as compared with eyes
open [73, 116]. This concept has been applied to the total COP
excursion [114] or the mean amplitude of oscillation [117]. Njiokikjien
and van Parys [90] used many of the above COP parameters and
performed a comparison with the Romberg Quotient. Results showed
that the Romberg Quotient is an easily calculated and reliable
parameter to identify proprioception impairments.

Much disagreement has occurred over the length of test duration.
Sway test duration in the literature range from a few seconds to a few
minutes. However, the typical test duration is within 20-80 seconds.
Woolley, et al [134] investigated several COP measures and how they
varied over 6 test durations ranging from 10-60 seconds. The data
indicated no significant change in the COP parameters used over the
different durations. Therefore a 10 second test would give the same
results as a 60 second test reducing the possibility of fatigue to the
subject. Some researchers have used only central portions of a test to
eliminate edge effects and instability as the subject steps onto the plate
and during the early portion of the trial [7 6, 113]. Others have used the
entire files for analysis. Hasan, Lichtenstein and Shiavi [36] noticed

that a loss of balance by a subject caused 0-3% increase in the area of

14

the COP during double stance. During single stance, area increased 16-
38% and velocity measures by up to 10% with loss of balance.
Therefore, he developed a method to locate and separate out a loss of
balance from the COP plot to be analyzed. A loss of balance was
defined as a touchdown of the non-supporting leg, during one-legged
stance, in an attempt to regain balance. They also quantified the
effects of loss of balance in different conditions. In a review of the 5th
International Symposium on Posturography in Amsterdam (1979),
Kapteyn, et al [5 1] expressed the need to standardize platform
stabilometry parameters such as test duration, stance, and other
methodology aspects to allow comparison between subjects and
researchers.

Frequency-Domain Measures - The other type of COP
measures, which are very useful but more difficult to read, fall into the
frequency-domain category. In one type, a Fast Fourier Transform
(FFT) is applied to the COP displacement measurements obtained from
the force platform. This provides the frequency spectrum and reveals
the total amount of energy in the NP and the ML spectra [29, 35, 107].
From the frequency spectrum of the COP movements, some researchers
have analyzed peak frequency [35, 7 3], mean frequency [98], and
frequency at which the magnitude decreases 3 decibels (dB) from the
maximum frequency [35], while others have conducted qualitative
characterization of the spectrum [7 3], such as identification of the wave
forms present in force measurements. The following frequency domain
measurements were also calculated for the frequency range of 0.147 -
10.010 Hz [97, 98]: total power, 50% and 95% power frequency [97, 98],

centroidal frequency, and frequency dispersion. Mean, standard

15

deviation, and coefficient of variation (CV) have all been used as
standard calculations for frequency domain parameters. Soames, Atha
and Harding [107] measured the NP and the NHL components of sway
and applied FFT to 4 consecutive minutes of feet together stance,
analyzing each minute separately to note changes in the distribution of
energy over time.

For clinical evaluations of postural imbalance, determination of
the efficiency of each of the three sensory control loops over a range of
frequencies may be useful. This may be done by comparing the power
spectra of sway in patients with isolated lesions of the visual, the
vestibular, or the somatosensory proprioceptive systems with the power
spectra of normals [16].

Results by Dichgans, et al [16] showed that in atactic patients,
the postural instability frequently exhibits an amplitude peak at about
0.6 Hz in the Fourier power spectrum of the COP. Patients with a
cerebellar disease exhibit a peak at 2.5-3 Hz. Thus, the frequency
analysis of the COP excursions when compared with normative data
can be useful in diagnosis and treatment of patients.

Soutas-Little, et a1.[110] took a different approach by conducting
an FFT of the torque data. A significant difference was found between
the power frequency spectrum of the norm and a Traumatic Brain
Injured patient. The power of the norm decayed between 4-5 Hz, while
the patient's power was beyond that of the norm, with additional peaks
in the 5-10 Hz frequency range.

3. Displacement of the body's Center of Gravity - In addition
to the displacement of the COP, center of gravity (CG) displacement has

16

also been studied [123]. A common source of error in evaluation of force
platform data is confusion of the COP with the CG. Whereas this
confusion might not be serious in a purely static case, it is crucial
during accelerated motion [50]. Winter [131] defined the difference
between the COP and CG and used an inverted pendulum model to
show that "the range of the COP must be somewhat greater than that
of the CG". Results of experiments by several researchers have
indicated that COP displacement is greater in magnitude and
frequency than that of the CG, and that the stabilogram gives an
exaggerated impression of the movements of the center of gravity [100,
11 1, 118].

Displacements of body segments have also been measured and
used in conjunction with CG displacements as an indicator of postural
sway [93]. Black, et a1 [7] measured A/P sway of the body center of
mass by attaching a potentiometer to the subjects hips with a belt and a
system of light rods. In some patients, a second potentiometer was
attached to the subject's back at shoulder height to measure the
contributions of hip as well as ankle joint motion to the NP sway.

Tokita, et al [124] measured sway of the head and the CG to
compare normals with various categories of patients. The patients, who
had different types of impaired sensory systems due to injury or
disease, showed definite differences in frequency and direction of sway.
Murray, Seireg and Scholz [80] measured vertical supportive forces
during squatting. He differentiated between changes in the applied
force and changes in the center of gravity of the body. He also
investigated the difference between the excursions of the line of gravity
and the action line of the vertical supportive force. Hasan, Robin and

l7

Shiavi [37] used fifteen targets to collect kinematic data and force
platform data to develop a relationship between COP and the CG data.

4. Motion of Body Segments and Joints - Some researchers
felt that kinematic data was essential to evaluate postural steadiness.
Angular displacement, velocity, and acceleration of various body
segments are all parameters that have been considered. Various
devices such as displacement transducers and accelerometers can be
used to measure these parameters.

Sway is often characterized by motion or displacement of body
segments. Displacement transducers have been attached to the pelvis
and hip [5] or to the sacrum and greater trochanter [23, 28] to measure
postural movements. Body segment positions in the NP plane were
measured with an opto-electrical movement analyzer and LED targets
[83]. Mauritz, Dichgans and Hufschmidta [7 3] used an electronic
goniometer fastened to a belt around the subject's waist or head.
Yoshizawa, et al [135, 136] measured head position on the horizontal
plane in an on-line real-time fashion by using an ultrasonic distance
sensor system. Lord, Clark and Webster [66] used a device consisting of
a rod attached at the subject's waist with a pen at the end which
recorded movements on graph paper. Another method was developed
by Hirashawa [40] to track movement of the gravitational force on
human subjects. He named this electro-gravitograph (EGG) and
showed quantifiable differences between normal subjects and patients
with chronic organophosphate intoxication. Others [30, 83] have used a
sensing potentiometer to detect body oscillations due to force plate
perturbations such as lower leg rotations [124].

18

In addition to measurement of body displacements, the
calculation of velocity (or speed) and acceleration of the body segments
has also provided useful information. Nashner, Schupert and Horak
[83] measured velocity of NP head rotation with an angular rate sensor
attached to a helmet. Fernie and Holliday [28] used the motion data,
he obtained with transducers, to calculate the mean speed of sway (the
length of the locus of sway in unit of time) and the range of movement
in the saggital and coronal planes. Accelerometers attached to the
subject have been used to measure A/P accelerations of the head, trunk,
and waist [118, 124]. Woloszko and J aeger [132] measured both body

angle and acceleration during quiet stance.

5. EMG Activity in Various Muscle Groups - EMG muscle
responses are often used in postural evaluations. Many experiments
have been conducted to present evidence that during stance,
functionally related postural muscles in the legs are activated according
to fixed patterns [2, 86]. Others revealed specific movement strategies
used in response to perturbations [16, 19, 20, 22, 42, 44, 56, 77, 78, 84,
92, 132]. The organizing principle of mechanical body motion has been
extensively studied from the perspectives of biomechanical, neurological
sciences, and control systems analysis. Coordination patterns may be
found in EMG recordings and the organization of such EMG activities
of leg muscles during rapid postural adjustments have been studied by
Nashner [83] and others [85]. These results supported hypotheses of

hierarchically organized groups of muscles.

19

2.3 Postural Stability

As discussed earlier, postural steadiness was a measurement of
static equilibrium during quiet standing. With respect to balance,
equilibrium is defined as a state of posture where there is zero
resultant torque or force on the body. Thus, the body is at rest or in
uniform motion [50]. However, balance may also be evaluated in terms
of postural stability which is the body's response to external
perturbations of the postural control system [50]. Postural stability can
be either static or dynamic. Static stability is when the body's
equilibrium is restored by a force or torque. Dynamic stability means
that equilibrium tends to be restored over time. There exists a
damping of the velocities such that oscillations about the equilibrium
are damped [50]. One's degree of stability is a measure of the body's
ability to counteract disturbances to the postural control system such as
force platform movements or other negative feedback.

Stability requires that small perturbations give rise only to a
small deviation away from equilibrium [50]. According to Black, et a1
[7], two main components are required for the maintenance of
equilibrium: (1) accurate sensory and perceptual information about the
body's position, orientation, and movements with respect to external
references, and (2) accurate motor system command to correct or
maintain the body's position with respect to the earth's vertical, placing
the body center of mass over the support base provided by the feet.

Combining head and body movements with muscle response to
sway, Nashner, Shupert and Horak [83] investigated head-trunk
movement coordination in standing posture. Nashner, Shupert and
Horak [89] and Black, et a1 [7] observed that when exposed to saggital

20

perturbations, a subject may regain equilibrium by two different
strategies. The first of these is the "ankle strategy" which, in response
to slow translations of the support surface, begins with muscle activity
in ankle muscles and then ascends the body to rotate the body around
the ankle joint. The second strategy, called "hip strategy", is a response
to platform rotations or standing on a narrow beam. This strategy is
more complex and involves muscle activity of the body and neck causing
hip translations and stable head position [96]. These strategies predict
that primary motion occurs at the ankle or hip and consider the knee
motionless, ignoring movements of the upper body. However,
examination of kinematic data of the responses to force platform
perturbations show the strategies to be more complex, involving both
knee and upper body motion, multisegmental interactions and inertial
influences on the system [1 10].

Postural steadiness, which quantifies an output of the postural
control system, fails to characterize the inputs which cause the sway to
occur. Thus, no predictions of response to various inputs can be made.
However, with postural stability, the known input allows an
input/output model of the postural control system to be identified.

Input perturbations can include surface displacements, visual
surrounding movements, or the application of other postural
perturbations. In most experiments, muscle response, angular
displacement of body segments, and COP displacements were measured
before, during, and after the perturbations were applied. This was done
in hope of defining more clearly the functional role of each sensory

input.

