The Effects of Varying Speed on the Biomechanics of Stair
Ascending and Descending in Healthy Young Adults: Inverse
Kinematics, Inverse Dynamics, Electromyography and a Pilot Study
for Computational Muscle Control and Forward Dynamics
A Thesis
Presented in Partial Fulfillment of the Requirements for the Degree
Master of Science in the Graduate School of The Ohio State
University
By
Rebecca Linn Routson, B.S.M.E.
Graduate Program in Mechanical Engineering
The Ohio State University
2010
Thesis Committee:
Dr. Robert Siston, Adviser
Dr. Gary Kinzel
Dr. Ajit Chaudhari
c Copyright by
!
Rebecca Linn Routson
2010
ABSTRACT
Stairs are a frequently encountered obstacle in daily life. The ability to negotiate
stairs without difficulty or pain is important to quality of life. Although it is a simple
task for healthy persons, ascending and descending stairs can be very challenging
when motor functions are diminished (e.g., in elderly persons, persons with physical
disabilities and in persons who have experienced trauma to their lower extremities).
Conditions such as stroke, cerebral palsy (CP), osteoarthritis (OA) both before and
after total knee replacement (TKR), and anterior cruciate ligament (ACL) injuries
impair the ability to negotiate stairs. Because many individuals with neuromuscular
impairments walk and ascend/descend stairs slowly, it is important to isolate functional task from other factors such as age, muscle weakness, etc. Previous studies
have developed the normative data for kinematics, kinetics and muscles or groups of
muscles that contribute to specific subtasks of walking at various speeds. However,
the normative data for various speeds of stair climbing, as prevalent a task and as
periodic as level over the ground walking, has yet to be established. The purpose of
this thesis is to create a normative database characterizing the effect of speed on the
biomechanics in healthy young adults while ascending and descending stairs.
Kinematic, kinetic and EMG data was collected for 12 healthy subjects while
ascending/descending stairs at three speeds (slow, self selected, and quick). Computational modeling was employed in ViconNexus and OpenSim to determine joint
ii
angles, joint flexion moments, ground reaction forces and muscle activations during
stair ascending/descending at the three speeds. Peak ground reaction forces, peak
flexion angles, peak flexion and extension moments and angles at foot strike, midtstance and foot off were compared during stair climbing for the three speeds using a
one-way ANOVA (p less than 0.05) with repeated measures. Post hoc analysis was
performed with paired t-tests and a bonferroni correction factor of p less than 0.025.
The work in this thesis determined the effects of changing stair climbing speed
on lower extremity joint kinematics and kinetics. Joint angles were found to vary
significantly for both ascending and descending stair trials, but less for descending.
Internal joint flexion moments did not change significantly for ascending stairs, but
were more varied in descending stairs. Peak ground reaction forces were found to vary
significantly with speed and increased with speed. Average peak EMG activations
and and activation timing was found to increase as speed increased, as well.
The research conducted in this thesis is the preliminary work towards creating a
normative database characterizing the effects of speed in ascending and descending
stairs in healthy young adults. In the future, data from other populations, especially
those with mobility disorders, can be compared with this normative database. Characterization of the biomechanics of stair climbing in individuals with disabilities may
direct innovative rehabilitative therapies to target and strengthen impaired muscle
groups so that these people can negotiate stairs with increased ease and independence.
iii
This thesis is dedicated to my students, past, present and future.
iv
ACKNOWLEDGMENTS
I would sincerely like to express my gratitude to a number of people without whom
this thesis would not have been written.
First, I would like to thank Dr. Robert Siston, for being my adviser during
my undergraduate and graduate careers at the Ohio State University and for his
support with this particular project. I would also like to thank the NeuroMuscular
Biomechanics Lab at the Ohio State University for their help; especially Brooke
Morin, Becky Lathrop and Julie Thompson.
I would like to thank Dr. Ajit Chaudhari and the Sports Biomechanics Lab at
OSU for allowing me to use the SBL to set up my experiment, and process my data. I
would like to thank Dr. John Borstad for allowing me to borrow his EMG equipment
for my data acquisition. Additionally, I would like to thank Dr. Laura Schmitt and
Lise Worthen-Chaudhari for assisting with the EMG placement and methodology.
I would like to thank the support team for OpenSim at Stanford University for
their help especially with RRA and CMC.
Additionally, I am very appreciative for the guidance that I have received during
my Masters from Dr. Gary Kinzel especially with the design aspect of this project
and with finding a PhD program.
v
I would like to express my gratitude to Dr. Richard Freuler for his love and
guidance during my entire seven year career at Ohio State. He has worn many hats
for me over the years and I am especially grateful for the roles he played as my mentor,
and my surrogate Dad. His words of encouragement and his support have meant the
world to me from my first confusing days as a freshman to my last few days as a
student at the Ohio State University.
And, also, I would like to thank the Freshman Engineering Program for funding
my graduate education at Ohio State and for providing me with a second family. I
would like to thank both my fellow teaching assistants and my students for helping
me find meaning and reward in my life that I couldn’t have found without them. I
would like to thank them for giving me their friendship and encouragement. I would
especially like to thank those of my fellow FEH TA’s who I recruited as research
subjects for this project.
Finally, and most importantly, I would like to express my gratitude to my family
and friends, who have provided support, inspiration and encouragement throughout
my life and especially during this project.
Rebecca Linn Routson
August 2010
vi
VITA
January 13, 1985 . . . . . . . . . . . . . . . . . . . . . . . . . . . Born - Colorado, USA
June, 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.S. Mechanical Engineering,
The Ohio State University.
2008-present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graduate Teaching Associate,
The Ohio State University.
PUBLICATIONS
Research Publications
Instructional Publications
FIELDS OF STUDY
Major Field: Mechanical Engineering
Studies in:
Studies in Biomechanics: Prof.Robert Siston
vii
TABLE OF CONTENTS
Page
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
Chapters:
1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1
1.2
1.3
2.
1
Focus of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Significance of Research . . . . . . . . . . . . . . . . . . . . . . . .
Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
9
10
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.1
2.2
11
19
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21
24
28
29
30
31
2.3
Design and Build Modular Staircase for Gait Laboratory
Experimental Data Acquisition . . . . . . . . . . . . . .
2.2.1 Marker Set . . . . . . . . . . . . . . . . . . . . .
2.2.2 EMG . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Testing Protocol . . . . . . . . . . . . . . . . . .
Musculoskeletal Simulation . . . . . . . . . . . . . . . .
2.3.1 ViconNexus . . . . . . . . . . . . . . . . . . . . .
2.3.2 Scale Model . . . . . . . . . . . . . . . . . . . . .
2.3.3 Inverse Kinematics (IK) . . . . . . . . . . . . . .
viii
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Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
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Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
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2.3.4 Inverse Dynamics (ID) . . . . . . . . .
2.3.5 Residual Reduction Algorithm (RRA)
2.3.6 Computational Muscle Control (CMC)
2.3.7 Forward Dynamics (FD) . . . . . . . .
Signal Processing . . . . . . . . . . . . . . . .
Statistics . . . . . . . . . . . . . . . . . . . .
Ascending Stairs . . . . . . . .
3.1.1 Ground Reaction Forces
3.1.2 Inverse Kinematics . . .
3.1.3 Inverse Dynamics . . . .
3.1.4 EMG . . . . . . . . . .
Descending Stairs . . . . . . . .
3.2.1 Ground Reaction Forces
3.2.2 Inverse Kinematics . . .
3.2.3 Inverse Dynamics . . . .
3.2.4 EMG . . . . . . . . . .
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Ascending Stairs . . . . . . . . . . . . . .
4.1.1 Ground Reaction Forces . . . . . .
4.1.2 Inverse Kinematics . . . . . . . . .
4.1.3 Inverse Dynamics . . . . . . . . . .
4.1.4 EMG . . . . . . . . . . . . . . . .
Descending Stairs . . . . . . . . . . . . . .
4.2.1 Ground Reaction Forces . . . . . .
4.2.2 Inverse Kinematics . . . . . . . . .
4.2.3 Inverse Dynamics . . . . . . . . . .
4.2.4 EMG . . . . . . . . . . . . . . . .
Summary of Effects of Speed in Ascending
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and Descending
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Stairs
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Pilot Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.1
5.2
5.3
5.4
Introduction . . . . . . .
Residual Reduction . . . .
Computed Muscle Control
Forward Dynamics . . . .
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102
102
105
109
6.
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.1
6.2
6.3
6.4
Contributions . . . . . .
Additional Applications
Future Work . . . . . .
Summary . . . . . . . .
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114
115
116
117
Appendices:
A.
Stair Climbing Experimental Protocol . . . . . . . . . . . . . . . . . . . 128
x
LIST OF TABLES
Table
Page
3.1
Statistical results for ascending stairs peak vertical GRF. . . . . . . .
39
3.2
Statistical results for ascending stairs peak hip angle. . . . . . . . . .
44
3.3
Statistical results for ascending stairs peak knee angle. . . . . . . . .
45
3.4
Statistical results for ascending stairs peak ankle angle. . . . . . . . .
45
3.5
Statistical results for ascending stairs IK Leg1 foot strike. . . . . . . .
46
3.6
Statistical results for ascending stairs IK Leg1 midstance. . . . . . . .
46
3.7
Statistical results for ascending stairs IK Leg1 foot off. . . . . . . . .
47
3.8
Statistical results for ascending stairs IK Leg1 foot strike. . . . . . . .
47
3.9
Statistical results for ascending stairs IK Leg2 foot strike. . . . . . . .
49
3.10 Statistical results for ascending stairs IK Leg2 early stance. . . . . . .
49
3.11 Statistical results for ascending stairs IK Leg2 midstance. . . . . . . .
49
3.12 Statistical results for ascending stairs IK Leg2 foot off. . . . . . . . .
50
3.13 Statistical results for ascending stairs peak hip moment.
. . . . . . .
51
3.14 Statistical results for ascending stairs peak knee moment. . . . . . . .
51
3.15 Statistical results for ascending stairs peak ankle dorsiflexion moment.
55
xi
3.16 Statistical results for ascending stairs peak hip extension moment. . .
55
3.17 Statistical results for ascending stairs min knee extension moment. . .
55
3.18 Statistical results for ascending stairs min ankle plantarflexion moment. 55
3.19 Statistical results for descending stairs peak vertical GRF. . . . . . .
62
3.20 Statistical results for descending stairs peak hip flexion angle. . . . .
69
3.21 Statistical results for descending stairs peak knee flexion angle. . . . .
69
3.22 Statistical results for descending stairs peak ankle dorsiflexion angle. .
69
3.23 Statistical results for descending stairs IK Leg1 foot strike. . . . . . .
70
3.24 Statistical results for descending stairs IK Leg1 midstance. . . . . . .
71
3.25 Statistical results for descending stairs IK Leg1 foot off. . . . . . . . .
71
3.26 Statistical results for descending stairs IK Leg1 foot strike. . . . . . .
71
3.27 Statistical results for descending stairs IK Leg2 foot strike. . . . . . .
73
3.28 Statistical results for descending stairs IK Leg2 early stance. . . . . .
73
3.30 Statistical results for descending stairs IK Leg2 foot off. . . . . . . . .
73
3.29 Statistical results for descending stairs IK Leg2 midstance. . . . . . .
74
3.31 Statistical results for descending stairs peak hip moment. . . . . . . .
78
3.32 Statistical results for descending stairs peak knee moment. . . . . . .
79
3.33 Statistical results for descending stairs peak ankle moment. . . . . . .
79
3.34 Statistical results for descending stairs min hip moment. . . . . . . .
79
3.35 Statistical results for descending stairs min knee moment. . . . . . . .
80
3.36 Statistical results for descending stairs min ankle moment. . . . . . .
80
xii
LIST OF FIGURES
Figure
Page
2.1
Force plate layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.2
Force plate layout with stepping pattern. . . . . . . . . . . . . . . . .
14
2.3
Solid model assembly of completed staircase. . . . . . . . . . . . . . .
15
2.4
Completed staircase in the Sports Biomechanics Lab.
. . . . . . . .
16
2.5
Finite element analysis of the 2nd step. . . . . . . . . . . . . . . . . .
17
2.6
The Sports Biomechanics Lab.
. . . . . . . . . . . . . . . . . . . . .
20
2.7
MXF40 Vicon high speed motion capture camera . . . . . . . . . . .
20
2.8
PCT marker set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.9
Torso Markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.10 Surface EMG placement. . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.11 Subject descending stairs with complete marker set. . . . . . . . . . .
27
3.1
Vertical GRF for ascending stairs . . . . . . . . . . . . . . . . . . . .
37
3.2
A-P GRF for ascending stairs . . . . . . . . . . . . . . . . . . . . . .
38
3.3
Stair climbing IK with forces in OpenSim . . . . . . . . . . . . . . . .
40
3.4
Stair climbing hip flexion angle . . . . . . . . . . . . . . . . . . . . .
41
xiii
3.5
Stair climbing knee flexion angle . . . . . . . . . . . . . . . . . . . . .
42
3.6
Stair climbing ankle flexion angle . . . . . . . . . . . . . . . . . . . .
43
3.7
Stair climbing ID for hip in OpenSim . . . . . . . . . . . . . . . . . .
52
3.8
Stair climbing ID for knee in OpenSim . . . . . . . . . . . . . . . . .
53
3.9
Stair climbing ID for ankle in OpenSim . . . . . . . . . . . . . . . . .
54
3.10 EMG results for GAS . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.11 EMG results for SOL . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.13 EMG results for VAS . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.12 EMG results for TA . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.14 Vertical GRF for descending stairs . . . . . . . . . . . . . . . . . . .
61
3.15 A-P GRF for descending stairs . . . . . . . . . . . . . . . . . . . . . .
63
3.16 Stair descending IK with forces in OpenSim . . . . . . . . . . . . . .
64
3.17 Stair descending hip angle in OpenSim . . . . . . . . . . . . . . . . .
66
3.18 Stair descending knee angle in OpenSim . . . . . . . . . . . . . . . .
67
3.19 Stair descending ankle angle in OpenSim . . . . . . . . . . . . . . . .
68
3.20 Stair descending ID for hip in OpenSim . . . . . . . . . . . . . . . . .
75
3.21 Stair descending ID for knee in OpenSim . . . . . . . . . . . . . . . .
76
3.22 Stair descending ID for ankle in OpenSim . . . . . . . . . . . . . . .
77
3.23 EMG results for GAS . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.24 EMG results for SOL . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
3.25 EMG results for TA . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
xiv
3.26 EMG results for VAS . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
5.1
Residuals after RRA for a typical trial. . . . . . . . . . . . . . . . . . 103
5.2
Residuals after RRA for a typical trial. . . . . . . . . . . . . . . . . . 104
5.3
Kinematic results after RRA for a typical trial. . . . . . . . . . . . . 105
5.4
Kinematic results after RRA for a typical trial. . . . . . . . . . . . . 106
5.5
CMC for a typical trial. . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.6
CMC for a typical trial. . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.7
CMC compared to EMG. . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.8
Forward Dynamics for a typical trial. . . . . . . . . . . . . . . . . . . 111
5.9
Forward Dynamics for a typical trial. . . . . . . . . . . . . . . . . . . 112
A.1 Placement of surface EMG electrodes [Konrad, 2005]. We will be placing GMax, GMed, BF, RF, VAS med, TA, GAS med, SOL. . . . . . . 135
A.2 Muscle fiber direction for GMax . . . . . . . . . . . . . . . . . . . . . 136
A.3 Example of vest setup. The belt in rear of vest can be used to help
keep wires out of the way. . . . . . . . . . . . . . . . . . . . . . . . . 136
A.4 MVIC exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
A.5 PCT marker set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.6 Placement of torso markers. Markers used from this image are RSHO,
LSHO, ASIS, PSIS, CLAV and STRN. . . . . . . . . . . . . . . . . . 139
xv
CHAPTER 1
INTRODUCTION
Stairs are a frequently encountered obstacle in daily life. Due to their abundance,
the ability to ascend and descend stairs without difficulty or pain is important to
quality of life. When individuals are unable to negotiate stairs, their ability to live
independently may become severely limited. Functionally, as well as biomechanically
different from level over-ground walking, stair climbing requires larger knee moments
and ranges of motion than those in level walking [Andriacchi et al., 1982]. Stair
climbing is often used as a measure to determine functional ability in persons with
physical disabilities such as knee osteoarthritis (OA) and injury to the anterior cruciate ligament (ACL) [Andriacchi and Mikosz, 1991]. Although it is a simple task for
healthy persons, ascending and descending stairs can be very challenging when motor
functions are diminished (e.g., in elderly persons, persons with physical disabilities
and in persons who have experienced trauma to their lower extremities).
