Analysis of the Forces on the Spine During a Fall with Application towards
Predicting Vertebral Fracture Risk
by
Sara E. Wilson
S.M. Mechanical Engineering, Massachusetts Institute of Technology (1994)
B.S. Biomedical Engineering, Rensselaer Polytechnic Institute (1992)
Submitted to the Harvard-MIT Division of Health Sciences and Technology
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Medical Engineering
At the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1999
© Massachusetts Institute of Technology 1999. All rights reserved.
Author..........................................................................
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Harvard-MIT Division of Health Sciences and Technology
May 21, 1999
Certified
by.. ........ ..............................
Certifie byElizab
Ri.Myers
Assistant Professor
.Thesis Supervisor
Acceptedby
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FTECHNLTGE
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L. Gray
J.W. Kieckhefer Professor of Electrical E gineering
Co-Director, Division of Health Sciences and Technology
MASSACHUSETS
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Analysis of the Forces on the Spine During a Fall with Application towards
Predicting Vertebral Fracture Risk
by
Sara E. Wilson
S.M. Mechanical Engineering, Massachusetts Institute of Technology (1994)
B.S. Biomedical Engineering, Rensselaer Polytechnic Institute (1992)
Submitted to the Harvard-MIT Division of Health Sciences and Technology
on May 21, 1999 in partial fulfillment of the requirements for the
degree of Doctor of Philosophy in Medical Engineering
Abstract
Age-related vertebral fractures are a common public health problem for the elderly with
an estimated 27 percent of U.S. women aged 65 years and over thought to have at least one
vertebral fracture. It is important, therefore, to characterize the "at risk" patient and to find
methods of reducing that risk. Fracture risk has been defined as the ratio of applied loads to the
force required to fracture a bone. Although studies have examined the force required to fracture,
few studies have tried to assess the applied loads associated with fractures. Epidemiological
studies have found that as many as 30 to 50 percent of vertebral fractures are associated with
falls. This work examines the forces on the spine during a backward fall.
Models of a passive fall, without tension in the torso musculature, were constructed in
order to examine the peak axial forces on the spine as a result of a passive fall. Muscle tension
elements were added to examine the effect of pre-compression of the spine by the musculature.
Three experimental and observational studies were performed to examine the input parameters of
these models. This included an experimental measurement of the stiffness and damping of the
spine segments, measurement and modeling of the fall dynamics in a backward fall, and
measurement of the geometry of the torso musculature.
The peak axial forces on the spine were found to range from 1100 Newtons to 3500
Newtons depending on a number of factors including the fall impact dynamics (fall velocity and
torso angle), the body weight of the individual, the properties of the soft tissue of the pelvis and
spine, and the amount of muscle tension in the torso musculature. These forces can be compared
to a mean compressive failure force around 2000 N in elderly thoracolumbar vertebrae. This
puts a portion of the elderly population at risk for a fracture simply from an upright passive fall
of average velocity. The highest forces were found in upright, fast falls in which the individual
had a high upper body weight and very tense torso musculature and little damping in the spine.
Thesis Supervisor: Elizabeth R. Myers
Title: Assistant Professor, Harvard Medical School
Acknowledgements
This work was possible through the generous support of the Whitaker Foundation and the
American Association of University Women. Fellowships from these two organizations have
been critical in the completion of this work and their support is greatly appreciated.
This work would not have been possible without the support, love and encouragement of many
people. There were many stumbling blocks that I might not have overcome without the support
of these friends. In particular I would like to acknowledge several people.
Dr. Thomas McMahon came to my rescue when things seemed the bleakest. He provided me
with encouragement and a safe and protective research home when I most needed it. He worked
behind the scenes many times to assure that I would not be lost or feel forced to give up. He did
this, even though I was not his student, showing once again his dedication to the students and his
love for the learning process.
C6cile Smeesters, soon to be Dr. Smeesters, has been my officemate, my compatriot and more.
She has come to my rescue, even when I sometimes didn't want her to. She has been an
understanding and sympathetic ear for any complaints and a true friend.
Dr. Elizabeth Myers has provided almost motherly support and encouragement during my
studies. She has shown, by example, that it is possible to be a compassionate human being and a
high caliber researcher.
Tara Arthur, Richard Courtemanche, and Richard Donovan have been good and loyal friends.
They have made sure that I don't forget to live life and have fun occasionally.
My parents and grandparents who have been proud of what I am doing, even if they really don't
know what it is exactly, and sent me cookies when I was down to show they love me.
Finally, I would like to thank my many friends in the Orthopedic Biomechanics Lab and the
Harvard Biomechanics Lab who have cheered my successes, encouraged me when I was down,
and made life bearable.
5
Contents
1
Introduction
15
1.1 Vertebral Fractures
15
1.2 Fall Mechanics
1.3 Impact Mechanics and Spine Modeling
1.3.1 Pilot Ejection
1.3.2 Vibration
1.3.3 Pilot Ejection and Vibration Summary
1.3.3 Controlled Action Models
1.3.4 Stability Models
1.4 Summary of Literature
1.5 Aims of the Thesis
1.6 References
18
19
19
20
22
22
23
25
25
26
2
Impact
2.1
2.2
2.3
33
33
33
36
36
37
40
41
41
41
41
42
46
50
52
57
3
Muscles and Impact Mechanics
61
Mechanics Modeling
Abstract
Introduction
Methods
2.3.1 Human Body Models
2.3.2 Selection of Input Parameters
2.3.3 Validation
2.3.4 Sensitivity
2.3.5 Force Prediction
2.4 Results
2.4.1 Validation
2.4.2 Sensitivity
2.4.3 Force Predictions
2.5 Discussion
2.6 References
Appendix 2.A Equations of Motion for the Four Models
3.1 Abstract
61
3.2 Introduction
3.3 Methods
3.3.1 Models
3.3.2 Validation
3.3.3 Stiffness Relation Sensitivity
3.3.4 Unequal Muscle Tension
3.4 Results
3.4.1 Validation
3.4.2 Stiffness Relation Sensitivity
61
63
63
63
64
64
64
64
66
7
4
5
3.4.3 Unequal Muscle Tension
3.5 Discussion
3.6 References
66
74
76
Mechanical Properties of the Spine
4.1 Abstract
4.2 Introduction
4.3 Methods
4.3.1 Specimens
4.3.2 Magnetic Resonance Imaging
4.3.3 Mechanical Testing
4.4 Results
4.5 Discussion
4.6 References
79
79
Fall Dynamics
5.1 Abstract
5.2 Introduction
5.3 Methods
5.3.1 Human Experiments
95
82
83
83
86
91
92
95
95
96
96
98
98
5.3.2 Dummy Experiment
5.3.3 Models
5.4 Results
5.4.1 Human Experiment
5.4.2 Dummy Experiment
5.4.3 Models
5.5 Discussion
5.6 References
6
80
82
105
105
105
105
107
110
113
113
Cross-sectional Anatomy
6.1 Abstract
6.2 Introduction
6.3 Methods
6.3.1 Subjects
6.3.2 Anthropometric Data
6.3.3 Digitization
6.3.4 Data Analysis
6.4 Results
6.5 Discussion
6.6 References
114
117
117
118
118
119
119
122
129
8
7
Conclusion
7.1 Summary
7.2
7.3
7.4
7.5
7.6
7.7
7.8
133
133
Predicted Risk
Contributors to Increasing the Forces on the Spine
Limitations and Weaknesses of the Models
Strength of This Work
Future Directions
Conclusion
References
9
133
134
137
138
138
139
140
List of Figures
Chapter
Chapter 2
Number
title
page number
2-1
2-2
2-3
2-4
2-5
2-6
2-7
Four Models to Examine Fall Dynamics
Relative Apparent Mass
Phase Shift
Sacral Transmissibility
L3 Vertebral Transmissibility
Seat to Head Transmissibility
Average Angle (,vg) Between Two Objects
38
43
44
45
47
48
59
3-1
3-2
Muscle Models
Seat to Head Transmissibility with Increasing
Muscle Stiffness
Seat to Head Transmissibility with Increasing Initial
Muscle Tension
Axial Spine Force Over Time
Peak Compressive Spine Force for Several
Constant Stiffnesses
Peak Compressive Spine Force for Several
Stiffness-Tension Relations
Motion of the 3 Centers of Mass
Motion of the 3 Centers of Mass
Compressive Force for the 2-dimensional Model at 45 °
65
85
4-3
4-4
The Pendulum Apparatus
Force Transmission After Impact Exhibits
Underdamped Oscillations
Stiffness Increased with Increasing Preload
T2 intensity of the Whole Disk
87
88
90
5-1
5-2
5-3
5-4
Constants for the Joint Angle-Torque Relations
Static Joint Angle-Torque Plots - Ankle
Static Joint Angle-Torque Plots - Knee
Static Joint Angle-Torque Plots - Hip
100
101
102
103
Chapter 3
3-3
3-4
3-5
3-6
3-7a
3-7b
3-8
67
68
69
70
71
72
73
75
Chapter 4
4-1
4-2
Chapter 5
11
List of Tables
Chapter
Chapter 2
page number
Number
title
2-1
2-2
Input Values
Sensitivity of Peak Compressive Force
4-1
Correlation Coefficients (r) Relating Stiffness Constants
with MRI Based Measurements
Correlation Coefficients (r) Relating Damping Constants
with MRI Based Measurements
39
49
Chapter 4
4-2
89
89
Chapter 5
99
5-3
Input Values for a 5% Female
Mean Velocity and Configuration Data for Human,
Dummy and Model Falls
Sensitivity of Vertical Velocity and Torso Angle
6-1
6-2
6-3
6-4
6-5
6-6
Studies of Cross-sectional Properties
Anthropometric Parameters Measured
Number of Images Available for Each Gender
Mean Moment Arm Lengths in the Thoracic Torso
Mean Moment Arm Lengths in the Lumbar Torso
Regressions of Major Muscle Groups
116
120
121
123
124
125
7-1
7-2
Factors of Risk for Fracture
Factors of Risk for Fracutre as a Function of T-score
135
136
5-1
5-2
106
108
Chapter 6
Chapter 7
13
Chapter 1 - Introduction and Overview
1.1 Vertebral Fractures
Age-related vertebral fractures are a common problem for the elderly with an estimated
27 percent of U.S. women aged 65 years and over thought to have at least one vertebral fracture
(Melton et al., 1989). These fractures are characterized by a decrease in height of the vertebral
body, a wedging of the anterior aspect of the vertebral body and/or a decrease in the height of the
center of the vertebral body relative to the heights on the anterior and posterior sides (SmithBindman et al., 1991). The incidence of vertebral fractures increases with age from 0.2 per 1,000
per year at ages less than 45 to 1.3 per 1,000 per year in men and 1.2 per 1,000 per year in
women over 85 years (Cooper et al., 1992). The lifetime risk of a clinically diagnosed vertebral
fracture is 16% in women and 5% in men (Melton, 1997). These fractures are thought to be due
to a decrease in bone density and strength with age, commonly known as osteoporosis.
Osteoporosis is a disease characterized by a bone mineral density (BMD) of the hip, spine
or forearm which is more than 2.5 standard deviations below the normal values for young adults
(Kanis, 1994). Approximately 30% of all postmenopausal white women in the United States are
within this range for at least one of the three bone regions (hip, spine, or forearm) (Melton,
1997). This lowered bone mineral density in the spine has been shown to significantly increase
the risk of a vertebral fracture (Black et al., 1992).
The consequences of a vertebral fracture can include pain, disability, loss of height, loss
of independence and increased morbidity and mortality. The five year survival relative to agematch controls for patients with clinically diagnosed vertebral fractures is 0.81 (Cooper et al,
15
1993). This is comparable with a five-year relative survival of 0.82 for hip fractures. The odds
of impairment in an activity such as cooking meals after a vertebral fracture is 6.9 fold that of
age-matched controls (Melton, 1997). The direct cost of vertebral fractures in the United States
in 1995 was 746 million dollars (Ray et al, 1997).
It is important, therefore, to characterize the "at risk" patient and to find methods of
reducing that risk. A bone will break when the loads placed upon the bone exceed the loads
required to break the bone. A patient can be said to be at risk when either the loads on the bone
are increased or the force required to fracture the bone is decreased. Activities and events such
as lifting heavy objects or falling can increase the loads on the spine. The failure load can be
decreased due to age- or disease-related changes in the structure or the material properties of the
bone.
The force required to fracture a vertebra has been investigated by several researchers. In
studies in which the intervertebral disks remained intact to transfer load, vertebrae from younger
adults were found to have compressive failure forces of approximately 8000 N. Vertebrae from
the elderly were found to have compressive failure forces averaging about 2000-3000 N (Moro et
al., 1995, Cody, 1985). Moro et al. (1995) found that vertebrae from cadavers with a mean age
of 72 years had an average failure load of 2080 (± 1420) N for the T11 vertebrae and 2620 (±
1510) N for the L2 vertebrae. They found the compressive force needed to fail a vertebra could
be as low as 500 N. These studies have also found good correlations between the failure force
and densitometric measurements such as bone mineral density using dual energy x-ray
absorptiometry (DXA) or computed tomography (CT). Moro et al. (1995) found that lumbar
bone mineral density of the L2 vertebra using DXA in the lateral plane correlated significantly
16
with L2 compressive failure force with a correlation coefficient of 0.89 and with T11
compressive failure force with a correlation coefficient of 0.94. Brinckmann et al. (1988) found
a correlation coefficient of 0.80 between a CT based estimate of bone density and failure force.
While several studies have looked at the decreases in the force required to fracture a
vertebra, its correlation with decreases in bone mineral density, and the effect of pharmacologic
intervention, few studies have examined the forces applied to the spine and how they might be
reduced. Such forces could be high both in controlled heavy loading situations such as lifting or
bending and in accidental events such as falls or trauma.
Two studies, using patient reports of the events preceding vertebral fracture, have shown
that a high proportion of patients associate a fall with their fracture. Ina population-based study,
Cooper et al. (1992) found that 86 of 228 vertebral fracture patients (37%) whose fractures were
not diagnosed incidentally and were not a result of severe trauma reported associating the onset
of pain with a fall from standing height. Of the other patients, 29 (13%) patients reported lifting
a heavy object and 113 (50%) patients reported no significant event associated with the onset of
pain. in a survey, Myers et al. (1997) found that 56% of patients seen in the emergency room for
a vertebral fracture associated falling with their fracture. In this study, 23% of the patients were
involved in controlled activities such as lifting and 18% did not associate a particular activity
with their injury. Of these patients 56 % reported a backward fall, 11% reported a sideways fall,
11% reported a forward fall, and 11% could not recall the fall direction (Myers, 1998).
Because falls account for as much as 56% of associated activities, it is essential therefore,
to try to assess the forces on the spine during a backward fall in order to understand fully the risk
of fracture.
17
1.2 Fall Mechanics
Several studies have examined aspects of falling and the elderly. Factors such as chronic
disease, medications, environmental hazards, changes in balance or gait, and changes in mental
cognition have been shown to predispose a person to fall (King et al., 1995, Tinetti et al., 1988,
Tinetti et al., 1995). Studies have also shown that interventions such as exercise, behavioral
instruction and reduction in sedatives decrease the likelihood of a fall (Tinetti et al., 1994,
Privince et al., 1995, Lord et al., 1995).
Other researchers have looked at the initiation of a fall and mechanisms for recovery.
Zhang et al. (1992) found that subjects used a combination of swaying and stepping to recover
from a lateral fall. They found that foot response times were significantly slowed in the healthy
elderly subjects compared with young subjects. Sprague et al. (1993) reported that older adults
took larger, slower steps than young adults in response to postural disturbances.
There have been very few studies of what occurs after a fall has been initiated. Most of
the work has focused on sideways falls because of the importance of side falls in the etiology of
hip fractures. Kroonenberg et al. (1996) studied the descent phase of sideways falls and found
average impact velocities of 3.09 ± 0.41 m/s for "relaxed" falls and 3.31 ± 0.43 m's for "active"
falls. In another paper, Kroonenberg et al. (1995) modeled sideways falls using 2 and 3 link
models of the human body. They found impact velocities in the models ranged from 2.47 to 4.34
m/s depending on the size of the person and torso angle at impact. Robinovitch et al. (1991,
1997) modeled the impact of a side impact fall and found forces on the hip varied between 1145
N to 8600 N depending on speed, torso angle, and stiffness properties of the pelvis soft tissue.
18
1.3 Impact Mechanics and Spine Modeling
While no researchers have examined the forces on the spine during a fall, researchers
have tried to examine forces on the spine or the acceleration of the spine during other events and
actions. These include examining pilots ejected from fighter aircraft, occupational exposure to
vibration, and lifting and bending, particularly in an occupational setting.
PilotEjection
In the early 1970s, several investigators examined the problem of vertebral fractures in
young healthy fighter pilots who were ejected from their aircraft during a crash. These fractures
were thought to be due to the high vertical acceleration needed for the pilots to clear the cockpit.
Models created to examine this event included lumped parameter models ranging from simple
one or two degree of freedom models to complex models with many degrees of freedom. One of
the earlier models (Terry and Roberts, 1968) considered the body to be a single mass over a
viscoelastic element. They concluded that a viscoelastic rod more closely approximates the
response of the spine acceleration of the spine due to an inpulse at the base than an elastic rod.
Orne and Liu (1971) created a model in which individual vertebrae were represented as masses
connected by stiffness and damping elements. They found that bending played a role in the
response of the spine to an input acceleration pulse and that the time to peak loading was
approximately 0.04 s. They predicted forces as high as 7000 N in response to a 10g acceleration
impulse. Prasad and King (1974) created a similar model, incorporating a second set of springs
to represent facet joint action and validated this model with experimental data on the facet joint
pressures. Belytschko et al. (1978) created a three-dimensional model in which the vertebrae
19
were represented as individual elements, the facets were represented by spring elements and the
abdomen was represented as a fluid column. Belyschko predicted axial forces of up to 4270 N
and moments of between -11.11 and 11.19 Nm in response to a 10g pelvis acceleration
depending on the level of the spine, angle of seat, and speed of onset of the acceleration pulse.
These models, in general, suffered from a lack of experimental data on the mechanical
properties of the body and from a lack of appropriate validation data. Prasad et al. (1974) were
able to validate a complex model of the body including components representing the facet joints
with cadaveric intrafacet force data from sled tests. They found that cadaveric intrafacet forces
followed a slightly underdamped pattern with a peak at around 50 ms in response to an
acceleration pulse. They also found that facet joints showed a pattern of compression followed
by tension. This pattern resembled the predicted forces seen in the model when exposed to the
same acceleration conditions.
Vibration
Models of vibrational dynamics have, in general, used simpler models than those used for
pilot ejection to represent the dynamics of the human body and spine. Patil and Palaichamy
(1988) represented a person sitting on a tractor as parallel spring-dashpot pairs connecting
masses representing the pelvis, abdomen, diaphragm thorax, back, torso and head. Wan and
Schimmels (1997) represented the human body with similar parallel spring-dashpot pairs
separating four masses representing the lower torso, viscera, upper torso and head. This model
was validated against data from several experimental studies of vibration dynamics of the torso
and used to examine the effect of different seat cushions. Broman et al. (1996) examined the
20
gain and phase of human body vibration response using a two-dimensional model with two
masses that are connected by a freely rotating rod. The first mass was connected to the ground
via horizontal and transverse spring-dashpot pairs. A rotational spring-dashpot pair resisted
rotation of the rod. This model was validated against an impact experiment in which the phase
and gain of the lumbar spine response were measured.
Several experiments were also performed in order to assess vibrational dynamics.
Experimental studies of vibration with human subjects have generally measured acceleration of a
marker attached to the body or force exerted by the body seated on a force platform when the
body is subjected to a seat vibration of varying frequencies. Griffin et al. (1982) measured
acceleration of a bite bar. Panjabi et al. (1986) measured acceleration of K-wires inserted in to
the sacrum and L3 vertebral spinous process. Fairley and Griffin (1989) measured force on a
seat platform. Kitazaki and Griffin (1998) measured modes of vibration using several
accelerometers attached to the skin over several spinous processes, a bite bar, and the skin of the
abdominal wall. Broman et al. (1991) examined motion of markers attached to the lumbar spine
as a result of an impact to the seat. In this experiment gain and phase of the resulting
acceleration were examined and used to validate the model by Broman et al. (1996). Gain and
phase results from Panjabi et al. (1986), Griffin et al. (1982), and Fairley and Griffin (1989) were
used to validate the model by Wan and Schimmels (1997).
The 5 Hz peak frequency often seen in the vibration experiments used for validation can
be explained as the resonance frequency of the body mass over the pelvis soft tissue. More
difficult to ascertain is the resonance characteristics of the spine and abdominal viscera. The
experimental data from Kitazaki et al. (1998) are useful for determining these frequencies.
21
Kitazaki reported visceral frequencies of 4.9 Hz. They reported that they did not measure above
10 Hz and did no find an axial spine vibration mode. This would indicate that the in situ spine
resonance is over 10 Hz.
Pilot Ejection and VibrationModel Summation
Both pilot ejection and vibration models attempt to model a dynamic motion of a seated
body in order to get information about what forces or motions the spine is exposed to. While
these models were developed for other applications, similar models could be used to examine the
forces on the spine during a fall. While some of the earlier models were more complex, the later
models, which were more often validated against experimental data, showed that a simpler model
with a few key elements could model the system dynamics. They also showed the importance of
validation in confirming the models. The variety in the predictions of force as a result of a 10g
acceleration impulse in the early, less validated models, also illustrates the need for good
validation of the models. Another limitation of most of these models is the lack of attention to
the sensitivity of final predictions to the input values chosen and often a lack of good input data.
Controlled Action Models
Controlled actions are slower, more deliberate actions such as lifting and bending, which
are often studied in order to analyze safety in the workplace. Many studies have examined these
types of actions using experiments and models (Cappozzo, 1985, Lee, 1989, McGill, 1985,
Schultz, 1982, McGill, 1986, Schultz, 1987, Hughes, 1991, Wilson, 1994). The models have, in
general, been quasi-static models in which the forces and moments of the upper or lower body
22
are balanced against the forces in a cross-section of the torso. The forces considered in this
cross-section include the compressive load on the spine and tensile forces of the muscle groups.
