Download LOW BACK BIOMECHANICS DURING WALKING OF INDIVIDUALS

LOW BACK BIOMECHANICS DURING WALKING OF
INDIVIDUALS WITH A LOWER-LIMB AMPUTATION
by
Adam Yoder
Copyright by Adam J. Yoder 2014
All Rights Reserved
A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of
Mines in partial fulfillment of the requirements for the degree of Master of Science (Engineering
- Mechanical).
Golden, Colorado
Date ___________________________
Signed: ___________________________
Adam Yoder
Signed: ___________________________
Dr. Anne Silverman
Thesis Advisor
Golden, Colorado
Date ___________________________
Signed: ___________________________
Dr. Greg Jackson
Professor and Head
Department of Mechanical Engineering
ii
ABSTRACT
Individuals with a lower-limb amputation have an increased prevalence of chronic low
back pain (LBP), relative to the general adult population.
Altered, dynamic whole-body
biomechanics resulting from limb loss are thought to be a primary cause of the increased
susceptibility. However, biomechanical LBP development is a multi-factorial problem, and a
definitive cause has yet to be ascertained using only traditional, laboratory methods.
Thus, the purpose of this work was to compare dynamic, in vivo low back biomechanics
between individuals with and without unilateral, transtibial amputation during walking, estimated
using patient-specific computational modeling and simulation. A generic, muscle-actuated
whole-body model with additional detail in the L1-L5 lumbar was adjusted to represent each
individual.
Experimentally-measured motion capture, ground reaction force, and surface
electromyography for each individual were used to simulate a gait cycle to estimate concurrent
internal low back biomechanics.
Results showed several group differences in computed low back metrics during particular
phases of the gait cycle. Most significant in individuals with an amputation was greater lateral
trunk motion towards the residual side during residual single limb stance, concurrently with
greater intact-side trunk muscle forces and a greater L4L5 lumbar joint contact force. A greater
range of axial trunk rotation near toe off of the residual limb was also found concurrently with
greater force in residual-side erector spinae and psoas.
The repetition of such abnormal
biomechanics over time has potential to cause deficiencies in muscular endurance, strength
asymmetries, inhibited proprioception, and myofascial pain, each associated with increased
susceptibility to chronic, biomechanical LBP and other secondary musculoskeletal disorders.
This work contributes to a broader goal of developing computational modeling and simulation
into a supplementary clinical tool to aid in diagnosis and treatment of biomechanical disorders.
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TABLE OF CONTENTS
ABSTRACT
............................................................................................................................ iii
LIST OF FIGURES ....................................................................................................................... vi
LIST OF ABBREVIATIONS ...................................................................................................... viii
CHAPTER 1
INTRODUCTION ............................................................................................... 1
CHAPTER 2
REVIEW OF LITERATURE .............................................................................. 4
2.1.
Low Back Pain ..................................................................................................... 4
2.1.1.
Body Segment Kinematics .................................................................... 6
2.1.2.
Muscle Function.................................................................................. 14
2.1.3.
Spinal Tissue Mechanisms .................................................................. 22
2.2.
Individuals with a Lower-Limb Amputation ..................................................... 30
2.3.
Musculoskeletal Modeling and Simulation ....................................................... 37
2.4.
Finite Element Analysis of the Spine................................................................. 48
2.5.
Summary ............................................................................................................ 55
CHAPTER 3
LOW BACK KINEMATICS, MUSCLE FORCES, AND JOINT CONTACT
FORCES DURING WALKING OF INDIVIDUALS WITH TRANSTIBIAL
AMPUTATION ................................................................................................. 57
3.1.
Abstract .............................................................................................................. 57
3.2.
Introduction ........................................................................................................ 58
3.3.
Methods.............................................................................................................. 60
3.4.
3.3.1.
Musculoskeletal Model ....................................................................... 61
3.3.2.
Simulation Framework........................................................................ 63
3.3.3.
Data Analysis ...................................................................................... 64
Results ................................................................................................................ 65
3.4.1.
Trunk-Pelvis Kinematics and Low Back Joint Contact Force ............ 65
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3.4.2.
Low Back Muscle Forces.................................................................... 68
3.5.
Discussion .......................................................................................................... 68
CHAPTER 4
SIMULATION AND MODEL DETAILS ........................................................ 75
4.1.