In particular, the elderly and persons with movement disorders and disabilities
experience difficulty performing daily tasks such as stepping over obstacles, moving
from seated to standing, walking and ascending/descending stairs. Due to its importance and prevalence in daily life, stair climbing is a functional measure in the lives
of persons with mobility disorders and disabilities [Stratford et al., 2006]. Conditions
1
such as stroke, cerebral palsy (CP), osteoarthritis (OA) both before and after total
knee replacement (TKR), and anterior cruciate ligament (ACL) injuries impair the
ability to negotiate stairs.
With over 700,000 strokes each year in the United States, stroke is the third
leading cause of death and causes more serious long-term disabilities than any other
disease [NINDS, 2004]. One of the most frequent disabilities resulting from stroke
is paralysis, although type and severity of disability following stroke depends on the
area of the brain in which the damage has occurred [NINDS, 2008]. Stroke not only
affects muscle endurance and range of motion, but also balance, coordination and
body posture [NINDS, 2008].
The survivors of strokes often experience traumatic and long-term disability associated with a diminished quality of life due to a limited ability to perform many
routine daily activities. Stroke damages the motor and sensory pathways within the
central nervous system [Sharp and Brouwer, 1997] and often leads to muscle weakness
and abnormal motor patterns that are frequently manifested by hemiparesis, a paralysis or weakness of one side of the body. Hemiparesis is a major contributing factor to
disability following stroke and significantly impairs ones ability to perform common
daily activities such as walking, dressing and ascending/descending stairs [deOliveira
et al., 2008]. Weight shifting, especially during stair climbing, to both the paretic
and the nonparetic limbs in stroke survivors is often impaired [Laufer et al., 2000].
Due to this, stair climbing ability in stroke survivors is often used as a predictor of
free-living [Alzahrani et al., 2009].
Cerebral palsy (CP) is a neuromuscular disorder that affects movement and body
posture. It is the most common cause of physical disability in childhood [Colver,
2
2000] with a reasonable estimate of 700,000 children and adults up to age 50 are
living with CP in the United States [UCPREF, 2008]. The rate of incidence of CP
has increased in recent years, paralleling increases in survival rates in infants with
low birth-weight and an increase in infants born prematurely [Stanley and Watson,
1992, Colver, 2000].
Cerebral palsy is often characterized by poor muscle tone and posture, spasticity
(a tightness in muscles that is characterized by continuous and painful muscle spasms
[NINDS, 2007a], unsteady gait and limited mobility [NINDS, 2007b]. Persons with CP
often experience difficulty controlling muscle movement, and, therefore, simple tasks
often become an overwhelming challenge to them. Walking, and even standing, can be
a major problem for people with this disability because of asymmetrical distribution
of muscle tone, poor ability to shift weight and a forward displacement of center of
gravity [Thompson-Rangel et al., 1992]. Due to this, CP interferes with the ability of
an individual to carry out daily activities such as walking and ascending/descending
stairs [Bjornson et al., 2007].
The most commonly injured ligament in the body requiring surgery is the anterior
cruciate ligament (ACL) [Spindler and Wright, 2008]. The cruciate ligaments in the
knee act to restrict sagittal knee translations [Vergis and Gillquist, 1998, Georgoulis
et al., 2003]. An injury to the ACL usually leads to difficulty in daily activities due
to the knee joint laxity and instability. The goal of cruciate ligament reconstruction
is to allow patients to resume normal activities by decreasing joint laxity [Vergis and
Gillquist, 1998]. An estimated 175,000 ACL reconstructions were performed in 2000
and the number is increasing [Spindler and Wright, 2008].
3
ACL injury not only changes the kinematics of the knee, but also changes the muscle activation patterns of the muscles that cross the knee joint [Rudolph et al., 2001].
ACL injury is associated with a high incidence of a coping strategy called quadricep
avoidance [Georgoulis et al., 2003, Berchuck et al., 1990]. Quadricep avoidance is assumed to be used when subjects who are ACL deficient are performing certain daily
activities such as ascending and descending stairs and walking or jogging. Previous
studies have investigated the consequences of ACL injury on level over the ground
walking in addition to the effects of ACL reconstruction and rehabilitation towards
walking [Andriacchi and Dyrby, 2005, Georgoulis et al., 2003, Vergis and Gillquist,
1998]. However, it is ascending and descending stairs that presents the most difficulty in individuals who have experienced an ACL injury [Berchuck et al., 1990]. Stair
climbing involves the use of both concentric and eccentric quadriceps muscle activity
which can produce knee translations in the ACL deficient [Vergis and Gillquist, 1998,
Berchuck et al., 1990].
Osteoarthritis (OA) is the leading cause of disability within the United States
[Lawrence et al., 1998, Borrero et al., 2006] The prevalence of knee OA makes it
the single greatest cause of chronic disability in community-dwelling adults in the
United States [Maly et al., 2006]. Some individuals begin to experience severe pain
and disability in their 40s [NIH, 2003], but OA most frequently affects individuals
over the age of 65. The onset of osteoarthritis increases with age; approximately 10
percent of individuals over the age of 55 [Baliunas, 2002], 30 percent of individuals
over the age of 65 [Jackson, 2004] and 80 percent of those over the age of 75 [Arden
and Nevitt, 2006] suffer from OA.
4
Osteoarthritis is characterized by cartilage degeneration and painful stiffness in
the joint leading to diminished physical function and ultimately joint replacement
surgery [Jackson, 2004]. Compared with healthy adults, people with knee OA walk
more slowly due to a shorter stride and decreased cadence [Maly et al., 2006]. In
person with osteoarthritic knees, the knee adduction moment is lower during stair
climbing and walking [Maly et al., 2006].
Approximately a quarter of those who suffer from OA are severely disabled [Baliunas, 2002] and can no longer perform important daily functions such as walking,
stepping over obstacles, moving from a seated to standing position, and stair ascending/descending. Often one of the first complaints for patients with early OA is
difficulty climbing stairs [Costigan et al., 2002]. Because walking, and stair climbing become painful and difficult tasks for individuals with OA, adaptive strategies to
walk and climb stairs are often formed to avoid severe pain. These strategies change
the kinematics and kinetics as well as the muscle groups that are recruited for the
activities . One of these compensation strategies is quadricep avoidance where the
subject learns to avoid complete extension of their knee by decreasing the activation
of their quadriceps [Slemenda et al., 1997].
Ultimately, when pain inhibits normal daily activities in individuals with OA, it
becomes necessary for them to have a Total Knee Replacement (TKR). TKR is a
surgical treatment to relieve pain and restore function to the knee joint in patients
with severe OA. According to an NIH census in 2003, approximately 300,000 TKR
surgeries are performed in the United States each year [NIH, 2003] and in recent years
that number has been climbing. Surgery aims at alleviating pain but does not repair
everything on a neuromuscular level. Therefore, it is unknown whether or not the
5
adaptive strategies developed to avoid pain before TKR carry over to the activities
after the surgery or if new ones develop. Some functional testing in the clinical setting
has identified deficits in locomotor abilities in persons post TKR including decreased
speed when walking and climbing stairs [Jacobs and Christensen, 2009, Walsh et al.,
1998].
Many individuals with neuromuscular impairments walk and ascend/descend stairs
slowly. It is important to isolate functional task from other factors such as age, muscle
weakness, etc. Evaluating a patients gait requires discriminating between deviations
caused by pathology and walking speed [Liu et al., 2008]. Isolating pathological locomotion from normal locomotion will establish whether characteristics of pathological
locomotion are due to muscle weakness, surgery, or other factors.
Of various functional tasks performed on a daily basis perhaps the most well
documented and understood is walking. Previous studies have analyzed the contributions of individual muscles to support and forward progression during level walking
[Neptune et al., 2004, Anderson and Pandy, 2003, Liu et al., 2006, Neptune et al.,
2008, Pandy, 2001]. These studies used dynamic optimization and musculoskeletal simulations to mimic experimental data. The models were used to determine
individual muscle contributions towards specific substasks in walking such as early
stance, late stance, progression and support. In these studies EMG recordings and
muscle-actuated forward dynamic simulations provided a means of estimating the
contribution of a particular muscle or groups of muscles to movement [Neptune et al.,
2004, 2008]. Collecting EMG data in addition to kinematic and kinetic data allows
for definitive evidence towards inferences that are made in its absence towards activations [Rudolph et al., 2001]. Normative muscle activations in groups of muscles and
6
in individual muscles serve as a basis for comparison to pathologic movement. This
comparison directs innovative surgical and rehabilitative therapies.
Many aspects of gait change with varying walking speeds. Kinematic and EMG
patterns have also been investigated at various speeds of walking [Murray et al.,
1984]. Studies showed a decrease in range of motion and decreased maximum flexion
for all joints and decreased magnitude of EMG while the subjects walked at slower
speeds. Thus, healthy slow walking would be better applied than self selected speeds
in evaluating pathological gait patterns which, typically, would be slower than healthy
persons’ self selected pace [Murray et al., 1984, Liu et al., 2008, Neptune et al., 2008].
Furthermore, the recovery of the ability to negotiate stairs is often used as a
factor to allow patients to return home after surgery or trauma [Startzell et al.,
2000]. There are multiple functional scales that use stair climbing as a measure for
locomotor ability post-stroke [Brott et al., 1989, Poole and Whitney, 1988, Holbrook
and Skilbeck, 1983], in the elderly [Pearlman, 1987, Washburn et al., 1993], in persons
after TKR[Jacobs and Christensen, 2009] and in children with CP [Bar-Haim et al.,
2004]. Studies have shown how climbing stairs affects joint kinematics [Andriacchi
et al., 1982], however the mechanisms by which muscles control the accelerations of
the center of mass are not well understood. Ascending and descending stairs, like level
walking, are rhythmic and periodic in nature recruiting similar muscles and producing
similar joint angles in each step [Ghafari et al., 2009]. The main differences between
walking and stair climbing are manifested in a significant increase in range of motion of
the lower limbs during stair climbing as well as changes in muscle activations [Ghafari
et al., 2009]. Characterization of the biomechanics of stair climbing in individuals
with these disabilities could direct innovative rehabilitative therapies to target and
7
strengthen impaired muscle groups so that they could negotiate stairs with increased
ease.
Because many aspects of gait have been shown to vary with walking speed [Andriacchi et al., 1982], it is hypothesized that biomechanical aspects of stair climbing
will also be affected by speed. Several studies have shown how muscles provide support and propulsion in over the ground walking [Pandy, 2001, Neptune et al., 2004,
Liu et al., 2006] and have shown the importance of walking speed when evaluating
muscle function [Liu et al., 2008]. However, individual muscle contributions towards
biomechanical tasks have not yet been quantified for stair climbing. Walking speed
influences each muscles contractile state (fiber length and velocity) which may alter
force and power generation in that muscle [Neptune et al., 2008]. It has been shown
that gait kinematics and muscle forces change with walking speed [Neptune et al.,
2008, Lelas et al., 2003]. As with level walking, it would be valuable to compare the
biomechanical properties of healthy normal stair climbing at various speeds to stair
climbing in individuals with physical disabilities since those with physical disabilities
tend to climb stairs at a self selected pace that is slower than that of healthy subjects.
1.1
Focus of Thesis
The purpose of this thesis is to create a normative database characterizing the
effect of speed in ascending and descending stairs in healthy normal subjects. This
was done by developing the experimental setup and collecting force, movement, and
muscle activation data. The main focus was to evaluate the kinematic, kinetic and
EMG data from the experiment. Additionally, a pilot study was performed to determine the force contributions of individual muscles in the lower extremities of healthy
8
young adults to understand normal function. This pilot study will be used to direct
future studies. All of the data for this study was collected from healthy subjects as
they ascended and descended stairs at various speeds: slow, self selected, and quick.
1.2
Significance of Research
The collection of normative biomechanical data for healthy young adults performing routine activities such as walking and ascending/descending stairs can serve as the
basis to compare pathological data allowing for innovations pre-, post- and interoperatively. People who have disabilities walk and perform other functional tasks such
as stair climbing more slowly than healthy subjects. Previous studies have developed
the normative muscles or groups of muscles that contribute to specific subtasks of
walking at various speeds. However, the normative data for various speeds of stair
climbing, as prevalent a task and as periodic as level over the ground walking, has
yet to be established.
This analysis will characterize the biomechanics of stair ascending/descending in
healthy persons so that future work can differentiate normal and pathological patterns in ascending and descending stairs. For example, one explanation for abnormal
characteristics of gait could be after total knee replacement the patients continued
to walk with a pattern that they had learned prior to treatment (TKR) [Andriacchi
et al., 1982]. The analysis and characterizations of parameters leading to impaired
movement and control can be used to guide therapeutic rehabilitation in these individuals.
9
1.3
Overview of Thesis
This masters thesis is comprised of six chapters. Chapter 2 discusses the methodology and protocol used to collect and analyze the data for the study. Chapter 3
presents the results of the study mostly in graphical form. Chapter 4 discusses the
results of the study. Chapter 5 is a completed pilot study for future work. Chapter 6,
the conclusion, is a summary of the thesis and addresses the future direction of this
work.
10
CHAPTER 2
METHODOLOGY
The goal of this study was to characterize the neuromuscular modifications responsible for ascending and descending stairs at various speeds using inverse kinematic
and inverse dynamic simulations that emulate the experimentally collected kinematic,
kinetic and EMG data of healthy young adults. Additionally, protocol to analyze the
muscle-actuated computational model for stair climbing was developed for this thesis.
What follows in this section is the background and protocol for both the collection of
the empirical data and the analysis using a subject-specific computational simulation.
2.1
Design and Build Modular Staircase for Gait Laboratory
Due to the orientation and size of the force plates within the testing facility at the
Sports Biomechanics Lab in the Martha Moorehouse Pavilion, stairs for this study
were specially designed and built for the facility. There are two conditions that must
exist in order for ground reaction forces to be accurately obtained from the force plates
in the gait lab. The first condition is that the foot must be completely within the force
plate that is measuring the ground reaction forces. The second condition is that there
must be no other forces applied to that force plate from the other foot or walking
aids [Oggero et al., 1998]. Therefore, when designing the stairs it was imperative that
11
each step for which ground reaction forces would be collected resided entirely within
its own force plate. The force plate layout (Figure 2.1 and Figure 2.2) shows one of
the possible stepping patterns for which the ground reaction forces can be measured.
Transition from level walking to stair climbing was of particular interest so the first
two force plates were used to measure level over the ground walking, potentially one
step with each foot. The next force plates measured the ground reaction forces placed
on the first and second steps respectively. Due to the isolation of the forces to each
independent step, the stairs created were of a modular design and the second step
was cantilevered over the first. In addition, the steps needed to be partially skeletal
so that as many of the cameras used for the motion capture as possible could detect
the reflection from the markers on the subjects.
The dimension of the stairs are what would be encountered in a standard building
and were based on previous studies[Nadeau et al., 2003, Ghafari et al., 2009, Andriacchi et al., 1980]. The important dimensions taken from the literature were the
rise and tread for each step which were 17 cm and 30 cm, respectively. Due to the
placement of the force plates, the second step was cantilevered in two directions. The
final design for the entire stair case mounted to the force plates is shown in Figure
2.3 and the staircase that was built can be seen in Figure 2.4.
A finite element analysis was performed for the middle, cantilevered step to asses
it’s displacement at the farthest corner from the base, where the load was meant
to be applied. This was done to verify that there would be minimal deflection and
that the stairs would be rigid for the data colection. In order for the entire step
to be approximated as steel, an equivalent section for the top wooden section was
determined with a constant cross section and loading from the top, but the thickness
12
Figure 2.1: Force plate layout in the Sports Biomechanics Lab in the Martha Moorehouse Pavilion.
13
Figure 2.2: Force plate layout in the Sports Biomechanics Lab in the Martha Moorehouse Pavilion with stepping pattern. R and L symbolize where the subject will step
with the right foot and left foot respectively.
14
Figure 2.3: Solid model assembly of completed staircase.
15
Figure 2.4: Completed staircase assembled in the Sports Biomechanics Lab. The
bottom two steps are bolted to force plates. There are two additional forceplates in
front of the steps.