21

A wide variety of different perturbations have been used by
various investigators. Maki [70] summarized the perturbation
parameters used by investigators from 1957-1984. The objective is to
eliminate only one form of sensory input at a time and compare balance
with and with out this input.

Vestibular disturbances - Vestibular feedback is essential for
orienting the head in space and with respect to gravity [50]. To
investigate vestibular contributions to postural stability, static
vestibular input is modified by tilting the head forward, backward, or to
either side prior to the force platform perturbations. DeWit [14] altered
vestibular input by having the subjects shake their head for 10 seconds
with eyes closed to stimulate the labyrinth. Still another type of
vestibular perturbation was used by Tokita, et al [123] who measured
changes in soleus muscle EMG and sway of the CG when galvanic
stimulation was applied to the labyrinth of one ear.

Proprioceptive disturbances - Postural perturbations can be
applied easily by moving a platform on which a subject stands. This» is
the most commonly used form of de stabilizing input. The force
platform can be translated horizontally in the NP [7 7, 98], or in the
MIL directions [7 7]. It may also be rotated about an axis coinciding
with the ankle joint axis of rotation [2, 4, 7, 7 7]. Force plate
perturbations are driven by several wave forms. Some are continuous
sinusoidal signals, while others are random or pseudo random. Still
other force platforms are driven by ramped and pulse signals [30, 88].
A combined input of horizontal translation and ankle rotation has been
used by Nashner [87 , 88] to evaluate changes in proprioceptive input.
This two degree of freedom force platform was translated horizontally

22

then rotated the amount of degrees needed to keep the ankle in a fixed
neutral standing position [21, 88]. This eliminated the proprioceptive
input from the ankle joint stretch receptors. Ischemic blocking of leg
afferents with pneumatic cuffs around each thigh have also been used
to decrease proprioceptive input [1, 7 4]. Nashner, Woollacott and Tuma
[84] combined the fixed-ankle angle with horizontal translation,
reciprocal vertical displacement, and synchronous vertical displacement
inputs.

Most studies in postural control using support rotation and
translation or body free fall induce ankle angular velocities which aren't
encountered in daily activities. Therefore, Woloszko and J aeger [132]
used perturbation generating step transients to alter the body center of
mass without generating high angular velocities at the ankle. He
restrained the body with the use of an orthosis which allowed A/P ankle
movements only, thus creating a single-link system. Woloszko also
dropped weights from the orthosis at random times and measured the
muscular response.

Another type of proprioceptive disturbance is foot positioning and
spacing. Stribley, et al [113] reported that posture, especially in the
M/L direction, was more stable with a large distance between the feet.
Various stances, such as tandem (heel to toe), feet apart, feet together,
and one-legged stance have been used. Goldie, Evans and Bach [32]
developed a reliable and feasible method for testing steadiness in one-
legged stance where the non-affected leg was used as a control. This
test has potential use in evaluations of unilateral injuries or disorders.

Visual disturbances - Postural response to visual, rather than
force platform inputs has also been investigated. Visual disturbances

23

have been applied in the form of closing of the eyes, displaying vertical
or horizontal black/white alternating stripes [104], moving rooms and
walls, moving lines or patterns on a projection screen, false vertical
domes, or a moving visual surround [7]. Also used in studies was the
varying of surrounding conditions such as normal lighting, reduced
lighting, normal visual acuity, and reduced visual acuity. This provides
information on how different environments affect COP excursions.
Data support the possibility that having adequate visual stimuli could
be an heuristic approach to optimize the role of vision in reducing risk
of falling for the elderly. It stresses the need for properly corrected
vision and high contrast environments. Bles and deWit [8] used a room
which tilted +/- 10° in the ML direction with an enclosed fixed position
force platform to apply visual perturbations. Another moving room
which moved horizontally in the NP direction has been used by Lee and
Lishman [60]. Visual stimulation may be induced by simulating an
optic flow field with moving walls and moving tunnels on a projection
screen [128]. Taguchi [115] used moving stripes displayed on a 270°
projection screen which encompassed the stationary force platform.
This optokinetic stimulation was applied at various angular frequencies
and postural response in terms of NP and WL sway was recorded.
Another type of visual input was the "roll vection stimulus" used
by Dichgans, et al [16]. This was a visual field which rotated in front of
the subject and consisted of a half spherical dome suspended above the
force platform. The inner surface of the dome was covered by randomly
distributed colored circular patches of different sizes. The dome was
rotated about its axis to induce postural sway. DeWit [15] used a
vertical light bar in a dark room placed in front of the subject as de

24

stabilizing input. This light bar was rotated +/- 10 degrees to induce
sway.

Other types of input create distorted visual feed-back.
Yoshizawa, et al [135] used visual feedback where the subject wore the
3D—VD and stood in front of a screen on which a vertical line is drawn.
The images of the line, taken by two CCD cameras on the subject's
head, are artificially altered by the personal computer and transferred
to the 3D-VD. Thus, the subject can watch altered stereoscopic image
depending on head motion. This device is called the "visual conflict
dome" and has been used by Lehmann, et a1 [62] and Ingersoll and
Armstrong [45]. This dome gives a visual feed-back of vertical lines
that changes with the movements of the head. Thus a false sense of
vertical is created for the subject. Barin [4] used a visual scene which
surrounded the subject on the force platform. The scene rotated
according to the subject's sway in order to provide false visual input.

Hlavacka and Litvinenkova [41, 65] have investigated the visual
feed-back gain influence on postural control by use of a force platform
and monitor. The subject's COP trajectories were displayed on a screen
in front of the subject. This allowed the subject to correct his/her
balance accordingly and visualize the change. Results showed that in
visual feed-back conditions, the postural control, gauged by stabilogram
area and velocity, was more stable. The postural movements were
quicker (i.e., increased average velocity), and the stabilogram area was
smaller.

Other disturbances - In addition to vestibular, proprioceptive,
and visual perturbations, other postural disturbances were

investigated. Chandler, Duncan and Studenski [11] designed a wall

25

mounted pulley system from which a weight attached to a belt around
the subjects waist is dropped along the pulley track providing a de
stabilizing force posteriorly. This method of disturbance was also used
by Luchies, et a1 [67] to investigate age effects on step response to
impending falls. Also used as de stabilizing inputs were movements of
the trunk and of upper extremities such as reaching forward [24].
Mechanical vibrations have been applied to the leg muscles as a
form of postural perturbation [25, 34]. Also, Mauritz, Schmitt and
Dichgans [7 5] applied electrical stimuli to the tibial nerves to induce
postural sway and study the body's response. Martin, Fletcher and
Park [7 2] investigated effects of hand vibration on postural control and
stability. He measured COP excursion while the subject held a
vibrating handle (sinusoidal 150 Hz. vibrations). In this experiment
alterations of hand proprioceptive cues caused by hand vibrations
resulted in a deterioration of balance stability and a change in postural
behavior. This information is important for the design of industrial

workplaces where hand-held vibrating tools are extensively used.

2.4 Postural Control System Models and Dynamic Equations

Many researchers have taken the control systems approach to
understanding the complex process of postural control. Two elements
work together to make up the postural control system: neural elements
(reflexive and voluntary) and mechanical elements (bones, muscles,
ligaments, and tendons). It is a dynamic system (i.e., concerned with
motions as it depends on forces and velocities as well as positions) [50].
A control system framework must explicitly describe system outputs,

inputs, and input-output relationships. This framework can be used to

26

analyze how the system operates at a given time or how it adapts to
changed conditions due to development, disease, trauma, and recovery
[61].

Many researchers have developed postural control systems [47 ,
49, 68, 69, 88, 95]. Johansson and Magnusson [50] presented a model of
sensory feedback in control of posture. However, most models were
used to predict ankle torque or body sway in the form of COP
displacements in response to external disturbances.

In 1984, Shimba and Takeshi [102] derived an equation from the
principles of dynamics for a system of particles forming a relationship
between force plate data, the center of gravity on the platform, and the
moment of momentum of the body about its center of gravity. This
equation allows the estimation of the center of gravity path or the time
rate of change of the angular momentum of the body. With the use of
equilibrium equations, Snijders and Verduin [106] developed a force
platform device to measure position of mass CG of erect standing
subjects or during lying posture. Barin [4] used measurement of the
COP and a mathematical model to estimate peak-to-peak ankle sway
angle which was then normalized by 12.50 (a theoretical maximum).

Maki, Holliday and Fernie [69] developed a posture control model
which defines relative stability by the degree to which a postural
perturbation causes the COP on the feet to approach the limits of the
base-of-support. He used a type of external perturbation as input,
resulting in a COP displacement output. Small amplitudes, random
and pseudo random translation accelerations in the NP direction were
used to define a linear transfer function. Also, three system

identification methodologies: ordinary least squares, cross-spectral

27

analysis, and maximum likelihood were used. Then the saturation
amplitude, which is the transient perturbation pulse amplitude at
which the resulting COP displacement would equal the length of the
base-of-support, was predicted.

Body movements were often described by segmented rigid-link
mechanics. These models are formulated using the methodology of
classical mechanics. Many different approaches have been used. The
most common of these is the inverted pendulum. Single or multi-link
biomechanical models have been developed which quantify the
relationship between body segment angles and joint torques. However,
a problem exists with the modeling of damping of perturbations in
posture [50].

Gurfinkel [33] in 1973 developed a biomechanical model to
quantify the relationship between body segment angles and joint
torques. The human body was simplified and modeled as a one-link
inverted pendulum with the axis of rotation at the ankle. The model
defined difference between the COP and the vertical projection of the
CG in terms of the following parameters: sway angles, the mass of the
body, and dimension of the body. Concluded from the test was that the
upper limit for frequencies which are reflected in the stabilogram with
an error less than 10% is 0.2 Hz.

In 197 2, Nashner [87] developed a model to describe the control of
body sway with only vestibular sensory input. Nashner used the two
degree of freedom force platform he created which rotates with body
sway to eliminate proprioceptive input thus creating a rigid body that
rotates about the ankle joint [88]. The assumed model was allowed
movement in the NP direction only. With this model, he was able to

28

estimate sway angle due to known perturbations and the relative
influence of semicircular canals and utricular otoliths, which act as
linear and angular accelerometers.

Smith [105] developed an ankle torque equation for postural sway
in the NP direction using a single-link inverted pendulum in 1957 .
Kadteyn [53] later developed a model for the M postural sway. This
model used ankle torque derived from stabilometer measurements to
predict body sway. A simplified differential equation was formulated
and tested in the same way as the equation for A/P sway given by
Smith [105]. Both the static and dynamic components of the stability
were estimated.