The simplest models consider only the erector spinae and rectus abdominous muscles in
sagittally symmetric flexion and extension tasks and erector spinae and oblique muscles in lateral
bending and flexion tasks (Cappozzo, 1985, Lee, 1989, Schultz, 1982). More sophisticated
models incorporate other muscles including the latissimus dorsi, psoas and quadratus lumborum
muscles (McGill, 1986, Schultz, 1987, Hughes, 1991). Because these models are indeterminant,
various techniques are used to determine the configuration of muscle activation. These
techniques, include: EMG based configuration, compressive force optimization, compressive
force optimization with incremented maximum stress and minimization of the maximum stress
followed by compressive force optimization.
These models are less helpful in the modeling of a fall because they are quasi-static.
However, they do illustrate the complexity of the torso musculature activity in even simple
controlled acitivites and the difficulties involved in estimating muscle tension.
Stability Models
Recent efforts in the low back pain literature have focused on the stability of the spine
(Bergmark, 1989, Crisco, 1991, Cholewicki, 1997, Gardner-Morse, 1998, Cholewicki, 1999).
Unlike the other models described here, stability models use the dynamic characteristics of the
torso musculature. Bergmark (1989) developed the first lumbar stability model with a model of
the spine as a single inverted pendulum held in place by several variable stiffness springs
representing the musculature. The stiffness of these springs was based on data from Morgan
23
(1977) who reported that stiffness (K) was proportional to active muscle tension (F) with the
function:
K=qF
where 1 is the length of the muscle and q is a constant. Morgan (1977) estimated the constant q
to be around 40. Crisco (1991) used several sources to estimate the q at between 0.5 and 42 with
a mean value of 10. Cholewicki (1997) used a q of 30. Also difficult to assess is the length of
the torso musculature and the contribution of a tendonous attachment. Cholewicki (1997) used a
length of 20 cm for abdominal and extensor musculature, giving an overall q/l of 150 m ' . Crisco
(1991) commented that although the relationship is noteworthy, it has not been sufficiently
researched experimentally for the human lumbar torso musculature.
The main purpose of these models has been to assess the potential for buckling in the
lumbar spine and the effect of antagonistic muscle activity. It is believed that antagonistic
muscle activity provides stability to the spine. For the purposes of this dissertation, the most
interesting aspect of these models is the use of muscle stiffness and tension in dynamic
modeling. The linear relationship between tension and stiffness found in animal studies and used
in these stability models can be used to examine the relationship of muscle tension and stiffness
to the peak compressive force on the spine.
1.4 Summary of Literature
In summary, vertebral fractures are a significant public health problem. While studies
exist examining the forces required to fracture a vertebra, few have tried to assess the force that
may be applied to the spine. Epidemiological data have shown that many of these fractures are
24
associated with backward falls, so it is important to examine what happens to the spine during a
backward fall in order to assess risk of a fracture. Previous work that aided in this investigation
included previous work done examining fall dynamics and work done examining the loads on the
spine during pilot ejection, controlled actions, or as a result of vibration.
1.5 Aims of the Thesis
The aim of this thesis was to answer the research question: What are the forces on the spine
during a fall? and Is the magnitude of the compressive force on the vertebra high enough to put
the osteoporotic subject at risk of fracture? This question was divided into several topics. First,
the impact phase of the fall and the resulting forces on the spine were modeled. Second, the
effect of variations in anthropometric parameters, soft tissue stiffness, and spine curvature on the
applied forces was investigated. Finally, the dynamics of a backward fall were explored.
This thesis is divided into 5 chapters. These include:
Chapter 1 - Introduction
- A literature review and introduction to the
problem
Chapter 2 - Impact Mechanics Modeling
- Modeling of the dynamics of the human body
and estimation of the forces on the spine
Chapter 3 - Active Muscle Modeling
- Adaptation of the impact models to examine the
effect of active torso musculature on the impact
forces
Chapter 4 - Dynamic spine properties
- Experimental assessment of dynamic spine
properties for input into models of spinal loading
25
and analysis of the effect of disc degeneration on
these properties
Chapter 5 - Fall modeling
- Analysis of fall dynamics and evaluation of the
impact configuration and velocity
Chapter 6 - Cross-sectional Anatomy
- Measurement of torso musculature geometry for
input into models of spinal loading
Chapter 7 - Conclusion
- Summation of findings and general conclusions
1.6 References
1. Belytschko, T., Schwer, L., Privitzer, E., "Theory and Application of a Three-Dimensional
Model of the Human Spine", 49(1), pp. 158-165, 1978.
2. Black, D.M., Cummings, S.R., Genant, H.K., Nevitt, M.C., Palermo, L., and Browner, W.,
"Axial and appendicular bone density predict fractures in older women", J Bone Miner Res, 7,
pp. 633-638, 1992.
3. Broman, H., Pope, M.H., Benda, M., Svensson, M., Ottosson, C., Hansson, T., "The Response
of the Seated Subject", J Orthop Res, 9, pp. 150-154, 1991.
4. Broman, H., Pope, M., Hansson, T., "A Mathematical Model of the Impact Response of the
Seated Subject", Med Eng Phys, 18(5), pp. 410-419, 1996.
5. Cappozzo, A., Felici, F., Figura,F., and Gazzani, F., "Lumbar Spine Loading During Halfsquat Exercises," Med. Sci. Sports Exerc., 17(5), pp. 613-620, 1985.
6. Cody, D.D., Goldstein, S.A., Flynn, M.J., and Brown, E.B., "Correlations between vertebral
regional bone density (rBMD) and whole bone fracture load", Spine, 16, pp. 146-154, 1991.
26
7. Cooper, C. Atkinson, E.J., Jacobsen, S.J., O'Fallon, W.M., and Melton, L.J., "PopulationBased Study of Survival after Osteoporotic Fractures", Amer. J. Epidem., 137(9), pp. 10011005,
1993.
8. Cooper, C., Atkinson, E.J., O'Fallon, W.M., Melton, L.J., "Incidence of Clinically Diagnosed
Vertebral Fractres: A Population-Based Study in Rochester, Minnesota, 1985-1989", 7(2), pp.
221-227, 1992.
9. Brinkmann, P. Biggemann, M., Hilweg, D., "Prediction of the Compressive Strength of
Human Lumbar Vertebrae", Spine, 14:6, p. 606-610, 1989.King, M.B., Tinetti, M.E., "Falls in
Community-Dwelling Older Persons", J Amer Geriatrics Soc, 43, pp. 1146-1154, 1995.
10. Fairley, T.E., Griffin, M.J., "The Apparent Mass of the Seated Human Body: Vertical
Vibration", 22(2), pp. 81-94, 1989.
11. Greendale GA, Barrett-Connor E, Inlges S, Haile R, "Late Physical and Functional Effects
of Osteoporotic Fracture in Women: The Rancho Bernardo Study", J Am Geriatr Soc 43, pp.
955-961, 1995.
12. Griffin, M.J., Whitman, E.M., Parson, K.C., "Vibration and Comfort. I. Translational Seat
Vibration", Ergonomics, 25(7), pp. 603-630, 1982.
13. Hughes, R.E., "Empirical Evaluation of Optimization-Based Lumbar Muscle Force
Prediction Models," Ch. 4, Ph.D. dissertation, University of Michigan, 1991.
14. Kanis, J.A., Melton, L.J., Christiansen, C., Johnston, C.C., Khaltaev, N., "The Diagnosis of
Osteoporosis", J. Bone Min. Res., 9, pp. 1137-1141, 1994.
15. Kitazaki, S., Griffin, M.J., "Resonance Behaviour of the Seated Human Body and Effects of
Posture", J Biomechanics, 21, pp. 143-149, 1998.
27
16. Kroonenberg, A.J.vd, Hayes, W.C., McMahon, T.A., "Hip Impact Velocities and Body
Configuration for Voluntary Falls from Standing Height", J. Biomechanics, 29(6), pp. 807-811,
1996.
17. Kroonenberg, A.J.vd, Hayes, W.C., McMahon, T.A., "Dynamic Models for Sideways Falls
from Standing Height", J Biomech Eng, 117(3), 309-318, 1995.
18. Lee, K.S., Chaffin, D.B., Waikar, A.M., and Chung, M.K., "Lower Back Muscle Forces in
Pushing and Pulling", Ergonomics, 32(12), pp. 1551-1563, 1989.
19. Lord, S.R., Ward,J.A., Williams, P. Strudwick, M., "The Effects of a 12-Month Exercise
Trial on Balance, Strength, and Falls in Older Women: A Radomized Controlled Trial", J Amer
Geriatrics Soc, 32, pp. 1198-1206, 1995.
20. McGill, S.M., and Norman, R.W., "Partitioning of the L4-L5 Dynamic Moments into Disc,
Ligamentous, and Muscular Components During Lifting", Spine, 11(7), pp. 666-678, 1986.
21. McGill, S.M. and Norman, R.W., "Dynamically and Statically Determined Low Back
Moments During Lifting," J. Biomech., 18(12), pp. 877-885, 1985.
22. Melton, L.J., Kan, S.H., Frye, M.A., Wahner, H.W., O'Fallon, W.M., and Riggs, B.L.,
"Epidemiology of Vertebral Fractures in Women", Amer. J. Epidem., 129 (5), pp. 1000-1011,
1989.
23. Melton, L.J., "Epidemiology of Spinal Osteoporsis", Spine, 22(24S), pp. 2-11, 1997.
24. Myers, E.R., private communication, 1998.
25. Moro, M., Hecker, A.T., Bouxsein, M.L., Myers, E.R., "Failure Load of Thoracic Vertebrae
Correlates with Lumbar Bone Mineral Density Measured by DXA", Calcif Tissue Int, 56, pp.
206-209, 1995.
28
26. Myers, E.R, Wilson S.E., "Biomechanics of Osteoporosis and Vertebral Fracture", Spine,
22(24S), pp. 25S-31S, 1997.
27. Orne, D., and Liu, Y.K., " A Mathematical Model of Spinal Response to Impact", J
Biomechanics, 4, pp. 49-71, 1971.
28. Panjabi, M.M, Andersson, G.B.J., Jorneus, L., Hult, E., Mattsson, L., "In Vivo
Measurements of Spinal Column Vibrations", J Bone Joint Surg, 68-A(5), pp. 695-702, 1986.
29. Patil, M.K., Palanichamy, M.S., "A Mathematical Model of Tractor-Occupant System with a
New Seat Suspension for Minimization of Vibration Response", Appl Math Modeling, 12, pp.
63-71, 1988.
30. Prasad, P., King, A.I., "An Experimentally Validated Dynamic Model of the Spine", J
Applied Mechanics, pp. 546-550, September, 1974.
31. Province, M.A., Haley, E.C., Hornbrook, M.C., Lipsitz, L.A., Miller, J.P., Mulrow, C.D.,
Ory, M.G., Sattin, R.W., Tinetti, M.E, Wolf, S.L., "The Effects of Exercise on Falls in Elderly
Patients", JAMA, 273(17), pp. 1341-1347, 1995.
32. Ray, N.F., Chan, J.K., Thamer, M. and Melton, L.J., "Medical Expenditures for the
Treatment of Osteoporotic Fractures in the United States in 1995: Report from the National
Osteoporosis Foundation", J. Bone Min. Res., 12(1), pp. 24-35, 1997.
33. Robinovitch, S.N., Hayes, W.C., McMahon, T.A., "Distribution of Contact Forces during
Impact to the Hip", Annals Biomed Eng, 25, pp. 499-508, 1997.
34. Robinovitch, S.N., Hayes,W.C., McMahon, T.A., "Prediction of Femoral Impact Forces in
Falls on the Hip", J Biomed Eng, 113, pp. 366-374, 1991.
35. Schultz, A., Cromwell, R., Warwick, D., and Andersson, G., "Lumbar Trunk Muscle Use in
29
Standing Isometric Heavy Exertions", J. Orthop. Res., 53, pp. 320-329, 1987.
36. Schultz, A., Andersson, G.B.J., Ortengren, R., Bjtrk, R., and Nordin, M., "Analysis and
Quantitative Myoelectric Measurements of Loads on the Lumbar Spine when Holding Weights
in Standing Postures," Spine, 7(4), pp. 390-397, 1982.
37. Smith-Bindman, R., Cummings, S.R., Steiger, P., Genant, H.K., "A Comparison of
Morphometric Definitions of Vertebral Fracture", J Bone Min Res, 6 (1), pp. 25-34, 1991.
38. Soechting, J.F., Paslay, P.R., "A Model for the Human Spine During Impact Including
Musculature Influence", J Biomechanics, 6, pp. 195-203, 1973.
39. Sprague, J.K., Ashton-Miller, J.A., Schultz, A.B., "A BIomechanical Analysis of the Use of
Stepping to Maintain Balance", 1993 ASME Bioengineering Conference, Vol. 24, pp. 412-414,
1993.
40. Terry, C.T. and Roberts, V.L., "A Viscoelastic Model of the Human Spine Subjected to +gz
Accelerations", J Biomechanics, 1, pp. 161-168, 1968.
41. Tinetti, M.E., Baker, D.I., McAvay, G., Claus, E.B., Garrett, P., Gottschalk, M., Koch, M.L.,
42. Tinetti, M.E., Doucette, J., Claus, E., Marottoli, R., "Risk Factors for Serious Injury During
Falls by Older Persons in the Community", J Amer Geriatrics Soc, 32, pp. 1214-1221, 1995.
43. Tinetti, M.E., Speechley, M., Ginter, S.F., "Risk Factors for Falls Among Elderly Persons
Living in the Community", The New England J of Medicine, 319(26), pp. 1701-1707, 1988.
44. Trainor, K., Horwitz, R.I., "A Multifactorial Intervention to Reduce the Risk of Falling
Among Elderly People Living in the Community", The New England J of Medicine, 331(13), pp.
821-827, 1994.
45. Wan, Y., Schimmels, J.M., "Optimal Seat Suspension Design Based on Minimum
30
'Simulated Subjective Response"', J Biomech Eng, 119, pp. 409-416, 1997.
46. Wilson, S.E., "Development of a Model to Predict the Compressive Forces on the Spine
Associated with Age-Related Vertebral Fractures", Master's thesis, Mechanical Engineering,
Massachusetts Institute of Technology, 1994.
47. Zhang, X., Ashton-Miller,J.A., Schultz, A.B., Alexander, N.B., "A Biomechanical Study of
the Effects of Age on Recovery from Impending Lateral Falls", Proceedings of the 16th Annual
Meeting of the American Society of Biomechanics, pp. 49-50, 1992.
31
Chapter 2 - Impact Mechanics Modeling
2.1 Abstract
With an estimated 27 percent of women over 65 years thought to have at least one
vertebral fracture, age-related vertebral fractures are a significant public health concern. Recent
surveys of patients entering the emergency room have shown that as many as half associated
their fracture with a fall. In this work, the impact phase of a backward fall was modeled in order
to estimate the maximum forces on the spine during a fall. These forces were found to vary
depending on the speed of impact, the angle of the torso and weight of the faller. The highest
forces on the spine were for upright falls with high impact speeds. Forces were found to be as
high as 2630 N for a woman of average height and weight in an upright fall at an impact speed of
2.53 m/s. Previous studies of the failure force of cadaveric vertebra have shown that this force is
enough to elderly vertebra of average or below average bone mineral density. This work shows
that falls put many elderly people at risk for vertebral fractures, suggesting that prevention efforts
be addressed at preventing falls as well as increasing bone strength.
2.2 Introduction
Age-related vertebral fractures are a growing public health problem. In the United States,
an estimated 27 percent of women aged 65 years and over are thought to have at least one
vertebral fracture (Melton et al., 1989). Patients with age-related vertebral fractures can suffer
pain, loss of height, and loss of independence. The mortality over five years of patients with
vertebral fractures relative to age-matched controls is 19 percent. The direct costs of vertebral
33
fractures in the United States in 1995 were 746 million dollars (Ray et al, 1997).
Recent studies have shown that falls may play a role in the etiology of vertebral fractures.
Cooper et al. (1992) found that 86 of 282 patients with vertebral fractures not resulting from
severe trauma reported associating the injury with a fall from standing height. In another study,
56 percent of patients diagnosed with a vertebral fracture and presenting at the emergency room
reported associating a fall with the onset of pain (Myers et al., 1996). Among these patients,
preliminary data suggests that backward falls are the most common type of fall (Myers, 1998).
While several studies exist looking at the forces required to fracture a vertebra (Moro et
al., 1995, Biggemann et al., 1995), no study to our knowledge has examined the forces on the
spine during a fall from standing height. The forces transmitted to the spine under such an
impact are not well understood.
While the propagation of force during the impact from a fall has not been assessed, the
propagation of force from the pelvis to the spine has been studied in the context of examining
pilot ejection and vibration dynamics. Modeling efforts in these two areas have included several
lumped parameter models of the human body. Experimental efforts have included several
studies with human subjects on the vibrational characteristics of the body.
The earliest models, developed for pilot ejection, included those by Orne, Prasad and
Belytschko (Orne and Liu, 1971, Prasad and King, 1974, Belytschko et al., 1978). These were
complex lumped parameter models of an upright seated human exposed to an acceleration pulse.
Later models of vibration dynamics of the body, including those by Patil, Broman and Wan,
modeled an upright seated human exposed to sinusoidal vibrations using simpler lumped
parameter models (Patil and Palanichamy, 1988, Broman et al., 1996, Wan and Schimmels,
34
I
1997). These models showed that it was possible to use lumped parameter techniques to model
the dynamics of the torso. The variety of different force predictions in the pilot ejection models
demonstrated the need for appropriate experimental validation and for good input data. Similar
models could be used to examine the forces on the spine during a fall.
Experimental studies of vibration with human subjects have generally measured
acceleration of a marker attached to the body or force exerted by the body seated on a force
platform when the body is subjected to a seat vibration of varying frequencies. Griffin et al.
(1982) measured acceleration of a bite bar. Panjabi et al. (1986) measured acceleration of Kwires inserted in to the sacrum and L3 vertebral spinous process. Fairley and Griffin (1989)
measured force on a seat platform. Kitazaki and Griffin measured modes of vibration using
several accelerometers attached to the skin over several spinous processes, a bite bar, and the
skin of the abdominal wall. These experiments have analyzed the propogation of the force and
acceleration through the body and can be used to validate models of the dynamics of the spine
and torso such as a model of fall impact mechanics.
There is a need to examine backward falls in order to understand the potential risk for
vertebral fracture in elderly individuals. While the dynamics of the torso and spine have been
examined in the context of pilot ejection and vibration exposure, no one has examined the
dynamics of the torso as a result of impact from a fall. Lumped parameter techniques have been
demonstrated to be successful in modeling the dynamics of the torso. However, such models
require accurate input data and careful validation.
The present study will use lumped parameter techniques to examine the forces on the
spine during the impact phase of a backward fall. The sensitivity of the model to changes in
35
input parameters and the validity of the models relative to previous experimental studies of
whole body vibration will also be assessed. With this model, the maximum compressive force
on the spine during a backward fall will be estimated and compared to the fracture force of the
vertebrae measured by other researchers.
2.3 Methods
Human Body Models
Four lumped parameter models were created to represent a human body in an impact
configuration. The simplest model was a one-dimensional model of a upright fall (Figure 2.1).
In this model the thorax, head and arms were represented by one mass, the abdominal viscera by
a second mass and the pelvis and upper legs as a third mass. The soft tissues of the pelvis, the
spine and the abdominal viscera were represented by a spring and dashpot in parallel (Appendix
A).
The second model was a two-dimensional version of the simple model. In this model, the
spine and pelvis soft tissue were represented by transverse (anterior-posterior), axial (caudalinferior) and torsional (flexion-extension) pairs of springs and dashpots. The abdominal viscera
was represented by a point mass connected to the pelvis and thorax by transverse and axial
stiffnesses. This model allowed consideration of angled impact configurations (Appendix A).
In the third and fourth models, the lumbar spine was represented by five masses
connected by parallel spring and dashpot pairs. The third model was a one-dimensional
representation of the upright impact and the fourth model was a two dimensional version. The
fourth model allowed for the consideration of spine curvature as well as angulation of the torso.
36
l
Selectionof Input Parameters
Input parameters including the spring stiffness and damping coefficients of the soft
tissues, the masses of the body segments, and the impact velocity and configuration were taken
from a variety of sources (Table 2.1). The distribution of mass was based on data collected by
Dempster and reanalyzed by Winter (1979). The mass of the arms, head, neck, and thorax were
lumped into the upper body mass. The mass of the pelvis and thighs was lumped into the lower
mass. The abdominal mass was divided into the viscera and the spine. In the models in which
the spine was modeled as one element the mass of the spine was added to the upper body mass.
In the segmented spine models, the spine mass was divided amongst the spine segments. For the
initial runs of the model data, a female of average height and weight was used. Average total
height and weight for elderly women were obtained from a previous study with 120 women over
the age of 60 (Greenspan et al., 1996). Inertial properties of the upper body and pelvis in the two
dimensional models were determined based on data from the Anthropometric Source Book
(1978). The geometry of the two dimensional models was calculated from data by Contini
(1972) and by Lui (1971). The lumbar curvature in the two dimensional model with a segmented
spine was obtained from Bernhardt (1989).
In Chapter 5, impact velocity and configuration of subjects under self-initiated backward
falls are reported. The mean impact velocities and torso angles from this study were used in this
model. The vertical impact velocities found in Chapter 5 were 2.18 + 0.34 m/s and the impact
torso angles were 47 ° + 24° .
To estimate the stiffness of the spine segments, instantaneous stiffness of spine segments
from creep studies and stiffness from studies of the vibrational properties of the spine were
37
IT
4
(b) l-dimensional model
(a) 1-dimensional model
with a segene d spine
I
___r
(c) 2-dimensional model
(d) 2-dimensionalmodel
with a segment d spine
Figure 2.1
Four models of fall dynamics were created to examine fall dynamics. Models were either
one-dimensional, (a) and (c), or two-dimensional, (b) and (d), with either a single element spine,
(a) and (b), or a five segment spine (c) and (d). A solid bar represents axial, transverse and
rotational elements in the two-dimensional models.
38
Table 2.1 - Input Values
Input values used in the four models were obtained from a variety of literature sources.
These sources included anthropometric data, experimental data from mechanical tests, and whole
body data from experiments with volunteers.