16
Figure 2.5: Finite element analysis of the 2nd step (cantilevered step) was conducted
to find the maximum displacement of the step. The 300 lb load applied to the front
right corner can be see by the yellow arrow. The maximum displacement is indicated
at the front right corner and is 0.0251 inches.
reduced according to equations 2.1 - 2.3. The maximum displacement of the step was
determined computationally in a finite element package to be approximately 0.0251
inches at the farthest cantilevered area and can be seen in Figure 2.5.
Because loading and bending should be the same on the equivalent section, therefore:
!w = !s =
σw
σs
Ew
=
=⇒ σw =
σs
Ew
Es
Es
17
(2.1)
and
Pw = Ps =⇒ Mw = Ms =⇒
σw 1 bt3
σs 1 bt3
σw Iw
σs Is
=
= 112 w = 112 s
cw
cs
t
t
2 w
2 s
(2.2)
Combining equations 2.1 and 2.2
!
Ew
tw = ts
Es
The variables used in equations 2.1 - 2.3 are as follows.
!w
strain in the plywood
!s
σw
stress in the plywood
σs
Ew
Es
Young’s Modulus in the steel
Pw
applied force in the plywood
Mw
applied force in the steel
applied moment in the plywood
Ms
Is
stress in the steel
Young’s Modulus in the plywood
Ps
Iw
strain in the steel
applied moment in the steel
area moment of inertia in the plywood
area moment of inertia in the steel
b base dimension
tw
thickness of the plywood
18
(2.3)
ts
cw
distance to the neutral axis of the plywood
cs
2.2
thickness of the steel
distance to the neutral axis of the steel
Experimental Data Acquisition
The Sports Biomechanics Gait Laboratory in the Martha Morehouse Pavilion was
the facility used to collect the data for the study. Figure 2.6 shows the gait lab facility.
Eight MXF40 Vicon high speed motion capture cameras (Figure 2.7) recorded 3D
motion performed by subjects while four Bertec force plates embedded in the floor
recorded forces applied to the ground and the corresponding centers of pressure. One
eight channel electromyography (EMG) system recorded muscle activations during
activity. This experiment was performed using these technologies and Vicon software
to capture and store the data.
2.2.1
Marker Set
Passive optical markers are spherical markers covered with reflective material that
are attached to various anatomical landmarks on the body [Shafiq et al., 2001]. Light
emitted from infared sources mounted near the cameras used for the data acquisition
is reflected off of the markers and captured by the cameras [Shafiq et al., 2001]. The
point cluster technique (PCT) marker placement and approach (discussed in Section
2.3.1) was employed by placing clusters of markers on the limb in order to decrease the
nonrigid body artifact [Andriacchi et al., 1998, Alexander and Andriacchi, 2001]. The
marker positions for PCT in the lower extremities are shown in Figure A.5. The PCT
uses an overabundance of markers on the soft tissue areas over the femur and tibia
19
Figure 2.6: The Sports Biomechanics Lab in the Martha Moorhouse Pavilion at the
Ohio State University. The stairs have been mounted on the force plates in the center
of the image. There are 8 Vicon cameras mounted around the gym.
Figure 2.7: MXF40 Vicon high speed motion capture camera.
20
(a) PCT right
(b) PCT left
Figure 2.8: Placement of PCT markers [Andriacchi et al., 1998].
to define anatomical coordinate systems [Andriacchi et al., 1998]. In this experiment,
nine markers were placed in a cluster on the thigh and six markers were placed for
the cluster on the shank of both legs. In addition to the markers used for the PCT,
markers were also placed on the right and left shoulder, the asis, the psis, the clavicle
and the sternum which are shown in Figure A.6. This is a total of 58 markers.
2.2.2
EMG
In this study, action potentials were collected in a pilot study for eight muscles
in each leg: rectus femoris, hamstrings (biceps femurous), tibialis anterior, medial
gastrocnemius, vastus lateralis, gluteus maximus, gluteus medius, and soleus. This
21
Figure 2.9: Placement of torso markers. Markers used from this image are RSHO,
LSHO, ASIS, PSIS, CLAV and STRN.
22
was based on availability of sensors, as well as previous studies [Ghafari et al., 2009,
Catani et al., 2003, Andriacchi et al., 1980, Thelen and Anderson, 2006, Liu et al.,
2008, Anderson and Pandy, 2001]. Neptune showed that seven muscles: gluteus
medius, vastus lateralis, rectus femoris, soleus, gastrocnemius, tibialis anterior, hamstrings are primary contributors to biomechanical subtasks during walking [Neptune
et al., 2009]. However, after significant struggles with the EMG setup, for 10 of the
12 subjects EMG data for four muscles were collected for each leg: tibialis anterior,
medial vastus, medial gastrocnemius, and soleus.
For motor studies like this one, the active electrode is placed over the region where
the greatest number of motor neurons synapse, typically in the center of the muscle,
midway between the origin and insertion of the muscle [Tan, 2004]. The placement of
the EMG electrodes can be seen in Figures A.1a and A.1b. The reference electrode
is placed over an inactive area of the body such as the collar bone or the elbow. The
preamplifier enlarges the initial physiological signal before passing the signal to the
amplifier which is located near the computer [Tan, 2004]. The EMG data in this
experiment was processed by using a bandpass filter between 5 and 400 Hz, rectification and a low pass filter at 70 Hz. The signals were then normalized using the
peak values from MVIC trials. Maximal voluntary isometric contraction (MVIC)
was used because it is the most common normalization method used [Araujo RC,
2000, Knutson LM, 1994, Soderberg and Knutson, 2000]. MVIC trials provide more
accurate insight into what the maximum excitation of a subject’s muscle would be
[Worrell et al., 2001, Soderberg and Knutson, 2000]. This is because taking the maximum excitation from a stair trial for all the muscles may not necessarily be the
maximum excitations those particular muscles are capable of exerting. MVIC is also
23
a more repeatable measure to use than taking the maximum excitation from a stair
climbing cycle (which may be varied especially for different speeds) and normalizing
over that. It however, may present problems in a pathological population because
MVIC trials may be painful or the muscles may be weak. No data are available on
the variability of neurophysiological parameters as compared with maximal voluntary
isometric contraction (MVIC) in the same muscles, in healthy subjects [de Carvalho
et al., 2001, Soderberg and Knutson, 2000]. Therefore MVIC normalization for subjects with pathological gait is a percentage of maximum values that the subject can
use without pain and are not taken as a percentage of what they could use if they
were healthy. Another alternative in pathological populations has been the use of
EMG data obtained from subjects who are simply resting or passive [Soderberg and
Knutson, 2000].
2.2.3
Testing Protocol
Twelve healthy subjects participated in this study, 7 female and 5 male. The
number of subjects was based off of what has been used in previous studies [Ghafari
et al., 2009, Murray et al., 1984, Neptune et al., 2008, Liu et al., 2008, Catani et al.,
2003, Andriacchi et al., 1980, Anderson and Pandy, 2001, Nadeau et al., 2003]. Their
average age, height, mass and BMI was 24 ± 2 years, 1.725 ± 0.068 meters, 72.20 ±
18.35 kg, and 24.1 ± 5, respectively. Subjects were recruited based upon responding to
fliers posted in the community, blurbs in newsletters, and short announcements made
during an event that they are attending (e.g., class, meeting, information session, etc).
None of these subjects experienced any of the following exclusion criteria: previous
ACL tear, other ligament tear, tendor tear, muscle tear or meniscus tear in either
24
25
(b) Dorsal View
Figure 2.10: Placement of surface EMG electrodes (Figure taken from [Konrad, 2005]). We will be placing GMax, GMed,
BF, RF, VAS med, TA, GAS med, SOL.
(a) Frontal View
lower limb, previous surgery to either lower limb, inability to climb stairs, women in
their second or third trimester of pregnancy. A detailed protocol document for the
experiment can be found in the Appendix of this thesis.
For the pilot study muscle activation data was collected bilaterally using 16 sets of
surface electrodes placed on 8 muslces of each leg: rectus femoris, hamstrings, tibialis
anterior, medial gastrocnemius, medial vastus, gluteus maximus, gluteus medius, and
soleus. In Figure 2.11 a subject is shown descending the stairs. Here the subject has
been fitted with passive optical skin markers and 16 channels of surface EMG. For
the rest of the subjects muscle activation data was collected bilaterally using 8 sets of
(DELSYS) surface electrodes placed on 4 muslces of each leg: medial gastrocnemius,
medial vastus, tibialis anterior, and soleus. Once the EMG electrodes were placed,
MVIC trials were performed according the the protocol (found in the Appendix) for
each of the 8 muscles.
Passive reflective markers were placed on both the left and the right sides of
the body to measure the three dimensional positions of the segments of the lower
extremities. The PCT marker placement was used on the legs and 8 additional
markers were placed on the torso. Spatiotemporal and kinematic data were obtained
using eight MXF40 Vicon cameras, a computer system for acquisition, and Vicon
Motion Measurement and Analysis system.
A static calibration trial was collected in addition to two hip joint center trials.
The hip joint center trials employed a range of motion of the subjects legs to determine
the location of the center of the hip joint [Comomilla et al., 2006]. The hip joint
center in addition to the PCT marker placement allows for the replacement of the
PCT markers in the simulation with a marker coordinate system for the thigh and
26
Figure 2.11: Subject with PCT markers for motions capture and 16 channels of EMG
descending the stairs in the Sports Biomechanics Lab.
27
the shank. The code for this was developed by Dr. Ajit Chaudhari of the Sports
Biomechanics Lab at OSU following equations described in previous publications
[Andriacchi et al., 1998, Alexander and Andriacchi, 2001].
Subjects were asked to climb the stairs at their own self selected speeds and
allowed to practice until a comfortable and consistent self selected pace was achieved
without targeting the steps or the force plates. Data for the self selected speed was
then collected for three trials. The subjects were then instructed to walk at speeds
which they would consider to be a slow stroll and quick pace (about 0.5 and 1.5 times
their self selected speed, respectively). Three trials were performed at each speed
and data was collected for these trials. Approximate speeds were regulated using a
stopwatch. Previous studies assessed self selected speeds using a similar methodology
[Murray et al., 1984, Baliunas, 2002].
2.3
Musculoskeletal Simulation
The majority of data analysis and modeling for this experiment was performed
using an open-source musculoskeletal simulation in OpenSim [Delp et al., 2007]. This
program uses the marker positions to create and optimize an anthropomorphic model
of each subject and their movement. OpenSim uses the movement files to output
kinematic data such as joint angles. Force plate data is used to assess the dynamics
of the subjects joints. For most of the subjects, the data was only processed through
Inverse Dynamics (ID), however, a pilot study was conducted where the data from the
first subject was processed through CMC and the results were compared to the EMG.
The contribution of this analysis to this thesis is only qualitative but presented many
28
areas for improvement with the data acquisition and created a pipeline for future
data analysis.
2.3.1
ViconNexus
The data for this experiment was collected using ViconNexus motion capture
software. In this software, each marker was labeled according to Figure A.5. Gaps
in data were recovered. Trials in which significant markers were not present for the
entire trial were discarded.
At this point, code developed by Dr. Chaudhari of the Sports Biomechanics
Lab at Ohio State was applied to the data to find the hip joint centers, reduce the
PCT marker system and develop the coordinate system for the shank and thigh. The
functional hip joint centers were found by moving the thigh segment through its range
of motion and labeling the origin of the rotation with a virtual marker for the hip joint
center. The point cluster technique was implemented using the static calibration trial
where the subjects were asked to stand still. This trial provides reference positions
of the markers to create the transformation matrix from a global coordinate system
to an anatomical coordinate system. A weighting factor is applied to each marker
in order to determine the center of mass of the cluster within the global coordinate
system [Alexander and Andriacchi, 2001]. The eingenvectors of the inertia tensor
for the discrete point clusters establish a transformation between the anatomical and
global coordinate system [Andriacchi et al., 1998].
The orientation matrix is determined for the thigh segment using the hip joint
center and markers on the femoral condyle [Andriacchi et al., 1998]. The eigenvector
for the thigh’s medial-lateral axis is found from a line drawn between the medial and
29
lateral epicondyles. The inferior-superior axis for the thigh segment runs along the
femur between the midpoint of the line between the medial and lateral epicondyles
and the hip joint center. The anterior-posterior axis is a cross product of the other
two axes in the thigh coordinate system.
The coordinate system for the tibia is determined similarly but using markers
on the tibial plateau [Andriacchi et al., 1998]. The medial-lateral axis is determined
from a line drawn between the medial and lateral tibial plateau. The superior-inferior
axis is perpendicular to the medial lateral axis and passes through its midpoint. The
anterior-posterior axis is found by taking the cross product of the other two axes.
The virtual markers for these axes and their origins were created in ViconNexus,
applied to the stair ascending and descending trials, and were used in further processing in OpenSim instead of the original clusters. The data was then exported
and converted to a MOT and TRC files for OpenSim using custom Matlab code
that was modified from code created by Becky Lathrop and Brooke Morin for the
Neuromuscular Biomechanics Lab at OSU.
2.3.2
Scale Model
In the first step of the simulation a generic musculoskeletal model is scaled to
anthropomorphically match each individual subject. This is done using the static
calibration file so that the virtual markers on the simulation match the ones that
were output from ViconNexus. Additionally, subject body mass and scale factors are
entered manually to adjust the limb sizes and marker locations on the model. The
entire marker set after the PCT has been reduced to the virtual markers for the local
coordinate systems was used to scale the model.
30
2.3.3
Inverse Kinematics (IK)
For each trial, the next part of the analysis is Inverse Kinematics (IK). Inverse
Kinematics is the calculation of motions independent of the forces which produce
the motions. The IK are assessed using the motion files and the scaled model to
determine joint angles and translations that best fit the experimental marker data.
OpenSim uses a frame-by-frame weighted least squares optimization to minimize the
differences between virtual and motion captured marker locations. This is all done
in absence of force plate data.
In IK, anatomical coordinate systems (defined in static posture) for each body
segment are used instead of a global coordinate system so that angles make sense
from a clinical perspective. The IK analysis uses transformation matrices between
anatomical coordinate systems of adjacent segments for each frame of motion. Joint
angles are then extracted from this transformation matrix.
2.3.4
Inverse Dynamics (ID)
Inverse Dynamics (ID) employs force and moment data collected from the force
plates. ID computes internal forces and torques at each joint which produce the
movement estimated in the kinematics. The external forces are input from the force
plate data and applied to specific body parts. In this experiment, the external forces
were applied to the right and left calcaneus only. Inverse dynamics is a common
measure used to asses movement (especially in walking and running) [Andriacchi
et al., 2004].
In OpenSim ID are calculated using traditional force and moments equations:
31
For the ankle:
Fa = mf ∗ af − Fg + mf ∗ g
(2.4)
Ma = −Tg − (rankleCOM p xFa ) − (rankleCOM d xFg ) + If ∗ αf
(2.5)
Fk = ms ∗ as − Fa + ms ∗ g
(2.6)
Mk = −Ma − (rkneeCOM p xFa ) − (rkneeCOM d xFa ) + Is ∗ αs
(2.7)
Fh = mt ∗ at − Fk + mt ∗ g
(2.8)
Mh = −Ma − (rhipCOM p xFh ) − (rhipCOM d xFh ) + It ∗ αt
(2.9)
For the knee:
For the hip:
Subscripts refer to the following: g refers to the force on the ground, f refers to the
foot segment, s refers to the shank segment, t refers to the thigh segment, a refers to
the ankle joint, k refers to the knee joint, and h refers to the hip joint. The distances
of the center of mass are denoted by COMp for proximal and COMd for distal.
2.3.5
Residual Reduction Algorithm (RRA)
In OpenSim errors in IK and ID create residuals, especially where there are not
external loads applied to the body and the simulation applies additional residual forces
and moments so the model follows the same motion as the subject. The Residual
Reduction Algorithm is used to alter the inverted kinematic solution and trunk mass
center to minimize the residual forces applied to the body during ID [John, 2008].
RRA adjusts the center of mass of model segments to alter the dynamic consistency
of kinematic motion. RRA makes the ground reaction forces and moments more
consistent with the kinematics. In this thesis, RRA was run twice, first to find the
32
change in mass that the algorithm recommends and rescale the model. RRA is then
run again to reduce the residuals on the new model.