Peeters, Caberg and M01 [95] in 1985 also used the single-link
inverted pendulum model. They calculated power gain spectrum, phase
angle, and coherence for the frequency relation between ankle joint
torque and sway angle. The values derived from the model were
compared with experimentally measured ankle torques and body
movements. Differences between simulated and measured spectra were
mainly noted for high frequencies (f > 1 Hz.), and could be attributed to
decreasing signal to noise ratio with increasing frequency, sway angle,
and the degree of biological coordination between parts of the body.

Modeling of the body by a single-link inverted pendulum uses the
force platform for measuring the reactive forces and treats the swaying
body as a structure with one equivalent support. However, this type of
modeling has been criticized by Valk-Fai [127] and Lestinne (1977).
The two reasons for the criticism were the existence of relative motion
between adjacent body segments which contribute to body correction,
and the failure of the inverted pendulum model to predict corrections

29

between sway magnitude and physique variables such as body height,
weight, and due to lack of symmetry of the actual body motion about
the vertical axis [7 6].

Winter [130] modeled frontal plane posture and balance of the
total body and head, arms, and trunk during walking with two inverted
pendulum systems in 1990. The first is the total body pivoting about
the subtalar and ankle joints with the total body CG medial to the foot
COP. Thus, the COP accelerates toward the midline during single
stance and is shifted to the weight accepting foot during double stance.
The second inverted pendulum requiring balance was the head, arms
and trunk which pivoted about the support limb hip. Dynamic
equilibrium equations were written for both pendulum models.
Although this information deals with balance during gait as do many
other studies [58, 129], the results will still be useful in the overall
understanding of postural control system.

Valk-Fai [127] developed a four-link inverted pendulum model to
determine the difference between the measured COP displacement from
the ground reaction forces and the calculated CG displacements.

Linear potentiometers were used to measure horizontal movement of
four points: the knee, femur, shoulders and the head. Angular
movements around the ankle joint, the knee, the hip and the neck were
then calculated. Results confirmed that COP displacements are greater
in magnitude and frequency than displacements of the CG. Also
concluded was that larger angular activity occurred at the ankle and
hip, rather than at the knee or neck.

Koozekanani, et al [57] developed a four-mass inverted pendulum

model which indirectly provided a measure of the movement of the COP

30

of the ground reaction forces. Sway angles were calculated with motion
data collected from television cameras. Equations for the COP and
CG's were developed and the results compared with COP displacements
measured with a force platform. The effects of j oint torques produced
by muscular contractions, as well as torques produced by external
perturbations were also included. Luchies, et a1 [67] used a nine-link
biomechanical model to calculate net reaction joint torques from
kinematic and kinetic data.

Hasan, Robin and Shiavi [37] aimed at development of a
mathematical model which would use measured COP excursions to
estimate movements of the COG and implement novel, clinically
relevant measures of postural stability. An eleven-rigid-segment model
was used and developed with kinematic data. Barin [4] created a
mathematical model of an N -link inverted pendulum atop a triangular
foot. The segments were considered rigid bodies with concentrated
mass. The study was conducted in order to extend the analysis of error
in force platform measurements of postural sway to dynamic testing

conditions.

2.5 Clinical Applications

Much research and experimentation has been done to investigate
the mechanisms which make up the postural control system. This
increase in understanding is very useful in the diagnosis and treatment
of patients. In the area of sports medicine, it is important to correctly
identify severity of injuries when deciding if an athlete is able to

resume competition. In addition, the use of postural sway to quantify

31

balance may be an important tool that can be used in comparing drug
effects in young and elderly [37].

Postural stability evaluations are useful with brain-inj ured
patients in determining the area of deficiency and identifying the type
of rehabilitation most beneficial for the specific patient. It could also be
used to monitor progress over periods of time and rehabilitation.
Mizrahi, et al [7 6] investigated postural stability in post-cerebral
vascular accident (CVA) hemiplegic patients and compared these values
to normative data. Sway activity was found to be significantly higher
in hemiplegics than in normal subjects. Ingersoll and Armstrong [45]
evaluated four levels of closed-head-inj ured patients. The levels were
determined by the presence and length of a loss of consciousness upon
injury. Results showed that closed-head-injured patients, especially
those who experienced long periods of unconsciousness, displayed
postural instability. Results of these studies along with that of
Lehman, et a1 [62], who looked at sway as an indicator of stability in
post-traumatic brain injured (TBI) patients, suggest that the
contributing factors of instability could be identified and an appropriate
rehabilitation program could be developed.

Postural steadiness evaluations have been conducted to evaluate
changes due to neurological disease [17 , 52, 73, 75, 92, 93]. Dichgans,
et a1 [16] conducted experiments to analyze the stabilizing and de-
stabilizing effect of vision in normals and atactic patients. Paulus,
Straube and Brandt [94] conducted a study of changes in balance
parameters when closing the eyes in subjects with severe deficits of the
vestibular and somatosensory systems. In these subjects, a loss of

balance occurred within one second after closing the eyes. Comparisons

32

have been done between normals and patients with vestibular lesions
[16, 116], cerebellar lesions [16, 17, 73, 116], tabes dorsalis [16], spinal
lesions [116], proprioceptive hyperactivity [116], and multiple sclerosis
[13, 92]. Results showed that in atactic patients, the postural
instability frequently exhibits an amplitude peak at about 0.6 Hz in the
Fourier power spectrum. Patients with a cerebellar disease exhibit a
peak at 2.5-3 Hz. In addition, patterns of postural movements in
patients with vestibular pathologies have shown to be different from
those of subjects with normally functioning vestibular systems [2, 7].

Murray, Seireg and Sepic [81] investigated in 1975 for further
sensitive parameters to measure postural steadiness. Murray's results
showed two characteristics by which normal upright balance can be
distinguished from that of patients with neuromuscular or skeletal
disability. The first of these was that the enclosed area of the COP
positions during sustained weight-shifting was larger for normal men.
This indicated a larger area of stability, or security, in normals. The
second mark of normal stance was the manner in which upright
stability was controlled. The shifts of force and movement for normal
subjects, as compared with patients with postural instability, were
balanced such that the center of pressure remained remarkably close to
its mean position [81].

Simoneau, Cavanagh and Ulbrecht [103] calculated the
correlation between different clinical evaluations and total COP
displacement. Somatosensory evaluations were found to be most
closely associated with postural stability measures in patients with
diabetic neuropathy. Since distal sensory neuropathy resulting from
diabetes mellitus significantly reduces the ability to maintain a stable

33

stance position, an evaluation technique closely associated with COP
measurement would be useful in conjunction with regression equations
in predicting postural stability in patients without making a direct
posture measurements.

Moffroid, et al [7 7] proposed the use of postural stability
evaluation techniques on patients with lower back pain. Surface EMG
was used to measure muscle latency in response to force platform
perturbations. Moffroid felt that patients with lower back pain may
have delayed postural response due to deconditioning, slowed nerve
conduction velocity and/or aberrant muscle recruitment patterns
related to postural changes or dysfunctional movement habits.

Postural stability testing is also important for the elderly [98].
There is a need to develop a reliable and appropriate balance evaluation
protocol which could be used to identify individuals at risk before they
experience a debilitating fall, thereby allowing preventative measures
to be taken. Some risk factor evaluations used only questionnaires and
clinical evaluations [89, 120, 121] while others have added the use of
biomechanical parameters [3, 91]. Bugchee and Bhattacharya [3] used
COP excursions near the stability boundary as a sign of decreased
stability and increased risk of falls. 'l‘inetti, Williams and Mayewski
developed nine risk factors used in evaluation of balance based on the
ability to complete various tasks, and identified chronic characteristics
associated with falling among the elderly [121].

Postural steadiness evaluations have been conducted to evaluate
changes due to age [23, 27 , 38, 46, 63, 64, 66, 71, 112, 133]. Some have
focused specifically on women's postural stability changes with age [38,
63, 64], while others have studied men [27 J. Panzer, Zeffiro and

34

Hallett [93] used kinematic and force platform data to identify
characteristics of Parkinson's Disease patients separable from aging
effects. Tests have been developed to try to classify an elderly patient
as a "faller" or "non-faller" [5]. Others have evaluated changes in
frequency of falls due to illness and age [122], or by a compilation of
various risk factors [9].

Panzer-Decius and McFarland [92] conducted a study to
determine which postural stability measurement best correlated to
clinical evaluations of multiple sclerosis (MS) patients. An example is
the correlation between the number of clinical exacerbations and bursts
of enhancing lesions detected by Magnetic Resonance Imaging (MRI)
and postural instability. It was determined that postural response
latency was a sensitive indicator of motor changes in MS,
demonstrating disease activity that is not clinically evident. Measures
of postural response appear to be a useful means of monitoring the

course of MS and may be useful as a clinical outcome measure.

CHAPTER III
EXPERIMENTAL METHODS

The purpose of this thesis was to develop a feasible and reliable
testing protocol which offered useful information in the assessment of
balance patients. To insure cost and time effectiveness while
preventing patient fatigue, a protocol using only force platform data
was developed which could be completed in approximately thirty
minutes. The testing protocol parallels that used in previous balance
studies by Lehmann, et al. [200].

3.1 Equipment

All data were collected at the Biomechanics Evaluation
Laboratory (BEL) at the St. Lawrence Hospital Health Sciences
Pavilion in East Lansing, Michigan. The BEL is equipped with three
means of data collection: kinetic, kinematic, and electromyographical
(EMG). .

Kinetic data can be collected on an AMTI Biomechanics Force
Platform, model OR6-6-1 which is mounted such that the surface of the
platform is flush with the floor. The force platform features graphite-
composite construction, has a capacity of 1000 pounds, and a resonant
frequency of 500 Hz. The platform uses strain gages to measure the 3
orthogonal ground reaction forces, Fx, Fy, and Fz, and the three
components of the moment about the instrument center for a total of six
outputs. Strain signals are amplified and sampled at 100 or 1000 Hz.
from an A/D Board and converted to forces. The force platform

coordinate system and dimensions are as shown in Figure 1.

35

36

 

Figure 1. Force platform ccoordinate system and dimensions.

Kinematic data, is obtainable at the BEL through the use of a
Motion Analysis System. Four 60 Hz video cameras are used to collect
motion data by viewing retroreflective skin targets placed upon the
subject's bony landmarks. The four cameras are synchronized by the
VP320 video processor and targets are digitized in pixel space.
Expertvision (ev3d) software then uses Direct Linear Transformation
algorithms to obtain three-dimensional data for each target in the
laboratory coordinate system.