Category
Mass
Input Parameter
Variable
Literature Source 1-dimensional 2-dimensional
simple model simple model
1-dimensional
segmented model
2-dimensional
segmented model
Thorax, head, and arms
Abdomen
Winter
Winter
30.92
4.08
30.92
4.08
25.92
4.08
25.92
4.08
kg
kg
Pelvis and upper legs
Winter
22.33
22.33
22.33
22.33
kg
Spine segments
Lui
1
1
kg
Axial
Pelvic soft tissue
Robinovitch, Kitazaki
56.5
56.5
56.5
56.5
kN/m
Stiffness
Abdomen
Kitazaki
4
4
4
4
kN/m
Lumbar spine
Kasra, Keller, Ch. 3
88.3
88.3
530.0
530.0
kN/m
Transverse
Pelvic soft tissue
56.5
56.5
kN/m
Stiffness
Abdomen
4
4
kN/m
Miller
25.2
120
kN/m
87
Lumbar spine
Rotational
Pelvic soft tissue
Stiffness
Lumbar spine
Miller
Axial
Pelvic soft tissue
Robinovitch
2000
500
500
Kasra, Chapter 4
124.5
124.5
Damping
0
Abdomen
Lumbar spine
2000
0 Nnm/rad
435 Nm/rad
2000
2000
Nstm
500
500
Ns/m
746.9
746.9
Ns/m
Rotational
Pelvic soft tissue
0
0 Nms/ra
Damping
Lumbar spine
Miller
10
50 Nms/ra
Geometry
abdomen eccentricity
Lui
0.0165
0.0165
m
spine eccentricity
Lui
0.032
0.032
m
pelvis to L5
Lui, Contini
0.0337
0.0337
m
thorax to L
Lui, Contini
0.1103
0.1103
m
lumbar spine length
Lui
0.0443
0.0443
m
Thoracic
NASA
0.941
0.941
kg m2
Pelvis
vertebrae
NASA
0.0513
0.0513
kg m2
0.01
kg m2
Intertia
Fall
impact velocity
Chapter 5
2.18
2.18
2.18
2.18
mn/s
theta
Chapter 5
0.83
0.83
0.83
0.83
rad
theta dot
Chapter 5
-1.3
-1.3
-1.3
-1.3
rad/s
39
compared (Keller et al., 1987, Kasra et al., 1991, Miller et al., 1986). Damping of the spine
segments was estimated based on damping ratios reported in vibration studies (Kasra et al.,
1991).
The pelvis soft tissue would include muscle, fat, and skin tissue under the bony pelvis.
Whole body vibration studies report natural frequencies of around 5 Hz regardless of size or
gender (Fairley and Griffin, 1989, Kitazaki and Griffin, 1998). This is generally attributed to the
pelvis soft tissue. With the masses for an average woman, this would give a pelvis soft tissue
stiffness constant of 56.6 kN/m. Robinovitch et al. (1997) measured the stiffness and damping
coefficients of pelvis soft tissue over the greater trochanter to be in the range of 14 to 70 kN/m
for the stiffness constant and 13 to 1380 Ns/m for the damping constant.
Stiffness of 56.6 kN/m
and damping of 2000 Ns/m were chosen.
Validation
To validate the models, we compared model predictions to the results of several
experimental studies of vibration dynamics of the human body from the literature (Figure 2.22.6). Fairley and Griffin used a hydraulic vibrator to expose volunteers to random vibrations in a
frequency range of 0.25 to 20 Hz. In that experiment, a force platform was placed over the
vibrator to measure the force exerted by the volunteer seated on the platform. Panjabi et al.
inserted Kirschner wires into the spinous process of two lumbar vertebrae and into the sacrum.
They measured the acceleration of these wires relative to the acceleration of a seat
vibrated at frequencies of 2 to 15 Hz. Griffin et al. measured the vibration of an accelerometer in
a bite bar relative to a acceleration of a seat vibrated at frequencies of 1 to 100 Hz.
40
The models were setup to replicate these experimental conditions. The two-dimensional
models were set to a torso angle of 0 degrees. Pelvis rotational stiffness in the two dimensional
models was set to 1000 kN/m in order to maintain an upright position. Axial ground vibrations
of varying frequencies were applied to the models. The output of the upper body mass, L3
vertebra and lower body mass motion as well as the force in the axial pelvis soft tissue elements,
were compared to the data reported by the three authors.
Sensitivity
The sensitivity of the models to changes or errors in the input parameters was analyzed
by varying, individually, each of input parameters by ±5 percent and calculating the change in
predicted maximum axial force in the L3-L4 intervertebral disk.
ForcePrediction
Once the models were validated and the sensitivity was examined, the predicted forces on
the spine were assessed. Several input parameters were varied to examine the effect of altered
impact conditions and increased or decreased total weight and height. The forces at different
levels of the spine were also compared.
2.4 Results
Validation
All of the models were found to agree closely with experimental vibrations data (Figures 2.22.6). The relative apparent mass response to varying frequencies predicted by the model closely
41
followed that measured by Fairley et al. (1989) with a peak around 5 Hz at approximately 1.5
followed by a decline to approximately 0.2 at high frequencies (Figure 2.2). The phase shift of
the force response to acceleration input was also found to follow the same pattern as that
measured by Fairley et al. with a slightly greater phase lag in the mid-frequency (8-12 Hz) range
(Figure 2.3). The amplitude ratio of the vibrations at the sacral level was found to peak at
approximately 5 Hz with a ratio slightly under that measured by Panjabi et al. (1986) (Figure
2.4). At the L3 vertebral level, the amplitude ratio of the vibrations was found to be within
experimental measurements by Panjabi et al., with the segmented models predicting slightly
lower amplitudes than the non-segmented models in which the upper body vibration is compared
(Figure 2.5). The upper body vibrations in the model compared well with bite bar vibration data
from Griffin et al. (1982) (Figure 2.6). The upper body vibrations of the model were found to
peak higher than experimental data at frequencies of approximately 5 Hz and attenuate lower
than experimental data at frequencies around 10 to 30 Hz.
Sensitivity
The predicted compressive forces from the models were found to be the most sensitive to
changes in the impact velocity, impact angle, upper body mass, and axial stiffness of the spine
and pelvic soft tissue (Table 2.2). Changes in velocity and angle of impact had the greatest effect
on the predicted force with a 10 percent change in the predicted force if either value is varied 10
percent. Changes in upper body mass also had a substantial effect on the predicted force, with a
1 to 2 ratio of change in the predicted force to change in the mass. Other variables with a lower
but still noticeable effect on the predicted force included the axial stiffness of the pelvic soft
42
Figure 2.2 - Relative Apparent Mass
The amplitude of the force on the seat relative to the amplitude of the seat acceleration divided
by the resting force (the relative apparent mass) was measured by Fairley and Griffin (1989) and
the mean values or each frequency are indicated by *. Vibration of the upper body mass relative
to the seat for the four models is indicated by a solid line for the 1-dimensional simple model, a
dashed line for the 2-dimensional simple model, a dotted line for the 1-dimensional segmented
model and a dash-dot line for the 2-dimensional segmented model. The four models behave
similarly to each other in response to vibration. The models also behaved similarly to the
experimental data with a peak frequency of approximately 5 Hz. A lower apparent mass was
predicted in the mid-frequency (10-15 Hz).
uc,
C,
a)
CZ
.>
a
0
5
10
Frequency (Hz)
43
15
20
Figure 2.3 - Phase shift
The phase shift between the force on the seat and the the seat acceleration was measured by
Fairley and Griffin (1989) and the mean data for each frequency are indicated by *. Vibration of
the upper body mass relative to the seat for the four models is indicated by a solid line for the 1dimensional simple model, a dashed line for the 2-dimensional simple model, a dotted line for
the 1-dimensional segmented model and a dash-dot line for the 2-dimensional segmented model.
The four models behave similarly to each other in response to vibration. The models had a
greater phase shift in the mid-frequency (5-15 Hz) region but otherwise followed the
experimental data.
U
LL -0
cu
C
a)
CD
a-
-2
0
5
10
Frequency (Hz)
44
15
20
Figure 2.4 - Sacral Transmissibility
The amplitude of the sacral acceleration relative to the amplitude of the seat acceleration (the
transmissibility) was measured by Panjabi et al. (1986) for four subjects and is indicated by *.
Vibration of the upper body mass relative to the seat for the four models is indicated by a solid
line for the 1-dimensional simple model, a dashed line for the 2-dimensional simple model, a
dotted line for the 1-dimensional segmented model and a dash-dot line for the 2-dimensional
segmented model. The four models behaved similarly to each other in response to vibration.
The models also behaved similarly to the experimental data with slightly less transmissibility in
the mid-range frequency region and with approximately the same frequency at peak and
minimum transmissibility.
I-
^
2
O
2
1.5
'=
1.5
E
c7
0
L.
O
0.5
0.5
n
0
5
10
Frequency (Hz)
45
15
tissue and the axial stiffness of the lumbar spine. Changes in most of the other variables had
very little effect on the final force predictions.
Forcepredictions
For an average woman (height of 1.59 meters and weight of 65.3 kilograms) impacting
upright (0 degrees) at a velocity of 2.18 m/s, the one and two-dimensional single element spine
models predicted peak forces of 2505 N and 2461 N. For the segmented spine models, the peak
force transmitted from the L3 vertebra to the upper body was 2376 N for the 1-dimensional
model and 2165 for the 2-dimensional model. The two-dimensional models predicted lower
forces due to rotation of the upper body.
Using the two-dimensional segmented spine model, a 50th percentile woman was found
to impact with a maximum axial force on the L3 vertebra of 1404 N for a fall with an impact
velocity of 2.18 m/s and an impact angle of -48 degrees. As expected, a larger body size resulted
in a larger force with the 95th percentile woman having a maximum impact force of 1567 N for
the same fall and a 5th percentile woman having a maximum impact force of 1223 N.
Upright, high impact velocity falls were found to have the highest impact forces. The
maximum axial force on the L3 vertebra for a 50th percentile woman varied from 2165 N for an
upright fall to 1046 N for a fall with the torso angle at 60 degrees. Increasing impact velocities
from 2.18 m/s to 2.5 m/s increased the predicted axial force on the L3 vertebra from 1404 N to
1585 N at an impact angle of 48 degrees.
46
Figure 2.5 - L3 Vertebral Transmissibility
The amplitude of the L3 vertebra acceleration relative to the amplitude of the seat acceleration
(the transmissibility) was measured by Panjabi et al. (1986) for five subjects and is indicated by
*. Vibration of the upper body mass relative to the seat for the four models is indicated by a
solid line for the 1-dimensional simple model, a dashed line for the 2-dimensional simple model,
a dotted line for the 1-dimensional segmented model and a dash-dot line for the 2-dimensional
segmented model. For the single spine segment models, the upper body motion was used instead
of the L3 motion giving a higher peak transmissibility. The models behaved similarly to the
experimental data with the same peak transmissibility at a frequency of approximately 5 Hz.
O
Cr
ci)
.0
E1
O
>
U
0
10
5
Frequency (Hz)
47
15
Figure 2.6 - Seat to Head Transmissibility
The amplitude of the head acceleration relative to the amplitude of the seat acceleration (the
transmissibility) was measured by Griffin et al. (1982) and the mean female and male values are
indicated by *. Vibration of the upper body mass relative to the seat for the four models is
indicated by a solid line for the 1-dimensional simple model, a dashed line for the 2-dimensional
simple model, a dotted line for the 1-dimensional segmented model and a dash-dot line for the 2dimensional segmented model. The four models behaved similarly to each other in response to
vibration. The models also behaved similarly to the experimental data with a slightly higher
peak transmissibility and no secondary peak at 15 Hz.
1.8
1.6
1 .4
co
E
u) 1.2
C
m1i'
I 0.8
"r
o
- 0.6
C)
C) 0.4
0.2
A
10
0
101
Frequency (Hz)
48
102
Table 2.2
Sensitivity of the peak compressive force on the spine to changes in input parameters in percent.
The input parameters that the peak compressive forces are most sensitive to are highlighted.
Changes in the fall dynamics (torso angle and impact velocity) had the greatest effect on the
predicted peak compressive force on the spine.
Category
Mass
Input Parameter
Variable
Thorax,head,andarms:r:
1-dimensional
simple model
:
2-dimensional
simple model
s
2-dimensional
segmented model
1-dimensional
segmented model
9:
Abdomen
0.1
0.0
0.2
0.1
Pelvis and upper legs
-0.5
1.1
-0.2
0.3
0.5
1.9
Spine segments
Axial
Pelvic soft tissue
2.2
1.7
2.0
1.8
Stiffness
Abdomen
-0.1
-0.1
-0.2
0.3
Lumbarspine
Transverse
Stiffness
..
Pelvic soft tissue
0.3
:
:i.iri
0.5
Abdomen
0.0
0.1
Lumbar spine
0.0
-1.1
Rotational
Pelvic soft tissue
0.0
0.0
Stiffness
Lumbar spine
0.0
0.0
Axial
Pelvic soft tissue
1.9
1.6
1.6
2.4
Abdomen
-0.5
-0.8
-1.0
-2.3
Lumbar spine
-1.4
-1.4
-0.6
-0.7
Damping
Rotational
Pelvic soft tissue
-0.1
0.0
Damping
Lumbar spine
0.3
0.0
Geometry
abdomen eccentricity
-0.4
-0.5
spine eccentricity
0.0
0.0
pelvis to LS
thorax to L1
-0.1
-0.1
0.1
0.4
lumbar spine length
-0.2
0.2
Thoracic
0.1
0.0
Pelvis
0.0
0.0
Intertia
vertebrae
Fall
0.0
impact velocity
theta
-0.3
theta dot
0.11
I
49
With the two-dimensional segmented spine model, small differences were seen in the
forces in the lower and upper lumbar vertebrae. For an average woman with a velocity of 2.18
m/s and an angle of 48 degrees, the T12/L1 compressive force peaked at 1215 N and the L5/S1
force peaked at 1482 N. The spinal curvature imposed on this model had the effect of making
the L4AL5intervertebral peak compressive force (1669 N) slightly higher than that at the other
levels. L1L2, L2/L3, and L3/L4 intervertebral peak forces were 1172, 1293, and 1401 N,
respectively.
Pelvis rotational stiffness and damping are a function of the muscular resistance to the
pelvis rotating backward. A completely relaxed fall would have a low pelvis rotational stiffness
and damping. Increased pelvis stiffness from 0 to 500 N/m increased spine loads less than 10%.
2.5 Discussion
This paper describes efforts to model the human body using lumped parameter
techniques, in order to predict the forces on the spine during the impact phase of a backward fall.
Four models were created adding a segemented spine and two-dimensional movement to the
simplest one-dimensional model. These models predicted forces of between 880 N and 2630 N
depending on the body configuration at impact, the velocity at impact, and the height and weight
of the body. This can be compared to experimental studies that have found the fracture forces for
thoracolumbar and lumbar vertebrae to vary from as low as 500 N (Moro et al., 1995) to 8000 N
(Biggemannn et al., 1995). One study from elderly cadaveric vertebrae had an average axial
failure force of approximately 2000 N, below that predicted by these models for an upright fall
(Moro et al., 1995).
50
The predictions of peak axial spine force in these models are sensitive to the dynamics of
the fall. It could therefore be possible to reduce the axial force below the fracture force by
decreasing the speed of impact or by increasing the torso angle. The models were less sensitive
to other input properties so that errors in these properties would not likely influence the
conclusions substantially.
One of the limitations of this study is that muscle forces are not included in the model.
This model describes the force on the spine during a limp fall as might occur if a person fainted.
However, activity in the torso musculature could change the force at least in three ways. First,
Bisdorff et al. (1995) has shown that the reflexes associated with the falling sensation cause the
abdominal muscles to contract. Such a contraction would rotate the torso forward causing it to
impact in a more upright configuration, increasing the fracture force. Second, models and
experimental studies of lifting have shown that contraction of the abdominal wall muscles and
the paraspinal muscles can cause high compressive loads on the spine. The force generated in
the torso musculature causes equal and opposite compressive forces on the spine. These forces
would be in addition to the force on the spine due to the impact. For instance, if the abdominal
wall muscles contracted with a force of 500 N, the force on the spine could peak at as high as
1500 N instead of 1000 N without contraction. Third, contraction of the abdominal musculature
would cause an increase in the abdominal stiffness component of the model. This increase would
cause a slight decrease in the maximum force on the spine. Overall, it is likely that muscle
activity, particularly trying to catch oneself using the abdominal wall muscles, would
substantially increase the force on the spine. Future work should look at the activity of the torso
musculature during a backward fall to examine the increase in force on the spine that might be
51
generated. However, it can be said that these passive impact models represent a low estimate and
that active torso musculature would probably increase the fracture risk.
Other areas which might be improved by further consideration include the decoupling of
the upper body mass to examine the effect of head and arm motion and the variability of pelvis
soft tissue properties as a function of torso angle and body habitus. Motion of the head and neck
could cause a decrease in the predicted force. Also the irregular shape of the bony pelvis and
sacrum could cause some torso angles to have different pelvis soft tissue thicknesses and
therefore different stiffness properties than other angles. A change in the pelvis soft tissue from
mostly muscular in a healthy athletic person to mostly fatty in a sedentary person or a change in
thickness of the fatty layer may cause changes in the properties as well.
In conclusion, this effort was a first step towards estimating the forces on the spine during
a backward fall. The dynamics of the fall were found to have a substantial influence on the axial
force on the spine. Falls that are more upright and faster would have higher spine forces. This
study did not consider muscle activity that might play a significant role in increasing spine forces
and should be investigated further. However, these passive impact models indicate that spine
forces in a fall can exceed the failure loads of the spine even before muscle forces are added and
therefore fall prevention should be considered in preventative measures to avoid vertebral
fracture.
2.6 References
1. Belytschko, T., Schwer, L., Privitzer, E., "Theory and Application of a Three-Dimensional
Model of the Human Spine", Aviation, Space and Environmental Medicine, 49(1), pp. 158-165,
52
1978.
2. Bernhardt, M., Bridwell, K.H., "Segmental Analysis of the Sagital Plane Alignment of the
Normal Thoracic and Lumbar Spine and Thoracolumbar Junction", Spine, 14(7), pp. 717-721,
1989.
3. Biggemann, M., Brinkmann, P., "Biomechanics of Osteoporotic Vertebral Fractures", In:
Genant, H.K., Jergas, M., van Kuijk, C, eds., Vertebral Fracture in Osteoporosis. San Francisco:
Osteoporosis Research Group, University of California, pp. 21-34, 1995.
4. Bisdorff, A.R., Bronstein, A.M., Gresty, M.A., Wolsley, C.J., Davies, A., and Young,A.,
"EMG-responses to Sudden Onset Free Fall", Acta Otolaryngol, Suppl 520, pp. 347-349, 1995.
5. Broman, H., Pope, M., Hansson, T., "A Mathematical Model of the Impact Response of the
Seated Subject", Med Eng Phys, 18(5), pp. 410-419, 1996.
6. Cooper, C. Atkinson, E.J., Jacobsen, S.J., O'Fallon, W.M., and Melton, L.J., "PopulationBased Study of Survival after Osteoporotic Fractures", Amer. J. Epidem., 137(9), pp. 10011005,
1993.
7. Cooper, C., Atkinson, E.J., O'Fallon, W.M., Melton, L.J., "Incidence of Clinically Diagnosed
Vertebral Fractures: A Population-Based Study in Rochester, Minnesota, 1985-1989", 7(2), pp.
221-227, 1992.
8. Contini, R., "Body Segment Parameters, Part II", Artificial Limbs, 16(1), pp. 1-19, 1972.
9. Fairley, T.E., Griffin, M.J., "The Apparent Mass of the Seated Human Body: Vertical
Vibration", 22(2), pp. 81-94, 1989.
10. Greenspan, S.L., Maitland-Ramsey, L., and Myers, E.R., "Classification of osteoporosis in
the elderly is dependent on site-specific analysis", Calcif Tissue Int, 58, pp. 409-414, 1996.
53
11. Griffin, M.J., Whitman, E.M., Parson, K.C., "Vibration and Comfort. I. Translational Seat
Vibration", Ergonomics, 25(7), pp. 603-630, 1982.
12. Kasra, M., Shrazi, A., and Drouin, G., "Dynamics of Human Lumbar Intervertebral Joints,
Experimental and Finite-Element Investigations", Spine, 17(1), pp. 93-102, 1992.
13. Keller, T.S., Spengler, D.M., and Hansson, T.H., "Mechanical Behavior of the Human
Lumbar Spine, I. Creep Analysis During Static Compressive Loading", J. Orthop Res, 5, pp.
467-478, 1987.
14. Kitazaki, S., Griffin, M.J., "Resonance Behaviour of the Seated Human Body and Effects of
Posture", J Biomechanics, 21, pp. 143-149, 1998.
15. Kroonenberg, A.vd., Wilson, S.E., Myers, E.R., Hayes, W.C., and McMahon, T.A., "Impact
Velocities and Body Configurations for Backward Falls from Standing Height", private
communication.
16. Lui, Y.K. and Wickstron, "Estimation of the Intertial Property Distribution of the Human
Torso from Segemented Cadaveric Data", Perspectives in Biomedical Engineering, University
Park Press, London, 1972.
17. Lui, Y.K., Laborde, J.M., and Van Buskirk, W.C.v., "Inertial Properties of a Segmented
Cadaveric Trunk: Their Implications in Acceleration Injuries", Aerospace Medicine, 42(6), pp.
650-657, 1971.
18. Melton, L.J., Kan, S.H., Frye, M.A., Wahner, H.W., O'Fallon, W.M., and Riggs, B.L.,
"Epidemiology of Vertebral Fractures in Women", Amer. J. Epidem., 129 (5), pp. 1000-1011,
1989.
19. Miller, J.A.A., Schultz, A.B., Warwick, D.N., and Spencer, D.L., "Mechanical Properties of
54
Lumbar Spine Motion Segment Under Large Loads", J Biomechanics, 19(1), pp. 79-84, 1986.
20. Moro M, Hecker A, Bouxsein M, Myers E., "Failure load of thoracic vertebrae correlates
with lumbar bone mineral density measured by DXA", Calcif Tissue Int., 56, pp. 206-209, 1995.
21. Myers, E.R., Wilson, S.E., "Biomechanics of Osteoporosis and Vertebral Fracture", Spine,
22(24S), pp. 25S-31S, 1997.
22. Myers, E.R. private communication, 1998.
23. National Aeronouatics and Space Administration, Staff of Anthropology Research Project,
"Anthropometric Source Book, Volume I: Anthropmetry for Designers", NASA REference
Pulbication 1024, 1978.
24. Ome, D., and Liu, Y.K., "A Mathematical Model of Spinal Response to Impact", J Biomech,
4, pp. 49-71, 1971.
25. Panjabi, M.M, Andersson, G.B.J., Jorneus, L., Hult, E., Mattsson, L., "In Vivo
Measurements of Spinal Column Vibrations", J Bone Joint Surg, 68-A(5), pp. 695-702, 1986.