2.3.6
Computational Muscle Control (CMC)
Computational Muscle Control (CMC) is used to compute muscle excitations that
drive the dynamics of the subjects movement [Thelen and Anderson, 2006]. In OpenSim the output of this step of the analysis can be controlled based off of the active
periods in the experimentally acquired EMG data. Alternatively, EMG data can be
used in comparison with the results of the CMC analysis to determine the validity of
the model. Another benefit of using CMC is to determine muscle activations outside
of the ones measured with EMG.
2.3.7
Forward Dynamics (FD)
Forward Dynamics (FD) can be computed using the muscle excitations determined by the CMC. FD is an open loop system requiring no optimization or feedback
to ensure accuracy in the simulation. In theory, using the controls computed in CMC
should produce the same trajectory seen in IK and ID. The output trajectory from
forward dynamics can be compared to the trajectories from IK and ID to validate the
CMC portion of the simulation. Forward dynamics simulations are driven by individual muscles and therefore can show muscle contributions to power and and moments
especially in situations where there might be cocontraction.However, because it has
an open loop control in OpenSim, longer simulations in FD diverge from the expected
trajectories and are not reliable.
33
2.4
Signal Processing
The EMG signal was conditioned using a three step process. First, a bandpass
filter was applied filtering out only data that wasn’t between 5 Hz and 400 Hz. Next,
the signal was rectified. And finally, a lowpass filter was applied only allowing frequencies below 70 Hz. This processing was based on Neptune et al. [2009], Soderberg
and Knutson [2000] and an FFT taken of signal. This conditioned signal was then
normalized over the MVIC trials for the particular muscle for each subject. These
EMG values were then averaged for all the trials at each speed.
2.5
Statistics
A statistical analysis was performed for a small number of key variables. A oneway general, linear model analysis of variance (ANOVA) with repeated measures
was employed to determine the significance of speed within each subject. Tables in
the results section of this thesis include the means and standard deviations for the
entire population. Repeated measures were used to compare the three speeds of stair
climbing within each subject. P values less than 0.05 were statistically significant. A
post-hoc analysis was used to compare slower and faster speeds to the baseline value
of the self selected speed using paired t-tests. Additionally, a paired t-test was used
to compare values at the quick speed to values at the slow speed. This comparison
was statistically significant for P values less than 0.025 according to the Bonferroni
Correlation Factor for multiple correlations.
Variables of interest from IK were ankle, knee and hip flexion for foot strike on
level ground, foot strike on the first step, foot off of the level ground, foot strike on
the 2nd step and foot off the 1st step. The angles for both the leg in which the event
34
occurred and the opposite leg were analyzed. One full cycle was treated as foot strike
to foot strike of the same leg. Foot strike was determined to be when 2.5 percent
of the maximum force applied to the force plate was applied while the subject was
placing their foot onto the ground or the step. Similarly, foot off was determined at
2.5 percent of the maximum force applied to the force plate as the subject removed
their foot from the ground or the step. The variables of interest from ID were peak
hip, knee and ankle flexion moments, peak knee flexion and extension moments,
and minimum hip, knee and ankle flexion moments. Peak vertical GRFs were also
analyzed.
35
CHAPTER 3
RESULTS AND ANALYSIS
3.1
3.1.1
Ascending Stairs
Ground Reaction Forces
Three dimensional ground reaction forces were collected for one step on level
ground, the first stair and the second stair. The average vertical ground reaction
forces (GRF) for the experimental trials are plotted in Figure 3.1. The average
anterior-posterior ground reaction forces for the simulation are plotted in Figure 3.2.
These plots show the curves at the three different speeds. Forces are a percentage of
body-weight. For ascending stair trials step one correlates to the step one the first
force plate which is one level ground, step two correlates to the step taken onto force
plate two which is under the first stair, and step three corresponds to the step taken
onto the third force plate which is under the second stair.
There are three main sets of curves for the GRF which are for three force plates,
one of the two level force plates, the first stair and the second stair. One stair cycle
is defined as foot strike on level ground to foot off of the second stair. Red represents
the quick speed, blue the self selected speed, and green the slow speed. Superficially,
based on the figure alone, the red lines on the graph have much higher peaks than
36
the green lines. The green lines have a much flatter shape and lower peak magnitudes
on the figure. From Figure 3.1 it can be inferred that as the speed of stair climbing
increases, the forces applied to the steps and the ground increase. The plot for the
average anterior/posterior GRF in Figure 3.2 shows more posterior forces than what
is typically seen in level walking. This means that there is more decelerating of the
subject than propulsion forward in stair climbing. This is especially true of the AP
GRF curve for the first stair (the second force plate).
Figure 3.1: Vertical GRF for ascending stairs. Red represents the quick speed, blue
the self selected speed, and green the slow speed. Forces are a percentage of bodyweight.
Table 3.1 shows a statistical comparison of the peak vertical ground reaction forces
of the three steps at the three different speeds. Vertical ground reaction forces that
37
Figure 3.2: Anterior-Posterior GRF for ascending stairs. Red represents the quick
speed, blue the self selected speed, and green the slow speed. Forces are a percentage
of body-weight.
changed significantly with speeds (p less than 0.05) are indicated with and asterisk.
The table shows that forces on all of the force plates increase with speed. Although
standard deviations are high, the ANOVA was run with repeated measures, so the
P value is representative of significant changes within each subject due to speed.
Columns in the table are marked with a asterisk if the force at that speed has a
significant difference from the baseline (which is the force at the self selected speed).
Rows that that have a double asterisk (**) in the column with the P value denote a
significant variation due to speed between the slow and quick speed. In Table 3.1, all of
the columns, but one are marked with an asterisk. This is determined by the post-hoc
paired t-tests where the bonferroni correction factor is used to determine statistical
38
significance (p less than 0.025). Peak vertical ground reaction forces increase with
statistical significance as speed increases.
Table 3.1: Statistical results for ascending stairs peak ground reaction forces in the
vertical direction. Force plate 1 refers to the first step which is taken on level ground.
Force plate 2 refers to the step taken on the first step. Force plate 3 refers to the step
taken on the second step. Forces are a percentage of body-weight.
3.1.2
Inverse Kinematics
The hip, knee and ankle flexion angles from the simulation in OpenSim are used
in this thesis to describe the kinematics of stair climbing. The values were averaged
for the trials that correspond to the three different speeds for both legs. Figure 3.3
shows the sagital plane for a typical subject in OpenSim ascending the stairs. The
green arrows represent the ground reaction forces.
Figures 3.4, 3.5 and 3.6 are the plots of the average hip, knee and ankle flexion
angles respectively while ascending the stairs. Flexion angles are in degrees. Positive
values are for flexion and negative values are for extension in both the hip and the
knee. For the ankle, positive values are for dorsiflexion and negative values are for
plantarflexion. One entire cycle is defined as foot strike on the level ground to foot off
of the second step. Light blue represents the slow speed, blue represents self selected
speed and pink represents the quick speed. The solid line depicts the first leg to
39
Figure 3.3: Stair climbing simulation to process IK with forces in OpenSim, forces
are indicated with green arrow.
contact the force plates. As seen in Figure 3.4 the range of average hip angles for a
stair cycle is approximately between -20 and 60 degrees. The range of average knee
angles for a stair cycle is approximately between 0 and 100 degrees (Figure 3.5). As
seen in Figure 3.6 the range of average ankle angles for a stair cycle is approximately
between -20 and 40 degrees.
Tables 3.2, 3.3, and 3.4 show the mean values and standard deviations of the
peak angles of the hip, knee and ankle respectively during swing. This is compared
across the three different speeds, slow, normal and quick, for each of the three steps
40
41
Figure 3.4: Stair Climbing IK Hip Flexion Angle output from OpenSim. Light blue represents the slow speed, blue
represents self selected speed and pink represents the quick speed. The solid line depicts the first leg to contact the force
plates.
42
Figure 3.5: Stair Climbing Knee flexion Angle output from OpenSim. Light blue represents the slow speed, blue represents
self selected speed and pink represents the quick speed. The solid line depicts the first leg to contact the force plates.
43
Figure 3.6: Stair Climbing Ankle Flexion Angle output from OpenSim. Positive values indicate dorsiflexion and negative
values indicate plantarflexion. Light blue represents the slow speed, blue represents self selected speed and pink represents
the quick speed. The solid line depicts the first leg to contact the force plates.
Table 3.2: Statistical results for ascending stairs kinematics. Flexion angles are in
degrees. Significant P values are marked with an asterisk both for the repeated
measures ANOVA and for the post-hoc.
taken. Peak values with significantly different means based on speed have P values
less than 0.05(marked in the tables with an asterisk). For the peak values that were
statistically significant, an asterisk denotes the speed (slow, fast, or both) that varies
significantly from the baseline (the self selected speed). Rows that that have a double
asterisk (**) in the column with the P value denote a significant variation due to
speed between the slow and quick speed. Table 3.2 shows two of the three peak hip
flexion angles vary significantly with speed (level ground and stair one). They increase
with speed. Table 3.3 shows all of the peak knee flexion angles increase with speed.
Table 3.4shows only one of the peak ankle dorsiflexion angles varies with speed. The
dorsiflexion on stair two increases with speed.
Leg one refers to the first leg to strike a force plate. The first event for leg one is
foot strike (Table 3.5) of the first leg on level ground. The second event for leg one
is approximately midstance (Table 3.6) and refers to the foot strike of the second leg
on the first step. The third event for leg one refers to the foot off (Table 3.7) of the
first force plate. The fourth event for leg one is foot strike (Table 3.8) of the first
leg on the second step. Each event was compared across the various speeds. Mean
44
Table 3.3: Statistical results for ascending stairs kinematics. Flexion angles are in
degrees. Significant P values are marked with an asterisk both for the repeated
measures ANOVA and for the post-hoc.
Table 3.4: Statistical results for ascending stairs kinematics. Flexion angles are in
degrees. Significant P values are marked with an asterisk both for the repeated
measures ANOVA and for the post-hoc.
45
Table 3.5: Statistical results for foot strike in ascending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Significant P values are marked with an
asterisk both for the repeated measures ANOVA and for the post-hoc.
Table 3.6: Statistical results for midstance in ascending stairs kinematics. Leg 1 refers
to the first leg to strike a force plate. Significant P values are marked with an asterisk
both for the repeated measures ANOVA and for the post-hoc.
values and standard deviations for hip flexion, knee flexion and ankle flexion for each
event for leg one are shown in Tables 3.5 - 3.8. The speeds are labeled as 0.5 x SS
speed for slow, 1 x SS speed for self selected speed and 1.5 x SS speed for quick. Any
angles that had significantly different means for the three speeds have a P value less
than 0.05 (marked in the tables with an asterisk). For the flexion angles that were
statistically significant, an asterisk denotes the speed (slow, fast, or both) that varies
significantly from the baseline (the self selected speed). Rows that that have a double
asterisk (**) in the column with the P value denote a significant variation due to
speed between the slow and quick speed.
46
Table 3.7: Statistical results for foot off in ascending stairs kinematics. Leg 1 refers
to the first leg to strike a force plate. Significant P values are marked with an asterisk
both for the repeated measures ANOVA and for the post-hoc.
Table 3.8: Statistical results for foot strike in ascending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Significant P values are marked with an
asterisk both for the repeated measures ANOVA and for the post-hoc.
47
All of the angles for all of the events for leg one vary significantly. For the first
foot strike and for foot off, all of the flexion angles increase with speed. For midstance
hip flexion and knee flexion increase with speed and ankle dorsiflexion decreases with
speed. For the second foot strike, there is no clear pattern of change with speed for
hip and knee flexion angles, but ankle dorsiflexion decreases with speed.
Leg two refers to the second leg to strike a force plate. The first event for leg
two is foot strike of the second leg on the first step. The second event for leg two
is early in stance and refers to the foot off of the first force plate. Third event for
leg two is about midstance for stair climbing and refers to the foot strike of the first
leg on the second step. Fourth event for leg two is foot off the first step. Each event
was compared across the various speeds. Mean values and standard deviations for
hip flexion, knee flexion and ankle flexion for each event for leg two are shown in
Tables 3.9 - 3.12. The speeds are labeled as 0.5 x SS speed for slow, 1 x SS speed for
self selected speed and 1.5 x SS speed for quick. Any angles that had significantly
different means for the three speeds has a P value less than 0.05 (marked in the tables
with an asterisk). For the flexion angles that were statistically significant, an asterisk
denotes the speed (slow, fast, or both) that varies significantly from the baseline (the
self selected speed). Rows that that have a double asterisk (**) in the column with
the P value denote a significant variation due to speed between the slow and quick
speed.
Most, but not all of the flexion angles vary for all of the events for leg two. Only
knee flexion varies for foot strike. It increases with speed. For early stance, knee and
ankle flexion both decrease with speed. All of the flexion angles increase with speed
48
Table 3.9: Statistical results for foot strike in ascending stairs kinematics. Leg 2
refers to the second leg to strike a force plate. Significant P values are marked with
an asterisk both for the repeated measures ANOVA and for the post-hoc.
Table 3.10: Statistical results for early stance in ascending stairs kinematics. Leg 2
refers to the second leg to strike a force plate. Significant P values are marked with
an asterisk both for the repeated measures ANOVA and for the post-hoc.
Table 3.11: Statistical results for midstance in ascending stairs kinematics. Leg 2
refers to the second leg to strike a force plate. Significant P values are marked with
an asterisk both for the repeated measures ANOVA and for the post-hoc.
49
Table 3.12: Statistical results for foot off in ascending stairs kinematics. Leg 2 refers
to the second leg to strike a force plate. Significant P values are marked with an
asterisk both for the repeated measures ANOVA and for the post-hoc.
in midstance. At foot off, hip and knee ankles increase with speed and ankle plantar
flexion increases with speed.
3.1.3
Inverse Dynamics
Figures 3.7, 3.8 and 3.9 are the plots of the average hip, knee and ankle internal
flexion and extension moments respectively for the ascending stair trials. One entire
cycle is defined as foot strike on the level step to foot off of the second step. Light
blue represents the slow speed, blue represents self selected speed and pink represents
the quick speed. The solid line depicts the first leg to contact the force plates and
the dotted line indicated the second foot to strike the force plates. The torque is
normalized over the body weight multiplied by the height of each individual subject
before it is averaged for all the trials of the same speed.
As seen in Figure 3.20, the range of average hip torque for a stair cycle is approximately between 2 and -5 percent bodyweight times height. As seen in Figure 3.21
the range of average knee torque for a stair cycle is approximately between 2 and -5
percent bodyweight times height. As seen in Figure 3.22 the range of average ankle
50
torque for a stair cycle is approximately between 0 and -8 percent bodyweight times
height.
Tables 3.13, 3.14, and 3.15 tabulate the mean and standard deviation for the peak
positive values of the hip, knee and ankle moments respectively. Tables 3.16, 3.17,
and 3.18 tabulate the mean and standard deviation for the peak negative values of
the hip, knee and ankle moments respectively for the three different speeds. A P
value less than 0.05 indicates a statistically significant difference between the means
of the moments for the three different speeds. Significant P values are marked with
an asterisk both for the repeated measures ANOVA and for the post-hoc t-tests.
Table 3.13: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
Table 3.14: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
51
52
Figure 3.7: Stair climbing ID hip torque. Light blue represents the slow speed, blue represents self selected speed and pink
represents the quick speed. The solid line depicts the first leg to contact the force plates and the dotted line indicated the
second foot to strike the force plates. The torque is normalized over the body weight multiplied by the height
53
Figure 3.8: Stair climbing ID knee torque. Light blue represents the slow speed, blue represents self selected speed and
pink represents the quick speed. The solid line depicts the first leg to contact the force plates and the dotted line indicated
the second foot to strike the force plates. The torque is normalized over the body weight multiplied by the height
54
Figure 3.9: Stair climbing ID ankle torque. Light blue represents the slow speed, blue represents self selected speed and
pink represents the quick speed. The solid line depicts the first leg to contact the force plates and the dotted line indicated
the second foot to strike the force plates. The torque is normalized over the body weight multiplied by the height
Table 3.15: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
Table 3.16: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
Table 3.17: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
Table 3.18: Statistical results for ascending stairs kinetics. Moments are a percentage
of bodyweight*height.
55
Many of the peak internal flexion and extension moments vary with speed for
stair ascending. The peak internal hip flexion moment increases for level ground and
for the first stair. The peak knee flexion moment decreases on level ground. The
peak dorsiflexion moment increases on level ground. All peak hip extension moments
increase with speed. The peak knee extension moment only increases on level ground.