The third and final type of data available is EMG, collected by
real telemetry on a Transkinetics system with 16 channel capabilities,
using Protrace surface silver/silver chloride electrodes on various
muscle groups. Files from all three types of data are then stored on a
Sun 4/26OC work station for analysis. The advantages of having

multiple data forms available are great and allow the researcher to

37

obtain a complete understanding of the functioning of different
mechanisms within the body. However, the use of all three types of
data is very labor intensive, too costly, and not feasible for desired
clinical balance tests. Therefore, only force platform data were used for
this methodology. A data collection program, "bel4.11", was used to
collect and view the data. Bel4.11 also allows the input of the trial
description and all header information as well as setting parameters

such as trial duration and trigger source.

3.2 Subjects

For this study, human subjects were recruited from Michigan
State University and St. Lawrence Hospital under the UCRIHS
approval [RB #89-559. Nineteen normative subjects were evaluated in
order to obtain base line data. The norm subjects consisted of 9 men
and 10 women from the ages 22 to 37, averaging 25.75 years old, who
had no connection with the BEL and did not know what parameters
were being measured. The norm subjects were given a questionnaire to
fill out and were screened for any past neurological problems or losses
of consciousness. See Appendix A. The patients evaluated in the study
were referred to the BEL by physicians for balance and stability
evaluations. Referred patients came with two different diagnoses,

either Traumatic Brain Injured (TBI) or exposure to toxic substances.

3.3 Experimental Preparation
Before any testing was done, all subjects were required to read
and sign an informed consent form for Michigan State University and

St. Lawrence Hospital. A balance and stability questionnaire was given

38

to the patients to obtain background information and details about
their present condition (see Appendix A). Each subject was then
weighed. A brief explanation of the testing procedure was given to the
subject and the specific stances to be used in the test were
demonstrated. The subject was also asked which foot he/she would use
when kicking a ball. The one stated was recorded as the dominant foot

and was placed in front of the other foot during tandem stance.

3.4 Testing Procedure

The subject information along with the first trial description was
entered into the computer. The condition was announced and the
subject stepped onto the plate. A spotter was nearby to insure proper
footing and provide assistance if needed. As soon as the subject looked
comfortable, the data collection was triggered manually. Data were
collected for 20 seconds at a sampling frequency of 100 Hz. The subject
was instructed to continue the test for the entire 20 seconds, even if a
loss of balance occurred such as shifting of the feet or stepping off the
plate. After the 20 seconds, the subject was asked to step off the plate,
and the instrument was re-zeroed. The data for the entire 20 seconds
was kept and analyzed no matter how much shifting of the feet
occurred. All data corresponding to loss of balance was included in
order to obtain a complete description of the subject's balance without
eliminating valuable information. The test continued by announcing
the next condition to the subject according to the following list:

1. feet apart with eyes open

2. feet apart with eyes closed
3. feet together with eyes open

39

4. feet together with eyes closed

5. feet in tandem with eyes open (dominant foot in front)
6. feet in tandem with eyes closed

7. right-footed stance with eyes open

8. left-footed stance with eyes open.

Prior to the beginning of the test, the force platform was prepared with
two narrow strips of masking tape as shown in Figure 2. The tape was
placed 18 cm. apart, measured f'rom each outside edge of the tape, to
insure consistent foot placement in the feet apart conditions between
trials and individuals. This was done in order to keep the base of
support between patients consistent within the variance in foot size.
When using parameters such as total excursion or radial displacement,
this consistency in foot placement is necessary to allow comparisons
between subjects. One goal of this thesis is to identify parameters such
as speed or torque which are unaffected by where on the plate a person
is standing. All conditions were performed in stocking feet with arms
crossed in front of the body. Having arms crossed eliminated the
different arm waving techniques used by subjects to maintain balance
and forced the body to rely on strictly hip and ankle strategies. To
allow comparison with the work done by others who evaluate the AIP
and MIL COP values separately, all conditions were performed facing
the negative y direction except for tandem stance which was performed
diagonally (see Figure 2.). This allowed the separation of
anterior/posterior and medial/lateral sway components for all
conditions except tandem. After completion of all 8 conditions, the
sequence was repeated 2 more times for a total of 3 trials per condition.

 

40

 

 

 

 

 

,yi—Q $2.
272 :9 ,

 

 

 

 

 

 

 

 

 

 

a) FAEO, FAEC d) FTEO, FTEC
i/ R:
/%.a/ /

l
_ c) TDEO, TDEC d) RLEO, LLEO

Figure 2. Foot placement protocol.

CHAPTER IV
ANALYTICAL METHODS

4.1 Calculation of the COP

As mentioned previously, the most often used measure of postural
stability is the center of pressure. There are two approaches to the
definition of the COP.

Vertical Torque Method - In the first approach, consider the
measured resultant ground reaction force it , and the moment about the
instrument center M. . These may be resolved into a single resultant
force it with a unique line of action and a vertical torque by the
following method [109, 110]:

ii = XCOPix'i’YCOPIy-diz (1)
i = Rail + Ryiy ‘1' Kris (2)
PxR+(GRT)i.=Mo (3)

where 1:, 1,, , and i. are unit vectors along the force platform coordinate
system, and d is 4.05 cm, the distance between the instrument center
and the surface of the force platform (see Figure 1, section 3.1). By
equating the it, i,, and i. components of each side in equation (3) we are
able to solve for the Xcop and Yoor positions which are the intercept of
the force system resultant with the horizontal surface of the force
platform, and the ground reaction torque.

41

42

 

me ='(M_’+R‘;d_) (4)
R.
pr=M (5)
GRT= M°’R (6)
F2

where P is the vector from the instrument center to the COP and
P.=—d. (see Figure 3.).

h)
N

 

Figure 3. Vertical torque method for calculation of the COP

Parallel Torque Method - Method two involves resolving the
force system into a wrench system where the torque T is in the same
direction as the resultant force vector [108, 110]. See Figure 4.

43

(T)In +13 x 1‘: = M. (7)

N...)

 

Figure 4. Parallel torque method for calculation of the COP
Equatingcomponents in equation (7 ) as before we obtain the following:

 

=-(M,+Rx.d)LR-M. R,

X‘“ R. - n R. (8)
_(M.-R,.d)_ft-M.&

Yw” R. M R. (9)

(T)ls= “'3 (10)

 

In balance studies, R. and R, are small compared to R. and the
two force systems are nearly equal [110]. Thus, the vertical torque
method was used for this study.

After calculation of the COP, many different methods of analysis
may be employed. These methods of analysis will involve parameters

in either the time or frequency domain.

4.2 Time Domain Analysis

One method which has been used by many researchers is the
cross plot of the X00» versus the Your components to obtain a spot
stabilogram, either displayed on a representative force platform or
centered at an origin by subtracting the mean values, 3? and V. This
may also be plotted in a polar coordinate system by the following
equations [62, 110]:

32' --’1-'-:Xcor(i) (11)
in!

l7 = l i Ycor(i') (12)
n i=1

Xcop(i)=xcop(i)-it' (13)

Ycop(i)=rcop(i)-Y (14)

 

r(i)=,fitcop(i)2 +rcopa)2 (15)

45

obtaining the radial displacement of the COP path from the mean. This
is then plotted verses the angle from the x-axis of the force platform
obtained by

so) = tan"(Ycop(i)/Xcor(i)) (16)

Radial average displacement (RAD) is often used as an overall measure

of sway. The average may be computed using equation (15) and
l " .

Radial and average speed may then be calculated using ASi, the

distance between the COP at times i and i+ 1.

 

ASi = J(Xcopi+1- Xcopi)2 +(Ycopi+1-Ycopi)2 (18)
State! = iASi (19)

i=1
v = 49533) (20)

where f is the collection frequency in Hertz. The speed v(i) will be
referred to as radial velocity from this point forward for continuity
purposes.

The ground reaction torque (GRT), which is a byproduct of the
COP calculation, also contains valuable information. The GRT may be

 

46

displayed versus a time file. This shows how a patient's GRT varied
during the entire test. However, one might wish to describe a patient's
overall torque for a specific trial with quantitative parameters. The
time series of the GRT measurement is averaged in two ways. The first
is an averaging of the raw torque signal termed the "average torque".
This value describes the direction of the overall torque. A zero would
indicate the subject had equal amounts of torque to the right and to the
left. Thus, the averaged signal is zero. A positive average torque
corresponds to the patient's twisting to the right, the floor resisting to
the left. The inverse is true for a negative average torque. The second
method of torque averaging is to rectify the signal, than average it.
This measure is termed the "active torque". This value will correspond
with the magnitude of the torque. Thus, a person doing more twisting
in order to maintain balance will have a higher active torque than
someone who does little twisting. The equations used to calculate these

torque measures are as follows:

Average Torque= l-21:GRT(i) (21)

iii

Active Torque = l i |GRT(i)| (22)
n 1::

4.3 Frequency Domain Analysis

In the frequency domain, the Xcop and Ycop displacements may be
analyzed with a Fast-Fourier Transform (FFT) algorithm. This
produces the power spectrum of the signal and reveals the frequencies
present within the COP components [29, 73, 107, 117]. However, in

47

addition to the COP, an FFT analysis may be conducted on the ground
reaction torque (GRT) [110] and dr/dt terms also.

To compare and build upon the work of Soutas-Little, et al. [110],
a frequency spectrum analysis was conducted for the X00» , Ycop, torque,
and radial speed. An FFT was used to obtain the power frequency
spectrum for these parameters. The spectrum was then processed to
obtain the spectral distribution and plotted versus frequency.

CHAPTER V
RESULTS AND DISCUSSION

Radial average displacement, or more simply combined Xcop and
Ycop excursions, was used extensively throughout the literature as an
instability parameter. What researchers aim to measure is how one's
balance changes with a change in test condition such as a change in
stance. However, this is very difficult to measure and therefore,
parameters which can be correlated to changes in balance are used
instead. It is desirable to use the parameter which will give the most
useful information abOut the specific condition. For this reason, RAD
as well at other parameters were evaluated in terms of sensitivity to
balance. For this evaluation the sensitivity, [3, of a parameter with

respect to a change in test condition, Ax, was defined according to

Aps = BzAx (23)

An; = M (24)

Sensitivity of i: [31 = 92 (25)
Ax

Sensitivity of k: B.=%" (26)

Here, Ax is the unknown change in balance from one test condition, i, to

another, k. The change in the parameter being considered for the same

two conditions is Ap, where

 

Ap = P2 " P‘ (27)
p1 ~

48

49

Note that Ax remains the same for all parameters. This is because the
subject's change in balance is independent of the measurement
parameter. However, Ax is dependent upon the two conditions being
tested and is not expected to be the same for all conditions. Ax may be
very different for comparison of FAEO and FAEC than for comparison
of FAEO and TDEO. Since this difference is unknown, and Ax is not
measured, the difference will be apparent by comparison of the
sensitivities for these conditions.