26. Patil, M.K., Palanichamy, M.S., "A Mathematical Model of Tractor-Occupant System with a
New Seat Suspension for Minimization of Vibration Response", Appl Math Modeling, 12, pp.
63-71, 1988.
27. Prasad, P., King, A.I., "An Experimentally Validated Dynamic Model of the Spine", J
Applied Mechanics, pp. 546-550, September 1974.
28. Ray, N.F., Chan, J.K., Thamer, M. and Melton, L.J., "Medical Expenditures for the
Treatment of Osteoporotic Fractures in the United States in 1995: Report from the National
Osteoporosis Foundation", J. Bone Min. Res., 12(1), pp. 24-35, 1997.
29. Robiovitch, S.N., Hayes, W.C., and McMahon, T.A, "Distribution of Contact Force during
55
Impact to the Hip", Annals Biomed Eng, 25, pp. 499-508, 1997.
30. Wan, Y., Schimmels, J.M., "Optimal Seat Suspension Design Based on Minimum
'Simulated Subjective Response"', J Biomech Eng, 119, pp. 409-416, 1997.
31. Winter, D.A., Biomechanics of Human Movement, Wiley, New York, 1979.
56
Appendix 2.A: Equations of motion for the four models
The dynamics of the four models were analyzed using MATLAB software (MathWorks,
Natick, MA). Equations of motion for the four models were created. A variable-order
differential equation solver from the MATLAB software package was used to solve the equations
of motion given the initial configuration and velocity.
For the simplest model, in which the spine was modeled as one unit and the masses were
allowed to move in one-dimension, the equations solved by the ordinary differential equation
slover were:
,
y
0
y
0
=A y +
-where:
where.
0
o
0
1
0
0
O
0
0
0
1
0
0
0
0
0
0
1
1/ mp (- Kp - KaI - Kpine) 1/ mp Kal
1/ ma Kal
1/ mub Kspine
1/ ma (- Ka - Ka)
1/ mub Ka2
1/ mp Kpine 1/mp (- Cp - Cal - Cspi)
1/ ma Ka2
1/mub (- K2 - Kpine)
1/ ma Ca
1/mp Cal
1/ m (- Cal C2)
1/mp Cs
1/ma Ca2
1/ mub Cspine 1/ mub Ca2 1/ mub ( Ca2 - Cspine)
The mass of the three segements were mp,ma,mb,the stiffness constant of the tissues was K and
the damping constant was C. The subscript p denotes the pelvis mass or soft tissue properties,
57
the subscript a, al and a2 denote the abdominal mass properties, the subscript ub denotes the
upper body mass and the subscript spine denotes the spine properties. The one-dimensional
model with a segmented spine included five additional equations of motion, one for each spine
segment. This increased the number of state-space equations and variables to 10.
The two-dimensional equations of motion were created by first estimating the
displacement of each object relative to the other objects (Figure 2.7). Forces between the objects
were then calculated as:
Fa = Ka(da- lo)+ Ca(d/dt)
Ft = K(dt)+ Ct(dt/dt)
M = Kr()+ Cr(dO/dt)
where F. is the axial force, F, is the transverse force and M is the moment. These forces were
applied to the objects in the direction of the displacement. The equations of motion were found
using the formula:
mi d 2 x i /dt 2 = ]Fasin(0vg) + FFtcos(Ovg)
mi d2Yi /dt
2
=
Ii d 20i /dt 2 =
FacOs(Oavg)
-Ft
sin(Oavg)
FaDFa+ FtDFt+ M
where DFAand DrF are the distance from the center of mass of the object to the force vector.
These equations were solved for d2x/dt2 , d2y/dt2 , and d2 0/dt2 to give the equations of state for the
ordinary differential equation solver.
58
\
i+l
I
I
I
iZ
aavg
0i
Figure 2.7
Average angle (vg) between two objects was used to find the direction of axial (do)and
transverse (dr) displacement. The difference in angles if the two objects was the angular
displacement.
59
Chapter 3 - Active Muscle Impact Mechanics Modeling
3.1 Abstract
In Chapter 2, peak compressive forces on the spine were predicted by lumped parameter
models to be approximately 2500 N in an upright fall of 2.18 m/s. In that chapter it was
speculated that muscular activity might increase this force by applying a pre-compression to the
spine. The objective in this chapter was to examine the effect applying initial muscle tensions
and spine compressions would have on the predicted peak compressive force. In this modeling
effort, the 1 and 2-dimensional models of impact with single unit spines were used to create a
muscular version of the models. Springs were added to represent the abdominal and extensor
musculature. These springs were placed under an initial tension and the stiffness was determined
using relations from literature. The peak compressive force was found to change little with small
initial muscle tensions but increased dramatically at large initial muscle tensions. These findings
would indicate that a relaxed or only slightly tense fall would put one at less risk of fracture than
in fall in which the muscles are tense.
3.2 Introduction
In Chapter 2, models of a passive backward fall impact were created. These models
calculate the forces that might occur during a faint or limp fall. However, it was noted in that
chapter that if the musculature were active, it would be possible to increase the force on the
spine. Bisdorff et al. (1995) found that one of the fall reflexes is rectus abdominus activity. Tang
et al. (1998) reported both rectus abdominus and erector spinae muscle activity in response to an
61
unexpected slip. Abdominal musculature can have the effect of compression the spine (McGill,
1985, Schultz, 1987, and Wilson, 1994) and can also provide extra stiffness (Bergmark, 1989,
Crisco, 1991, Cholewicki, 1997, Crisco, 1990, and Gardner-Morse, 1998). It is important,
therefore to understand what role contraction of the torso musculature might play in the impact
phase of a fall.
Dynamic models of the torso musculature have included models examining the issues of
spinal stability. Bergmark (1989) used a model in which a linear relationship was used between
active muscle tension and muscle stiffness. This relation was based on work by Morgan et al.
(1977) who examined the relation in anesthetized cat, soleus muscles. This work found stiffness
was a function of the muscle tension:
K=q F/
Where q was a constant and 1 was the length of the muscle. The value q has been estimated by
several researchers to be between 0.5 and 42 (Crisco, 1991, Bergmark, 1989). The relationship
was used again by Cholewicki (1997), Crisco (1990) and Gardner-Morse (1998). Cholewicki
used a q/l of 150 (1997). Crisco, however, remarked that the relation was not well characterized
for the torso musculature (1991).
In this work, the models developed in Chapter 2 are adapted to include muscle tension
and stiffness. Several relations of muscle stiffness and tension are examined to understand the
effect of this relation on the final maximum compressive spine force estimates.
62
3.3 Methods
Models
The single spine element, one and two-dimensional models of the impact phase of a
backwards fall were used as the base model for this analysis (Figure 3.1). The models contain
masses representing the upper body, pelvis and abdominal mass and parallel spring-dashpot pairs
representing the spine, pelvis soft tissue and abdominal contents. To these models two muscle
tension springs was added (Figure 1). These springs, which represent the abdominal wall
musculature and erector spinae musculature, were place 11.24 cm anterior and 5.32 cm posterior
to the spine elements. These distances are the mean anterior-posterior distance for the erector
spinae and rectus abdominus muscle groups found in Chapter 6 for women over 60.
Validation
The 1-dimensional model was validated by comparing transmissibility of sinusoidal seat
vibrations against the seat to head transmissibility reported by Griffin (1982) in order to show
that the models still exhibited the same resonance behavior. In the paper by Griffin, which was
also used in Chapter 2 to validate the passive impact models, volunteers were seated on vibrating
platforms, while accelerometers were attached a bite bar (Griffin, 1982) to measure transmission
of the vibratory acceleration. The model was setup to replicate these experimental conditions.
Axial ground vibrations of varying frequencies were applied to the model. The output of the
upper body mass motion was compared to the data reported by Griffin (1982). Stiffnesses were
varied from 10 to 500 kN/m while initial muscle tension was held constant at 500 N for both
groups. Initial muscle tension was then varied independently from 1 to 1500 N for both muscle
63
groups at a constant stiffness of 100 KN/m.
Stiffness Relation Sensitivity
Runs of the one-dimensional model were made keeping the stiffness constant while the
initial muscle tension was varied equally in both muscle groups. These runs were then
performed using linear stiffness-tension relations with several different proportionality constants.
An impact velocity of 2.18 m/s was used. These runs were designed to answer basic questions
about the effect of muscle stiffness and initial muscle tension on the peak impact force.
Unequal Muscle Tension
Using the stiffness-tension relation, K = 150F, for both muscle groups the abdominal and
then the erector spinae muscle group tensions were varied independently in order to see the effect
of each muscle group. The function K = 150F is the same as that used by Cholewicki in
modeling spine stability (1997) and is based on a q of 30 and a length of 20 cm. First a run was
made with all the initial muscle tensions at zero. Then 5 runs were made with a total muscle
tension of 1000 N. These varied from 1000 N tension in the abdominal muscle group and none
in the extensor muscle group to 1000 N tension in the extensor muscle group and none in the
abdominal muscle group.
3.4 Results
Validation
As in the passive model, the active muscle model was shown to have a resonance
64
Figure 3.1 Muscle Models.
Muscle Models were created by adding two "muscle tension" springs
to the 1 and 2 dimensional, single spine element models described in Chapter 2. These springs
were considered to have a constant stiffness in tension and no stiffness in compression. (a) is the
original 1-dimensional model and (b) is the model with added muscle tension springs.
F1
(a)
(b)
65
frequency of approximately 5 Hz. Increasing muscle stiffness caused to peak attenuation to
decrease for seat to head transmission (Figure 3.2). Muscle tension also created a secondary
attenuation peak at 10-25 Hz similar to that seen in the experiment by Griffin (1982) (Figure
3.2). Changing the initial muscle tension by itself did not change the transmissibility
significantly except at a muscle tension of 0 N, where the muscle springs are no longer always in
tension and stiffness is not present in compression (Figure 3.3).
Stiffness Relation Sensitivity
The spine compressive force was set to be equal to the total muscle tension at the onset of
the run. It was seen to rise to a peak compression and then settle to the total muscle tension as
expected (Figure 4). The peak compressive force remained approximately the same for low
initial muscle tension and then increase linearly with muscle tension at high muscle tension
(Figures 3.5 and 3.6). When stiffness was held constant relative to muscle tension, the size of the
"toe-region", in which the peak compressive force did not change significantly, was found to
extend to higher muscle tensions with lower stiffnesses (Figure 3.5). When stiffness was allowed
to vary linearly with initial muscle tension, the "toe-region" was found to be smaller with higher
proportionality constant.
UnequalMuscle Tension
Using the 2-dimensional model and a stiffness-tension proportionality constant of 150,
the effect of abdominal versus extensor muscle activity was examined. The motion patterns for
different combinations of initial muscle tension were similar for upright falls (Figure 3.7).
66
Figure 3.2 - Seat to head transmissibility with increasing muscle stiffness.
The amplitude of the head acceleration relative to the amplitude of the seat acceleration (the
transmissibility) was measured by Griffin et al. (1982) and the mean female and male values are
indicated here by *. The 1-D model was run with an initial tension of 500 N in both muscle
groups and a sinusoidal input vibration of the seat. Stiffness was set at 10 kN/m (solid line), 50
kN/m (dotted line), 100 kN/m (dashed line) and 500 kN/m (dot-dash line). Increasing muscle
stiffness caused to peak transmisibility to decrease and become closer to that seen
experimentally. Muscle tension also created a secondary attenuation peak at 10-25 Hz similar to
that seen in the experiment.
1.8
1 r
1.4
co
n 1.2
Ca
0 0.8
"r
· 0.6
(D
) 0.4
0.2
n
100
101
Frequency (Hz)
67
102
Figure 3.3 - Seat to head transmissibility with increasing initial muscle tension. The amplitude of
the head acceleration relative to the amplitude of the seat acceleration (the transmissibility) was
measured by Griffin et al. (1982) and the mean female and male values are indicated here by *.
The 1-D model was run with muscle stiffness of 100 kN/m in both muscle groups and a
sinusoidal input vibration of the seat. Initial Muscle Tension in both groups was set at 0 N (solid
line), 500 N (dotted line), 1000 N (dashed line) and 1500 N (dot-dash line). Other than the 0 N
case, in which the muscle is not always in tension and the stiffness is 0 kN/m when in
compression, the transmissibility is similar for all of the muscle tensions.
1
.4
i1
-
._
E
Cl
I
.o
CD
CD U
0
10 0
101
Frequency (Hz)
68
102
Figure 3.4
Axial spine force over time for the 1-dimensional model with a muscle stiffness proportional to
the initial tension of K = 150F. Initial tension was varied from 0 to 1500 N and the model was
allowed to impact with a velocity of 2.18 m/s. The peak compressive force within 0.05 s and
increased with increasing muscle tension.
.
AA~
1 UUU
0
_..,
0I0
a)
._
&-2000
-3000
_Aftnn
0
0.1
0.2
Time (s)
69
0.3
0.4
Figure 3.5
Peak compressive spine force as a function of initial tension for several constant stiffnesses for
the one-dimensional model with equal initial tensions in the extensor and abdominal muscle
groups. Muscle stiffness was varied from 10 to 100 kN/m. Even when stiffness is held constant,
a toe-region is seen in which the peak compressive force on the spine does not increase with
increasing initial tension. This toe-region occurs at higher initial tension when the stiffness is
higher.
000
AL6OOO
K = 100 kN/m
K = 50 kN/m
K = 25 kN/m
u5000
--.
E
04000
K = 10 kN/m
I
E
r·
.e
r
.·
··
.·
'
;r
r
.
'.·
8 3000
.
·
C
0e
.. ·
··
II
I·I'
''
I IIII
c
·C
Onnn
0
500
1000
Initial Tension (Each Muscle Group) (N)
70
1500
Figure 3.6
Peak compressive spine force as a function of initial tension for several stiffnesses-tension
relations for the one-dimensional model with equal initial muscle tensions in the abdominal and
extensor muscles. Muscle stiffness was set as proportional to the initial muscle tension with a
proportionality constant of between 50 to 250. A toe-region in seen in which the predicted
maximum compressive force on the spine does not increase with increasing initial muscle
tension. This region is larger for stiffness relations in which the stiffness is higher.
Z
OD
0
_,
E
E
.m
Il
fl
0
500
1000
Initial Tension (Each Muscle Group) (N)
71
1500
Figure 7a - Motion of the 3 center of mass in the 2-dimensional model at 0 and 45 ° . The 2dimensional model was run with the stiffness equal to 150 times the inital muscle tension. In (a)
and (b) the initial muscle tensions are both zero. In (c) and (d) the initial abdominal muscle
tension is 1000 N. In (d) and (e) the initial abdominal and the initial extensor muscle tensions
are both 500 N. In (f) and (g) the initial extensor muscle tension is 1000 N. The motion patterns
were similar for upright falls. The upper body descended more slowly with active muscle
tension in angled torso falls. This slow in descent was greater for falls involving the extensor
muscles as they remained in tension as the upper body rotated.
(b) 45 - no muscle tension
(a) 0 - no muscle tension
0.2
0.15
u-
IpbodwC
Iln
I
0.1
.
a
fb d
simV
-0.1
,0 pi
.- 0.1 at mm
.
.
0
2
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-0.15
-01
-0.05
0.
0
0
0
.
-0.15
-0.1
-005
0
.0 5
(d) 45 ° - 1000 N initial abdominal muscle tension
(c) 0 - 1000 N initial abdominal muscle tension
0.2
0.2
0.15. WWboc aueiad
.1
O p
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-0.2
oTed
-0.15
0.1
fma
,
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,
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0
-0 .5
G-ASi
-'-0.2
0.05
72
01
i
-0.15
-0.1
,
-0.1
0.056
0
0.05
Figure 7b - Motion of the 3 center of mass in the 2-dimensional model at 0 and 45 ° . The 2dimensional model was run with the stiffness equal to 150 times the inital muscle tension. In (a)
and (b) the initial muscle tensions are both zero. In (c) and (d) the initial abdominal muscle
tension is 1000 N. In (e) and (f) the initial abdominal and the initial extensor muscle tensions are
both 500 N. In (g) and (h) the initial extensor muscle tension is 1000 N.
(e) 0° - 500 N initial muscle tensions
(f) 45 - 500 N initial muscle tensions
0.2
0.15 .p
0.1
botOw
d mm
i
m
0.1
0.05
I
bdome oener efm.
-
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radimaze
II
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t
M WMt
nte' kO
mm
-0.05
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-0.15
-0.1
.0s
0
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(g) 0 - 1000 N initial extensor muscle tension
2'
bodw EMr d an
t
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a
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amn
pa
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-
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r
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.
(h) 45 - 1000 N initial extensor muscle tension
0.2
0.05
-15
i
o
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. odmt
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-0.15
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-0.1
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Met
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73
-15
-0.1
-5
0
0.05
However, for angled falls (45°), the upper body descended more slowly with active muscle
tension. This slow in descent is greater for falls involving the extensor muscles. The
compressive force on the spine during a 45 ° fall is higher for falls in which the extensor muscles
are under a specific tension relative to falls in which the abdominal muscles are under the same
tension (Figure 3.8). This is due to the rotation of the upper body compressing the abdominal
spring and stretching the extensor springs. As the abdominal springs are compressed they lose
their tension and no longer contribute to the motion or to compressive forces on the spine.
3.5 Discussion
These models show that with muscular activity it is possible to raise the peak
compressive force on the spine during an upright fall at 2.18 m/s from 2500 N to as much as
3500 to 4000 N. This is well above the approximately 2000N mean axial force found to fracture
elderly thoracolumbar cadaveric vertebrae in experimental studies (Moro et al., 1995). This
would mean that although those elderly individuals with above average fracture forces would not
be at risk in a purely passive fall, they could be at risk if their torso muscles were tense.
These models also showed that small amounts of initial muscle tension have very little
effect on the predicted peak compressive force. This pattern depends on the function used to
assign the muscle stiffness as a function of initial muscle tension. The functions that made the
muscles stiffer caused a larger "toe-region" in which the predicted maximum compressive spine
force did not increase with increasing initial muscle tension.
These results have shown the need for better assessment of the relation between force and
stiffness for human torso musculature. Although a linear relation was found for isolated animal
74
Figure 3.8 - Compressive force for the 2-dimensional model at 45 ° . Tracing lines represent
different initial muscle tensions. The lowest tracing on the page is 1000 N of initial tension in
the extensor muscles. The highest tracing on the page is 1000 N of initial tension in the
abdominal muscles. Intermediate tracings are for 750N abdominal/250N extensor, 500N
abdominal/500N extensor, and 250N abdominal/750N extensor initial tensions (from top to
bottom). Higher activity in the extensor muscles has a greater predicited maximum compressive
force due to the forward rotation of the upper body during a fall stretching the muscle spring.
rAA
OUU
0
-500
Z -1000
0
'i -1500
a.
Cn
' -2000
0E
-2500
-3000
-3500
-4000
0
0.02
0.04
0.06
0.08
0.1
time (s)
75
0.12
0.14
0.16
0.18
0.2
muscles (Morgan, 1977), this may be changed by the presence of tendinous connections
(Cholewicki, 1995) and has not been demonstrated in the human torso musculature. The
proportionality constant of a linear relationship between torso muscle force and stiffness has also
never been measured. A potential experiment would be to measure stiffness of the torso of
human subjects in conjunction with EMG-based assessments of the force in the musculature.
Stiffness could be measure by applying small perterbations such as adding a load to the amount a
subject is carrying and measuring the resulting vibratory motion. Such an experiment would
help to elucidate the relation between stiffness and force for the torso musculature.
There is still work to be done to understand the influence active torso musculature on the
compressive forces on the spine. However, we now know that a passive fall could impact with
as much as 2500 N and that although small muscle forces do not increase the impact force, large
muscle forces can increase the compressive spine force significantly. A potential fall strategy
resulting from this work and that of chapters 2 and 6 would be to use muscle forces to reduce fall
velocity and torso angle being careful to keep torso musculature activity low at impact.
3.6 References
1. Bergmark, A., "Stability of the Lumbar Spine: A Study in Mechanical Engineering", Acta
Orthop. Scand., 230(60), pp. 1-54, 1989.
2. Bisdorff, A.R., Bronstein, A.M., Gresty, M.A., Wolsley, C.J., Davies, A., and Young, A.,
"EMG-Responses to Sudden Onset Free Fall", Acta Otolaryngol Suppl, 20(2), pp. 347-349,
1995.
3. Cholewicki, J., Panjabi, M.M., and Khachatryan, A., "Stabilizing Function of Trunk Flexor-
76
Extensor Muscles Around a Neutral Posture", Spine, 22(19), pp. 2207-2212, 1997.
4. Cholewicki, J., Juluru, K., and McGill, S.M., "Intra-abdominal Pressure Mechanism for
Stabilizing the Lumbar Spine", J. Biomech., 32, pp. 13-17, 1999.
5. Cholewicki, J., McGill, S.M., "Relationship Between Muscle Force and Stiffness in the
Whole Mammalian Muscle: A Simulation Study", J. Biomech. Eng., 117, pp. 339-342, 1995.
6. Crisco, J.J., and Panjabi, M.M., 'The Intersegmental and Multisegmental Muscles of the
Lumbar Spine", Spine, 16(7), pp. 793-799, 1991.
5. Fairley, T.E., Griffin, M.J., "The Apparent Mass of the Seated Human Body: Vertical
Vibration", 22(2), pp. 81-94, 1989.
6. Griffin, M.J., Whitman, E.M., Parson, K.C., "Vibration and Comfort. I. Translational Seat
Vibration", Ergonomics, 25(7), pp. 603-630, 1982.
7. Gardner-Morse, M.G., and Stokes, I.A.F., "The Effects of Abdominal Muscle Coactivation on
Lumbar Spine Stability", Spine, 23(1), pp. 86-92, 1998.
8. McGill, S.M. and Norman, R.W., "Dynamically and Statically Determined Low Back
Moments During Lifting," J. Biomech., 18(12), pp. 877-885, 1985.
9. Morgan, D.L., "Separation of Active and Passive Components of Short-Range Stiffness of
Muscle", Am. J. Physiol., 232(1), pp. C45-C49, 1977.
10. Moro M, Hecker A, Bouxsein M, Myers E., "Failure load of thoracic vertebrae correlates
with lumbar bone mineral density measured by DXA", Calcif Tissue Int., 56, pp. 206-209, 1995.