All of the peak plantarflexion moments increase with speed.
3.1.4
EMG
Electromyography data was collected experimentally for four muscles bilaterally.
The average EMG signal after being conditioned can be seen in Figures 3.10, 3.11,
3.12 and 3.13. EMG data was only taken for subjects 06-12 because of problems
limited by EMG system while collecting data for the first five subjects. One stair
climbing cycle is defined from foot strike on level ground to foot off of the second
step. Values of muscle activation are a percentage of the MVIC. Red represents the
quick speed, blue the self selected speed and green the slow speed.
56
Figure 3.10: The average EMG activation for the gastroc muscle (GAS). Values of
muscle activation are a percentage of the MVIC. Red represents the quick speed, blue
the self selected speed and green the slow speed.
57
Figure 3.11: The average EMG activation for soleus muscle (SOL). Values of muscle
activation are a percentage of the MVIC. Red represents the quick speed, blue the
self selected speed and green the slow speed.
Figure 3.13: The average EMG activation for the vastus (VAS). Values of muscle
activation are a percentage of the MVIC. Red represents the quick speed, blue the
self selected speed and green the slow speed.
58
Figure 3.12: The average EMG activation for the tibialis anterior (TA). Values of
muscle activation are a percentage of the MVIC. Red represents the quick speed,
blue the self selected speed and green the slow speed.
Figure 3.10 shows the average activation for the medial gastroc (GAS) muscle
during one stair cycle. There are some variations in phase and magnitude for the
EMG at the different speeds, but the general shape has peaks at foot off and very
little activity during early stance. Slower speeds, especially the slowest, has decreased
activation in the gastroc muscles. The gastroc muscles are also active earlier in stance
at slower speeds than in quicker speeds.
Figure 3.11 shows the average activation for the soleus (SOL) muscle during one
stair cycle. The soleus muscles are active for longer in stance than the gastroc muscles,
but the peaks for the soleus muscles also occur at toe off and the beginning of the
swing phase. Where the subjects progress to stair climbing from level walking, a
second peak in soleus activity occurs after weight acceptance.
59
Figure 3.12 shows the activation of the tibialis anterior (TA) muscle for one stair
cycle. The TA is active during most of the stair climbing cycle. Peak activations
occur during swing. The peak magnitude of the TA is smaller for the slowest speed.
Figure 3.13 shows the average activation of the medial head of the vastus (VAS)
muscle for one stair cycle. The first step taken on level ground has typical vastus
activations for level walking where the highest activations are in the beginning of
stance to decelerate the center of mass. The peaks for the vastus during stance on
the first step and the second step are much greater than the activation on level ground.
Slower speeds have lower peak magnitudes.
3.2
3.2.1
Descending Stairs
Ground Reaction Forces
For descending stair trials, three dimensional ground reaction force data were
collected for the second stair, the first stair and level ground. The average vertical
ground reaction forces (GRF) for descending stairs are plotted in Figure 3.14. The
average anterior-posterior ground reaction forces for the simulation are plotted in Figure 3.15. These plots show the differences at the three speeds. Forces are normalized
over body-weight. For descending stairs, step one is taken onto the first force plate
which is under the second stair, step two is taken onto the second force plate which
is under the first stair, and step three is taken onto the third force plate which is on
level ground.
There are three main sets of curves for the GRF which are for three force plates,
the second step, the first step and one of the two level force plates. One stair cycle is
defined as foot strike on second step to foot off of the level ground. Red represents
60
the quick speed, blue the self selected speed, and green the slow speed. Based on
the figures alone, it can be inferred that stair descending trials at faster speeds have
higher ground reaction forces. The plot for the average anterior/posterior GRF in
Figure 3.15 shows significant anterior forces. This means that, when the subject
is descending staris, there is a lot more acceleration and propulsion than there are
breaking forces. This is especially true of the AP GRF curve for the first stair (the
second force plate) and the last step which is on level ground.
Figure 3.14: Vertical GRF for descending stairs. Red represents the quick speed,
blue the self selected speed and green the slow speed. Forces are a percentage of
body-weight.
Table 3.19 shows a statistical comparison of the peak vertical ground reaction
forces (normalized over body-weight) on the three steps for each of the three speeds
61
Table 3.19: Statistical results for descending stairs peak vertical ground reaction
forces. Forces are a percentage of body-weight. Significant P values are marked with
an asterisk both for the repeated measures ANOVA and for the post-hoc t-tests.
(slow, self selected and quick). Vertical ground reaction forces with significantly
different means for the three speeds have P values less than 0.05 (denoted by an
asterisk) . The table shows that forces on all of the force plates increase with speed.
Although standard deviations are high, the ANOVA was run with repeated measures,
so the P value is representative of signicant changes within each subject due to speed.
Columns in the table that show the mean and standard deviation of the forces are
marked with a asterisk if the force at that speed that for the specic force plate that
has a significant difference from the baseline (which is the force on that force plate
at the self selected speed). Rows that that have a double asterisk (**) in the column
with the P value denote a significant variation due to speed between the slow and
quick speed. For descending stairs, all of the peak vertical ground reaction forces
increase with speed.
62
Figure 3.15: Anterior-Posterior GRF for descending stairs. Red represents the quick
speed, blue the self selected speed and green the slow speed. Forces are a percentage
of body-weight.
3.2.2
Inverse Kinematics
Hip, knee and ankle flexion angles are used to describe the kinematics of stair
descending in this thesis. Figure 3.16 shows the sagital plane for a typical subject
in OpenSim descending the stairs. The green arrows represent the ground reaction
forces.
63
Figure 3.16: Stair descending IK with forces in OpenSim, forces are indicated with
green arrow.
Figures 3.17, 3.18 and 3.19 are the plots of the average hip, knee and ankle flexion angles respectively while descending the stairs. Angles are measure in degrees.
Positive angles indicate flexion and negative angles indicate extension for the hip and
knee. For the ankle, positive angles indicate dorsiflexion and negative angles indicate
plantar flexion. One entire cycle is defined as foot strike on the second step to foot
off of the level ground. Light blue represents the slow speed, blue represents self
64
selected speed and pink represents the quick speed. The solid line depicts the first
leg to contact the force plates.
As seen in Figure 3.17 the range of average hip angles for a stair cycle is approximately between -30 and 30 degrees. As seen in Figure 3.18 the range of average knee
angles for a stair cycle is approximately between 0 and 100 degrees. As seen in Figure
3.19 the range of average ankle angles for a stair cycle is approximately between -30
and 40 degrees.
Tables 3.20, 3.21, and 3.22 show the mean values and standard deviations of the
peak angles of the hip, knee and ankle respectively during swing. This is compared
across the three different speeds: slow, normal and quick for each step. Peak angles
with significantly different means for the three speeds have P values less than 0.05
(marked by an asterisk). Within rows with significant P values, the columns (slow
or quick speed) representing a significant difference in angle from the baseline (self
selected speed) are also marked with an asterisk. Rows that that have a double
asterisk (**) in the column with the P value denote a significant variation due to
speed between the slow and quick speed. For these tables, although the standard
deviations are large, they are large for the whole population and P values are based
on variations within a given subject’s moment (repeated measures ANOVA).
65
66
Figure 3.17: Stair descending average hip flexion angle results from OpenSim. Light blue represents the slow speed, blue
represents self selected speed and pink represents the quick speed. The solid line depicts the first leg to contact the force
plates. Flexion angle is in degrees.
67
Figure 3.18: Stair descending average knee angle results from OpenSim. Light blue represents the slow speed, blue
represents self selected speed and pink represents the quick speed. The solid line depicts the first leg to contact the force
plates. Flexion angle is in degrees.
68
Figure 3.19: Stair descending average ankle angle results from OpenSim. Light blue represents the slow speed, blue
represents self selected speed and pink represents the quick speed. The solid line depicts the first leg to contact the force
plates. Flexion angle is in degrees.
Table 3.20: Statistical results for descending stairs kinematics. Flexion angle is in
degrees.
Table 3.21: Statistical results for descending stairs kinematics. Flexion angle is in
degrees.
Table 3.22: Statistical results for descending stairs kinematics. Flexion angle is in
degrees.
The following peak flexion angles change significantly with speed. Hip flexion
angle increases with speed for the second stair. Peak knee flexion increases between
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the slow speed and self selected speed for the first stair. Peak ankle dorsiflexion
decreases with speed for stair two, level ground and between the self selected and
quick speed for stair one.
Leg one refers to the first leg to strike a force plate. The first event for leg one is
foot strike of the first leg on step two. The second event for leg one is approximately
midstance and refers to the foot strike of the second leg on the first step. The third
event for leg one is foot off of the second step. The fourth event for leg one is foot
strike of the first leg on the level ground. Mean values and standard deviations for
hip flexion, knee flexion and ankle flexion for each event for leg one are shown in
Tables 3.23 - 3.26. Each event was compared across the various speeds. The speeds
are labeled as 0.5 x SS speed for slow, 1 x SS speed for self selected speed and 1.5 x
SS speed for quick. Any angles that had significantly different means for the three
speeds have a P value less than 0.05 (marked with an asterisk). Within rows that
have significant P values, the columns (slow or quick speed) representing a significant
difference in angle from the baseline (self selected speed) are also marked with an
asterisk. Rows that that have a double asterisk (**) in the column with the P value
denote a significant variation due to speed between the slow and quick speed.
Table 3.23: Statistical results for foot strike in descending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Flexion angle is in degrees.
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Table 3.24: Statistical results for midstance in descending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Flexion angle is in degrees.
Table 3.25: Statistical results for foot off in descending stairs kinematics. Leg 1 refers
to the first leg to strike a force plate. Flexion angle is in degrees.
Table 3.26: Statistical results for foot strike in descending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Flexion angle is in degrees.
Only a few of the angles in the events for leg one change significantly with speed.
For the first foot strike, knee flexion increases between the self selected speed and the
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quick speed. Ankle plantar flexion for foot strike decreases with speed. For midstance,
only the ankle dorsiflexion angle changes with speed; it decreases. At foot off, knee
flexion increases from slow speed to self select, but decreases from self selected speed
to quick. For the second foot strike, knee flexion decreases with speed.
Leg two refers to the second leg to strike a force plate. The first event for leg
two is foot strike of the second leg on the first step. The second event for leg two
is early stance and refers to the foot off of the second step. The third event for leg
two is at approximately midstance and refers to the foot strike of the first leg on
the level ground. The fourth event for leg two is foot off the first step. Each event
was compared across the various speeds. Mean values and standard deviations for
hip flexion, knee flexion and ankle flexion for each event for leg two are shown in
Tables 3.27 - 3.30. The speeds are labeled as 0.5 x SS speed for slow, 1 x SS speed
for self selected speed and 1.5 x SS speed for quick. Any angles that had significantly
different means for the three speeds have a P value less than 0.05 (marked with an
asterisk). Within rows that have significant P values, the columns (slow or quick
speed) representing a significant difference in angle from the baseline (self selected
speed) are also marked with an asterisk. Rows that that have a double asterisk (**)
in the column with the P value denote a significant variation due to speed between
the slow and quick speed.
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Table 3.27: Statistical results for foot strike in descending stairs kinematics. Leg 2
refers to the second leg to strike a force plate. Flexion angle is in degrees.
Table 3.28: Statistical results for early stance in descending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Flexion angle is in degrees.
Table 3.30: Statistical results for foot off in descending stairs kinematics. Leg 1 refers
to the first leg to strike a force plate. Flexion angle is in degrees.
For foot strike only knee flexion is affected by speed and increases as speed increases. Knee flexion increases from slow speed to self selected speed for early stance.
At midtance there is increased hip extension and decreased ankle dorsiflexion with
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Table 3.29: Statistical results for midstance in descending stairs kinematics. Leg 1
refers to the first leg to strike a force plate. Flexion angle is in degrees.
increased speed. At foot off for leg two, all flexion angles decrease with increasing
speed.
3.2.3
Inverse Dynamics
Figures 3.20, 3.21 and 3.22 are the plots of the average hip, knee and ankle internal
flexion and extension moments respectively for descending stair trials. Moments were
normalized over body-weight multiplied by height for each individual subject. One
entire cycle is defined as foot strike on the second step to foot off of the level ground.
Light blue represents the slow speed, blue represents self selected speed and pink
represents the quick speed. The solid line depicts the first leg to contact the force
plates. The torque is normalized over the body weight multiplied by the height of
each individual subject before it is averaged for all the trials of the same speed.
As seen in Figure 3.20, the range of average hip torque for a stair cycle is approximately between 4 and -4 percent body weight * height. As seen in Figure 3.21 the
range of average knee torque for a stair cycle is approximately between 4 and -8 percent body weight * height. As seen in Figure 3.22 the range of average ankle torque
for a stair cycle is approximately between 2 and -8 percent body weight * height.
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Figure 3.20: Stair descending ID hip torque. Light blue represents the slow speed, blue represents self selected speed and
pink represents the quick speed. The solid line depicts the first leg to contact the force plates. Moments are a percentage
of body-weight * height.
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Figure 3.21: Stair Climbing ID Knee Torque. Light blue represents the slow speed, blue represents self selected speed and
pink represents the quick speed. The solid line depicts the first leg to contact the force plates. Moments are a percentage
of body-weight * height.
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Figure 3.22: Stair Climbing ID Ankle Torque. Light blue represents the slow speed, blue represents self selected speed and
pink represents the quick speed. The solid line depicts the first leg to contact the force plates. Moments are a percentage
of body-weight * height.
Tables 3.31, 3.32, and 3.33 tabulate the mean and standard deviation for the peak
positive values of the hip, knee and ankle moments respectively. Tables 3.34, 3.35,
and 3.36 tabulate the mean and standard deviation for the peak internal extension
moments of the hip, knee and ankle plantar flexion moments respectively for the three
different speeds. A P value less than 0.05 indicates a statistically significant difference
between the means of the moments for the three speeds (denoted by an asterisk next
to the Pvalue). Rows that that have a double asterisk (**) in the column with the P
value denote a significant variation due to speed between the slow and quick speed.
Columns corresponding to values that have significant differences from the baseline
vales (at self selected speed) are also marked with an asterisk.
Table 3.31: Statistical results for descending stairs kinetics Step 1 refers to the step
which is taken on the second stair. Step 2 refers to the step taken on the first step.
Step 3 refers to the step taken on level ground. Moments are a percentage of bodyweight * height.
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Table 3.32: Statistical results for descending stairs kinetics. Step 1 refers to the
step which is taken on the second stair. Step 2 refers to the step taken on the first
step. Step 3 refers to the step taken on level ground. Moments are a percentage of
body-weight * height.
Table 3.33: Statistical results for descending stairs kinetics. Step 1 refers to the
step which is taken on the second stair. Step 2 refers to the step taken on the first
step. Step 3 refers to the step taken on level ground. Moments are a percentage of
body-weight * height.
Table 3.34: Statistical results for descending stairs kinetics Step 1 refers to the step
which is taken on the second stair. Step 2 refers to the step taken on the first step.
Step 3 refers to the step taken on level ground. Moments are a percentage of bodyweight * height.
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Table 3.35: Statistical results for descending stairs kinetics. Step 1 refers to the step
which is taken on the second stair. Step 2 refers to the step taken on the first step.
Step 3 refers to the step taken on level ground.
Table 3.36: Statistical results for descending stairs kinetics. Step 1 refers to the
step which is taken on the second stair. Step 2 refers to the step taken on the first
step. Step 3 refers to the step taken on level ground. Moments are a percentage of
body-weight * height.
Most, but not all, of the peak flexion and extension moments change with speed.
All peak hip flexion moments increase with speed. Peak knee flexion moments increases with speed for stair one. For stair two peak knee flexion moments increase
from slow speed to self selected speed, but decrease from self selected speed to quick.
Peak ankle dorsiflexion moments increase with speed. Peak hip extension moments
decrease with speed for stair two and increase for stair one. Peak knee extension moments increase with speed for stair two. Peak ankle plantarflexion moments increase
with speed.
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3.2.4
EMG
The average EMG signal after being conditioned can be seen in Figures 3.23,
3.24, 3.25 and 3.26. These averages were only taken for the data from subjects 06-12
because of issues with the EMG data for the first five. Muscle activations are shown
as a percentage of the MVIC. One stair descending cycle is defined from foot strike
on step two to foot off of the level ground. Red represents the quick speed, blue the
self selected speed and green the slow speed. The solid line indicates the second leg
to contact a force plate.