The sensitivities B: and B: of the two parameters, with respect to

the same measure, can be compared by

E=fl (28)
Bk 11

Thus, ipr: > Ap, then B: >Bn. Likewise, if Ap < Apr, then [3; <Bx. This
allows a sensitivity comparison to be made between any two
parameters for a single condition change.

Displacement of the COP provided some useful information about
sway, but it failed to accurately characterize a subject's balance in
several instances, an example of which is shown in Figures 5 and 6.
Figure 5 is a plot of Xcop versus Ycop displacement for two conditions:
(a) FTEC, and (b) TDEO for the same subject. Although the patient
was observed having difficulty in maintaining balance in tandem
stance, the cross plot suggests little or no change in sway between the
two conditions. Therefore, the B of the RAD would be low. Calculations
show that the RAD actually increased by 14% (B=0.14) from condition a
to condition b. Figure 6, however, which is a plot of torque versus time

50

 

AJAL‘ALAI'LLL

 

O . o
.u'
A; 1 AAA L AJlL LAI

 

 

 

 

‘

-

C

q

4

I

d

‘

4

‘

I

‘1“ 1

‘

"""“"'""""""" V " 'l".""'"' ‘V '

one: o que-

(a) Feet together with eyes closed

 

 

 

 

 

 

'V‘VV'YVVV'YYVV‘WV' V'VI'VVVVIYV'V'YVV‘I'VVV'

02k. 0 on:-

(b) Tandem stance with eyes open
Figure 5. Xcop versus Ycop

 

51

 

JO<

I.‘

.3. .
I

.41

 

0401

 

-? 6
the (use)

(a) Feet together with eyes closed

‘
fl

 

 

 

 

J 0'
use «on

(b) Tandem stance with eyes open
Figure 6. Ground reaction torque

t.

'
l.

 

 

 

52

for the same patient and conditions, shows a torque increase of 56%
(5:056) from condition a to b. Thus, the torque sensitivity was four
times greater than the radial average displacement sensitivity. The
velocity parameter increased 45% (B=O.45) from condition a to b and
therefore was approximately three times more sensitive than RAD.
Therefore, using this definition of sensitivity, RAD was found to be less
sensitive than both velocity and torque.

Clearly, if radial average displacement alone was the measure
used to determine if a balance difficulty existed in tandem with eyes
open, the result would be that no change was present. However, if
velocity and torque are also used, there would be evidence that some
change in maintenance of balance occurred between FTEC and TDEO.
Thus, consideration of only radial average displacement, which is a
combination of Xcop and Ycop, could lead to a false conclusion in
assessing balance by comparing these two conditions. This illustrates
the importance in determining which variable(s) will give the most
useful information for balance evaluations.

Another reason why radial average displacement should not be
used as a sole means of evaluating balance is because the COP
excursions are limited by the area between and under the feet or more
accurately, the "functional base of support" as defined earlier [37].
Thus, comparison may not be conducted between a one-footed stance
and a wide comfortable stance. Clearly the two bases of support are
very different and the limits of COP excursion are different. In addition
to intra-subject comparison, inter-subject comparison is also incorrect
in some cases due to variance in foot size. One way to combat these

comparison obstacles was to calculate COP excursions in terms of a

53

percentage of total base support, or as a percentage of maximum
allowable sway without falling [3, 37 , 38, 40]. However, this does not
eliminate the problem when a balance impaired person maintains
balance through small quick ankle movements and has observable
difficulty in maintenance of balance, thus does not create large COP
excursions.

It has been suggested that dynamic parameters such as velocity
and torque are more sensitive than static ones, such as COP
displacement or area [109]. This is due to the fact that static
parameters do not measure the state of balance at any particular
instant in time. They are usually an averaged value over the entire
trial duration. The dynamic parameters, however, give information
about balance at each time during the trial. Therefore, trends are
noticeable in addition to the onset of a fall or presence of a recovery.

The objective of this thesis was to identify balance evaluation
parameters that are sensitive to postural instabilities, characterize the
subject's postural responses and can be used as a comparison measure,
thereby providing a quantitative approach in addition to already
conducted qualitative analyses. In order to evaluate patients, a
normative population was recruited to provide base line data for
comparison. Normative data and results collected from nineteen
subjects are shown in Table 1 as a comparison between the calculated
and reported normative results found in the literature [62]. Although
the analytical approach was identical for the two systems being
compared, there is a discrepancy, approximately a factor of two, in the
velocity values for all conditions between the reported and calculated

mean values. The only difference between the two

54

Table 1. Comparison between reported and experimental norms

REPORTED AND MEASURED NORMATIVE BALANCE DATA

REPORTED REPORTED BEL BEL
CONDI'I'ION NORM NORM NORM NORM
(mean) (SD) (mean) (SD)

Comfortable stance. eyes open

Radial Ave. Disp.(cm) 0.42 0.12 0.52 0.19

Velocity (cal/sec) 1.55 0.39 3.54 0.57

Active Torque (N -m) 0.20 0.23
Comfortable stance. eyes closed

Radial Ave. Disp.(cm) 0.44 0.09 0.54 0.16

Velocity (cm/sec) 1.69 0.37 3.64 0.51

Active Torque (N -m) 0.22 0.10
Narrow stance, eyes open

Radial Ave. Disp.(cm) 0.60 0.17 0.76 0.18

Velocity (cm/sec) 1.87 0.42 3.91 0.60

Active Torque (N -m) 0.22 0.08
Narrow stance eyes closed

Radial Ave. Disp.(cm) 0.72 0.21 0.91 0.21

Velocity (cm/sec) 2.41 0.54 4.47 0.53

Active Torque (N-m) 0.22 0.08
‘Tandem stance, eyes open

Radial Ave. Disp.(cm) 0.65 0.12 0.91 0.29

Velocity (cm/sec) 3.23 0.62 5.61 0.79

Active Torque (N-m) 0.28 0.10
‘Tandem stance. eyes closed

Radial Ave. Disp.(cm) 1.07 0.22 1.23 0.41

Velocity (cm/sec) 5.54 1.46 7.77 1.64

Active Torque (N-m) 0.36 0.13
Right leg stance, eyes Open

Radial Ave. Disp.(cm) 1.03 0.19

Velocity (cm/we) 6.35 1.01

Active Torque (N-m) 0.35 0.10
Left leg stance eyes open

Radial Ave. Disp.(cm) 1.02 0.19

Velocity (cm/sec) 6.28 0.92

Active Torque (N -m) 0.31 0.10

"' Tandem stance is performed with the dominant foot in front.

55

systems, which would cause this difference in the velocity and not the
RAD was the sampling rate. The reported data were sampled at 50 Hz,
while the calculated norms were sampled at 100 Hz. This is one
possibility for the error. However, without inspection of the actual
program used by Lehmann, et al. [62], this cause is not verifiable. The
velocity equations used in this thesis, restated below from Chapter IV,

were checked and correctly account for a 100 Hz. sampling rate.

 

AS: = J(Xcopi + 1 - Xcopi)2 + (Y copi + 1 - Ycopi)2 (18)

v=-1£0-[iASi] (20)

n i=1
The calculated norms, noted as "BEL norms", were then used as
baseline data for evaluation of patients.

Figure 7 is an example of a patient's data compared with
normative values for 8 conditions. Radial average displacement,
velocity and torque are shown here. The white boxes represent
normative values while the gray area is one standard deviation above
the norm mean. The black boxes represent patient values with respect
to the norm and are labeled with the percentage above norm mean. A
patient value lying within the white or gray area is considered to be
within normative range and have no apparent balance difficulties. For
the patient shown here, all values were above the normative range.
This type of plot is very useful for patient reports since it displays the
data in a convenient layout for quick comparisons with normative

values.

FOB!
FAEO:
FEET APART E0

FAEC :
FEET APART Ec

FTEC:
FEET TOGETHER Eo

FTEC :
FEET TOGETHER EC

TDEO
FEET TANDEM EO

TDEC:
EEET TANDEM Ec

RLEO:
RIGHT LEG EC

LLEO:
LEFT LEG E0

EO=EYES OPEN
EC=EYES CLOSED

56

Numbers represent %above norm mean

 

 

 

 

 

 

 

 

 

 

 

C::::3NOMA 535m£a130 """'Nman
ww- AVERAGE 365% 467%
6'00 DISPLACEMENT F _ _ _. ‘
' ‘ 3599:.
5Q) ' ‘
632% 350% , i
4.00 .‘ .I _ - --
2 l l l
o 3.00 25195' 1001.
2.00 I: .
If!) m... a
0.00.l lle'fll '1'”le
FAEOFAECFTEOFIECTDEOTDECMOUEO
CONDmoN
120.m" VELOCITY 122“
100.00.. ‘I‘
8 80.m ‘- l. “‘883%
Q 6000 , I‘
z ' ~ 514%
‘J 4030.. 4m%
4701. 334% ‘ ‘-
20.00-- “"x'u 67*.—I'
"OWN
FAEOFAECFIEO mommmECRLEOLLEo
‘CONDNKMQ
4§%
2.00 ACTIVE TORQUE I ~ _
.‘ ‘- 352% 423%
533% 3921. .I - _ --
1.50 I. - _ --
E
z

 

HEO FEC TDEO TDEC RUE)
conomou

 

Figure .7. Balance summary chart

 

57

In addition to time-domain parameters, five parameters were
studied in the frequency domain: Xcop, Ycop, torque, radial
displacement, and radial velocity. The spectral distributions for these
parameters were calculated and plotted for comparison. A method was
devised to isolate the frequency at which the maximum amplitudes
occurred in the power spectrums. These values correspond to the
frequencies that are most prevalent and used for maintenance of
balance.

For interpretation of this data, a model was constructed using
fimdamental vibration theory. It was necessary to begin with a simple
model in order to investigate the variables and their effects on the
system. The model considered was a damped second-order single
degree-of-freedom (DOF) linear system, with harmonic excitation.
Using the model and free body diagram shown in Figure 8, a
summation of the forces and Newton's second law, 2F = ma, allows the
development of the differential equation of motion for this system. One
can then solve for the amplitude, X. The differential equation of motion

is

mi+ci+la=F.sinmt (28)

See Appendix B for the development of the following equation for gain

in terms of frequency ratio.

= (29)

58

 

Figure 8. Forced harmonic oscillation 1 DOF model
with free body diagram.

The natural frequency, (a. , is that at which the system oscillates

with maximum amplitude. According to vibration theory for this
simple model, the natural frequency of oscillation is equal to .Ik/m ,

[119]. The symbol C is the damping ratio which is the ratio between the
actual damping and the critical damping, c I c. . The critical damping is
the amount of damping necessary for the limiting case between non-
oscillatory and oscillatory motion. When c = Cc, §=1 and no oscillations
are present. When c = 0 , §= 0 and the system oscillates with a
maximum amplitude. This occurs at the natural frequency. Actual
postural damping, which is produced by the muscles and soft tissues of
the body, is somewhere between 0 and Cc.