Additional Musculoskeletal Model Background ............................................... 75
4.2.
Simulation Settings & Parameter Optimization ................................................. 75
4.3.
Muscle Fiber and Tendon Calibration ............................................................... 82
4.4.
Joint Angle Conventions .................................................................................... 82
4.5.
Lower Extremity EMG constraints .................................................................... 84
CHAPTER 5
FINITE ELEMENT LUMBAR SPINE GEOMETERY
FOR MULTI-SCALE SIMULATION .............................................................. 86
5.1.
Methods & Results ............................................................................................. 86
CHAPTER 6
GENERAL CONCLUSIONS ............................................................................ 96
6.1.
Recommendations for Future Research ............................................................. 96
REFERENCES CITED ............................................................................................................... 100
APPENDIX A SUBJECT PARAMETERS ............................................................................. 113
APPENDIX B HILL MUSCLE TENDON/FIBER CALIBRATION ..................................... 114
APPENDIX C PARAMETER OPTMIZATION AND MARKER
TRACKING SETTINGS ................................................................................. 116
APPENDIX D LOWER EXTREMITY EMG VALIDATION ............................................... 117
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LIST OF FIGURES
Figure 1.1
Categories of, and interactions between, degenerative and biomechanical LBP ..... 3
Figure 1.2
A patient-specific, computational simulation workflow .......................................... 3
Figure 2.1
Illustration of in-phase and anti-phase modes of trunk-pelvis coordination ............ 9
Figure 2.2
Selected musculature of the hip, pelvis, and low back ........................................... 15
Figure 2.3
Representation of a scoliotic, spinal deformity ...................................................... 29
Figure 2.4
Anatomical FSU compared to a representative finite element model. ................... 49
Figure 3.1
Whole-body musculoskeletal model ...................................................................... 62
Figure 3.2
Group average results for trunk-pelvis relative angle and joint contact force ....... 66
Figure 3.3
Group average results for cumulative force within ipsilateral and contralateral
low back muscle groups throughout the gait cycle ................................................ 69
Figure 4.1
The generic musculoskeletal model (MoCapModel, Model Repository v1.6,
AnyBody Modeling System v6.0) .......................................................................... 76
Figure 4.2
Optimization settings for the iliac crest marker ..................................................... 79
Figure 4.3
Example of model parameters after applying the optimization sequence. ............. 80
Figure 4.4
Minimization of marker tracking errors ................................................................. 81
Figure 4.5
Frames created to measure thorax 3DOF rotation relative to pelvis ...................... 83
Figure 4.6
Joint coordinate system in the L4L5 joint .............................................................. 84
Figure 4.7
Processing steps to compute EMG-based lower bound activation constraints ...... 85
Figure 5.1
Cadaver-based L1-L5 finite element model (Huls, 2010) ...................................... 87
Figure 5.2
Bone geometry from the AnyBody model in comparison to the cadaver .............. 87
Figure 5.3
Rigid-body similarity transform for initial alignment. ........................................... 89
Figure 5.4
Representation of three-step sequential transform process .................................... 90
Figure 5.5
Lumbar muscle nodes in the AnyBody model ....................................................... 92
Figure 5.6
Bone geometry aligned after step one rigid-body registration ............................... 92
Figure 5.7
Comparison of transform methods ......................................................................... 93
Figure 5.8
Representative facet cartilage created at each of the four joint levels. .................. 94
Figure 5.9
Creation of baseline, sagittally-symmetric spinal geometry .................................. 95
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LIST OF TABLES
Table 2.1
In vivo disc pressure in the L4L5 joint measured during various activities ............ 26
Table 2.2
Total facet loads during tri-planar motions.............................................................. 28
Table 3.1
Mean (SD) of participant characteristics. ................................................................ 61
Table 3.2
Group mean (SD) of outcome metrics that were significantly different ................. 67
Table 4.1
Modeled lower extremity muscle groups in generic lower extremity model .......... 77
Table 4.2
Modeled trunk muscle groups.................................................................................. 77
Table A.1
Parameters of subjects selected for simulation. .................................................... 113
Table C.1
Settings applied in the AnyBody parameter optimization process ....................... 116
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LIST OF ABBREVIATIONS
LBP
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOWER BACK PAIN
TFA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRANSFEMORAL AMPUTATION
TTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRANSTIBIAL AMPUTATION
EMG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ELECTROMYOGRAPHY
ROM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RANGE OF MOTION
LLD
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LEG LENGTH DISCREPANCY
IVD
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTEVERTEBRAL DISC
FEM
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FINITE ELMENT METHOD
FSU
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FUNCTIONAL SPINAL UNIT
OA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OSTEOARTHRITIS
RBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RADIAL BASIS FUNCTION
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1.CHAPTER 1
INTRODUCTION
Low back pain (LBP) is a widespread clinical issue in the general population with large
impacts on healthcare each year. Certain patient populations, such as lower-limb amputees, have
an increased prevalence of persistent, bothersome (chronic) LBP relative to the able-bodied
population. Due to the complex anatomy and physiology of the spine, diagnosing and treating
the underlying etiology of a patient’s LBP is difficult, as illustrated in Figure 1.1. Experimental
comparisons of chronic LBP patients with respect to LBP-free individuals have proven useful to
characterize potential associations between LBP and whole-body biomechanics. In particular,
abnormal posture and motion, altered muscular recruitment, and altered low back stability are
often characteristic of individuals with chronic LBP. However, biomechanical and degenerative
factors that may be sources of LBP are not independent (Figure 1.1), and cause/effect
relationships between them are difficult to ascertain using only traditional experimental methods.