Figure 3.23: The average EMG activation of GAS. Muscle activations are a percentage
of the MVIC. Red represents the quick speed, blue the self selected speed and green
the slow speed.
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Figure 3.24: The average EMG activation of SOL. Muscle activations are a percentage
of the MVIC. Red represents the quick speed, blue the self selected speed and green
the slow speed.
Figure 3.25: The average EMG activation of TA. Muscle activations are a percentage
of the MVIC. Red represents the quick speed, blue the self selected speed and green
the slow speed.
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Figure 3.26: The average EMG activation of VAS. Muscle activations are a percentage
of the MVIC. Red represents the quick speed, blue the self selected speed and green
the slow speed.
Figure 3.23 shows the average activation for the medial gastroc (GAS) muscle
during one stair cycle. Figure 3.23 shows that the GAS is active during stance. The
peak activation values of the GAS increase with speed.
Figure 3.24 shows the average activation for the soleus (SOL) muscle during one
stair cycle. As was found with stair climbing, with descending stairs, the SOL muscles
are active during the whole stair cycle. Peak activations occur during stance. The
activations are close in magnitude for the lower speeds, but at the fast speed the
activations of the SOL are higher.
Figure 3.25 shows the activation of the tibialis anterior (TA) muscle for one stair
cycle. The TA are active for the entire stair climbing cycle. The activations of the
TA are higher at faster speeds.
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Figure 3.26 shows the average activation of the medial head of the vastus (VAS)
muscle for one stair cycle. The VAS are active in end of stance and in the beginning
of swing. Most of the curves have two separate peaks. The first peak is to decelerate
the center of mass in stance and the second peak occurs during the downward swing.
The last step taken on level ground has only one peak, this is for decelerating the
center of mass. The magnitudes are close for these curves, but are slightly higher for
faster speeds.
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CHAPTER 4
DISCUSSION
4.1
4.1.1
Ascending Stairs
Ground Reaction Forces
The plot for the average vertical GRF in Figure 3.1 shows the GRF applied to
three force plates. The first force plate is on level ground, the second force plate has
the first stair bolted to it, and the third force plate has the second stair bolted to it.
Each of the force plates has the same general shape for the forces that are applied to
it during the stair climbing. There are, however, some differences in the curves at the
three speeds. The slowest speed has a much flatter curve for the three force plates
and has a smaller magnitude. This is more clearly defined in Table 3.1 which shows
that for all three of the steps there is a statistically significant difference in the mean
values for the peak forces. Post-hoc analysis shows that as the speed of stair climbing
increases, the forces applied to the steps and the ground increase.
The plot for the average anterior/posterior GRF in Figure 3.2 shows more posterior
forces than what is typically seen in level walking. This was also seen in a study done
by Riener et al. [2002]. This means that there is more decelerating of the subject than
propulsion forward in stair climbing. This is especially true of the AP GRF curve
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for level ground and the first stair (the second force plate). On the second stair, the
magnitudes of the anterior and posterior portions of the curve become more similar.
This may mean that the steady state stair climbing has been reached by the second
stair.
4.1.2
Inverse Kinematics
The shapes of the hip flexion curves seen in Figure 3.4 are periodic with the
maximum flexion during the swing. The stair climbing cycle begins with foot strike
on the level force plate and ends at foot off the second stair. The maximum flexions
are compared at the three speeds (slow, self selected and quick) in Table 3.2. Peak
hip flexion increases with speed on level ground and for stair one. This is evident in
Figure 3.4, as well. Peak hip flexion in swing was about 50 degrees. These values
are close to and between values found by Andriacchi in 1980 [Andriacchi et al., 1980]
(about 41 degrees of flexion during the swing phase of stair climbing) and Nadeau
[Nadeau et al., 2003] in 2003 (about 60 degrees at peak flexion).
The shapes of the knee flexion curves in Figure 3.5 are periodic with the maximum
flexion during the swing. These maximum flexions are compared at the three speeds
in Table 3.3. The peak knee flexion angles change significantly with speed for the first
step on level ground and for the step that is taken on the first stair. For these steps,
peak knee flexion increases as speed increases. This is evident in Figure 3.5, especially
for the second step which is on the first stair. Peak knee flexion was between 80 and
100 degrees for all of the stairs, less for the first step. These values are close to, but
slightly higher than, what was found by Andriacchi in 1980 [Andriacchi et al., 1980]
which was between 70 and 80 degrees for the swing phase of ascending stairs. Catani
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[Catani et al., 2003] and Nadeau [Nadeau et al., 2003], however, found maximum
knee flexion to be about 89 and 93 degrees, which are both in the middle of the range
found in this thesis.
The shapes of the ankle flexion curves in Figure 3.6 are periodic with the positive values indicating dorsiflexion and negative values indicating plantarflexion. The
maximum dorsiflexion are compared at the three speeds in Table 3.4. None of the
peak ankle flexion angles change significantly with speed. This is evident in Figure
3.6, especially for the first and last steps where the curves are on top of each other.
The average peak flexion of the ankle is about 30 degrees. This is different from
what was found by Andriacchi in 1980 [Andriacchi et al., 1980] where the maximum
ankle flexion is only about 13 degrees, but consistent with what Nadeau found in
2003 [Nadeau et al., 2003] which was 30 degrees. In Figure 3.6 dorsiflexion occurs in
both swing and in weight acceptance. Plantarflexion occurs mainly at foot off.
During stair climbing for the level foot strike on the ground before ascending, all
of the angles increase with speed. In midtstance, hip and knee flexion increase with
speed and ankle dorsiflexion decreases with speed. At foot off, hip and knee flexion
increase with speed. At foot strike, onto a step hip flexion decreases with speed.
Overall, in the kinematic results there is a decrease in knee flexion during foot
strike for faster speeds and an increase in knee extension at midstance at slower
speeds. This indicates a smaller range of motion for the knee at faster speeds during
stair climbing. The first step on level ground does not exhibit the limited range of
motion in the knee. This is depicted for the average knee flexion angles in Figure
3.5 where the pink lines representing the fast speeds appear to have a more limited
range of motion. When changing speed on level ground, a subject can vary both
87
step length and the frequency of those steps. While climbing stairs, step length is
fixed and therefore the subject must target each step and not vary their stride. So
when the subjects are asked to climb stairs quickly the only variable that they have
is frequency at which the steps are taken. It may be possible that the ROM becomes
smaller at higher speeds to increase efficiency and therefore meet the higher frequency
more easily.
4.1.3
Inverse Dynamics
The general shape of the hip flexion torque curves for stair climbing can be seen
in Figure 3.7. The moment curve generally peaks early in stance and decreases back
to zero around foot off. The highest values are negative in this plot. The shapes of
the flexion moment curves for stair climbing are similar in shape to what was found
by Riener et al. [2002].
The statistics for the maximum and minimum values during stance are shown in
Tables 3.13 and 3.16. Level ground, the first step and second step moments vary
significantly with speed. The hip flexion moments on level ground and the first stair
increase as speed increases. The moment on stair two decreases with speed. For
all of the steps, peak hip extension torques increase significantly with speed. Peak
hip moments range between 1.5 and 5 which is consistent with previous studies [Yun
et al., 1997].
The plot of the knee flexion moments for stair climbing can be seen in Figure 3.8.
The knee moment curves generally have the highest extension moment values early in
stance and increases back to about zero after foot off. The highest values of torques
seen in the figure are internal knee extension moments which occur shortly after foot
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strike. The shapes of the flexion moment curves for stair climbing are similar in shape
to what was found by Riener et al. [2002] and Yun et al. [1997] but the magnitudes
of the moments in these studies are only normalized over body weight so there is not
a direct comparison of magnitudes between the three studies.
The statistics for the maximum and minimum values during stance are shown in
Tables 3.14 and 3.17. The maximum knee flexion moments do not vary significantly
with speed except for on level ground where it increases with speed. The maximum
knee extension moment also increases with speed for the step taken on level ground.
Peak knee moments ranged from between 3 and 4.5 which is consistent with previous
studies [Catani et al., 2003, Asay et al., 2009, Yun et al., 1997].
The step on level ground has lower average peak knee extension moments that the
first and second stairs. This correlates to a larger power production needed in the
joint to extend from the peak knee flexion angle of around 90 degrees at foot strike
to about zero degrees of flexion at midstance and is reflected in an increased activity
in the vastus muscle in Figure 3.13. This is because the vastus is a knee extensor
muscle. Peak knee extension moments do not change significantly with speed on the
stairs. The vastus magnitudes are very close on the first and second step, but increase
with speed for level ground, which is reflected in an increase the peak knee extension
moment on level ground.
The ankle flexion moments for stair climbing are shown in Figure 3.8. The ankle moment curves generally have the highest plantarflexion moment values early in
stance and increase slightly before a second peak in plantarflexion at toe off before
increasing back to zero. The shapes of the flexion moment curves for stair climbing
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are similar in shape to what was found by Riener et al. [2002] but are normalized
differently so there is not a direct comparison of magnitudes.
The statistics for the maximum and minimum values during stance are shown
in Tables 3.15 and 3.18. The maximum ankle dorsiflexion moments do not vary
significantly with speed. The peak plantarflexion moments increase in magnitude
with speed.
The shapes of the ankle flexion moments are similar to the shapes of the vertical
ground reaction forces. The second peak in the ground reaction forces correlates to
toe off in level walking. This also corresponds to activity in the soleus and gastroc
muscles as seen in Figures 3.10 and 3.11. This is why for level ground there is only one
peak for the ankle flexion moment. On the stairs there are two peaks for the plantar
flexion moments. This is most likely due to the fact that foot strike occurs with the
forefoot in stair climbing and not at the heel. For the stairs, both peaks in the GRF
correlate with peaks in plantarflexion. As speed increases so do peak vertical GRF,
peak plantarflexion moments and muscle activations in the gastroc and soleus.
4.1.4
EMG
In level walking, the gastroc (GAS) muscle is mainly used for swing initiation and
is mostly active in late stance and early swing. Both the soleus and the gastroc are
important for toe off [Neptune et al., 2008, 2004]. Figure 3.10 shows the activity in
the medial gastroc muscles during a stair climbing cycle. There are some variations in
phase and magnitude for the EMG at the different speeds, but the general shape has
peaks at foot off and very little activity during early stance. This is consistent with
level walking. The shape of the GAS activation is consistent as was found for stair
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ascending by Ghafari et al. [2009]. Slower speeds, especially the slowest, has decreased
activation in the gastroc muscles. The gastroc muscles are also active earlier in stance
at slower speeds than in quicker speeds.
In level walking, the soleus (SOL) muscle is mostly active during late stance and
early swing. It is important for forward propulsion especially in toe off [Neptune
et al., 2008, 2004]. Figure 3.11 shows the average activations of the soleus muscle
during percentage of stair climbing cycle. The soleus muscles are active for longer in
stance than the gastroc muscles, but the peaks for the soleus muscles also occur at
toe off and the beginning of the swing phase. This is consistent with level walking.
However, where the subjects progress to stair climbing from level walking, a second
peak in soleus activity occurs after weight acceptance. This activity in the soleus
muscle is most likely to propel the subject upwards into midstance on that step. The
peak magnitude of the soleus muscle increases as speed increases.
In level walking, the tibialis anterior (TA) muscle is active only during swing and
contributes to dorsiflexion of the ankle [Neptune et al., 2004]. Figure 3.12 shows the
average activations for the tibialis anterior muscle. The TA is active during most of
the stair climbing cycle which is consistent with what was found in previous studies
[Ghafari et al., 2009]. Peak activations occur during swing. This is consistent with
level walking because it is where the ankle changes from plantarflexion to dorisiflexion.
The added activation of the TA muscle during stance is most likely due to the constant
changes in the ankle joint angle and the fact that foot strike most likely occurs with
the forefoot for stair climbing. The peak magnitude of the TA is smaller for the
slowest speed.
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In level walking, the vastus (VAS) muscle is used primarily to decelerate the
center of mass and to provide trunk support during stance [Neptune et al., 2008,
2004]. Figure 3.13 shows the average activations of the vastus muscle during one stair
cycle. The activations for stair ascent is consistent with Ghafari et al. [2009]. The
first step taken on level ground has typical vastus activations for level walking where
the highest activations are in the beginning of stance to decelerate the center of mass.
The peaks for the vastus during stance on the first step and the second step are much
greater than the activation on level ground. This is because the quadriceps muscles
are important in stair climbing for knee extension which is evident when comparing
EMG in Figure 3.2 to knee extension moments seen in Figure 3.8. Slower speeds have
lower peak magnitudes for the step on level ground and similar activation magnitudes
for the stairs.
In level walking, EMG activity has been shown to increase with speed [Murray
et al., 1984]. In Figures 3.10 - 3.13, it can be seen that stair climbing at higher speeds
has higher activations for the GAS, SOL, and TA muscles.
4.2
4.2.1
Descending Stairs
Ground Reaction Forces
The plot for the average vertical GRF in Figure 3.14 shows the GRF applied to
three force plates. The first force is applied to the second step which is bolted into
the third force plate; the second step is applied to the second plate which has the
first stair bolted to it and the third step is onto the first force plate which is on level
ground. Each of the force plates seem to have the same general shape for the forces
that are applied to it during the stair climbing, although the magnitude varies slightly
92
between them. The general shape of the vertical GRF force while descending stairs
is similar to what was seen in previous studies [Riener et al., 2002] where the first
peak in the vertical GRF is much larger than the second. Stacoff et al. [2005] showed
that there is very little difference in the vertical GRF for ascending stairs but a large
difference in descending, like the ones seen in Figure 3.14 compared to Figure 3.1.
There are some differences in the vertical GRF curves at the three speeds. The
slowest speed has a much flatter curve for the three force plates, similar to what
was in Figure 3.1 for ascending stairs, and has a smaller magnitude. This is more
clearly defined in Table 3.19 which shows that for all three of the steps there is a
statistically significant difference in the mean values for the peak forces. As the
speed of descending stairs increases, the forces applied to the steps and the ground
increase.
The plot for the average anterior/posterior GRF in Figure 3.15 shows significant
anterior forces. This was also seen in a study done by Riener et al. [2002]. This
means that, when the subject is descending staris, there is a lot more acceleration
and propulsion than there are breaking or posterior forces. This is especially true of
the AP GRF curve for the first stair (the second force plate) and the last step which
is on level ground. For these steps the subjects are transitioning from descent to the
forward progression of walking which may explain the acceleration forward.
4.2.2
Inverse Kinematics
The shapes of the hip flexion curves seen in Figure 3.17 are periodic with the
maximum flexion during the swing. The stair climbing cycle begins with foot strike
on the second stair and ends at foot off the level ground at the base of the staircase.
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The maximum hip flexions are compared at three speeds (slow, self selected and
quick) in Table 3.20. Only the hip flexion for the top step changes significantly with
speed. For this step average hip flexion increases about 8 degrees from the lowest
to the highest speed. For descending stairs peak hip flexion in swing was about
25 degrees. These values are consistent with the values found in previous studies
[Andriacchi et al., 1980, Zachazewski et al., 1993] which were between 23 and 28
degrees of flexion during the swing phase of stair descending. Both of these sets of
results deviate from what was found by Ghafari [Ghafari et al., 2009], which was hip
flexion angles between 20 and 60 degrees for stair descent.
The shapes of the knee flexion curves in Figure 3.18 are periodic with the maximum
flexion occurring during the swing phase. These maximum flexions are compared at
three speeds in Table 3.21. The peak knee flexion angles only changes significantly
with speed for stair one, increasing in flexion between slow and self selected speeds.
In Figure 3.18, the peak magnitudes for the slowest speed are highest for all three
steps during swing (not reflected in Table 3.21). This would be consistent with what
was previously noted with knee flexion in stair climbing, that the range of motion
decreases for the average of the population for fasters speeds. Peak knee flexion
was between 90 and 100 degrees for all of the stairs, less for the last step. These
values are close to, but slightly higher hip flexion peaks found by both Andriacchi in
1980 [Andriacchi et al., 1980] and Ghafari in 2009 [Ghafari et al., 2009] which were
between 80 and 90 degrees for the swing phase of descending stairs. Values found by
Zachazewski et al. [1993], however, were much higher at around 115 degrees.