11. Panjabi, M.M., Krag, M., Summers, D., and Videman, T., "Biomechanical Time-Tolerance
of Fresh Cadaveric Human Spine Specimens", J. Orthop. Res., 3, pp. 292-300, 1985.
12. Panjabi, M.M, Andersson, G.B.J., Jorneus, L., Hult, E., Mattsson, L., "In Vivo
77
Measurements of Spinal Column Vibrations", J Bone Joint Surg, 68-A(5), pp. 695-702, 1986.
13. Schultz, A., Cromwell, R., Warwick, D., and Andersson, G., "Lumbar Trunk Muscle Use in
Standing Isometric Heavy Exertions", J. Orthop. Res., 53, pp. 320-329, 1987.
14. Tang, P.F., and Woolacott, M.H., "Inefficient Postural Responses to Unexpected Slips
During Walking in Older Adults", J. Gerontology: Medical Sciences, 53A(6), pp. M471-M480,
1998.
15. Wilson, S.E., "Development of a Model to Predict the Compressive Forces on the Spine
Associated with Age-Related Vertebral Fractures", Master's thesis, Mechanical Engineering,
Massachusetts Institute of Technology, 1994.
78
Chapter 4 - Mechanical Properties of the Spine
4.1 Abstract
In chapter 2, changes in the stiffness or damping characteristics of the spine of 10% were
shown to change the predicted maximum compressive force by approximately 2%. While
several studies have looked at stiffness during slow speed creep, relatively few have examined
high rate stiffness and fewer still have also assessed damping characteristics. These
characteristics were also not reflected much in the whole body response to vibration used to
validate the model in chapter 2. It was, therefore, important to assess the characteristics
experimentally in order to assure accuracy of the impact models.
In this experiment the stiffness and damping were measured by using a pendulum
apparatus to impact L1 to L3 spine segments. The frequency and decay of the resulting
oscillations were fit to a parallel spring and dashpot model to obtain stiffness and damping
constants. Preload was applied to the spine segments using rubber bands stretched around the
specimen and load cell. Magnetic resonance images of the spine segments were also taken in
order to obtain an assessment of disk quality. Correlation between such a non-invasive
measurement and the stiffness and damping characteristics might be used to examine the effect
of degeneration on the impact dynamics.
Stiffness, but not damping, was related significantly to preload. MRI based
measurements that reflect T2 relaxation time were found to weakly correlate with stiffness at low
preloads.
79
4.2 Introduction
In Chapter 2, it was shown that an accurate assessment of axial spine properties was
important in the prediction of compressive force. Changes in the stiffness or damping
characteristics of the spine of 10% were shown to change the predicted maximum compressive
force by approximately 2%. It was therefore necessary to carefully assess the stiffness and
damping constants of the spine in order to assure that these predictions are accurate. It would
also be useful to understand how degeneration of the spine might affect these constants.
Previous estimates of spine stiffness and damping constants have often focused on the
long-term creep behavior of the functional spinal unit (FSU) or two vertebrae and a central
intervertebral disk (Keller, 1987, Bums, 1984). These experiments have shown that the FSU
exhibits a visco-elastic behavior with time constants on the order of hours. Keller et al. also
showed that the stiffness of these FSUs varied with a degenerative rating.
In this experiment, interest was focused on the high speed behavior of a spine segment
such as during a fall. Two other papers have looked at higher speed behavior. Kasra et al.
(1992) examined the stiffness of functional spinal units under cyclic loading (0.5-50 Hz) with
varying preload. Rostedt et al. (1998) examined changes in impact stiffness with over time.
Both of these experiments used a single functional spinal unit, in which movement of the
vertebrae was constrained. Kasra sampled 7 specimens including 6 L2-L3 specimens and 1 T12L1 specimen. They found peak transmission frequencies of between 23.5 and 33 Hz and
damping ratios of 0.05 and 0.13 for a mass of 40 kg. This corresponds to a single FSU stiffness
of 872 to 1720 kN/m and damping constant of 590 to 2156 Ns/m. Rosedt sampled 6 lumbar
specimens of several levels and found stiffnesses of between 1400 and 2800 kN/m with stiffness
80
increasing with preload. Rosedt did not examine the damping characteristics. These stiffnesses
were generally much higher than the instantaneous stiffness found in creep studies. This would
indicate that rate is an important contributor to stiffness measurements.
Keller et al (1987) found that degenerated disks had a slightly increased instantaneous
stiffness in creep studies using radiograph examinations and a grading scale of 1 to 4. Magnetic
resonance imaging is often used clinically to assess degeneration. T2-weighted images, which
show a bright nucleus and darker annulus in healthy disks, are often used (Gundry, 1997).
Panagiotacopulos (1987) found that T2 relaxation time correlated with water content in the
intervertebral disk. Boos (1995) commented that T2 relaxation time reflects both water content
and the biochemical composition. Gunzberg (1992) compared the ratio of nucleus to annulus
ratio in T2-weighted images to torsional mobility of the intervertebral joint and found a trend of
increased mobility with decrease nucleus to annulus ratio.
A simple parallel spring and dashpot was used to model the spine functional spinal units
(FSUs) in the impact model. Previous works modeling the FSU have used this simple model,
linear solid models (with an additional series spring) and even finite element analysis (Burns,
1984, Kasra, 1992). The simple parallel spring-dashpot model is limited in its ability to describe
the long-term creep behavior. The other models were mathematically too complex to include in
the impact model. For the application of modeling vertebral fractures due to high rate impacts,
however, the long-term behavior is less important.
The simple parallel model exhibits second order behavior when exposed to an impulse or
impact. When the mass is sufficient the response is an underdamped, decaying oscillation. The
stiffness used in the impact models was linear but could potentially be non-linear reflecting a
81
more linear solid behavior. Like many soft tissues the non-linearity would be expected to
increase in stiffness with increased total force.
Factors that might affect the stiffness and damping characteristics include the
degenerative or hydration state of the disk, the cross-sectional size of the disk and the height of
the disk. These factors would affect the material properties or geometry of the disk. The effect
of disc degeneration on the stiffness of the spine under impact was important to assess as this
may play an important role in increasing or decreasing the risk of a vertebral fracture.
The experiment presented here examined the impact mechanics of two functional spinal
units in which the central vertebra was unconstrained. The spine segment was modeled as a
parallel spring and dashpot pair. The model exhibits second order characteristics and allows
examination of the damping characteristics. The relation between the stiffness and damping
constants and magnetic resonance based measures of disc degeneration were also examined in
order to find non-invasive measures that could be used to predict the dynamic properties.
4.3 Methods
Specimens: 5 male and 14 female, cadaveric, L1 to L3 spine segments from the Harvard
Anatomic Gifts program were dissected leaving the posterior structures and ligaments intact.
These specimens ranged from 62 to 85 years of age (mean age 75.5 ± 6.9 years). They
represented a consecutive sample from the Harvard Anatomic Gifts program. Specimens with a
history of metastatic cancer involving the spine were excluded. These specimens were wrapped
in saline soaked gauze in plastic bags and stored in a -20
°
freezer. Two male samples of the
original consecutively sampled population were not included because they were too large to fit in
82
the test rig and imaging tube. This was unusual as previous experiments have used the same
potting rings and imaging tubes and have not run into this problem.
Magnetic Resonanace Imaging: The specimens were removed from the freezer and allowed to
thaw in a refrigerator for approximately 12 hours. The specimens were placed in polyethelene
tubes filled with saline. These tubes were then put under vacuum and sealed. A GE 1.5 Tesla
magnetic resonance scanner (General Electric Medical Systems, Waukesha, Wisconsin) was used
to obtain sagittal T2-weighted (2000/80) images and three sets of axial images (2000/80,
2000/60, 2000/20). The first and last axial image represented T2 weighted and proton weight
images. Phatoms made of solutions of water and D2 0Owere placed under the tubes during
imaging.
The whole disk, annulus and nucleus of the mid-disk axial images were traced using
Application Visualization Systems software (Advanced Visualization Systems, Waltham,
Massachusetts). The area and the average intensity of these regions were recorded. The middisk sagittal images were used to measure the heights of the intervertebral disks. Anterior,
central and posterior heights were obtained. Relative intensities of the disk areas to phantom
intensity were obtained by fitting the phantom intensities to the percent 1-H
2O present.
The spine specimens were returned to the freezer between imaging and testing. This was
necessary because of the time constraints of both the imaging and testing.
Mechanical Testing: An impact test configuration was used to simulate impact loading on the
spine (Figure 4.1). A 6-degree of freedom load cell (AMTI MC5, Advanced Mechanical
83
Technology, Watertown, Massachusetts) on the anterior side of the specimen was used to obtain
the transmitted force. The pendulum impacted the end mass (20.9 kg) with an estimated kinetic
energy of 2.50 J. Data were sampled at a frequency of 3000 Hz.
In preparation for testing, the specimens were thawed and placed in a saline bath at room
temperature. A compressive load of 178 N was applied to the segments in the bath for
approximately one hour. This load represented the upper body mass of the lightest specimen and
was chosen to avoid the potential of fracturing the more osteoporotic spines. The specimens
were then removed from the bath, wrapped loosely in plastic to prevent dehydration, and placed
in the impact apparatus.
Seven-inch rubber bands were wrapped around the load cell and specimen to apply a
preload to the specimen. Sets of 0, 4, 8 and 12 rubber bands were used to create the preload.
The order of preloads was randomized. Three tests at each preload were performed.
Force data from the experiment were brought into the MATLAB software (Mathworks,
Natick, MA) for post-processing. A fast fourier transform was performed on the signal starting
at the point where the pendulum leaves the end mass to obtain the peak frequency. A finite
impulse response (FIR), low pass filter with a Hamming windowing and with a cutoff frequency
of twice the peak frequency was used to filter the signal. A linear regression of the logarithms of
several successive peaks was used to obtain the damping ratio. Using a parallel stiffness and
damping model and the end mass of 20.9 kg, stiffness (K) and damping (B) constants were
obtained.
The effect of preload was assessed using an analysis of variance between the 4 preload
groups for both stiffness and damping constants as independent variables. Within each preload
84
cimen
tnsducer
Figure 4.1. The pendulum apparatus consisted of a pendulum arm that struck and end mass (20.9
kg). The end mass attached to the posterior potted end of the spine segment. The anterior,
potted end was attached to a force transducer that was mounted to the wall.
85
group, the correlation between stiffness and damping values and data obtained from the MRI
analysis was calculated.
4.4 Results
Spine segments were found to exhibit second-order, underdamped oscillations when
attached to an end mass of 20.9 kg (Figure 4.2). Predicted stiffness and damping fits matched
closely with the original force signal. Stiffness values were found to range between 17.9 and
754.5 kN/m with a mean of 264.9 ± 194.0 kN/m. Damping values were found to range between
133.6 and 905.3 Ns/m with a mean of 373.3 ± 139.8 Ns/m.
Using an analysis of variance between the 4 preload groups (0, 4, 8, and 12 rubber
bands), significant differences in the stiffness (p < 0.001) but not the damping were found
(Figure 4.3 and 4.4). The rubber band groups corresponded to preloads of 0 N for 0 bands, 30.47
+ 7.84 N for 4 bands, 78.90 ± 10.93 N for 8 bands, and 111.69 ± 14.03 N for 12 bands. The
stiffnesses at these groups were 135.3 ± 127.6 kN/m, 210.6 ± 164.1 kN/m, 293.4 + 157.6 kN/m
and 420.4 ± 203.8 kN/m (Figure 3).
Within preload groups, correlations of stiffness and damping with MRI assessed data and
with age, height and gender (0=females, 1= males) were assessed (Table 1 and 2). Correlation of
T2 relaxation time based measures (T2 relaxation time and T2 image intensity) were negatively
correlated with stiffness. This correlation was only barely significant at low preloads but was not
significant at higher preloads. This result would indicate that lower T2 intense intervertebral
disks are stiffer. The T2 based measures were correlated with each other with correlation
coefficients (r) of between 0.55 and 0.95.
86
Preload of 0 N
Preload of 38 N
4nMAI
I UVU
.4 P
I UUU
800
800
z.
600
600
0D
400
400
O
L
200
200
0
_nn 0-vv
0
no s^^
-_nn
0.05
0.1
0.15
00ru
0.2
0.1
0.15
0.2
Preload o 112 N
Preload of 76 N
4
I UUU
~Itdq
IUUU
800
800
600
600
0 400
.o
400
z-.
0.05
200
O 200
0
-9_
-___
0
0.05
0.1
0.15
0
0.2
time (s)
0.05
0.1
time (s)
0.15
0.2
Figure 4.2. Force transmission after impact exhibits underdamped oscillations. Fit of the
oscillations with Kelvin model is shown as a dark, thick line. For this specimen, the frequency
increases with preload reflecting increases in stiffness.
87
800
* 0 bands
m 4 bands
700
A
8 bands
12 bands
x
600
J
x
.
500
A
*
A
x
X
A
A
.
A
x
x
E 300
gj
A
A
U
.
200
.
A
x
K
X
A
Eu
&
U
A
100
0
I
-_
.
!
I
I
0
20
40
I
1
60
I
l
80
100
120
I
I
140
Preload (N)
Figure 4.3
Stiffness increased with increasing preload. The bar graphs represent the means and standard
deviations of the four preload groups.
88
Table 5.1. Correlation coefficients (r) relating stiffness constants with MRI based measurements
and with age, height and gender. Gender was assigned as 0 for women and 1 for men. Values
marked with a * are significant. Intensities are relative to the heavy water phantoms % of H2 0.
Measured property
Mean ± S.D.
Preload (N)
0 rubber
bands
Correlation (r)
0.00
4 rubber bands
Correlation (r)
8 rubber bands
Correlation (r)
-0.11
-0.32
12 rubber
bands
Correlation (r)
0.19
Age
75.5 + 6.9
-0.40
-0.54*
-0.31
-0.11
Gender (0 - women)
---------
0.32
0.41
0.38
0.24
Height (cm)
163 ± 33
0.20
0.06
-0.01
0.12
Disk Area (cm2)
16.8 ± 3.2
-0.05
-0.09
0.01
0.04
Mean Disk Height (cm)
0.93 + 0.16
0.52*
0.46*
0.05
0.07
5.56
0.22
-0.47*
-0.39
-0.12
0.04
T2 intensity (nucleus)
5.81 + 0.27
-0.42
-0.34
-0.31
-0.13
T2 relaxation time (disk) (ms)
65.6 ± 16
-0.39
-0.38
-0.06
0.21
T2 relax. time (nucleus) (ms)
75.6 ± 24.8
-0.38
-0.37
-0.22
0.07
T2 nucleus/annulus intensity
1.33 ± 0.38
-0.20
-0.21
-0.42
-0.09
Proton-dens. intensity (disk)
6.82
-0.17
-0.05
0.09
0.04
T2 intensity (disk)
0.09
Table 4.2. Correlation of damping constants with MRI based measurements and with age, height
and gender. Gender was assigned as 0 for women and 1 for men.
Measured property
Preload (N)
0 rubber bands 4 rubber bands
Correlation (r)Correlation (r)
0.00
-0.20
8 rubber bands
Correlation (r)
-0.06
12 rubber bands
Correlation (r)
0.46
Age
-0.09
-0.04
0.40
0.37
Gender (0 - women)
0.13
0.02
-0.29
0.10
Height
-0.32
0.14
-0.29
-0.09
Disk Area
0.00
0.01
0.12
0.44
Mean Disk Height
-0.01
-0.11
-0.40
0.17
T2 intensity (disk)
0.17
-0.16
0.12
-0.19
T2 intensity (nucleus)
0.04
-0.29
-0.02
-0.25
T2 relaxation time (disk)
-0.05
-0.04
0.17
0.10
T2 relax. time (nucleus)
-0.10
-0.19
0.12
0.01
T2 nucleus/annulus intensity
-0.15
-0.31
-0.06
-0.11
Proton-dens. intensity (disk)
0.45
-0.09
-0.20
-0.60
89
Figure 4.4
T2 intensity of the whole disk correlates with stiffness at low preloads but not at high preloads.
In (a), the 0 and 4 bands preload groups can be seen to decrease with increased T2 intensity. In
(b), the 8 and 12 bands preload groups can men seen to have little correlation with T2 intensity.
T2 intensity is reported relative to the scale of the heavy water phantoms where 0 is equivalent to
the D2 0 phantom and 100 is equivalent to the H20 phantom.
a. (0) and (4) band preload groups
,,
/ LJ
600
500
*
[
400
-Regression (4)
-
300
Stiffness(0)
Stiffness(4)
Regresion(0)
200
100
0
5.2
5.4
5.6
T2Intensityrelativeto % H20
5.8
6
b. (8) and (12) band preload groups
800
700
0
600
500
A
400
e
*
300
* 0', I
A
A
A
-
S
200
l _~~~~~~~~~~~I
100
n
.
'A
I
v
5.2
5.4
5.6
5.8
T2Intensity
relativeto %H20
90
6
-
Stffness(8)
Stiffness(12)
Regression(8)
Regression(12)
Taller disks were found to be stiffer than shorter disks at low preloads.
4.5 Discussion
In summary, stiffness was predicted to increase with increasing preload. Damping was
not shown to change with preload. Magnetic resonance based assessments of disc degeneration
were found to correlate only weakly with stiffness properties. Both increased age and decreased
disk height corresponded to decreases in the stiffness properties in this experiment.
Measures
of degeneration and loss of water content (including T2 relaxation time and T2-weighted image
intensities) correlated with an increase in stiffness at low preloads. This was only significant at
low preloads, probably because these MRI measurements are made with no preload applied.
A limitation of this study was the number of freeze-thaw cycles. Although Panjabi
(1995) has found that biomechanical properties of the spine did not change with freezing, the
specimens in this study were forced to go through several cycles, including one between imaging
and testing which may have had some effect on the properties. This study was also performed at
room temperature rather than at body temperature. Little is known about the effects of
temperature on the viscoelastic behavior of the intervertebral joint, but it is possible that
temperature could play a role.
Stiffness and damping in this experiment can be compared to experiments with a single
functional spinal unit by doubling the stiffness and damping values. Values found here for
stiffness were higher than the instantaneous stiffness found by researchers examining the creep
behavior of spine (Keller, 1987). The stiffness range was similar to the cyclic experiment by
Kasra (1992) but lower than the other impact experiment (Rostedt, 1998). Unlike the other
experiments, all of our specimens were elderly, and often with moderately to severely
91
degenerative disks. This sample more accurately represents the population that might be
susceptible to osteoporotic vertebral fractures. A larger sample size was also used than in
previous studies. Finally, the impact-based experiment more accurately reproduced the rate of a
fall impact than the cyclic experiments of Kasra.
Variations in stiffness and damping of one standard deviation from the mean would
change the predicted force as much as 18%, using the fall impact model. A decrease in damping
by one standard deviation and an increase in stiffness by one standard deviation would cause the
predicted axial force of the 1 dimensional, single element spine, passive impact model to increase
from 2505 N to 2948 N.
In conclusion, stiffness and damping data from this experiment will be useful in modeling
the forces on the spine due to impact from a fall. This experiment focused on stiffness and
damping characteristics of an elderly spine during an impact such as might occur during a fall. A
nonlinear stiffness may be necessary in the models of Chapter 2 in order to reflect the changes of
the stiffness at different force levels seen in this experiment. MRI-based measures of the
degeneration showed a modest increase in stiffness with increasing degeneration.
4.6 References
1. Boos, N., and Boesch, C., "Quantitative Magnetic Resonance Imaging of the Lumbar Spine",
Spine, 20(21), pp. 2358-2366, 1995.
2. Bums, M.L., Kaleps, I., and Kazarian, L.E., "Analysis of Compressive Creep Behavior of the
Vertebral Unit Subjected to a Uniform Axial Loading Using Exact Paramentric Solution
Equations of Kelvin-Solid Models - Part 1. Human Intervertebral Joints", J. Biomech., 17(2) pp.
92
113-130, 1984.
3. Gundry, C.R. and Fritts, H.M., "Magnetic Resonance Imaging of the Musculoskeletal System,
Part 8. The Spine", Clin. Orthop. Rel . Res., 38, pp. 275-287, 1997.
4. Gunzburg, R., Parkinson, R., Moore, R., Catraine, F., Hutton, W., Vernon-Roberts, B., and
Fraser, R., "A Cadaveric Study Comparing Discography, Magnetic Resonance Imaging,
Histology, and Mechanical Behavior of the Human Lumbar Disc", Spine, 17(4), pp. 417-426,
1992.
5. Kasra, M, Shirazi-Adl, A., and Drouin, G., "Dynamics of Human Lumbar Intervetebral
Joints", Spine 17(1), pp. 93-102, 1992.
6. Keller, T.S., Spengler, D.M., and Hansson, T.H., "Mechanical Behavior of the Human
Lumbar Spine. I. Creep Analysis During Static Compressive Loading", J. Orthop. Res., 5, pp.
467-468, 1987.
7. Panagiotacopulos, N.D., Pope, M.H., Krag, M.H., and Block, R., "Water Content in Human
Intervertebral Discs, Part I., Measurement by Magnetic Resonanace Imaging", Spine, 12(9), pp.
912-917, 1987.
8. Panjabi, M.M., Karg, M., Summers, D., and Videman, T., "Biomechanical Time-Tolerance of
Fresh Cadaveric Human Spine Specimens", J. Orthop. Res., 3, pp. 292-300, 1985.
9. Rostedt, M., Ekstrom, L., Broman, H., and Hansson, T., "Axial Stiffness of Human Lumbar
Segments, Force Dependence", J. Biomechanics, 31, pp. 503-509, 1998.
93
Chapter 5 - Fall Dynamics - Experiments and Modeling
5.1 Abstract
Vertical impact velocity and torso angle both have a large effect on the predicted axial
forces on the spine during a fall. It was necessary, therefore, to determine what these values
might be in a fall from standing height. A previously performed experiment in which human
volunteers were asked to fall, self-initiated, onto soft landing mats was analyzed to determine
these variables for a fall. A 5h percentile crash test dummy was also used to examine the
dynamics of limp falls. Finally, 3 and 4-link models of the backward fall dynamics were used to
examine the effect of changes in range of motion of the knee, hip and ankle joints on the
dynamics of the fall. Vertical impact velocities of 1.62 m/s to 3.05 m/s were measured. These
velocities, in an upright fall with little tension in the abdominal musculature, could result in a
peak compressive force on the spine of 1925 and 3327 N in an average woman. Future work will
need to look at the effect of muscle forces on the dynamics of a fall.