However, in order to develop effective rehabilitative and therapeutic interventions to treat LBP
within a particular category of patients, such as individuals with a lower limb amputation,
associations between abnormal whole-body biomechanics and internal, tissue-level metrics must
be established.
Particular altered whole-body biomechanics of individuals with a lower-limb amputation
during walking, relative to able-bodied individuals, include muscle compensations, kinematic
asymmetries, and abnormal coordination between body segments. Even though these differences
are frequently apparent through purely visual observations, underlying biomechanical
mechanisms that contribute to increased LBP susceptibility in individuals with a lower-limb
amputation have not been established. This may be due in part to limitations of traditional,
1
clinical measurement tools to fully characterize in vivo biomechanical quantities that are known
or suspected tissue-level contributors to LBP, especially when these quantities must be
monitored during dynamic patient motions. Advancements in computational biomechanics and
simulation have recently gained attention as potential tools to address these limitations; by
computing estimates of whole-body movements and accompanying, internal tissue-level
mechanics that are costly, invasive, or impossible to measure in a laboratory environment.
Therefore, the objective of this research was to compare the low back biomechanics
of individuals with and without a lower-limb amputation during walking, using a patientspecific computational simulation workflow. The broader, long-term goal of this work is to
establish baseline data, biomechanical models, and simulation tools and that will be part of a
computational workflow, with potential clinical applications to aid in diagnoses and
rehabilitation of patients with biomechanical LBP (Figure 1.2).
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Figure 1.1 – Categories of, and interactions between, degenerative and biomechanical LBP. The
most prevalent, competing theories of chronic LBP development are adaptation to pain versus
biomechanical mechanisms that drive degeneration. Abnormal motion and muscle recruitment
have been suggested as the most likely causes of LBP in individuals with a lower-limb
amputation. Full background of each cited references are discussed in the Literature Review
(Chapter 0), and documented in References Cited.
Figure 1.2 – A patient-specific, computational simulation workflow for the evaluation of
biomechanical LBP. Components developed or investigated within the scope of thesis work are
designated with shading.
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2.CHAPTER 2
REVIEW OF LITERATURE
A background of low back pain (LBP) in individuals with a lower-limb amputation is
available through a review of literature in the areas of low back biomechanics, clinical gait
analysis, and spinal tissue degeneration.
The review collectively suggests biomechanical
alterations in upper and lower extremity motion, muscle function, and low back stability in
individuals with a lower-limb amputation, which may be associated with increased susceptibility
to chronic LBP.
2.1.
Low Back Pain
Low back pain is a prominent disability in the general population of the United States,
with quantitative evidence suggesting that between 50-80% of all individuals will be affected by
an episode of LBP at some point in their life (Rubin, 2007). More specifically, the 2006
National Health Interview Survey of U.S. adults (n=31,044) found 26% to report at least one day
of LBP within the last three months (Deyo et al., 2006). Investigations of healthcare visit trends
found that ~90% of cases resolved as acute instances and patients recovered quickly (Freburger
et al., 2009). However, 10% of the adult population appears to develop LBP that is persistent and
bothersome in excess of 3 months, at which point a chronic classification is appropriate. This
category of chronic LBP is among the most common reasons to seek medical care (Becker and
Stumbo, 2013), and the result each year with the United States is associated direct and indirect
costs of $100-200billion, primarily due to lost time and disability wages (Freburger et al., 2009;
Katz, 2006; Salzberg, 2012).