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The shapes of the ankle flexion curves in Figure 3.19 are periodic with the positive
values indicating dorsiflexion and negative values indicating plantarflexion. Dorsiflexion occurs in early swing and late stance at foot off. Plantarflexion occurs in early
stance at foot strike and late swing. This was seen in previous stair climbing studies
[Riener et al., 2002]. The maximum dorsiflexion angles are compared at the three
speeds in Table 3.22. All of the peak ankle dorsiflexion angles decrease significantly
with speed. This is evident in Figure 3.19. The average peak flexion angle of the
ankle is about 40 degrees. This is different from what was found by Andriacchi et al.
[1980] and Ghafari et al. [2009] where the maximum ankle dorsiflexion angle is only
about 20-25 degrees.
During stair descent, not as many angles are affected by speed as was seen for
ascending stair trials. For foot strike onto a step, knee flexion angles increase with
speed. This is the only event that has flexion affected by speed for both legs. In
midtstance for the second leg knee flexion increases and ankle dorsiflexion decreases
with speed. For the second leg at foot off all of the flexion angles decrease with speed.
Knee flexion angle for foot strike onto level ground decreases with speed.
Overall, in the kinematic results for descending stairs there is a lack of change in
the angles at events for all of the joints across the three speeds. There is no significant
change in hip flexion, even peak hip flexion. This is most likely due to the fact that it
would be unstable to lean the center of mass of the body forward over the legs while
walking downward. The joint that shows the most consistent variability with speed
is the knee.
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4.2.3
Inverse Dynamics
The general shape of the hip flexion moment curves for descending stairs can
be seen in Figure 3.20. The hip flexion moment curve generally peaks for internal
extension early in stance and increases to a flexion peak during late stance.
The statistics for the maximum and minimum values during stance are shown in
Tables 3.31 and 3.34. The first step refers to the step taken on the second stair. The
second step is the step taken onto the first stair. The third step is the step taken
onto the level ground. Peak hip flexion moments increase for all of the steps as speed
increases. Peak hip extension moments decrease with speed for stair two and increase
with speed for stair one.
The plot of the knee flexion moments for stair climbing can be seen in Figure 3.21.
The knee moment curves generally have the highest internal extension moments late
in stance and increase to flexion moments after foot off. The extension moments for
stair two and stair one are similar to the descending stair extension moments seen in
a previous study by Riener et al. [2002], however the moments on level ground are
more similar to extension and flexion moments seen in the knee joint for level walking
which were shown in the same study.
The statistics for the maximum and minimum values during stance are shown in
Tables 3.32 and 3.35. The peak knee flexion moments are affected by speed on stair
one and stair two. On stair one knee flexion moment increases with speed. Peak knee
extension moment increases with speed only for stair two.
Overall the average knee flexion moments for descending stairs are much larger
than the knee flexion moments in ascending stairs. The step on level ground has a
much lower magnitude for knee flexion and extension than the moments in the knee
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while descending stairs, with stair two having the highest moments. This correlates
with the curves for vastus activation in Figure 3.26. In Figure 3.26 it can also be
clearly seen that the peak values for vastus activation increase with speed on stair
two similar to how the peak knee extension moments increase on that stair.
The ankle flexion moments for stair climbing are shown in Figure 3.21. The ankle
moment curves generally have the highest plantarflexion values early in stance and
have a second peak in plantarflexion moment before increasing back to zero after foot
off. The results are similar as what was seen by Riener et al. [2002]. The descending
stair moments for the ankle are very similar in shape to the ascending stair moments
seen in Figure 3.21. However the initial peak in plantarflexion moments during stair
descent is correlated with foot strike occurring in plantar flexion, as well as the peak
in vertical GRF which occurs at the same timing.
The statistics for the maximum and minimum values during stance are shown
in Tables 3.15 and 3.36. The maximum ankle dorsiflexion moments increase with
speed for stair two and stair one. The peak ankle plantarflexion moments increase
in magnitude with speed for all of the steps. This correlated to the fact that as the
speed of descending stairs increases, the forces applied to the steps and the ground
increase.
Overall in stair descent there is a large initial peak in plantarflexion moment at
foot strike due to the fact that foot strike occurs with the forefoot. At foot strike there
is also peak activations for the soleus and gastroc muscles as can be seen in Figures
3.23 and 3.24. This is due to the fact that these muscles are the ankle plantarflexors.
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4.2.4
EMG
In level walking, the gastroc (GAS) muscle is used mainly for swing initiation
and is active mostly in late stance and early swing. Both the soleus and the gastroc
are important for toe off [Neptune et al., 2008, 2004]. Andriacchi [Andriacchi et al.,
1980] showed that in descending stairs the GAS is active mainly in stance. Figure
3.23 shows the activity in the medial gastroc muscles during a stair climbing cycle.
A stair climbing cycle in this thesis is defined as beginning when the first leg strikes
the first force plate on level ground and ending when the last foot comes off of the
third force plate which is under the second stair. Figure 3.23 shows that the GAS
is active during early stance. This is consistent with Andriacchi and is due to the
fact that foot strike occurs in plantarflexion and foot off occurs in dorsiflexion for the
ankle joint. The average peak activation values of the GAS increase with speed.
In level walking, the soleus (SOL) muscle is active mostly during late stance and
early swing. It is important for forward propulsion especially in toe off [Neptune et al.,
2008, 2004]. Andriacchi [Andriacchi et al., 1980] showed that in descending stairs the
SOL is active in stance. Figure 3.24 shows the average activations of the soleus
muscle during percentage of stair climbing cycle. As was found with stair climbing,
with descending stairs, the SOL muscles are active during the whole stair cycle. Peak
activations occur during stance which is consistent with Andriacchi. The activations
are close in magnitude for the lower speeds, but at the fast speed the activations
of the SOL are higher. The slower speeds also have two peaks of activation during
stance which is consistent with what was found by Ghafari et al. [2009]. The first
during foot strike and the second for foot off. This is because foot strike occurs with
the forefoot. Higher speeds have only one peak in soleus activation.
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In level walking, the tibialis anterior (TA) muscle is active only during swing and
contributes to dorsiflexion of the ankle [Neptune et al., 2004]. Andriacchi [Andriacchi
et al., 1980] showed that in descending stairs the TA is active mainly in swing. Figure
3.25 shows the average activations for the tibialis anterior muscle. The TA are active
for the entire stair climbing cycle which is consistent with what Ghafari found in
2009 [Ghafari et al., 2009]. Peaks in activation occur for both swing and stance. This
is most likely due to the fact that the ankle is in dorsiflexion in both swing and at
midstance and foot off. The activations of the TA are higher at faster speeds.
In level walking, the vastus (VAS) muscle is used primarily to decelerate the
center of mass and to provide trunk support during stance [Neptune et al., 2008,
2004]. Andriacchi [Andriacchi et al., 1980] showed that in descending stairs the VAS
is active at the end of stance and the beginning of swing. Figure 3.26 shows the
average activations of the vastus muscle during one stair cycle. The VAS are active
in end of stance and in the beginning of swing. This is consistent with previous
studies [Andriacchi et al., 1980, Ghafari et al., 2009]. Most of the curves have two
separate peaks. The first peak is to decelerate the center of mass in stance and the
second peak occurs during the downward swing when the knee angle changes from
flexion to extension. The last step taken on level ground has only one peak, this is
for decelerating the center of mass. The magnitudes are close for these curves, but
are slightly higher for faster speeds.
In level walking, EMG activity has been shown to increase with speed [Murray
et al., 1984]. In Figures 3.10 - 3.13, it can be seen that stair descent at higher speeds
has higher activations for the GAS, SOL, VAS and TA muscles.
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4.3
Summary of Effects of Speed in Ascending and Descending Stairs
In order to provide rehabilitative therapists with a clearer picture of the biomechanics of stair ascending and descending, a wider range of studies need to be conducted in stair climbing. Previous studies have determined the kinematics, kinetics
and EMG of stair climbing in various populations [Nadeau et al., 2003, Andriacchi
et al., 1980, Ghafari et al., 2009, Riener et al., 2002]. It is known that subjects with
mobility disorders walk more slowly than healthy subjects [Murray et al., 1984, Dingwell et al., 2000]. However, stair climbing has yet to be characterized for various
speeds in healthy subjects. Therefore, this study is an attempt to broaden the understanding of stair climbing by characterizing stair ascending and descending at three
speeds in healthy young adults.
Many aspects of gait change with varying walking speeds. Kinematic and EMG
patterns have been investigated at various speeds of walking [Murray et al., 1984] and
have shown a decrease in the magnitudes of joint moments and muscle activations
with a decrease in speed. Studies showed a decrease in range of motion and decreased
maximum flexion for all joints and decreased magnitude of EMG while the subjects
walked at slower speeds [Liu et al., 2008].
In this thesis, many variables investigated in ascending stair trials were affected by
speed. Joint angles were found to vary significantly. Internal joint flexion moments
did not change significantly for ascending stairs. Peak ground reaction forces were
found to vary significantly with speed and increased with speed. Average peak EMG
activations and and activation timing was found to increase as speed increased for
most of the muscles, as well.
100
In this thesis, descending stair trials were also shown to be affected by speed. Joint
angles were found to vary significantly for descending stair trials, but less for descending than ascending. Internal joint flexion moments varied in descending stairs. Peak
ground reaction forces were found to vary significantly with speed and increased with
speed for descending stair trials. Average peak EMG activations and and activation
timing was found to increase as speed increased, as well.
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CHAPTER 5
PILOT STUDY
5.1
Introduction
The results and discussion in this section pertain to a pilot study where the first
subject’s data was processed through Residual Reduction (RRA), Computed Muscle
Control (CMC) and Forward Dynamics (FD). A full analysis of CMC can be used
to determine and validate the muscle excitation patterns of the lower limbs during
stair ascending and descending. The analysis was performed for only one subject,
and therefore, the discussion of these results may not be statistically significant.
However, there is relevance for future studies and consideration for decisions made
while compiling the data of the eleven remaining subjects.
The following sections include the sample results from the RRA, CMC and FD
for ascending and descending the stairs and are labeled accordingly.
5.2
Residual Reduction
Residual Reduction was run in two iterations for the trials. In the first iteration,
a change in the model’s mass was determined. This change in mass was scaled in
the model and then a second pass at RRA was taken to further reduce the residuals.
102
Figure 5.1: Residuals after RRA for a typical trial ascending stairs at a self selected
pace.
An acceptable range of residuals was determined to be between ± 15 Newtons. The
residuals in the times where forces were applied to the force plates was predominantly
within the acceptable range. Plots for residuals in ascending and descending stairs can
be seen in Figures 5.1 and 5.2. These plots show the residuals in the x (red), y (blue)
and z (green) directions. The greatest residuals occur along the y axis. Typically
there were higher residual peaks in the descending stair trials as can be seen when
Figures 5.1 and 5.2 are compared.
Running RRA twice smoothed the kinematic results. Examples of the kinematic
plots after the RRA was run can be seen for ascending stairs in Figure 5.3 and
103
Figure 5.2: Residuals after RRA for a typical trial descending stairs at a self selected
pace.
104
Figure 5.3: Right and Left knee angles after RRA for a typical trial ascending stairs
at a self selected pace. Red indicates the leg that is originally in stance and blue
indicates the leg that was originally in swing. The knee flexion angles are negative
here by convention in OpenSim and range from -10 degrees to -100 degrees.
descending stairs in Figure 5.4. These plots were made within OpenSim so they use
the OpenSim convention of making knee flexion negative.
5.3
Computed Muscle Control
CMC is used to computationally determine the muscle activations that should
produce the movements and forces in the IK and ID results. Running CMC in OpenSim results in a simulation with blue muscles that become red as they are activated.
The results of these simulations were plotted along with EMG results to compare the
105
Figure 5.4: Right and Left knee angles after RRA for a typical trial descending stairs
at a self selected pace. Red indicates the leg that is originally in stance and blue
indicates the leg that was originally in swing. The knee flexion angles are negative
here by convention in OpenSim and range from -10 degrees to -100 degrees.
106
Figure 5.5: CMC for a typical trial ascending stairs at a self selected pace. Green
and red show GAS and blue and pink show SOL.
confidence in the simulation. Figures 5.5 and 5.6 show typical results in OpenSim for
the Soleus and Gastroc muscles during stair ascending and descending respectively.
The CMC portion of the pilot study was extremely valuable because it showed
that there was a lack in consistency in the two different EMG systems used in the
experimental setup. Figure 5.7 shows both the EMG and the CMC results for all
16 muscles for a typical trial for subject one. The channels of EMG that did get
good data agree well with the activation times of the simulation(e.g., left Gmax, left
and right Vas, and left Sol). The best data for the EMG was taken in the proximal
muscles. The data for these muscles came from the same EMG system that was used
107
Figure 5.6: CMC for a typical trial descending stairs at a self selected pace. Green
and red show GAS and blue and pink show SOL.
108
in the final protocol, but the problems with the EMG system used to take the data
for the distal muscles were never worked out.
5.4
Forward Dynamics
Forward Dynamics for typical trials for ascending and descending stairs are seen
in Figures 5.8 and 5.9 respectively. The results of FD can be compared to the results
from ID. FD in OpenSim has an open loop control, unlike ID. And because of this, it
will only process for a maximum of one second for any trial. This makes it difficult
to have complete confidence in the usefulness FD results for this application where
the shortest trials are at least 2.5 seconds in duration.
109
110
Figure 5.7: CMC compared with EMG for 16 muscles in the lower extremities for ascending stairs at a self selected speed.
Each muscle is labeled with a corresponding abbreviation. The top (green and red) trials are of the left leg and the bottom
(blue) trials are the right leg.
Figure 5.8: Forward Dynamics for a typical trial ascending stairs at a self selected
pace. Note that the maximum amount of time that FD could be processed for any
trial was between 0.5 and 1 second.
111
Figure 5.9: Forward Dynamics for a typical trial descending stairs at a self selected
pace. Note that the maximum amount of time that FD could be processed for any
trial was between 0.5 and 1 second.
112
CHAPTER 6
CONCLUSION
Stairs are encountered frequently in day-to-day life. The ability to ascend and
descend stairs without difficulty and without pain is important to quality of life.
When individuals are unable to negotiate a staircase, they may loose their ability
to live independently. Because many individuals with neuromuscular impairments
walk and ascend/descend stairs more slowly than healthy individuals, it is imperative
to isolate functional tasks from other factors such as age, muscle weakness, walking
cadence, etc. Evaluating a patients gait requires discriminating between deviations
caused by pathology and walking speed [Liu et al., 2008].
The work in this thesis determined the effects of changing stair climbing speed
on lower extremity joint kinematics and kinetics. Joint angles were found to vary
significantly for both ascending and descending stair trials, but less for descending.
Internal joint flexion moments did not change significantly for ascending stairs, but
were more varied in descending stairs. Peak ground reaction forces were found to vary
significantly with speed and increased with speed. Average peak EMG activations
and and activation timing was found to increase as speed increased, as well.
These results represent preliminary steps in an analysis that will provide experimentalists and therapists with the information necessary to make more informed
113
decisions when choosing therapy programs to help patients ascend and descend stairs
with increased ease, efficiency and independence.
6.1
Contributions
The main contributions of this thesis are as follows.
Design stair climbing experimental setup and experimental protocol. Some
of the work performed for this thesis was to design a set of stairs that could be
bolted to the existing force plate setup in the Sports Biomechanics Lab in the
Martha Moorehouse Pavilion at OSU. Additionally, a stair climbing protocol
with this staircase, motion capture and EMG was created, tested and established. This stair setup and protocol will be used in future testing with stair
ascending/descending in the NeuroMuscular Biomechanics Lab at OSU.
Pipeline to process experimentally collected stair climbing data in OpenSim.
Experimental data collected underwent a significant processing in Vicon, in
Matlab and in OpenSim. Matlab code was used to extract data from Vicon
to OpenSim and for post processing and extracting values for statistical analysis. This code was updated during this thesis to include four forces plates,
walking in two directions and adjustments for stair climbing. Additionally code
was added for post processing that pulled out events specific to stair climbing.
Custom EMG conditioning code was also created in Matlab. XML files and
pipelines for OpenSim were created to process stair ascending/descending data
for IK, ID, RRA, CMC, and FD. This OpenSim pipeline and the XML files will
be used in future testing with stair ascending/descending and other research in
the NeuroMuscular Biomechanics Lab at OSU.
114
Effects of varying speed on GRF, kinematics, kinetics and EMG in stairs.