5.2 Introduction
In Chapter 2, parametric analysis of the impact mechanics models showed the predicted
force results were most sensitive to the fall dynamic properties, vertical velocity and torso angle.
A 10% change in either vertical velocity or torso angle resulted in an approximately 10% change
in the predicted impact force. Because the velocity and torso angle played a critical role in
determining the compressive forces on the spine as the result of a fall, it was important,
therefore, to address what the velocity and torso angle would be in a typical fall and how that
95
velocity might change.
This work began by examining some previously recorded backwards falls of human
volunteers. These experiments had been performed (but not analyzed) in conjunction with a
study of sideways falls. The sideways fall study found that falls to the side impacted the ground
with a vertical velocity of 2.75 ± 0.42 m/s and a sideways trunk angle of 17.3 ± 11.50
(Kroonenberg, 1996). Kroonenberg went on to estimate hip impact energy at 168 J.
Hsiao (1998) in an experiment examining protective movements in a fall, also measured
impact velocity, reporting average pelvis impact velocities of 2.55 ± 0.85 m/s in falls resulting
from movement of the floor in several directions. The velocities in this study were not broken
down into direction of perturbation or fall direction. Neither of these two previous studies
examined the impact velocities and torso angles of a backward fall.
The primary objective of this research was to examine backwards falls using backwards
human falls, falls of a crash test dummy and simple link models in order to better assess the
range of impact velocities and torso angles. A second objective as to compare active and passive
falls. A final objective, using the link models, was to answer the research question "Do
decreases in range of motion in the joints of the leg change the impact velocity and torso angle?"
5.3 Methods
Human Experiments
Participants included six subjects (3 males and 3 females) ranging in age from 19 to 30
years (mean: 23.7 + 3.67 years), in height from 1.63 to 1.93 m (mean: 1.76 + 0.12 m), and in
weight from 534 to 801 N (mean: 651 + 116 N), respectively. They were instructed to stand on a
'96
platform in front of a landing mattress and to fall backwards as naturally as possible. The
subjects were asked to fall either normally or "relaxed". The falls were videotaped from the side
with one camera at 60 frames/s. The study was approved by the Institutional Review Board
(Committee on Use of Human Subjects in Teaching and Research) at Harvard University. This
experiment was performed previously by Aya van den Kroonenberg.
Markers at the ankle, knee, hip, shoulder and ear were hand-digitized from video records.
A reference length and the initial heel position at floor height were also digitized. The
coordinates of the body markers versus time were then fit to third-order polynomials. Impact
was defined as the point at which the hip marker was a height from the original heel position
equal to 5% of the body height for men and 5.7% of the body height for women, based on
anthropometric estimates of hip height by Contini (1972). This definition was used because the
landing mattress made assessing the time of impact difficult. Using the polynomial of the
coordinates and the derivatives of those polynomials, we obtained at the time of impact the hip
position xhp,the torso angle 0, the pelvic impact velocity vp, and the torso angular velocity dO/dt.
The hip position x.P was defined as the distance between the hip marker and the initial heel
position. The torso angle 0 was defined as the angle of the trunk with the vertical. The pelvic
impact velocity vbipwas defined as the velocity of the hip marker. The means of these values for
each subject were used for the statistical analysis. For each variable, a paired t-test was
performed comparing active muscle falls with those in which the volunteers were asked to fall
passively.
97
Dummy Experiment
A 5" percentile, female, crash test dummy was suspended by the head from a support
frame in an upright position. The initial dummy position was set up with a slight backwards tilt
and knee bend. The dummy was released from the frame and allowed to fall. Markers, placed at
center of the head, shoulder, hip, knee and ankle of the dummy, were video taped at 60
frames/second and hand digitized. Seven falls were recorded. A reference length and the initial
heel position at floor height were also digitized. Digitization and analysis followed the same
protocol as that of the human subjects.
Models
Two-dimensional three-link (leg, thigh and torso) and four-link (leg, thigh, torso, and
head) models were created. The leg links were connected to the floor via a pin joint. Literature
values were used to estimate link length, mass and inertial properties (Contini, 1972, Winter,
1979, NASA, 1978) (Table 5.1). The ankle, knee and hip were given a flexion-extension
moment versus angle relation representing the passive stiffness and damping characteristics. The
moment was set to a nonlinear equation:
M = AeC' ( 4° ) + A2e2(
°2)
+ BO
using literature data for the passive stiffnesses and damping of the joints (Figures 5.1-5.4). This
function was based on a function proposed by Yoon and Mansour (1982). The function provides
a low torque, neutral region with a continuous function that works well in computer processing.
The literature passive data was fit by first setting the stop angles (01 and
02)
as the range of
minimal static resistance. C and C2 were set to mimic the shape of the experimental data and
98
Table 5.1
Input values for a 5th percentile female. These values were used for
validating against the passive dummy falls and for sensitivity analysis.
8.03
7.21
Lower leg
Thigh
Torso (3-link)
34.75
Torso (4-link)
30.70
Head (4-link)
4.05
Lower leg
0.35
Thigh
Torso
Head and Neck
0.38
0.62
Center of
Lower leg
0.23
Mass (m)
Thigh
Torso
Head and Neck
0.19
Moment of Inertia
Lower leg
Thigh
0.16
0.33
(kg m2)
Torso (3-link)
1.20
Torso (4-link)
Head (4-link)
1.20
Mass (kg)
Length (m)
(from lower joint)
0.18
0.21
0.10
0.10
99
Figure 5.1
Constants for the joint angle-torque relations using the equation:
M = A,eC1(6 'L) + A2 eC2(
°:
+ BO
ankle
knee
hip
Al
-0.57
-7.5
-0.16
A2
1.42
1.3
3
C1
C2
01
0.1
-0.1
30
0.05
-0.1
110
0.1
-0.11
80
02
8
30
20
B
0.2
0.2
0.2
where flexion (plantarflexion in the ankle) is in the positive direction:
I
I
iknee
hip
ankle
100
Figure 5.2
Static joint angle-torque plots relative to literature data. Equation was fit to the data. Equations
were adjusted within the extrapolated regions to give realistic ranges of motion. The range of
motion was decreased by 20 ° by increasing the stop angle 0l and decreasing the
stop angle 02by 10° each.
Ankle Joint:
zE
a)
L_
0
F-
Flexion in degrees
101
Figure 5.3
Static joint angle-torque plots relative to literature data. Equation was fit to the data. Equations
were adjusted within the extrapolated regions to give realistic ranges of motion. The range of
motion was decreased by 20° by increasing the stop angle 0, and decreasing
the stop angle 02 by 10° each.
Knee Joint:
Vlll~l~llll1·11------
I
LmI
I
1[]
4
40
U
\ \I
*
*
Mansour
Magnusson
l
Ma
____ Passive Torque Equation
\
---- 20 degree reduction in ROM
* Stop Angles
Ill
20U
E
-IU-
%I.
A*
a
U1)
or
L -2 3
0
Af
*
llw
I
·
3V
80
"N
-20-
-40
_
Ifn
m-
I ...
\I
___
_
__
Flexion in degrees
102
____
Figure 5.4
Static joint angle-torque plots relative to literature data. Equation was fit to the data. Equations
were adjusted within the extrapolated regions to give realistic ranges of motion. The range of
motion was decreased by 20° by increasing the stop angle 0, and decreasing
the stop angle 02by 10° each.
Hip Joint:
|
:
-
-
------
-
--
Lt
A
-_
1-'
---
-
---
-
--
--
-
-
----
----
_
%'.1
:-
Yoon
x
Ma
Passive Torque Equation
40\
-.-..- 20 degree reduction in ROM
Stop Angles
0
30
z
A
In
a)
1W
20
i!Ut:'
..
:':E:-
L
'11!:
:: Z::
.....
0
·
· -.
X:
..
HE
I
...
:_..:
,,
_
bi-i_.i,
v
_
-5 )
_
I.
CI
ii8
-
-10-
l O
iiii
.i..
\\X
\
I
-20 -30
I
I
-
-
A11
-
v
-
\ \xl
\
-
Flexion in Degrees
103
then the A, and A2 values were varied to minimize the standard error. C, and C2 were then varied
to minimize the standard error. For flexion limits of the hip and knee, experimental data were
not available. However, Ma et al. (1995) published a fit to their own experimental data, and this
fit was used for the flexion portions of the hip and knee equations.
The models were checked for accuracy over time by removing the joint functions and
measuring the total kinetic and potential energies over time. The joints were then locked using
high stiffness linear joint functions, and final rotational velocities were compared to those
predicted by a simple falling rod.
Initial conditions for falls were taken from the digitized dummy fall data. The initial
point in the dummy data was considered to be the moment the hip marker began to descend.
Sensitivity of the two models to changes in the mass distribution and link length was determined
by varying each input quantity by 10% for one set of initial conditions. Each set of initial
conditions from the dummy falls was then used with the 3 and 4-link models to get impact
configuration and velocity. The impact point for the dummy was defined as the moment the hip
pin joint hit the ground. At this point the torso angle, torso angular velocity, the horizontal
position of the hip and the horizontal and vertical velocities of the hip were calculated. Finally,
the effect of decreases in the range of motion of the joints was examined by decreasing the
difference between 01 and 02, 20° for each joint and repeating the 7 runs with the initial
conditions from the dummy falls.
104
5.4 Results
Human Experiment
The mean magnitude of the total pelvic impact velocity was 2.73 + 0.33 m/s, with the x
component of -1.57 + 0.44 m/s, and the y component of -2.18 + 0.34 m/s. Values for hip
position, x,,, at impact were 0.80 + 0.20 m. Values for the torso angle and torso angular velocity
were between -112 ° and -7° and between -165°/s and -2.4°/s, respectively (means of -47° + 24 °
and -74.25 + 38°/s, respectively).
We found a significant 10% increase in total pelvic impact velocity, a significant 39%
increase in the x component of pelvic impact velocity, and a significant 42% increase in hip
position for the muscle-active falls, compared with the muscle-relaxed falls (Table 5.2). Trunk
angular velocity was not significantly different for the muscle-active case versus for the musclerelaxed case. Finally, muscle activity did not significantly affect the torso angle or the y
component of pelvic velocity at impact.
Dummy Experiment
Mean magnitude of the total pelvic impact velocity for the 5" percentile, female, crash
test dummy were 2.39 ± 0.54 m/s, with an x component of -0.03 ± 0.63 m/s and a y component
of -2.33 ± 0.52 m/s. The x position of the hip averaged at 0.38 ± 0.15 m. The torso angle and
angular velocity were -4° ± 23 ° and -285.4 ± 70.00/s (Table 5.2).
Models
Accuracy tests using total energy assessment of the models without joint torque functions
105
Table 5.2
Mean velocity and configuration data for human, dummy and 3 and 4-link model falls. The
dummy and the models, which represent a truly passive fall, fell more upright and closer to the
feet with slightly higher impact velocities.
Average
Human
Subjects
Active
Human
Subjects
Relaxed
Human
Subjects
5* percentile
Crash Test
Dummy
5" percentile
3-link Model
with Dummy
init. conditions
hip position
from feet
horizontal
velocity
(m)
(m/s)
-0.81
vertical
velocity (m/s)
total velocity
(m/s)
torso angle
(degrees)
torso angular
velocity (°/s)
0.20
-1.57 + 0.44
-2.18
0.34
-2.73
0.33
-47 + 24
-74 + 38
-0.94 + 0.10
-1.82 ± 0.32
-2.18
0.31
-2.86
0.35
-47
22
-63
35
-0.66 ± 0.18
-1.31 + 0.39
-2.19
0.41
-2.59
0.27
-48
27
-85
40
-0.38 ± 0.15
-0.03 + 0.63
-2.33 ± 0.52
-2.90 ± 0.54
-4
23
-235
70
-0.20 ± 0.10
1.64 + 0.50
-2.32 ± 0.40
-2.90 ± 0.23
-20 ± 15
-377 + 76
-0.16 ± 0.09
1.89 + 0.48
-2.06 ± 0.47
-2.83 ± 0.44
-28 ± 16
-453
-0.17 ± 0.08
1.66
0.38
-1.98 ± 0.26
-2.61 ± 0.19
-24 ± 11
-422 ± 54
-0.14 ± 0.07
1.76 ± 0.43
-1.71 ± 0.28
2.48 ± 0.41
-33 ± 11
-470 + 54
5' percentile
4-link Model
with Dummy
init. conditions
3-link model
20 ° decrease
in range of
motion
4-link model
20 ° decrease
in range of
motion
±
106
75
and using locked joints to examine the rotational velocity of straight rod falls found variations in
the total energy and deviations of rotational velocity of less than 1%. By varying each input
parameter by 10%, it was possible to examine sensitivity of the model and, in particular, the
vertical impact velocity and torso angle, to changes in the input parameters. The prediction of
vertical impact velocity was most sensitive to the length of the links (Table 3). The prediction of
torso angle was most sensitive to the length of the links and the moment of inertia of the torso
segment. Of the joint passive stiffness and damping properties, only the flexion stop angle of the
knee resulted in changes greater than 5% in the vertical impact velocity and torso angle. The
knee flexion stop angle resulted in a 10.2% change in the torso angle.
Using initial conditions from the dummy experiment, the model landed with a similar
impact velocity to the dummy falls (Table 2). However, the models landed less upright and
impacted closer to the feet. The 4-link model impacted with slower velocity and higher impact
angle than the 3-link model. With a 20 ° decrease in the range of motion (difference between the
two stop angles), the models impacted slower with a larger torso angle.
5.5 Discussion
In this series of human and crash test dummy experiments, vertical impact velocities
ranged from 1.62 m/s to 3.05 m/s. For a passive fall, in which the torso musculature was not
active, this could result in as much as 1925 and 3327 N of compressive force on the spine using
the 1-D simple spine model from chapter 2 and the anthropometric parameters of a
50 h
percentile
woman. Torso angle at impact varied from 45 ° to -95 °. Torso angles of 0° would have the
highest compressive forces on the spine during a fall using the models of chapter 2.
107
Table 5.3
Sensitivity of vertical velocity and torso angle to changes in input properties. The vertical
impact velocity was most sensitive to the length of the links. The torso angle was sensitive to the
length of the links and the moment of inertia of the torso link.
Change in Torso Angle (%)
4-link model
3-link model
Change in Velocity (%)
4-link model
3-link model
0
0
0
Moment of
Lower leg
Intertia
Thigh
-1
0
1
1
Torso
2
-1
-10
-10
0
Mass
-1
-1
1
1
Thigh
1
2
-1
-2
Torso
2
2
1
0
-18
-26
25
26
24
34
-14
-23
Lower leg
Lower leg
Thigh
Lower leg
Gravity
Thigh
Position
Torso
13
-5
Torso
Center of
0
-2
Head and Neck
Length
0
0
Head and Neck
-2
-1
1
2
2
-3
1
-3
-2
2
1
-2
Head and Neck
0
108
0
The model performed similarly to the entirely passive dummy falls when using similar
initial conditions, mass, and height. Difference between the model and the crash test dummy in
torso angle and impact location may be explained by the use of joint stiffness characteristics
from human experiments rather than those of the crash test dummy in the model. The dummy
joints consist of a pin joint connected by a bolt that can be tightened down. These joints also
have limitations in range of motion when segments such as the thigh and lower leg begin to
contact.
Decreasing the range of motion in the model caused the models to hit the limits of knee
flexion sooner and rotate back rather than falling straight down. This caused a decrease in
vertical impact velocity and increase in torso angle.
Although the crash test dummy was a 5th percentile dummy and therefore smaller than
the human volunteers, the impact velocities were higher. This is probably due to the active
muscle use in the human subjects, even in the "passive" falls. Because the human falls were selfinitiated from a standing position, the fallers tended to throw their torso back to initiate the fall.
This can be seen most strikingly in the one human volunteer whose torso angle at impact was
greater than 90 ° indicating that he actually impacted his head first. Future experiments should
use more realistic fall initiation such as a slip, trip or push.
These models did not get into what effect muscle activity might have on the dynamics of
such a fall. Bisdorff et al. (1995) has shown that with falling sensation, the abdominal,
quadripcep, and tibialis anterior muscles show EMG activity. Tang et al. (1998) reported both
rectus abdominus and erector spinae muscle activity in response to an unexpected slip. A next
step for these models would be to add the muscle forces and see how they affect the dynamics of
109
the fall. With such a model it would be possible to examine the benefit of throwing the torso
back in decreasing the impact velocity as seen in the human subjects.
In conclusion, the crash test dummy and the link models, which represent limp falls,
impact at velocities on the order of 2-3 m/s. Torso angles for these falls depend on the initial
conditions and can vary from a forward to a backward tilt. With the human falls lower velocities
and higher angles were seen, probably because the volunteers had to throw their torso back to
initiate the fall. Future research and modeling should examine the effect various muscle forces
might have on the dynamics of a fall.
5.6 References
1. Bisdorff, A.R., Bronstein, A.M., Gresty, M.A., Wolsley, C.J., Davies, A. and Young, A.,
"EMG-response to sudden onset free fall", Acta Otolaryngol. Suppl. 520(2), pp. 347-349, 1995.
2. Chesworth, B.M., and Vandervoort, A.A., "Age and Passive Stiffness in Healthy Women",
Phys. Ther. 69, pp. 217.224, 1989.
3. Contini, R., "Body Segment Parameters, Part II", Artificial Limbs, 16(1), pp. 1-19, 1972.
4. Hsaio, E.T. and Robinovitch, S.N., "Common Protective Movements Govern Unexpected
Falls from Standing Height", J. Biomechanics, 31, pp. 1-9, 1998.
5. Kroonenberg, A.J.v.d., Hayes, W.C., and McMahon, T.A., "Hip Impact Velocities and Body
Configurations for Voluntary Falls from Standing Height", J. Biomechanics, 29(6), pp. 807-811,
1996.
6. Ma, D., Obergefell, L.A., and Rizer, A.L., "Development of Human Articulating Joint Model
Parameters for Crash Dynamics Simulations", SAE Technical Paper Series, No. 952726, 39h
110
Stapp Car Crash Conference, San Diego, 1995.
7. Magnusson, S.P., Simonsen, E.B., Aagard, P., Boesen, J., Johannsen, F., and Kjaer, M.,
"Determinants of Musculosketal Flexibility: Viscoelastic Properties, Cross-sectional Area, EMG
and Stretch Tolerance", Scand. J. Med. Sci. Sports, 7, pp. 195-292, 1997.
8. Mansour, J.M., and Audu, M.L., '"The Passive Elastic Moment at the Knee and its Influence
on Human Gait", J. Biomechanics, 19(5), pp. 369-373, 1986.
9. National Aeronouatics and Space Administration, Staff of Anthropology Research Project,
"Anthropometric Source Book, Volume I: Anthropmetry for Designers", NASA Reference
Pulbication 1024, 1978.
10. Weiss, P.L., Kearney, R.E., and Hunter, I.W., "Position Dependence of Ankle Joint
Dynamics - I. Passive Mechanics", J. Biomechanics, 19 (9), pp. 727-735, 1986.
11. Winter, D.A., Biomechanics of Human Movement, Wiley, New York, 1979.
12. Yoon, Y.S., and Mansour, J.M., 'The Passive Elastic Moment at the Hip", J. Biomechanics,
15(12), pp. 905-910, 1982.
111
Chapter 6 - Cross-sectional Anatomy
6.1 Abstract
Accurate knowledge of the cross-sectional anatomy of the torso is important in
computational models used to calculate forces on the spine. While data are available in the
literature for working-aged adults, few data exist for the elderly. Few papers also examine the
anatomy in the thoracolumbar regions of the torso. The objective of this study was to generate
an information base of cross-sectional anatomy data by examining the cross-sectional anatomy in
an elderly sample at both thoracic and lumbar levels. A second objective was to evaluate the
correlation between external, anthropometric measures and this data.
Twenty seven men and twenty nine women, over 60 years of age, were recruited from
patients having torso, thoracic or lumbar computed tomography (CT) scans as outpatients at a
local hospital. Height, weight and other anthropometric variables such as abdominal width and
depth were measured. CT images at the levels of the eighth thoracic to the fifth lumbar vertebrae
were digitized to obtain moment arms and cross-sectional areas of the musculature and three rib
cage sections. Stepwise linear regression was performed to find correlations between the
moment arms or areas and the anthropometric variables.
21% of the variance in the moment arms and areas can be explained by gender. The
addition of height, weight, body mass index, and age to gender in a linear regression explains an
additional 16% of the variance (coefficient of determination (R2) of 0.37). Adding all of the
anthropometric properties to the linear regression analysis, increases the mean coefficient of
determination to 0.42.
This study adds important information to the musculature geometry
113
data used for biomechanical modeling by including both lower thoracic and lumbar data for an
elderly population. Externally measured data including anthropometric measures and gender
were found to have modest correlations with muscle moment arms and areas.
6.2 Introduction
Age-related vertebral fractures represent a significant public health problem. It is
estimated that 500,000 age-related vertebral fractures occur in the United States each year
(Cooper, 1993). In women over 50 years of age, 18% have sustained at least one vertebral
fracture (Melton, 1989). The health care expenditures attributed to these fractures is estimated at
$746 million in the United States (Ray, 1997). The 5-year survival rate of individuals with
vertebral fractures is 0.81 relative to age-matched controls, close to the 5-year survival rate of
0.82 for hip fracture patients (Cooper, 1993).
This problem has led to significant research into the etiology and prevention of vertebral
fractures. This investigation has included research on ways to improve the strength of the
vertebrae as well as research on ways to limit excessive loading of the vertebrae (Myers, 1998).
Current research into vertebral loading has been directed towards modeling the loads on the spine
at the time of fracture in order to gain a better understanding of how to limit excessive loading on
the vertebrae (Wilson, 1996). Such biomechanical models require detailed information on the
positions and size of torso musculature. The positions of muscle groups are needed for
calculating the moment arm of a muscle around the spine. The cross-sectional areas of the
muscles are used to estimate the relative contributions of different muscle groups. The
biomechanical models have also used estimates of the rib cage geometry when analyzing the
114
loads on the spine in the thoracic region.
Models similar to the models used to examine the forces associated with vertebral
fractures are also used to model the loads on the spine associated with low back pain (McGill,
1992, Schultz, 1988). These computations also require the same detailed information on the
position and size of torso musculature in the lumbar region.
Previous studies of the cross-sectional area and position of torso muscles have used
Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) images of cross-sections of
the torso (Table 6.1). These studies have in general looked at working age adults in order to
provide data for biomechanical models examining the etiology of lower back pain. However,
age-related vertebral fractures more frequently occur in the upper lumbar and lower thoracic
regions of the spine and in a much older population than working age adults (Cooper, 1993).