Figure 9 is a plot of gain, Xk/F. , the amplitude ratio of the forcing
function and the response, versus frequency ratio. The frequency ratio,
to I (o. , is the ratio of excitation frequency to the natural frequency. Note
that both the peak amplitude and frequency of oscillation depend on the

59

value of C . Refer to Equation 28 for the equation relating amplitude
and frequency ratio to the damping ratio. For a fixed frequency ratio,
the amplitude decreases with increased damping. Likewise, the

‘ frequency ratio at which the maximum amplitude occurs will decrease
with increased damping. Thus, two important parameters may be
investigated, the peak frequency and amplitude.

This simple model may be related to the complex postural control
model by correlating both damping and spring control mechanisms with
the role played by. control mechanisms within the body. The specific
values for k and c depend on the amount of elasticity and damping
present within the musculoskeletal system. The amount of damping in
the postural control system corresponds to the ability to remove energy

 

 

 

 

 

 

 

o 0.5 1 i 1.5 2 2.5

Figure 9. Gain versus frequency ratio plot for l-DOF model

60

from the system [119]. By this model and for balance analysis,
damping corresponds to the subject's ability to reduce oscillations and
maintain balance. If the postural control system has the same
parametric relationships as shown in Figure 9, then a person with more
control, i.e., damping, will have a lower peak frequency and/or a lower
amplitude. Both must be considered since a patient may exhibit a
lower peak frequency but higher amplitude.

A dependence exists between the response of the system and the
variables k and c, in terms of (0! and C, respectively. This same
parametric influence must also apply to more complex models of the
human postural control system. The model considered for COP
displacement parameters consisted of a double inverted pendulum with
two DOF. This is similar to the simple two-link pendulum models used
in the literature[130]. The model has one point of rotation at the ankle,
and one at the hip, corresponding to the ankle and hip strategy
rotations mentioned in section 2.3 on postural stability. The
mathematics corresponding to this more complex model were
unnecessary for this thesis since the model is used for interpretations
only. However, it is important to note that the spring and damping
parameters are represented as matrices containing values for each link
within the system rather than a single value for the entire system. The
model and corresponding modes of oscillation, with spring and damping
matrices, denoted as K and C respectively, are shown in Figure 10. All
joints are hinge joints and have both spring and damping constraints as
shown in Figure 10a.

This system has two modes of oscillation. The first mode consists
only of oscillation about the base, as depicted in Figure 10c. This has

61

 

 

 

 

 

" K c \

. g g I

\ l

\ /

\\ ///
(a) (b)
“*6:
at

(c) ((1)

Figure 10. Inverted double pendulum 2-DOF model

two DOF where 81: 92. The type of motion associated with this mode
has been termed ankle strategy and is where the hip joint remains rigid
and the entire body rotates about the ankle joint. The second mode of
oscillation is more complex and is shown in Figure 10d. The two
degrees of freedom are more noticeable since 91¢ 92. They are usually
opposite in sign and exactly out of phase. The rotations occurring

correspond to rotation about both the ankle and hip joints. The modes

62

of oscillation have been solved for in many vibration text books and
show that the first mode is less than the second mode of oscillation
[119]. This information is useful later in the interpretation of spectral
distribution plots for Xcop, Ycop, and radial power.

The response of this system, like the simple one DOF model
depends highly upon both elasticity and damping, and therefore, will
characterize the amount of control exhibited by the subject; increased
peak amplitude and frequency with decreased damping.

The torque power distribution is a more difficult parameter,
conceptually. A different model which allows torsional movements is
necessary for interpretation of the torque data. The model consists of a
double inverted torsional rod system shown in Figure 11.

 

 

 

/" C2
92 5
K2
' C1
‘

 

 

 

 

Figure 11. Torsional 2-DOF model for postural stability

63

The torsional system has two natural modes of oscillation:
rotations that are in phase and those that are out of phase. If in phase
rotations occur, only ankle strategy is present and the rotation about
the hip is greater than rotation about the ankle. However, the
frequencies of ankle and hip oscillation are equal. Thus, only one peak
will occur in the spectral distribution. If out of phase rotations occur,
then two frequencies will be present in the distribution and both modes
of oscillation are present, the lower one being ankle rotation.

The final frequency domain parameter considered is radial
velocity or the rate of change of the radial displacement. Interpretation
of this parameter is even more difficult than the ground reaction
torque. The plots are very irregular and peaks occur at very large
frequencies. The proposed interpretation of this parameter is as a
measure of balance recruitment, assuming a person with good postural
control recruits only the control mechanisms necessary to maintain
balance. The recruitment is quick, but controlled. However, a subject
with reduced postural control most likely overcompensates and recruits
more than is required to maintain balance, thus causing an imbalance
in the other direction. Hence, more control mechanisms are recruited
and postural response becomes more disordered. This interpretation
agrees with and is demonstrated in the radial velocity plots. Patients'
data displayed much higher peak amplitudes and frequencies and often
many peaks occurred suggesting many modes of oscillation and
attempts to maintain balance.

This type of model was not intended to predict human motion
since the body is a multi-linked system with complex joints and

64

intricate control mechanisms. The model was used only as a basis for
interpretation of the data with regards to vibration theory.

The spectral distribution plots for one normative and one balance
impaired subject can be found in Figures 12— 15 and in Appendix C.
Inspection of the COP power plots revealed instances where more than
one peak existed. If the double inverted pendulum model in Figure 10
is taken as an anterior view allowing motion in the MIL direction, then
movement correlates with the Xcop displacement. M/L motions are
allowed at the ankle and hip for a two degree of freedom system. A
more complex model would account for additional movements of the
body. If the model is turned 90 degrees to a saggital view, movements
correspond to the Ycop or A/P motion and one could easily account for a
third mode of oscillation by adding a knee joint to the model. Again, a
more complex model would allow for knee flexion and extension. This
demonstrates the idea that the human body is a multi-link system
which may have more than two modes of oscillation.

In addition to the spectral distribution plots, a program was
developed which identified the peak frequency and amplitude for each
plot. These values are listed in table 2, along with the patient's
percentage above norm listed in table 3. The program picked the
frequency for the largest peak only. This information was very useful
in interpretation of the data and allowed quick comparison between
patient and norm. However, if more than one peak was present, there
existed a potential for misinterpretation of the data. With only the
maximum peak recorded, one has no way of knowing where other peaks
occur, if any, which explains the need to include and inspect the

frequency distribution plots. The presence of additional peaks may

65

suggest multiple strategies being used for postural control and should
not be dismissed.

Some additional interpretation can be made from the spectral
plots with regards to balance control strategy. Assuming the
correlation between the postural control system and the inverted double
pendulum is correct, the first mode of oscillation, ankle strategy, has a
lower frequency than the second mode of oscillation, ankle-hip strategy.
If only one peak occurs in the spectral distribution, ankle strategy was
used. However, if two peaks occur in a spectral distribution, ankle-hip
strategy was used and the lower frequency of the two peaks is for ankle
strategy, the other peak is for hip strategy.

In table 3a, the patient's percentages above norm are listed for all
conditions and parameters. In the FAEO condition, the patient's peak
frequency remained below or equal to that of the normative subject for
all parameters except dr/dt. However, the peak amplitude was below
norm for torque power only. The large amplitudes for this patient
suggest balance difficulties are present. Since the radius is made up of
the two COP components, the large percent difference in the Ycop
contributed to the difference in the radius as well. For this condition,
only one large peak occurred in each plot in Figures 12 and 14 and thus
the program selected the appropriate data.

As an example of two peaks, the FAEC condition shown in
Figure 13 for the norm and Figure 15 for the patient was analyzed.
Again, the data collected by the program are listed in tables 2 and 3.
Inspection of the plot in Figure 15 reveals the cause of the large
frequency shift for the Xcop power from the FAEO to the FAEC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xooppowaz YCOPPOWER
12 25
l 2
0.8 a:
15
S05 5
04 2 '
02 0.5
O- o.
012345070910 012045070910
momma!) FREQUENCYG-ll)
toneusmwen momma:
005 2
0.05
0.04 «'5
$000 5 1
002 905
0.01
0- o.
012345570910 012345070910
momma mummcm
dr/dtPOWER
3
25
2
$15
1
0.5
0- #A
012 3 4 5 0 7 0 91011121314151017101920
mummnm

 

 

Figure 12. Norm spectral distribution for FAEO condition

 

67

 

 

 

 

 

 

 

 

 

 

 

 

 

xooppowea YOOPPOWER
1 3
0.0 25
00 g 2
15
0‘ 1
0.2 Q5
0- o.
012345070910 012345070910
5150091011011) mumam
TORQUEPOWER mama:
0025 25
002 2
0015 15
001 1
0005 0.5
O- 0.
012345070910 012345070910
musucvam mousucvam
dr/leOWER
3
2.5
2
5..
1
0.5
012 3 4 5 0 7 0 91011121314151017101920
mausucvmz)

 

 

 

Figure 13. Norm spectral distribution for FAEC condition

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOWER YCOPPOWER
1.4 5
1.2 4
1
0.8 3
0.6 2
0A
02 ‘
O- 0.
012345678910 012345678910
FREQUENCYM FREQUENCY“
TORQUEPOWER RADIALPOWB?
0.05 5
0.04 4
0.03 3
0.02 2
0.01 1
0- o.
012345678910 12345678910
FREQUENCY“ FREQUENCY“
dr/dfPOWER

 

4
$3
2

1
0

012 34 56 7 8 91011121314151617181920

FREQUENCY“

 

 

Figure 14. Patient spectral distribution for FAEO condition

 

 

69

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

XCOPPOWER YOOPPOWER
5" 12'-
4 10"
£3
6“
2 41
1" 2.1
0 . - . . 0 -;-;-: vvvvvvvvv r-:.~.~
012345678910 012345678910
memo-12) mm
TORQUEPOWER RADIALPOWER
0.25" 10..
0.2“ 8"
0.15" 6“
g 0.1" 4..
0.05“ 2”
o :4; ¢A;-;A; : :41: 01: - 5 :
012345678910 012345678910
FREQUENCY“ FREQUENCY”
dr/dtPOWER
251’
2m
$151.
101*
5..
o 4 #- - 3:- enfw

 

012 3 4 5 6 7 8 91011121314151017101920
FREQUENCY“

 

 

Figure 15. Patient spectral distribution for FAEC condition

 

70

Table 2. Patient values compared to norm

 

 

 

 

 

 

 

 

 

 