Kinematic, kinetic and emg data were collected for twelve healthy subjects while
ascending and descending an instrumented staircase in a gait lab. The data was
processed in Vicon, Matlab and OpenSim to determine joint angles and joint
moments produced during various speeds. Joint angles, joint moments, EMG
and GRFs were shown to affected varying speed of ascending and descending
stairs. The characterization of the effects of speed and stair climbing kinematics
and kinetics will be helpful in combination with future studies towards helping
therapists make more informed decisions when setting rehabilitation programs
for people who have difficulty negotiating stairs.
6.2
Additional Applications
Additional applications of this work might include the following.
Determine effects of varying speed in computational muscle control. The inverse kinematics and inverse dynamics used in this thesis showed how varying
speed effects joint angles and flexion moments, and EMG data gives insight into
the muscle contributions towards the movements that are produced. However,
CMC was only performed for a pilot study. Using CMC to determine muscle
activations and contributions for various speeds would be useful when comparing muscle activity in people with disabilities to healthy subjects. This analysis
would aid in the creation of more efficient rehabilitation programs.
Characterization of stair ascending/descending in various pathologies. The
present study characterized stair ascending/descending in healthy young adults.
This protocol and procedure would be effective towards characterizing stair
115
climbing in various other populations. This could include, but not be limited
to, the elderly, individuals with osteoarthritis, people who have had total knee
replacement, individuals who have suffered from a stroke and people who have
cerebral palsy. Like in this study, these characterizations would provide information about joint angles, range of motion, joint loadings and muscle activations. A comparison of this data to a normative data set like the one created in
this thesis could direct innovative rehabilitation to help people with pathologies
climb stairs.
Validation of rehabilitation therapy. The present study characterized walking in
healthy subjects. Further work could provide insight that leads to rehabilitative
programs to assist with the negotiation of stairs. These rehabilitative programs
could then be validated by comparing data from before and after rehabilitation
to the normative database.
6.3
Future Work
This thesis only presents the results of the inverse kinematics, inverse dynamics,
ground reaction forces and conditioned EMG data. In a pilot study, the data was
processed through RRA and CMC in OpenSim. These analysis should be performed
for all twelve subjects. The CMC portion of the analysis will be particularly interesting especially if the results end up matching the EMG data. This entire analysis will
then serve as a normative data set for healthy young adults climbing stairs at various
speeds. The effect of speed will be able to be quantified for muscle activation in the
simulation. Previous studies have developed the normative muscles or groups of muscles that contribute to specific subtasks of walking at various speeds [Liu et al., 2008,
116
Murray et al., 1984]. However, the normative data for muscle activations at various
speeds of stair climbing has yet to be established. The simulation would be valuable
in adding incite into muscle activations outside those which had data collected using
EMG. In addition studies can be performed investigating how changes in the allowed
muscle activations change the kinematics and dynamics of the simulation.
The next step after this analysis is completed is to use the experimental protocol
outlined in the Appendix to have various other populations, such as people with
OA and people who have had TKA, walk up and down the stairs. Data from other
populations can be compared with this normative database. Characterization of the
biomechanics of stair climbing in individuals with disabilities could direct innovative
rehabilitative therapies to target and strengthen impaired muscle groups so that they
could negotiate stairs with increased ease and independence.
6.4
Summary
The ability to negotiate stairs is important in being able to live independently. Because individuals who have mobility disorders climb up and down stairs at decreased
speeds from healthy subjects it is important to separate the effects of speed from the
effects of the pathology. This is especially true when finding therapies to specifically
target the ability to ascend/descend stairs. This thesis is the first step towards giving
therapists a complete assessment of how different pathologies affect joint kinematics,
kinetics and muscle recruitment during stair ascending/descending independently of
speed.
117
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APPENDIX A
STAIR CLIMBING EXPERIMENTAL PROTOCOL
RESEARCH PROTOCOL: Determining the Biomechanics of Stair
Ascent and Descent
Rebecca Routson
[email protected]
I. OBJECTIVES
1. Create a normative database of healthy adults for biomechanics of the lower extremity
during activities of daily living such as walking and ascending/descending stairs.
2. Create a database of lower extremity biomechanics during activities of daily living in
adults with knee pathologies.
3. Determine the effects of age and knee pathology on the lower extremity during stair
climbing.
4. Determine the correlation between movement impairments and the biomechanics of
the lower extremity during activities of daily living.
5. Identify correlations that may be predictive of musculoskeletal injuries experienced
during activities of daily living.
II. BACKGROUND AND RATIONALE Stairs are a common obstacle encountered in daily
life. Due to their frequency, the ability to ascend and descend stairs without difficulty or
pain is important to quality of life. Additionally, when people are not able to negotiate
stairs it severely restricts their area of living and ability to live independently. Due to its
importance and prevalence in daily life, stair climbing is a functional measure in the daily
lives of persons’ with mobility disorders and disabilities [Stratford et al., 2006].
Most research on stair ascending and descending, both from the physics-based mathematical perspective and the clinical observation perspective, has focused on mostly the
movements that are executed when people negotiate stairs. However, this does not allow
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clinicians or scientists to understand what the muscles are doing to actuate these movements. Contributions of a particular muscle or groups of muscles towards movement can be
estimated by collecting data from sensors placed over muscles on the body [Neptune et al.,
2004].
Several studies have analyzed the contributions of individual muscles to support and
forward progression during level walking [Anderson and Pandy, 2003, Neptune et al., 2004].
The main differences between walking and stair climbing are manifested in a significant
increase in range of motion of the lower limbs during stair climbing, as well as, changes
in muscle activations [Ghafari et al., 2009]. Characterization of the biomechanics of stair
climbing in individuals with movement disorders and disabilities could direct innovative
surgical and rehabilitative therapies to enable these individuals to negotiate stairs with
increased ease.
III. PROCEDURES
A. RESEARCH DESIGN This combined cross-sectional and prospective longitudinal
correlational laboratory study will involve recording the motion of subjects while performing
various activities of daily living. All subjects will make one visit to the Sports Biomechanics
Laboratory within the OSU Sports Medicine Center where all measurements will be taken.
B. SAMPLING APPROACH To create a representative normative database for a healthy
adult population, data from a previous study of a similar population was used to estimate
the sample size needed for this study. To determine the normative database for healthy
young adults climbing stairs there should be 10 subjects that participate in the study [Andriacchi et al., 1980, Liu et al., 2008, Ghafari et al., 2009].
All healthy subjects must meet the following inclusion/exclusion criteria:
INCLUSION:
• Able to walk without pain or antalgic gait (i.e. a limp) at the time of motion test
• No history of serious injury to either leg that required surgery or involved ligament/tendon/muscle/meniscus tear
• Over 18 yrs old at time of testing
EXCLUSION:
• Previous ACL tear, other ligament tear, tendon tear, muscle tear, or meniscus tear
in either lower limb
• Previous surgery to either lower limb
• Woman in her second or third trimester of pregnancy
All subjects in the knee pathology group must meet the following inclusion/exclusion
criteria:
INCLUSION:
• Having a clinical diagnosis of: osteoarthritis of the knee, meniscal injury, anterior
cruciate ligament (ACL) injury, cartilage defect following a total knee replacement.
• Over 18 yrs old at time of testing
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EXCLUSION:
• Unable/unwilling to walk or climb stairs as an activity of daily living
• Woman in her second or third trimester of pregnancy
• Instability or balance problems that would make it unsafe for a person to ascend and
descend stairs.
Women in their second or third trimester of pregnancy are excluded because they experience large changes in weight and hormone balances that can be expected to alter their
biomechanical loading on their joints. Women in their first trimester of pregnancy are not
excluded because under a normal pregnancy, these women typically have no restrictions
placed on their activities of daily living.
MEASUREMENT/INSTRUMENTATION
This study will use motion analysis testing, which has been extensively validated by
many researchers over the past 30 years for use in understanding the biomechanical loading
on the joints during activities of daily living [Andriacchi et al., 1985, 1998].
1. Muscle activations. During each activity of daily living, we will estimate the activations of the muscles within the lower extremities.
2. Biomechanical loading. During each activity of daily living, we will estimate the profiles of net forces and torques acting at the ankle, knee, hip, and torso.
DETAILED STUDY PROCEDURES
List of Testing Supplies
• Stairs
– 3 piece modular staircase
– bolts and washers
– allen key
• EMG
– table
– 2 chairs
– 8 electrodes (John’s system)
– 1 ground electrodes
– athletic tape
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– double sided tape for John’s system
– power chords
– John’s EMG system
– alcohol prep pads
– vest
– MVIC straps
• Motion Capture
– 58 markers
– double sided tape
Testing Protocol
• Calibrate Motion Capture without steps.
• Setup Steps: this should take about 10-15 minutes.
– Bolt 1st and 2nd step to the force plates in the long part of the L.
– The black rubber mat on the floor will need to be removed from these force
plates, and only these force plates.
– 1st step gets 2 bolts and 2 washers on the front side of the step in the green
brackets. Tighten bolts with allen key.
– 2nd step should be bolted with no less than 3 bolts. If there are only 3 bolts,
preference will be given to the back two corners farthest from the cantilevered
portion. Tighten bolts with allen key.
– Line the 3rd step up with the black marks on the 2nd step. Be sure that the
3rd step does not rest on any of the force plates.
• Setup EMG: this should take about 10-15 minutes.
– If it is not already there, move table next to Vicon DAQ computer.
– If not already there, move chair next to Vicon DAQ computer.
– Uncoil wires for electrodes and lay untangled over the back of a chair.
– Apply double sided tape to John’s system with green tab facing away from wire.
– Wires for the EMG systems are plugged into the Vicon DAQ board using BNC
connectors labeled with tape: J1-8 and D1-8 corresponding to the channels from
the respective systems.
– If the BNC cables are not connected to the DAQ board:
∗ John’s system J1-8 get plugged into channels 33-40, respectively.
– Plug both EMG systems into power and turn on.
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• All subjects will be asked to participate in the entire testing procedure on one occasion, lasting approximately 2 hours.
• Prior to testing, subjects will be instructed to wear athletic short pants, briefs, and
comfortable low-top walking shoes. Since we place sensors on the torso, males will be
asked to wear no shirt, while females will be asked to wear only a sports bra.
– Subject will sign the consent form at this time.
• Measure and record the subjects height, and weight with the scale just outside the
Sports Biomechanics Lab.
• Place electrodes: this should take about 25-30 minutes. The skin over certain muscles
may need to be shaved and/or cleaned with alcohol prep pads prior to applying these
sensors (see Figures A.1a and A.1b for placement). One system of EMG will require
double sided tape to be applied to the electrodes; the other system will require the
electrodes to be taped to the skin.
– In total, there will be 8 electrodes placed in the following order (parenthesis
indicate channels; J for John’s system):
1.
2.
3.
4.
5.
Left (J1) and right (J5) VAS (med)
Left (J2) and right (J6) GAS (med)
Left (J3) and right (J7) SOL
Left (J4) and right (J8) TA
Ground electrode on elbow
– This will be a two step process...
1. Use a skin marker to draw a dot for electrode placement.
2. Place electrodes on dots.
– Apply electrodes in parallel to the muscle fiber direction.
– Use the middle portion of the muscle belly.
– Place one reference electrode per system on a bony area of the elbow or the
collar bone.
– A table should be placed near the Vicon DAQ computer for assisting with EMG
placement and for the MVIC trials.
• Additional EMG system setup: this should take about 5-10 minutes.
– EMG systems may be hung on or attached to a vest that will be provided to
subjects during testing. This vest will not obstruct the marker placement.
∗ John’s system can be clipped onto one of the tabs on the back of the vest.
Excess wires can be taped into a loop attached to the metal ring on the
left side of the vest and/or looped through the velcro belt in the rear of the
vest.
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– Excess wires will be taped out of the way of subjects, but if done so must
not restrict movement in the limbs or pull off electrodes. (See Figures A.3 for
example.)
• Perform MVIC trials to find the maximum activation of each muscle noted above
and to make sure that all channels of EMG are receiving good data: this should take
about 5-10 minutes. In total, there will be at least 8 exercises (4 for each leg) each
taking about 5 seconds with 10 seconds rest in between repetitions 30-45 seconds
rest/change position in between exercises. Example MVIC exercises can be seen in
Figure A.4.
– VAS: Place foam roll under the knee while the subject lies flat on back on top
of the table. Resistance can be applied to the shin from above as the subject
completely extends their leg.
– GAS: A. Face chair towards wall. With one foot at a time, press with toe so
heel comes off of the wall. B. Standing on one foot, lean torso into wall as to
stretch calf muscle andpress with toe so heel comes off of the floor.
– SOL: Seated using a theraband around toes and knee of one leg, press with toe
so heel comes off of the floor. Resistance can also be applied on the knee from
above.
– TA: Subject stands and resistance is applied at toes while subject lifts toes off
of the floor. (see Figure A.4)
– ALL: Subject will be asked to perform 2 squat jumps.
– This data can be taken in one continuous trial or separate trials that can be
strung together in post processing.
– Each MVIC exercise should be performed at least twice.
• Place tape over reflective material on the subjects clothing or shoes as required.
Clothing may also be bunched/rolled up and taped to expose bony landmarks where
reflective balls (markers) are to be placed.
• Place markers on the subjects skin using double-sided tape: this should take about
15 minutes. Markers will be placed according to the Point Cluster Technique on the
lower limbs (see Figure A.5 for placement). Additional torso markers include the
clavicle, sternum, right and left anterior /posterior superior iliac crests, and the right
and left shoulders (see Figure A.6 for placement). The STRN marker may need to
be placed on the vest. This is a total of 58 markers.
• Subjects will then perform a series of activities of daily living while being recorded:
this should take about 20-25 minutes. Subjects will only be asked to perform activities that they feel comfortable performing without pain or discomfort or fear of
injury. In total, there will be at least 21 trials with motion capture and EMG each
taking approximately 30 seconds with 30 seconds rest in between. These activities
will include:
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– 1 static calibration
– 2 hip joint center
– 3 ascending self-selected speed
– 3 descending self-selected speed
– 3 ascending slow speed
– 3 descending slow speed
– 3 ascending quick speed
– 3 descending quick speed
– Self-selected speeds will be monitored by stop watch to ensure quick and slow
are approximately 1.5 and 0.5 times the self-selected pace.
• Remove all markers and tape: this should take about 5 minutes.
• Subjects are free to change clothes and leave.
• Total time for motion testing should be less than 2 hours.
• Tear Down Steps: this should take about 10-15 minutes.
– Take off bolts with allen key.
– Store steps to the side of the testing area.
– Replace black rubber mat over the force plates. Apply new double sided tape
where necessary.
• Clean up EMG
– Unplug all wires.
– Coil electrode wires for Debbie’s system and secure with tape.
– Replace Debbie’s system as found before Stair Testing.
– Place John’s system back into box.
Potential risks of participation
Discomfort/embarrassment of wearing clothes that expose the skin during motion testing. Slipping or falling during motion testing (no greater than during daily activities outside
of the study).
Methods for avoiding/minimizing risks
Motion analysis will be limited to activities of daily living and present no elevated risk to
subjects. Only study personnel will be present during testing, and only study personnel will
be permitted to view video images of testing to minimize the risk of undesired identification
of subjects by other individuals. A physician will be on call at the Sports Medicine Center to
immediately attend to subjects in the case of any adverse events requiring medical attention
(such as slipping and falling while walking).
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(b) Dorsal View
Figure A.1: Placement of surface EMG electrodes [Konrad, 2005]. We will be placing GMax, GMed, BF, RF, VAS med,
TA, GAS med, SOL.
(a) Frontal View
Figure A.2: Muscle fiber direction for GMax
(a) To tie wires out of the way.
(b) example setup
Figure A.3: Example of vest setup. The belt in rear of vest can be used to help keep
wires out of the way.
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Figure A.4: MVIC trial exercises. The black thin arrow indicates movement direction, the white thick arrows the resistance
direction [Konrad, 2005]. Parenthesis indicates trial order. The 1st 3 trials require the table. The next 3 require a chair.
The last trial will be done while subject stands. For GAS and SOL resistance against the feet/knees (per white arrow)
will be applied by hand.
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(b) PCT left
Figure A.5: Placement of PCT markers [Andriacchi et al., 1998].
(a) PCT right
Figure A.6: Placement of torso markers. Markers used from this image are RSHO,
LSHO, ASIS, PSIS, CLAV and STRN.
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