Although Kumar and McGill et al. both measured muscles in the lower thoracic and upper
lumbar regions, both only measured the transversus spinalis, erector spinae and latissimus dorsi
muscles and neither reported any data on the rib cage (Kumar, 1988, McGill, 1992). Kumar also
found that moment arms of muscles differed significantly between individuals over 60 years of
age and individuals from 41 to 60 years of age or individuals under 40 but did not go on to report
this age group separately.
Many of these papers report mean data for the moment arms and areas. However, it
would be useful if easily measured anthropometric data could be used to better predict moment
arm and area data. Reid et al. examined correlations between 27 anthropometric parameters and
trunk muscle and moment arm areas at the L5 level and found coefficients of determination (R2 )
of between 0.6 and 0.85 for all the measured data except the moment arm of the rectus
115
Table 6.1 - Studies of Cross-section properties
Authors
Year
Sample
Age
Trunk Levels
McGill,Patt, and
1988
13 males
21-65 years
L4/L5
Norman
7
Kumar s
Chafin et al.'
(mean of 40.5)
1988
1990
35 males
23-90 years
21 females
(mean of 60)
96 females
40-63 years
T7,T12,L3,L5
L2/L3,L3/L4,
L4/L5
Reid et al.17
1987
20 males
unknown
L5
Nemeth and
1986
11 males
(mean of 67 years)
L5/S1
17-57 years
L2/L3,L3/L4,
(mean of 27)
L4/L5,L5/S
unknown
T1O/T 11 through
Ohlsen 4
Tracy et al.'9
Moga et al."
10 females
1989
1993
26 males
11 males
L4/L5
8 females
McGill et. al.s
1992
25.3
15 males
116
3.6 years
T5-L5
1
abdominus (Reid, 1987). Moga et al. found coefficients of determination of between 0.16 and
0.93 for musculature at the L3/1L4A
level (Moga, 1993).
To create a complete data set for biomechanical modeling, it is necessary to collect
moment arms and areas of muscles for elderly individuals in both the lower thoracic and lumbar
regions. It is also important to collect data on rib cage geometry in order to model the thoracic
regions. The research questions asked in this paper are: What are the mean moment arms and
areas of the muscles in the torso from the T8 vertebral level to the L5 vertebral level? What is
the cross-sectional rib cage geometry in the torso? Do the moment arms or areas of the muscles
or the geometry of the rib cage correlate with height, weight, or body mass index? and Do the
moment arms or areas of the muscles or the geometry of the rib cage correlate with any other
measurable anthropometric property?
6.3 Methods
Subjects
The subjects of this study were outpatients over 60 years of age who were scheduled for
diagnostic CT scans of the chest, abdomen or torso. English-speaking, ambulatory outpatients
were asked to volunteer for the study. Subjects with a history of musculoskeletal disease
involving the spine or torso musculature as determined from previous radiological exams were
excluded. Patients with evidence of significant kyphosis, scoliosis or previous identifiable
vertebral fractures in the anterior-posterior or lateral scout images were also excluded. This
study was approved by the Committee on Clinical Investigations of the Beth Israel Deaconess
Medical Center.
117
AnthropometricData
Anthropometric data were measured immediately prior to or following the CT scans.
Sitting height and torso length were measured sitting upright from the sitting surface to the top of
the head and the spinous process of the seventh cervical vertebra respectively. Abdominal width,
depth and circumference were measured at the waist, chest width, depth and circumference were
measured at the level of the base of the scapula. Width and depth of the abdomen and chest were
measured with large anthropometric calipers (Lafayette Instruments, Lafayette, Indiana). Arm
length was measured from the axilla to the tips of the fingers. Arm circumference was measured
midway between the acromion and the elbow using a Measurator (Lafayette Instruments,
Lafayette, Indiana). Weight and height were also measured. Body mass index was calculated
from weight and height by dividing the weight by the height squared.
Digitization
The CT images were taken using a GE Highlight Advantage CT scanner (Milwaukee,
Wisconsin). Anterior-posterior and lateral scout images were used to select slices corresponding
to the center of the each vertebral body. Images were processed using Application Visualization
Systems software (Advanced Visualization Systems, Waltham, Massachusetts). The outline of
each muscle, the vertebral body and the rib cage sections were traced. The rib cage was traced in
three sections; the right rib cage wall (ribs and intercostal muscles), the left rib cage wall, and the
sternum and costal cartilage. Centroid and area of each traced outline were found using the slice
algorithm of Nagurka and Hayes (1980). Right and left values of moment arms and areas were
averaged.
118
Data Analysis
At each level, muscles with a mean area greater than 1 cm2 and rib cage sections which
occurred in at least 10 of the images at that level were analyzed. Muscles that were not present
in a section were considered to have an area of 0 cm2 and were not included in the regression or
mean of the moment arm data. Mean values for each of the moment arms and areas at a vertebral
level were calculated for both gender groups. Stepwise linear regressions were performed with
the moment arm or area as a dependent variable and age, gender and the anthropometric
properties as independent variables. The independent variables were entered into the stepwise
regression in the following order: 1. age and gender, 2. height, weight, and body mass index, 3.
abdominal and chest width, depth and circumference measurements, and 4. all other variables.
Gender was assigned a value of 0 for a female and 1 for a male. In the first set of analyses, only
height, weight, body mass index and gender were considered as independent variables. In the
second set of analyses, all of the anthropometric properties and gender were included.
6.4 Results
Volunteers in this study included 27 men and 29 women with an average age of 69.8
years. There was no significant difference between the ages of the women and the men (Table
2).
There were at least 16 volunteers scanned at each level for both genders (Table 3).
Mean values of the moment arms and areas for each gender were found (Table 4 and 5).
The correlation coefficient (R) for gender alone varied from 0 to 0.66 depending on muscle
119
Table 6.2. Anthropometric Variables measured.
Means and standard deviations of the anthropometric parameters and age are reported
with statistically different parameters marked by an asterisk.
female
male
age -
69.91 _ 6.64 years
69.77 + 7.27 years
height* -
160.07 ± 7.32 cm
173.43 ± 6.43 cm
weight * -
68.71 ± 16.96 kg
81.55 ± 14.29 kg
body mass index -
26.94 ± 6.75 kg/m2
27.11 ± 4.03 kg/m2
least chest width*-
28.87 ± 3.66 cm
32.46 ± 2.25 cm
least chest depth*-
24.61 + 5.01 cm
27.54 ± 3.92 cm
least chest circumference*-
90.15 ± 14.54 cm
99.49 ± 7.93 cm
least abdominal width*-
29.22 ± 3.42 cm
31.91 + 3.32 cm
least abdominal depth -
25.66 ± 6.01 cm
27.50 ± 3.94 cm
least abdominal circumference*-
90.39 ± 15.22 cm
100.37 ± 9.30 cm
sitting height*-
77.83 ± 7.95 cm
84.30 ± 3.43 cm
torso length -
59.92 ± 8.69 cm
61.70 + 3.68 cm
straight arm circumference -
29.47 ± 3.44 cm
30.05 ± 3.78 cm
arm length*-
63.76 ± 9.33 cm
70.36 ± 10.03 cm
* Significantly different (p<0.05) between male and female.
120
Table 6.3. Number of images available at each level for each gender.
At least 16 CT images of each gender were used at
each thoracolumbar level from T8 to L5.
Region
Level
number of female images
number of male images
Thoracic
8
18
17
9
19
20
10
22
24
11
28
27
12
29
27
1
29
27
2
28
24
3
24
20
4
22
19
5
20
16
Lumbar
121
group, variable, and level with a mean correlation coefficient of 0.21 for all moment arms and
areas. The addition of height, weight, body mass index, and age to gender in a linear increased
the mean correlation coefficient (R) to 0.38 with a range of 0 to 0.95. Using a stepwise
regression with the measured anthropometric properties to the linear regression analysis increases
the mean correlation coefficient to 0.43 with a range of 0 to 0.99. The increase in the correlation
coefficient between using gender alone and using the measured anthropometric properties is
modest with only a few variables increasing noticeably. This is seen in the modest increases in
the means of the correlation coefficients. Certain muscle groups appeared to correlate well with
the measured anthropometric properties. These included the rectus abdominus, erector spinae,
external oblique, internal oblique, and latissimus dorsi muscles (Table 6).
6.5 Discussion
Using volunteers coming in for CT scans of the chest or abdomen, we measured height,
weight and other anthropometric properties. From the CT scans we obtained the moment arms
and areas of the musculature in the torso and moment arms of three sections of the rib cage. The
moment arms and areas were found to correlate modestly with measurable anthropometric values
and gender. Gender alone was found to explain, on average, 21% of the variance in the moment
arm and area data.
Relative to other papers in which the moment arms and/or areas of the musculature in the
third or fourth lumbar levels was measured (Chaffin, 1990, Kumar, 1988, Tracy, 1989), the
paraspinal muscle moment arms were approximately the same. However abdominal wall muscle
moment arms were generally longer than those found in other studies with young adult subjects.
122
Table 6.4. Mean moment arm lengths relative to the vertebral body centroid in the lateral (x) and anterior-posterior (y)
directions and mean cross-sectional area of the muscles and rib cage segments in the thoracic torso.
x (cm)
T8 level -
T9 level -
T10 level -
Sternum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Trapezius
Major Pectoralis
Latissimus Dorsi
Anterior Serratus
Sternum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Trapezius
Major Pectoralis
Latissimus Dorsi
Anterior Serratus
Sternum
Rib Cage Half
T11 level-
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
Anterior Serratus
Sternum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
Anterior Serratus
External Oblique
T12 level -
7.88
1.09
4.13
2.74
6.18
12.26
12.21
A (cm 2 )
x (cm)
1.63
9.28
1.24
4.15
Male
y (cm)
16.22
4.31
-4.32
-4.73
2.78
-5.70
6.21
14.46
14.07
16.11
0.36
6.02
16.77
9.62
4.48
4.00
2.64
2.53
10.77
7.93
14.73
8.36
1.07
3.73
2.18
4.98
11.52
12.49
8.70
1.06
3.83
4.29
10.95
12.86
9.33
1.03
3.83
3.73
10.59
12.99
12.31
Sternum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
External Oblique
Female
y (cm)
14.75
5.10
-3.83
-4.13
-4.99
14.35
0.12
4.50
9.61
0.98
3.87
4.07
10.29
12.43
4.29
-4.01
-4.36
-5.21
15.00
-0.62
4.42
14.56
4.32
-4.04
-4.51
15.05
-1.25
4.61
14.08
3.52
-4.13
-4.56
15.05
-1.77
4.74
9.13
12.65
2.85
-4.31
-4.73
14.35
-2.51
8.08
123
A (cm2)
2.55
5.29
3.11
3.59
15.04
13.63
1.87
1.19
-4.47
2.59
4.82
4.22
-4.94
1.47
1.18
8.75
9.50
2.14
6.08
13.48
14.61
2.14
6.66
1.68
7.68
6.65
10.15
1.12
4.29
5.79
12.81
14.90
-5.95
16.50
-0.52
5.90
16.73
3.89
-4.50
-5.04
17.69
-1.26
5.30
16.43
3.87
-4.49
-5.09
17.65
-2.14
4.25
12.06
14.99
2.43
-4.61
-5.21
17.34
-2.79
10.40
5.63
1.54
2.29
10.71
1.10
4.29
4.88
12.23
15.30
13.67
1.92
10.39
3.98
5.35
3.95
11.09
1.02
4.50
5.24
12.06
14.41
2.09
8.58
3.64
6.75
2.11
1.45
12.88
14.24
2.65
8.66
2.71
11.41
11.20
2.91
11.29
5.93
10.29
3.48
4.34
2.51
15.21
6.34
8.66
6.72
Table 6.5. Mean moment arm lengths relative to the vertebral body centroid in the lateral (x) and anterior-posterior (y)
directions and mean cross-sectional area of the muscles and rib cage segments in the lumbar torso.
Male
Female
x (cm)
L1 level-
L2 level -
Sternum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
External Oblique
Transversus Abdominus
Psoas
Quadratus Lumborum
Rib Cage Half
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
External Oblique
Internal Oblique
Transversus Abdominus
Psoas
L3 level -
Quadratus Lumborum
Transversus Spinalis
Erector Spinae
Rectus Abdominus
Latissimus Dorsi
External Oblique
Internal Oblique
Transversus Abdominus
Psoas
L4 level -
L5 level -
Quadratus Lumborum
Transversus Spinalis
Erector Spinae
Rectus Abdominus
External Oblique
Internal Oblique
Transversus Abdominus
Psoas
Quadratus Lumborum
Transversus Spinalis
Erector Spinae
Rectus Abdominus
External Oblique
Internal Oblique
Transversus Abdominus
Psoas
10.66
1.02
4.24
4.41
10.09
12.77
9.65
2.41
4.01
11.24
1.14
4.22
4.82
9.74
13.05
12.90
10.94
2.92
4.93
1.35
4.06
4.90
9.93
12.94
12.53
11.69
3.40
6.29
1.39
3.87
4.92
13.20
12.51
12.38
3.96
7.20
1.07
3.08
4.68
12.96
12.19
11.95
4.47
y (cm)
11.35
2.11
-4.56
-4.96
13.51
-3.21
6.82
10.97
-0.91
-2.96
1.27
-4.91
-5.27
12.31
-3.82
4.67
5.54
7.36
-1.01
-3.33
-5.08
-5.48
11.24
-3.43
2.75
3.52
4.08
-0.82
-3.56
-5.08
-5.39
10.68
2.99
4.03
3.59
-0.14
-3.03
-5.40
-5.32
11.17
5.38
6.08
5.46
1.11
124
A (cm2 )
2.07
13.08
4.23
4.22
5.34
1.37
1.20
0.84
3.03
14.23
4.24
2.50
6.11
2.37
3.73
3.87
2.01
3.75
14.75
4.47
0.92
6.85
5.83
4.02
6.58
3.04
2.81
16.49
4.82
6.64
6.29
2.87
8.86
3.80
0.45
13.69
4.83
3.99
4.20
2.17
8.68
A (cm2 )
12.42
1.03
4.91
5.87
11.78
14.95
10.50
2.76
4.55
13.05
1.12
4.84
5.78
11.27
15.01
14.78
12.49
3.30
5.39
1.38
v (cm)
11.82
2.12
-4.81
-5.48
16.27
-3.66
7.86
13.81
-0.87
-3.01
0.29
-5.11
-5.67
15.15
-4.29
5.65
7.87
10.41
-0.78
-3.37
-5.47
4.50
-5.86
5.8
11.34
14.80
14.17
13:59
3.55
6.74
1.31
4.02
5.48
14.46
13.96
13.42
4.45
7.85
1.41
3.06
5.05
14.37
13.45
13.12
5.01
14.12
-3.97
3.12
3.98
5.36
-0.71
-3.69
-5.32
-5.78
13.24
2.76
4.54
4.28
-0.21
-3.42
-5.50
-6.08
12.78
4.98
6.32
5.37
0.71
19.36
7.54
x (cm)
2.82
19.29
6.41
6.41
8.25
3.19
1.38
1.41
3.56
21.61
6.24
5.03
9.50
3.51
4.81
5.74
3.22
4.70
1.81
11.08
10.18
6.51
10.34
5.04
4.02
19.52
7.45
10.82
10.19
5.44
14.29
6.15
1.23
15.13
7.09
7.30
7.52
3.44
14.15
Table 6.6 Regressions between major muscle groups and height (ht), weight (wt), least chest width (lcw), least chest
depth (Icd), least chest circumference (Icc), least abdominal width (law), least abdominal depth (lad), least abdominal
circumference (lac), sitting height (sitht). torso length (torsol), straight arm circumference (sac) and arm length (al).
Erector Spinae -
T8 level -
T9 level -
T10 level -
T11 level -
x = 3.74 + 0.409 gender
y = -2.48 - 0.0548 law - 0.520 gender
r2 = 0.12
r2 = 0.61
A = 1.16 + 0.100 bmi + 1.45 gender
x = -1.27 + 0.0314 height
r2 = 0.35
r2 = 0.29
y = -3.83 - 0.0188 bmi - 0.602 gender
r2 = 0.53
A = 1.55 + 0.116 bmi + 1.71 gender
r2 = 0.29
r2 = 0.49
x = -1.35 + 0.08324 height
y = -3.94 - 0.00789 weight - 0.460 gender
A = 2.77 + 0.137 bmi + 2.21 gender
r2 = 0.45
x = -0.287 + 0.0102 weight + 0.0215 height
r2 =0.44
r2 = 0.37
r2 = 0.61
y = -3.70 - 0.0123 weight + 0.382 gender
A = 10.6 + 0.303 lcd - 0.137 age + 1.95 gender
T12 level -
L1 level-
L2 level -
x = 3.11 + 0.0111 weight + 0.492 gender
y = -3.86 - 0.0126 weight - 0.320 gender
r2 = 0.51
r2 = 0.30
A = 2.63 + 0.113 weight + 3.36 gender
x = 3.63 + 0.555 gender + 0.00886 weight
y = -4.61 - 0.0360 weight + 0.0774 bmi
r2 = 0.58
r2 = 0.58
r2= 0.31
A = 17.3 + 4.98 gender + 0.0946 weight - 0.153 age
x = 3.77 + 0.545 gender + 0.00654 weight
r2
r2
r2
r2
r2
y = -1.39 - 0.0244 height
A = 17.3 + 6.25 gender - 0.145 age + 0.102 weight
L3 level -
L4 level -
L5 level-
r2 = 0.40
x = -0.478 + 0.0244 height + 0.00706 lcc
y = -5.48 - 0.381 gender
A = 20.9 + 0.258 bmi - 0.185 age + 4.54 gender
x = -1.78 + 0.0350 height - 0.288 gender
= 0.71
= 0.54
= 0.22
= 0.71
= 0.54
r2=0.17
y = -5.51 - 0.0192 weight - 0.0184 sitht + 0.0969 sac
r2 = 0.52
r2 = 0.46
r2 = 0.45
A = 53.1 - 0.141 height - 0.201 age + 4.98 gender
r2 = 0.41
x =3.07
y = -5.32 - 0.759 gender
r2 = 0.25
A = 14.3
Rectus Abdominus T10 level -
T1l level -
x = 0.876 + 0.055 al + 1.16 gender
y = 4.44 + 0.398 Icd + 2.23 gender
A = -5.39 + 0.0449 weight
x = 0.722 + 0.114 lad + 1.02 gender
y = 2.64 + 0.254 lad + 0.0821 age + 2.28 gender
r2 = 0.49
r2 = 0.76
r2 = 0.35
r2 = 0.54
r2 = 0.62
A = 3.23 + 0.197 bmi - 0.0717 age + 2.35 genderr2 = 0.51
T12 level -
L1 level-
y = 2.92 + 0.290 lad + 0.0564 age + 2.52 gender
A = -1.02 + 0.195 lad + 2.00 gender
x = -1.71 + 0.0826 lad + 0.138 lcw + 0.819 gender
y = 5.18 + 0.477 lad - 0.146 bmi + 1.90 gender
r2 = 0.59
r2 = 0.73
r2 = 0.64
r2 = 0.76
r2 = 0.77
A = 7.59 - 0.0734 sitht + 0.149 sac + 0.114 lcw
- 0.0760 age + 2.15 gender
r2 = 0.75
x = -1.20 + 0.181 lcw + 0.536 gender
125
Table 6.6 (continued)
L2 level -
L3 level-
L4 level -
L5 level -
x = -5.27 + 0.0360 height + 0.0797 lad + 0.0927 lcd
y = 0.147 + 0.473 lad + 2.02 gender
A = 0.882 + 0.0487 weight + 1.405 gender
x = -3.33 + 0.284 lcw
y = -2.43 + 0.545 lad + 1.46 gender
A = -1.37 + 0.0872 weight + 1.82 gender
x = 1.08 + 0.156 lad
y = -3.50 + 0.585 lad
A = -2.25 + 0.280 bmi + 2.12 gender
x =0.389 + 0.169 bmi
y = -1.50 + 0.51 lad
A = -15.7 + 0.109 sitht + 0.295 lcw + 0.141 lcd
External Oblique
T11 level-
T12 level -
L1 level-
L2 level -
L3 level-
L4 level -
L5 level -
r2 = 0.65
r2 = 0.79
r2 = 0.58
r2 = 0.64
r2 = 0.85
r2 = 0.74
r2 = 0.51
r2 = 0.84
r2 = 0.66
- r2 = 0.51
r2 = 0.80
r2 = 0.70
x = 11.5 + 0.227 lcw - 0.0870 age + 0.827 gender
y = -8.69 + 0.0534 weight + 0.203 age + 2.08 gender
A = 27.1 - 0.152 height + 0.297 lad - 0.118 age
+ 3.66 gender
x = 3.06 + 0.103 law + 0.216 lcw + 1.07 gender
y = 6.09 - 0.178 lac + 0.290 lcd + 0.119 lcc
+ 2.35 gender
A = -6.21 - 0.0538 al + 0.301 lcw + 0.181 bmi
+ 2.01 gender
x = 4.71 + 0.0241 weight + 0.222 lcw + 1.07 gender
y = 2.72 - 0.107 lac + 0.161 lcc
A = -8.39 + 0.360 lcw + 0.124 bmi + 1.60 gender
x = 3.46 + 0.0273 weight + 0.266 lcw + 0.713 gender
y = -5.21 + 0.181 sac + 0.0648 age + 0.864 gender
A = -9.48 + 0.0660 weight + 0.382 lcw + 1.27 gender
x = 2.34 + 0.0477 weight + 0.261 lcw
y = -0.324 + 0.0667 weight - 0.180 law + 0.0539 age
A = -1.91 + 0.337 bmi + 3.96 gender
x = 3.96 + 0.0888 weight + 0.0477 age
y = -1.68 - 0.0477 weight + 0.308 bmi
A = -6.02 + 0.0651 weight+ 0.296 law + 1.84 gender
x = 0.483 + 0.0937 weight + 0.0892 age
y = 3.78 - 0.310 lcw + 0.116 lcc
A = -14.6 + 0.658 lcw
r2 = 0.53
r2 = 0.49
x = 0.124 - 0.165 sac + 0.646 lecd+ 1.51 gender
y = 1.63 + 0.232 torsol - 0.229 bmi
A =-2.71 + 0.119 bmi
x = -0.175 + 0.449 lcw
r2 = 0.99
r2 = 0.62
r2 = 0.71
r2 = 0.50
r2 = 0.71
r2 = 0.81
r2 = 0.24
r2 = 0.73
r2 = 0.81
r2 = 0.25
r2 = 0.68
r2 = 0.84
r2 = 0.29
r2 = 0.60
r2 = 0.77
r2 = 0.41
r2 = 0.69
r2 = 0.46
r2 = 0.23
r2 = 0.61
Internal Oblique.