 

b) Characteristic amplitude comparison

 

x0011 170011 101100: 114010: 01101
CONDITION NORM PATIENT NORM PATIENT NORM PATIENT NORM PATIENT NORM PARENT
FAEO 0.68 0.54 0.54 0.54 1.56 1.51 0.59 0.49 1.27 1.32
FAEC 0.63 1.66 0.54 0.54 2.15 1.61 0.59 0.63 1.07 1.51
FI'EO 0.68 0.54 0.63 0.68 1.56 1.81 0.68 0.59 1.32 1.42
FI'EC 0.93 1.42 0.63 0.68 1.17 1.90 0.59 0.59 2.34 2.59
TDEO 0.59 0.63 0.68 0.59 1.81 2.20 0.59 0.59 1.76 26.37
TDEC 0.63 0.73 0.63 0.73 4.30 3.17 0.54 0.59 2.29 23.39
RLEO 0.63 0.68 0.54 0.63 1.71 1.32 0.63 0.59 3.03 23.00
LLEO 0.68 0.73 0.54 0.63 1.61 1.76 0.59 0.59 1.86 18.26

a) Characteristic frequency comparison
x0011 YOOP 101100: was: 011/01
common now 94111210 NORM 11411911 NORM 941151111 NORM 9411911 NORM 9411311
FAEO 1.15 1.24 2.47 4.87 0.05 0.04 1.69 4.18 2.51 4.18
FAEC 0.99 4.28 2.57 10.01 0.02 0.20 2.03 8.14 2.58 20.15
FTEO 1.74 3.82 2.17 2.49 0.03 0.09 1.56 2.80 3.67 7.26
FTEC 1.37 9.23 1.79 6.95 0.06 0.33 1.34 9.19 5.00 41.16
TDEO 1.98 27.81 1.38 14.00 0.06 0.24 1.32 24.33 5.33 199.02
TDEC 2.42 16.09 2.92 23.94 0.06 0.34 1.33 26.45 5.93 21 1 .63
RIEO 2.16 30.46 2.20 27.74 0.15 0.31 1.74 20.27 6.32 203.67
LLEO 2.14 12.05 2.59 19.01 0.08 0.43 2.22 13.45 4.43 54.44

71

Table 3. Patient percentage above norm

 

 

 

 

 

 

 

common xeop vcor 101160: 114010: 4:101
FAEO -21% 0% -3% -17% 4%
FAEC 163% 0% -25% 7% 41%
FTEO -21% 8% 16% -13% 8%
FTEC 53% 8% 62% 0% 11%
TDEO 7% -13% 22% 0% 1398%
TDEC 16% 16% -26% 9% 921%
RLEO 8% 17% ~23% -6% 659%
LLEO 7% 17% 9% 0% 882%

a) Characteristic frequency comparison

common xeop YCOP 1011005 1140103 07/01
FAEO 8% 97% -20% 147% 67%
FAEC 332% 289% 900% 301% 681%
FTEC 120% 15% 203% 79% 98%
FTEC 574% 288% 450% 586% 723%
TDEO 1305% 914% 300% 1743% 3634%
TDEC 565% 720% 467% 1889% 3469%
RLEO 1310% 1161% 107% 1065% 3123%
LLEO 463% 634% 438% 506% 1 129%

 

b) Characteristic amplitude comparison

 

 

 

 

 

72

conditions. The second peak amplitude increased dramatically with
eyes closed thus producing two dominant peaks. The program identified
the second peak amplitude and frequency, even though the peak near
0.54 Hz still exists also. There are two large peaks and two dominant
modes of oscillation. Since this is for Xcop which describes M/L sway,
the peaks correspond to both the hip and ankle strategies of
maintaining balance. Without inspection of the distribution plots, the
conclusion could have been drawn that the patient had a much larger
peak frequency for ankle only strategy in the FAEC condition, rather
than the correct observation that the patient increased both ankle and
hip strategy amplitudes with eyes closed. This observation could be
very important in determination of proper treatment for the patient.

CHAPTER VI
CONCLUSIONS

The purpose of this thesis was to determine the most informative
and reliable means of measuring postural balance, develop a feasible
testing protocol for clinical use, and explore differences between normal
and balance impaired subjects. Several balance parameters were
evaluated, which included experimentally proposed measures such as
frequency domain parameters as well as currently accepted ones. In
addition, a parameter's sensitivity with respect to a change in condition
was defined and used as a comparison measure.

Force platform ground reaction forces and moments were
collected for nineteen normative subjects and over one hundred patients
with possible balance impairment. Data were then analyzed for one
norm and one balance impaired subject, both in the time and frequency
domains, to isolate which parameters more effectively identify postural
instabilities.

In time domain, the conventional "spot stabilogram" method of .
balance evaluation, the cross plot of X and Y COP, was shown to have
some inadequacies. This parameter was found to be less sensitive, as
defined, in identifying balance instabilities than dynamic measures
such as radial velocity or ground reaction torque. The dynamic
measures also allow for proper comparison within a subject or inter-
subject, regardless of condition or foot size.

The frequency distribution of the five balance parameters proved

to be another way to evaluate balance. Frequency parameters were

73

74

interpreted using a dynamic model which consisted of a second order
mass-spring-damper system. The model correlated the amount of
damping within the system to the amount of postural control exhibited
by the subject. Using the proposed model, the frequency distribution
plots could be interpreted as to balance strategy according to the
number of peaks present, peak frequency, peak amplitude and the
number of modes of oscillation present. These values were compared
for the balance patient and a norm to evaluate balance instabilities.
Relationships were proposed between postural stability and peak
frequencies and amplitudes. Patient peak amplitudes were larger than
norm for all conditions except one, corresponding to decreased postural
stability.

The methodology presented meets all the requirements as a
useful clinical evaluation. The test procedure is uncomplicated, yet
thorough, and is easily compared with norm and can be presented in a
clear manner for physician review. In addition, the parameters were
found to be more sensitive than previously used parameters and may
characterize each patient's unique postural control system in terms of
balance strategy, peak amplitude and peak frequency. The evaluation
provided quantifiable data and adds valuable information to qualitative
approaches currently used.

In addition to fulfilling the objectives of this thesis, many new
areas of research were found. Research should be conducted on
identification of postural strategies used in each condition. Addition of
EMG data would offer insight to muscle recruitment and allow
development of relationships between muscle activity and the various

force platform parameters. Kinematic data may serve very useful to

75

obtain relationships between specific body movements and force
platform parameters, such as pelvic movement to the ground reaction
torque. All three types of data combined together would allow a more
complete understanding of the postural control system in quiet stance
or in response to perturbations. Initially, this type of research would
be very cost and labor intensive and is not currently considered to be a
feasible test for clinical use.

The importance of every new clinical tool is the benefit of the test
to physicians, therapists, and patients. The information provided by
this type of postural evaluation has various applications.
Determination of appropriate treatment and rehabilitation focus,
evaluation during rehabilitation to monitor progress, and use as a
screening device for toxic exposure are just a few of its many

applications.

APPENDICES

APPENDIX A

APPENDIX A

Balance and Stability Questionnaire

BIOMECHANICS EVALUATION LABORATORY
s1. Lawrence Health Science Pavfllon
2900 Hannah Blvd” Suite 8-114
East Lanslng, MI 48824
517/336-4560

BALANCE AND INSTABILITY QUESTIONNAIRE

' Date:
Name: ‘ Bldhdate: Sex:
HISTORY:
1.8pecllealy.whatlsyourmahcomemorconplah? Pleasedescrbethesynptomsyouamexpeflemku.

 

 

 

 

armamspanayoummmpleasemwpammmmam.

 

 

 

 

3. When did your synptoms begin? _at birth _slowty __abmptly
Explain:
4. Have you ever had anything similar before? __yes _no

76

BalancesndlnstablityOuestionnalre
BlomechanicsEvaluationLaboratory

Pagez

5. Have you had a previous muscle. bone, cartilage. ligament.

ornervelnlury?

6. Priortothlseplcode.wereyoucorrpletelysyrr1ptomtree?

__yes
yes
yes

8. Are you better with:
Best?

Activity?
Neither?

9.Durkrgthelollowhgactivlties.areyoursyrrptorr1s:

Bending
Llano

LEM
sum

Richg
Standing
Walkhg

10. Is this conplalnt most aggravating or debilitating at:
Work? yes
DalyActlvltles? yes
Recreation? yes

11.1001isoonplalmcaushgdisruptionotsleep?
12. Doyouhaveanylocsotbladderorbowelcontrcl?

no

no

no

Better

__yes_no
__yes—no
_yes_no
__yes—no
_yes_no
_yes_no
_yes_no
_no
_no
__no

13.Haveyoueverhad.ordoyoumwhave.ar1yottheiollowingconditlons?
Arthritis

Cancer

HIghBlood Pressure

Heart Problems

Diabetes

Nerve Injury
Cereme Palsy

Muscular Dystrophy
Multiple Sclerosis

14. is there any possbaity that you are pregnant?
15.00 you stroke?
16. Doyou use alcoholor recreational dnrgs?

8.711.
8.01.
8.01.

yes

Worse

_yes_no
_yes_no
__yes-no
__yes—no
__yes__no
__yes—no

8.111.

8.111.

I8 '3 l8 l8 l8 '3 I8 '8 '3 I8 '8 l3 l3 l8

Balanceand instability Questionnaire
Biomechanics Evaluation Laboratory

78

 

 

 

 

 

 

 

Page 3
17. Haveyoutailenhthepast12 months? __yes no
Frequency of tale?
18. 00 you test rnuscie weakness, rnuscie spasticlty,
orhaveproblernsinwaiidngorstanding? ~ __yes _no
lico.onwhichsidedoestheproblemoccur? _rtgtl __lett
Descrbe:
19.Haveyoueverhadany'lossotconsciousness"
(LOO)? _yes _no
liyes, howlongwasthe LOO?
(mirutesihoursldays/rmnths)
20. Was there any “post-traumatic anrresia“ (PTA)?
(Loss of memory after traumatic brain injury
wlh loss 01 consciousness). _yes _no
it yes, how long was the PTA?
(minutesmoursldayslmomhs)
21.Whattypeotathietic activitiesdoyoudo?
Presently in the Past
Welsh! We _ _
Runnhg _ _
Tennis _ _
Basketball _ _
Soccer _ _
Bldno I I
Dance _ _
Snow skiing _ _
Aerobics _ _
Other
PREVIOUS TREATMENT: What previous treatments have recently been tried tor this problem?
Sorcery __yes —"°
Nerve Blocks _ . __yes __00
Injections _yes _no
Brace/Support . _yes _no
Exercise _yes __no
Traction __yes _no
Manbulatlon __yes _no
Medications .___yes __00

Balance and Instability Questionnaire
Biomechanics Evahatlon Laboratory
Page4

79

 

PREVIOUS TESTS: Which oi the following tests have been done tor your problem(s)?