L1 level-
L2 level -
y = -18.1 + 0.148 height
L3 level-
A = -6.88 + 0.369 lad
x = 7.97 + 0.0933 weight + 0.124 lad - 0.167 sac
y = 4.17 - 0.173 law + 0.185 lcd
A = -9.75 + 0.341 law + 0.224 bmi + 2.99 gender
126
r2 = 0.70
r2
r2
r2
r2
r2
= 0.20
= 0.67
= 0.38
= 0.35
= 0.86
r2 = 0.26
r2 = 0.57
Table 6.6 (continued)
L4 level -
L5 level -
Latissimus Dorsi
T8 level-
T9 level -
T10 level -
T11 level -
T12 level -
L1 level-
L2 level -
L3 level -
L4 level -
x = 7.03 + 0.0586 weight + 0.206 lad - 0.121 sac
y = -0.0351 + 0.164 bmi
A = 0.466 + 0.230 bmi + 3.49 gender
x = 4.98 + 0.294 lad
y = 3.16 + 0.115 bmi
A = -9.65 + 0.481 lcw + 1.43 gender
r2 = 0.88
r2 = 0.35
x = 4.29 + 0.0495 height + 1.57 gender
y = 3.02 - 0.101 bmi
A = -16.2 + 0.173 sitht + 0.439 law + 2.79 gender
r2 = 0.64
r2 = 0.18
x = 4.73 + 0.0421 height + 1.46 gender
y = 2.03 - 0.0943 bmi
A = 1.56 + 0.256 bmi + 4.41 gender
x = -2.41 + 0.0531 height + 1.18 gender
y = -2.48 - 0.0654 bmi + 0.439 age
A = 1.57 + 0.215 bmi + 4.05 gender
x = 2.43 + 0.0362 height + 0.0799 law + 0.963 gender
y = -4.02 - 0.0614 bmi + 0.0537 age
A = -9.12 + 0.219 law + 0.318 sac + 2.88 gender
x = -1.53 + 0.0407 height + 0.0981 law + 0.0350 age
+ 0.970 gender
y = -4.77 - 0.0164 weight + 0.0480 age
A = -0.307 + 0.210 bmi + 3.28 gender
x = 10.1 + 1.69 gender
y = -5.11 - 0.0194 weight + 0.0449 age
A = 1.03 + 0.118 bmi + 2.17 gender
x = 6.60 + 0.108 lcw + 1.16 gender
y = -1.04 - 0.0443 al
A = 2.50 + 2.53 gender
x = -2.04 + 0.0615 height + 0.0906 lcd
y = 2.52 - 0.0371 height
A = 0.917 + 0.890 gender
r2 = 0.45
r2 = 0.53
r2 = 0.20
r2 = 0.69
r2 = 0.58
r2 = 0.70
r2 = 0.19
r2 = 0.53
r2 = 0.65
r2 = 0.21
r2 = 0.55
r2 = 0.63
r2 = 0.24
r2 = 0.70
r2 = 0.67
r2 = 0.23
r2 = 0.63
r2 = 0.48
r2 = 0.26
r2 = 0.44
r2 = 0.51
r2 = 0.18
r2 = 0.41
r2 = 0.54
r2 =0.14
r2=0.19
x= 12.02
y = -0.636 - 0.444 bmi + 0.130 age
A=0.162
127
r2 = 0.95
Erector spinae and psoas areas were also smaller in this study than in previous studies (Chaffin,
1990, Tracy, 1989).
One of the limitations of this study is that the population may not completely represent
the population at large. One factor that could contribute to this was that patients were being
scanned for other medical reasons including cancers and gastrointestinal disease that might effect
body habitus.
The muscle moment arm data is subject to several limitations. The supine position of the
volunteers during the CT scan is the first limitation. Most biomechanical models are used to
model activities in an upright position. McGill et al. found that rectus abdominus moment arms
in the lumbar region measured in the supine position needed to be increase by 30% to accurately
represent the upright standing position (McGill, 1996). The second limitation when using this
data in a biomechanical model is the assumption that the centroid is at the same location as the
center of the force generated by the muscle.
The rib cage data also has some limitations. The rib cage is known to expand and
contract with each breath. CT images are taken while the volunteer is holding his or her breath.
This could increase the lengths of the moment arms. The rib cage moment arms are also
susceptible to the same limitations as the muscle moment arms.
Despite these limitations, this data will be of great use in biomechanical modeling of the
elderly. It provides new information on the geometry of the torso musculature in both the
thoracic and lumbar region in people over 60 years of age. Previous studies have focused on
young adults and the lumbar region. Abdominal wall muscle moment arms in this population
were larger than previous young adult data and muscle cross-sectional area was smaller. This
128
information is important for the accuracy of biomechanical models that examine the etiology of
vertebral fractures or low back pain in the elderly.
6.6 References
1. Chaffin, DB, Redfern, MS, Erig, M, and Goldstein, SA., "Lumbar muscle size and locations
from CT scans of 96 women of age 40 to 63 years", Clin Biomech, 5, pp. 9-16, 1990.
2. Cooper, C, Atkinson, EJ, OFallon, WM, and Melton, LJ., "Incidence of clinically diagnosed
vertebral fractures: A population-based study in Rochester, Minnesota, 1985-1989", J Bone Min
Res, 7, pp. 221-227, 1993.
3. Cooper, C, Atkinson, EJ, Jacobsen, SJ, O'Fallon, WM, and Melton, U., "Population-based
study of survival after osteoporotic fractures", Amer J Epidemiol, 137, pp. 1001-1005, 1992.
4. Engstrom, CM, Loeb, GE, Reid, JG, Forrest, WJ, and Avruch, L., "Morphometry of the
human thigh muscles. A comparison between anatomical section and computer tomographic and
magnetic resonance images", J Anat, 176, pp. 136-156, 1991.
5. Kumar, S., "Moment arms of spinal muscluature determined from CT scans", Clin Biomech,
3, pp. 137-144, 1988.
6. McGill, SM, Juker, D, and Axler, C., "Correcting trunk muscle geometry obtained from MRI
and CT scans of supine postures for use in standing postures", J Biomechanics, 29, pp. 643-646,
1996.
7. McGill, SM, Patt, N, and Norman, RW., "Measurement of the trunk musculature of active
males using CT scan radiography: Implcations for force and moment generating capacity about
the L41L5joint", J Biomechanics, 21, 329-341, 1988.
129
8. McGill, SM, Santaguida, L, and Stevens, J., "Measurement of the trunk muscluature from T5
to L5 using MRI scans of 15 young males corrected for muscle fibre and orientation", Clin
Biomech, 8, pp. 171-178, 1992.
9. McGill, SM, Juker, D, and Axler, C., "Correcting trunk muscle geometry obtained from MRI
and CT scans of supine postures for use in standing postures", J Biomechanics, 29, pp. 643-646,
1996.
10. Melton LJ, Kan, SH, Fryw, MA, Wahner, H.W., O'Fallon, WM, and Riggs, BL.,
"Epidemiology of vertebral fractures in women", Amer J Epidem, 129. pp. 1000-1011, 1989.
11. Moga, PJ, Erig, M, Chaffin, DB, and Nusssbaum, MA., 'Torso muscle moment arms at
intervertebral levels T10 through L5 from CT scans on eleven male and eight female subjects",
Spine, 18, pp. 2305-2309, 1993.
12. Myers, ER, and Wilson, SE., "Biomechanics of osteoporosis and vertebral fracture", Spine,
22(24S), pp. 25S-31S, 1998.
13. Nagurka, ML, and Hayes, WC., "An interactive graphics package for calculating crosssectional properties of complex shapes", J Biomechanics, 13, pp. 59-64, 1980.
14. Nemeth, G, and Ohls6n, H., "Moment arm lengths of trunk muscles to the lumbosacral joint
obtained in vivo with computed tomography", Spine, 11, pp. 158-160, 1986.
15. Ray, NF, Chan, JK, Thamer, M, and Melton, LJ., "Medical expenditures for the treatment of
osteoporotic fractures in the United States in 1995: Report from the National Osteoporosis
Foundation", J Bone Min Res, 12, pp. 24-35, 1997.
16. Reid, JG, and Costigan, PA., "Geometry of adult rectus abdominus and erector spniae
muscles", J Orthop Sports Phys Ther, 6, pp. 278-280, 1985.
130
17. Reid, JG, Costigan, PA, and Comrie, W., "Prediction of trunk muscle areas and moment
arms by use of anthropometric measures", Spine, 12, pp. 273-275, 1987.
18. Schultz, A, Haderspeck, K, Warwick, D, and Portillo, D. "Use of lumbar trunk muscles in
isometric performance of mechanically complex standing tasks", J Orthop Res, 1, pp. 77-91,
1988.
19. Tracy, MF, Gibson, MJ, Szypryt, EP, Rutherford, A, and Corlett, EN., '"The Geometry of
muscles of the lumbar spine determined by matnetic resonance imaging", Spine, 14, pp. 186-193
1989.
20. Wilson, SE, and Myers, ER., "A model to predict the compressive forces associated with
age-related vertebral fracutres of the thoracolumbar vertebrae", Presented at the annual meeting
of the Orthopaedic Research Society, Atlanta, Georgia, February 22, 1996.
131
Chapter 7- Conclusion
7.1 Summary
In this thesis, the research questions, "What are the forces on the spine during a backward
fall from standing height?" and "Are the forces on the spine during a backward fall high enough
to cause fractures in the elderly with osteoporosis?" were addressed using both models of the fall
and impact dynamics and experimental measurement of the input properties. Models of a
passive fall, without tension in the torso musculature, were constructed first. Then muscle
tension elements were added to examine the effect of a pre-compression of the spine by the
musculature. Three studies were performed to examine the input parameters of these models.
This included an experimental measurement of the stiffness and damping of the spine segments,
measurement and modeling of the fall dynamics in a backward fall, and measurement of the
geometry of the torso musculature.
The axial compressive forces on the spine were found to range from 1100 Newtons to as
much as 3500 Newtons depending on a number of factors including the fall impact dynamics
(fall velocity and torso angle), the body weight of the individual, the properties of the soft tissue
of the pelvis and spine, and the amount of muscle tension in the torso musculature. The highest
forces were found in upright, fast falls in which the individual had a high upper body weight and
very tense torso musculature and little damping in the spine.
7.2 Predicted Risk
Using relationships between the failure force of spine segments and dual energy x-ray
133
absorptiometry based assessment of bone mineral density from Moro et al. (1995), it is possible
to estimate the risk at a given level of bone mineral density or bone mineral density based t-score
under several fall conditions (Table 7.1 and 7.2). The t-score is the number of standard deviations
from the mean bone mineral density relative of a young (20-29 years of age), normal cohort. For
example, a t-score of -1 means that the bone mineral density value is one standard deviation
below the average for young adults.
It can be seen that even passive falls of a woman of average height and weight can put her
at risk if her bone density is below 0.6 g/cm2 . As a reference, a mean of 0.61 ± 0.13 g/cm2 for the
total lateral lumbar bone mineral density was measured in an elderly cadaveric sample (Moro,
1995). Using stiffness proportional to tension with a constant of 150 Cholewicki (1997), muscle
tensions of 1000 N put a large proportion of the elderly population at risk of fracture.
Two limitations of this analysis are that the stiffness-tension curve is not well understood
and the measurement of failure force by Moro et al. (1995) was performed at low rates of
loading. Decreased proportionality constants between muscle stiffness and tension would cause
an increase in the predicted risk. It is unknown how high loading rates might change the failure
force in cadaveric vertebrae.
7.3 Contributors to Increasing the Force on the Spine
Several factors increase the force on the spine. These include increased muscle tension,
increased fall velocity, decreased torso angle, increased spine or pelvis stiffness, decreased spine
or pelvis damping, and increased upper body mass. Initial muscle tension and spine precompression were found to have little effect on the peak axial compressive force on the spine at
134
Table 7.1
Factors of risk for fracture during a backward fall as a function of total, lumbar, lateral, bone
mineral density from Dual Energy X-ray Absorptiometry (DXA). Relations of bone mineral
density to compressive failure force from Moro et al. were used to compute these factors of risk.
A factor of risk greater than one would indicate a prediction of fracture. Because these
predictions have errors associated with them, factors of risk from 0.7 to 1 could also be
potentially at risk. High, initial, muscle tensions, upright fall postures, and high body weight
increased the factor of risk. Torso angle was varied between 0 and 45 degrees.
..: ,.-E..r- .·.
-'.......' III._'_-_.II__l
....
·
.I
'<
TC
Sb.w:toxwi&Si:&aiSffieiee;Y:v>_
1·- :O~A--·
.;-11
.0tIt,,.:8ge
Muscle
.%
A.
VM
o
O
V
A
SA..9
woma
XXIIXCIUXIXI
vowII
,.,,...-..,u
. .- . . . ..
::v
Ad<_qstsa:o:ffis_;
~U:
m-..i.....
:ss.vv
Bone Mineral Density (g/cm2)
XIIIIYII
_,..,..
0.4
·
,,,
0.5
,,,
.....
, ....
0.6
avid
I -·-r-·uCrx·Xi··
·---------------.....
·-
IAr_·--·~·--~·-·
0.9
0.8
0.7
I^YXXIXX~"XI~IXII*`I
0.4
0.5
0.6
·IIXIII·X·LIIII*XII*
V.V
50th
woma
n_4
fiHA
AV
qua
g~
0_
1_,
0.6
0.5
0.5
0.4
0.5
0.4
0.5
0.4
0.4
0.4
50th
woma
0.5
0.4
1000 NAB
50th
woma
0.5
1000 N ES
50th
woma
0.5
none
~
·· ·.
-
·
· ·...........................
. . .
_A%~II....
^.0.
,,.A5W.VVA=5.:h**···....
95th
woma
none
I.X··ll···X·ll··.·l
· ··· *·XIXXX-II·.·lt*
_
··· ·I I·.··l·lil· IIIX*X* ·I*···tl··*XI·WUIIIXX··*U
_
woma
··--··-·····-·
I
0*I*II~i~·
50th
500 N AB
.
W~~·l
50th
woma
500 N ES
..
50th
woma
500 N both
..
W
50th
! 500 N both
.
By
woma
....
WW
, 1000 N ES
.··-·· ··----- ·---·-------···-----------
a
g
e
r
m
50th
0.4: 0.3
0.5
0.6
woma
w
0.4
0.6
woma
:
1000 N both
k&:~.
', ::.~:.
Iq aws11_
i
I
i
0.4
"x"'*11~~~'~~~"1'`"'
x .. ...
_l0th
- 1000 N both
~
x
· 50th
woma
1000 N AB
~
, L ,.,,,.,,,,
,
50th
Hew
.9>s
,.,,
Angle
WA^
none
a,
Fall
,_.. .
V.4
.,
:-.v. ..............
. .........
......_....v..·
. v.......·I .
_
_
Size
Activity
*
W =..
.~,~~~1.~.~...
A
_ 1~xl~l
_ _~=.-.-= ...
%
so
V11:V
~
I-
B~X)*X~
135
0.5
IB.:.E:
<~x
God
Table 7.2
Factors of risk for fracture during a backward fall as a function of t-score from Dual Energy Xray Absorptiometry (DXA). T-score is the amount the bone mineral density is less than the mean
of young (20-29 years old) normals in standard deviations. Relations of bone mineral density to
compressive failure force from Moro et al. were used to compute these factors of risk. A factor
of risk greater than one would indicate a prediction of fracture. Because these predictions have
errors associated with them, factors of risk from 0.7 to 1 could also be potentially at risk. High,
initial, muscle tensions, upright fall postures, and high body weight increased the factor of risk.
Torso angle was varied between 0 and 45 degrees.
Muscle
Size
_W
V^
VVVVWVVV
Activity
none
none
none
500 N ES
500 N AB
500 N both
500 N both
1000 N ES
1000 N AB
..
II nnnl II·i ,.C
' 1000 N AB
50th
0
1
0.5
woman
50th
woman
95th
woman
0.3
" ''"""
~ . ,.
' S'~
-- i-
I1
a
50th
woman
50th
~
---_ 0.6
ktA,
0.5
0.5
woman
50th
I
woman
50th
woman
t'.a
a
0.5
VnW
Di
I/L"
50th
woman
0.4
50th
t1000 N both
50th
woman
0.5
I··
VIN
50th
woman
50th
woman
50th
woman
woman
:.
T-score
~UI"
Angle
1000 N both
S
Fall
W4WV^
o.
'.
136
l"
0.6
-1
I
wrw~~~~~~~~~~~~~
~xlx
xl~xxl~llxlx-ux
i
-3
-5
low tension by increased linearly with tension at high tension. The peak axial compressive force
also increased approximately linearly with increases in velocity or torso angle. Spine and pelvis
soft tissue properties and upper body mass had a lesser effect on the peak axial force.
These contributing factors suggest possible interventions that might lower risk. Possible
prevention strategies include decreasing the pelvis stiffness by adding padding to the body or
floor, decreasing impact velocity through changing the fall dynamics and relaxing the torso
musculature during the impact to keep muscle tension low. Ideally one might use muscles to
decrease the impact velocity and increasing the torso angle at impact being sure to relax the torso
musculature before impact to reduce risk.
7.4 Limitations and Weaknesses of the Models
These models represent a first attempt to estimate the forces on the spine during a fall.
There are several areas, however, that still need work in order to solidify these estimates. First,
experimental assessment of the relationship of muscle stiffness to muscle tension needs to be
done in order better predict the effect of active muscle tension and pre-compression of the spine
on the peak compressive force on the spine. Presently, the best available estimates come from
research on isolated muscles of small animals and previous modeling of spine stability. No one
has yet tried to measure human torso musculature stiffness. In Chapter 3 it was shown that, even
with the linear relationship between muscle tension and stiffness found in the animal studies, the
predicted peak compressive force was a function of the proportionality constant that was used.
This constant has never been measured experimentally.
Another much needed area of information is in the dynamics of falling. The modeling
137
and work here primarily examined passive fall dynamics. However, it is important to understand
what fall velocities and torso angles might result from more realistic fall disturbances such as
slipping, tripping or stepping down unexpectedly. Also it is important to examine the effect of
walking velocity and muscle activity on these dynamics. Future studies should try to incorporate
some of these elements in examining the fall dynamics.
Some of the other input parameters used in the models could also be obtained more
accurately. The pelvis soft tissue properties in this model are not considered to change with torso
angle and have not been examined relative to body habitus or physical fitness. All of these
factors could change the pelvis soft tissue properties. The stiffness and damping properties of the
pelvis soft tissue and the spine are also considered to be linear in the impact models. However,
the spine properties experiments demonstrated that the stiffness increases with preload. A nonlinear relation of stiffness may be more appropriate.
7.5 Strengths of This Work
The major strength of this work is the validated, simple model of the dynamics of impact
from a fall that can be confidently used to estimate the peak axial forces on the spine during a
fall. Sensitivity has been assessed carefully and in many cases the data used in the model have
been measured experimentally. This model is the first to answer, or even address, the questions
"What are the forces on the spine during a fall?" and "Are the forces on the spine during a
backward fall high enough to cause fractures in the elderly with osteoporosis?". It provides a
first step in examining the risk an individual might have of sustaining a fracture under a number
of fall conditions. It also shows potential opportunities to reduce risk through intervention. Such
138
interventions include changing the pelvis stiffness and damping through padding the hip or the
floor, changing the impact velocity of torso angle through change in the fall dynamics and
reducing muscle tension during a fall through relaxation.
7.6 Future Directions
Future work should focus on examining the stiffness-tension relations of muscles in the
human torso. This information would not only be useful in modeling fall dynamics but also in
examining issues around spine stability as well. A proposed experiment would be to use a
combination of EMG-based assessment of muscle tension and small, impulse-like, anterior and
posterior perturbations of the torso. The rocking of the torso in response to these perturbations in
both a relaxed posture and when the volunteer was performing a Valsalva maneuver and
contracting the torso musculature could be compared. The frequency of this rocking could be
used to examine the stiffness and damping effect of the torso musculature.
Another important area of investigation is the effect of muscle activity on torso dynamics.
This could be examine experimentally by creating a realistic fall condition and using EMGbased assessments of torso musculature tension to validate a muscle-active model of the fall
dynamics. This model could be based on the simple passive model presented in Chapter 5 but
would include muscle elements.
Finally, investigation of the non-linearity of force-deflection relation of the spine and
pelvis tissues at very high loads should be continued. In this thesis it was found that the spine
stiffness increased with increasing preload. However, in the experiments performed here high
loads were not investigated. It is expected that the pelvis soft tissue would also display a non-
139
linearity of the force-deflection relation at high loads. The deflections of the pelvis tissue in
Figure 5.8 are close to the thickness of the soft tissue. However, a non-linearity of pelvis soft
tissue would explain this somewhat unrealistic result. Non-linear force-deflection curves should
also be incorporated into the models. Such increased stiffness at high loads would increase the
predicted maximum axial compressive force.
7.7 Conclusion
In conclusion, the research questions "What are the forces on the spine during a fall?" and
"Are the forces on the spine during a backward fall high enough to cause fractures in the elderly
with osteoporosis?" have been answered using a combination of models and experimental data.
Peak axial forces were found to range from 1100 to 3500 Newtons depending on the dynamics of
the fall, the size of the individual and the torso muscle tension and initial spine compression.
Elderly (over 60 years of age) individuals with lower than average bone density were found to be
at risk for sustaining a vertebral fracture during a fall. Future work needs to examine more
closely the effect of torso musculature tension and stiffness on the peak axial force on the spine
and to examine more closely the dynamics of a backward fall concentrating on the effect torso
musculature activity might play in changing the dynamics.
140
7.8 References
1. Cholewicki, J., Panjabi, M.M., and Khachatryan, A., "Stabilizing Function of Trunk FlexorExtensor Muscles Around a Neutral Posture", Spine, 22(19), pp. 2207-2212, 1997.
2. Moro, M., Hecker, A.T., Bouxsein, M.L., Myers, E.R., "Failure Load of Thoracic Vertebrae
Correlates with Lumbar Bone Mineral Density Measured by DXA", Calcif Tissue Int, 56, pp.
206-209, 1995.
141