SURGERIES: List all surgeries you have had:

W

 

Prosthesis __yes _no
Stress yes no
Assistive Devices __yes __no
Physical Therapy __yes _no
Intracraniai Pressure Monitoring
. _yes _no
Steroid Administration
yes no
Mannltol Administration
yes no
Other
x-rays yes no
Myelogram yes no
__yes ___no
CAT scan __yes _no
EMG _yes __no
MRI __yes _no
Lab Tests __yes _no
Nerve Conduction Test __yes _no
Work Tolerance _yes _no
Biomechanlcal Test _yes __no
Doppler _yes __no
Bone Scan __yes _no
Other
Data

 

 

 

 

ALLERGIES: List alergles to foods. medications. and other substances.

 

 

MEDICATIONS: List an medications currently being taken.

 

 

 

 

 

 

 

 

 

 

THE INFORMATION PROVIDED HERE IS USED IN STRUCTURING YOUR
BIOMECHANICS EVALUATION. WE APPRECIATE YOUR RETURNING THIS
SgggmgfiilRE AS SOON AS POSSIBLE PRIOR TO YOUR SCHEDULED

APPENDIX B

APPENDIX B

Mathematical Development of
Gain versus Frequency Ratio Expression

The equation of motion can be written from the free body diagram

shown in Figure 8 as follows
m£+cfr+kx = Fosinnr

The assumed particular solution for this differential equation will be
differentiated twice

x = Xsin(00t -¢)
)1 = mXcos((ut-¢)

ii = -to’X sin(rot - 1b)

where X is the amplitude of oscillation and 0 is the phase shift.
Substitute into the equation of motion to obtain

-m0)2Xsin((0t - ¢)+ crux 003(0): - ¢)+ szin(0)t - 0) = F. sin 0):

Recall,

sin(10t-0) =sinr0tcos0-cosmtsin0
cos(01t — 0) = costutcos¢+sin00tsin¢

81

82

Substitute the above identities and equate the coefficients for

sin (or and cos (0t . Thus obtaining the system equations:

X[cos¢(k - mm’)+ 00) sin 0] = F.

X[sin 11>(m0)2 — k)+ 0100030] = 0

Solving the above system for X, and 0 (1, 2)

 

 

X = Fa
cos¢(k —m0)2)+ ctusinq)
X _ Fo/coso

-k-mm’+ccotan¢

From the second system equation we obtain an expression for the phase

angle

 

 

¢ = tan-(k .0202) (1)
x _ M" (2)

83

J1?
(Dn=—
m

cc=2mtun

Define

§=C/Cc

21;

£9. 2.
k (on

Utilizing the above definitions in equations 1 and 2 , the gain and phase

angle expressions become

APPENDIX C

APPENDIX C

Spectral Distribution Plots for Norm and Patient

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xcoppowen vcoppowen
2 2.5
1.5 2
a
15
g 1 5
2 1
0.5 as
0- o.
012345070910 012345070910
mammal!) mutucvtI-IZ)
TORQUEPOWER RADIALPOWER
000 10
14
0.025 12
0.02 E 1
0.015 00
001 200
04
005 02
0- o.
012345070910 012345070910
mousucvrrrz) mourncvarz)
dr/dtPOWER
4
3.5
3
912.5
g 2
1.5
1
0.5
o.
012 3 4 5 0 7 0 91011121314151017101920
FREQUENCYG'ID

 

 

 

Figure 16. Norm spectral distribution for F'TEO

84

 

 

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOMEK YCOPPOWER
1.4 2
1.2
1 1.5
0.0 °‘ 1
0.6
0‘ 0.5
0.2
0- o.
012345678910 012345678910
FREQUENCYO‘IZ) FREQUENCYMZ)
TORQUEPOWER RADIALPOWER
0.07 1.4
0% 1.2
0.05 1
0.04 0.8
0.03 0.6
0.02 CA
0.01 0.2
0- o.
012345678910 012345678910
FREQUENCY” FREQUENCY“
dt/d‘I’PQNER
6
5
4
$3
2
1
o.
012 3 4 5 6 7 8 91011121314151617181920

 

FREQUENCY (HZ)

 

 

Figure 17. Norm spectral distribution for FTEC

 

 

 

 
 
   

 

 

 

 

 

 

 

 

 

XCOPPOWB? YCOPPOWER
2.. 14v
1.2‘
1.5" 111
1" “0.01
0.61:
05" ' 041'
0.2
O Ac‘:‘:*e;:‘- .A.v. a 0--:<4fi:-:-:-:-:-:-:-:
012345678910 012345678910
FREQUENCY“ FREQIENCYM
TORQUEPOWER

 

  

 

 

 

012345678910

 

 

 

 

 

 

 

 

FREQUENCY“
dt/diPOWER
6"
50
4..
5311
20
1..
0 . 4 4*: :*:-;-:4; :::.:..v :-:-:-:-: 3-:
012 3 4 5 6 7‘8 91011121314151017101920

REQUENCYCHD

 

 

 

Figure 18. Norm spectral distribution for TDEO

 

 

 

XOOP POWER

 

 

 

 

012345678910

YCOPPOWER

 

A A AA

012345678910

 

POWER
Ogegrgv

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FREQUENCY“ mm
TORQUEPOWER
0.07"
omit
005"
0.04"
003‘»
0021»
001‘»
o 24%: 3% :4: 3 : ofi:-: :; : 3 :44.
012345678910 012345678910
FREQUENCY“ FREQUENCYCHZ)
dr/dtPOWER

 

 

 

012 3 4 5 6 7 8 91011121314151017101920

A A A A A A A
1 v—v

FREQUENCY“

 

 

Figure 19. Norm spectral distribution for TDEC

 

 

 

XCOP POWER

AAAAAAAAAAAAAAA

YCOPPOVER

 

 

 

 

12345678910 012345678910

FREQUENCY“

FREQIENCYG'D

 

 

 

 

 

 

0.16"

our.

TORQUEPOWER

 

RADIALPOWER

A‘
v

 

A A A A A

 

 

12345678910
FREQUENCY”

 

 

 

 

 

 

 

A AAAAA AA AA A
ifivffi‘vvvvvvvvvvfi‘fiVv'V‘4j vvv w v fi vvvv w v

012 3 4 5 6 7 8 910111213141516171819”

dr/dt POWER

A A A

FREQUENCY“

 

 

Figure 20. Norm spectral distribution for RLEO

 

89

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOWER vcoppowez
2.5 3
2 2.5
51.5 E2
1.5
1 2 1
05 05
0- 0. A
012345070910 012345070910
momma Recurrrcvom
TORQUEPOWER RADIALPOWER
0.1 25
000 2
0.00 “15
0.04 g I
0.02 05
0- o.
012345070910 012345070910
FREQUENCYOIZ) menstrual)
dr/dtPOWER
5
4
$3
2
1
0.
012 3 4 5 0 7 0 91011121314151017101920

 

FREQUENCY (I'll)

 

 

Figure 21. Norm spectral distribution for LLEO

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOWER YCOPPOWER
4 25
3.5
3 2
2.5 1.5
2
1.5 1
1
Q5 0.5
0. .
012345678910 012345070910
5115911901011) 1:11:00thva
TORQUEPOWER RADIALPOWER
0.1
000 25
000 1:
004 '1
cm 0.5
0- . o
012345070910 012345070910
manual!) FREQUENCYO‘IZ)
dr/dIPOWER
0
7
0
g 6
4
2 3
2
1
0

 

012 3 4 56 7 8 91011121314151617181920

FREQUENCY (HZ)

 

 

Figure 22. Patient spectral distribution for FTEO

 

 

91

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOWER YCOPPOWER
71?
61}
51.
40
311
21.
‘1
: : : :44+- 04;;43-3‘: -33-:
12345678910 012345678910
REGENCY” REGENCY“
TOTQUEPOWER RADIALPOWER
10"
81.
61.
4..
21.
3 3 : : :‘sfi;+< ft: 0 e 0-: : c : .T‘Sm
12345678910 012345678910
REGENCY” REGENCY“
dIdIPOWER
001»
a”
$19
at.
101.
O e;e;*:::‘:::44i:‘:e:‘:::-:‘:‘:-:4:;;::-:
012 3 4 5 6 7 8 91011121314151617181920
REGENCY“

 

 

Figure 23. Patient spectral distribution for FTEC

 

 

92

 

 

 

 

 

 

 

 

 

 

 

 

 

5“”

o8888

xcoppowsn vcoppowen
30 14
25 12
20 10
g 15 8
0
10 4
5 2
0- o.
012345070910 012345070910
material) FREQUENCYCHZ)
roneuepowen RADIALPOWER
025 25
02 20
015 15
01 10
005 5
0- see 0
012345070910 012345070910
mercuric FREQUENCYtl-IZ)
dr/leOWER
100
140
120

 

 

012 3 4 5 6 7 8 9101112131415161718192)
FREQIENCYO‘ID

 

 

Figure 24. Patient spectral distribution for TDEO

 

 

93

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XCOPPOWER YCOPPOWER
20» 254
151» 20‘
1611
‘01}
'04.
60 64.

O-%:‘~:T:-:~: :-;-: c o :‘:‘:44¢4-‘-
012345678910 012345070910
REGENCY” FREQUENCY”
TOTOUEPOWER RADIALPOWER

0.35'[ mi.
0.3‘ 25..
021 1:.
0.159
011 10“
015‘ 5..
0T3 3 3 3 van:-‘ 3‘3 0 t 3 : $i‘:‘: . 0:?
012345678910 012345678910
WINCYOID REGENCY”
d/dIPOWB?

 

 

 

o ---c-ll-- .---- ---l-
0123456789101112131415161718191)
REGENCY“

 

 

 

Figure 25. Patient spectral distribution for TDEC

 

 

XCOP POWER

 

 

YCOP POWER

 

 

 

 

 

2345678910
REGENCY”

 

 

35 30
a) 25
95 20
2° 15
15
,0 10 p
5 5
0- °_ /
0 2345070910 012345070910
mtmvm 1:115thch
TORQUEPOWER RADIALPOWER
25
20
15
10
5
0.

 

012345678910
FREQUENCY“

 

 

 

dr/dI POWER

0

 

012 34 5 6 7 8 91011121314151617181920
REGENCY“

 

 

Figure 26. Patient spectral distribution for RLEO

 

 

95

 

XCOP POWER YCOP POWER

    

 

 

 

 

: : : c e : : 4—5=' , , - , - 0
0 1 2 3 4 5 6 7 9 10 0 1 2 3 4 5 6 7 8 9 10
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Figure 27 . Patient spectral distribution for LLEO

 

 

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