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Recommended treatments may range from topical pain medication and therapy protocols
at a minimum, to medical imaging and invasive surgery at the most severe. A review of the
procedures typically followed in clinical management of LBP provides and distinguishes the
generally accepted physiological links between diagnostic findings and potential etiologies
(Becker and Stumbo, 2013). Examinations by physicians and physical therapists may include
evaluation of standing posture and lumbar lordosis, range of motion (ROM) tests, gait analyses,
supine lower extremity and low back endurance tests, and evaluation of the lower extremity
neurovascular system. Immediate medical imaging has been suggested not to improve outcomes
for a majority of individuals, and is thus only recommended in the presence of serious “red flag”
symptoms during repeated, physical examination. Approximately 90% of LBP patients receive a
nonspecific diagnosis, in which a particular etiology cannot be ascertained (van Tulder et al.,
2002). Upon chronic classification after LBP persistence in excess of 3 months, injection and
nerve block therapies are considered, followed by indication for surgery. Surgical intervention is
a last resort in the clinical management process, although the yearly frequency of low back
surgeries in the U.S. has been found to be on the increase since 1990 (Freburger et al., 2009).
Difficulties in investigating complex, interrelated biomechanical and degenerative
etiological factors has resulted in many studies over the past several decades seeking to
determine what, if any, biomechanical factors are different between individuals with LBP
relative to healthy individuals. These experimental designs generally cannot ascertain potential
cause and effect relationships. Nonetheless, such findings can be valuable, and generally fall
into one of three categories: (1) body-segment kinematics, (2) muscle function, and (3) lumbar
tissue-level. Unless explicitly stated otherwise, the LBP subject sampling in all studies collected
in this literature were individuals with clinically-nonspecific, chronic LBP.
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2.1.1. Body Segment Kinematics
Studies of whole-body movement characteristics associated with LBP have primarily
focused on motions of the thorax, lumbar spine, pelvis, and thighs. Furthermore, segmental
motions within a single stride, versus coordinative between-stride measures, have been
characterized. Studies investigating lifting exertions and sitting postures, while a large body of
the LBP literature, are not generally discussed here. Rather, the primary focus is altered body
segment kinematics of individuals with LBP during walking.
Distinct, angular displacements of the pelvis and lower lumbar spine in the three
anatomical planes have been compared between individuals with LBP and pain-free subjects
during treadmill walking (1.25m/s, angles normalized to standing) (Vogt et al., 2001). Withinstride patterns and amplitudes of segmental angular displacements were similar in subjects with
chronic LBP relative to healthy subjects; however between-stride variability of lumbar and
pelvic oscillations were greater in subjects with LBP. In contrast to a majority of previous work
that analyzed within-stride metrics, these findings highlighted that intrasubject variability across
repetitive motion may be a further important consideration with respect to chronic LBP, either as
a cause or result of pain.
Dynamical systems approaches use increased, between-stride
variability to distinguish coordination changes and low movement stability (Hamill et al., 1999).
Building on these findings, an additional similar work supplemented the experimental design of
current-LBP versus no-pain, with a resolved-LBP condition (Taylor et al. 2004). The subjects
used for the current-LBP condition were re-tested once the LBP had resolved. This work also
concluded that distinct, segmental amplitude measurements (max minus min, all three
anatomical planes, projected onto lab global) of lumbar and pelvic motion during walking were
insufficient to distinguish between people with current-LBP and healthy subjects with no history
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of LBP. However, range of lumbar bending in the frontal plane, and also of pelvic rotation in the
transverse plane, were significantly reduced in paired comparisons of resolved-LBP and currentLBP.
Additionally, a strong negative correlation (r=-0.74) was observed between average
(between-stride) angular displacement, and subject-reported pain intensity.
Subjects were
seemingly modulating segmental motion to avoid aggravating pain (pain-adaptation).
The
collective findings of these two studies suggest that if segmental motion is being analyzed,
robust, dynamic measures of relative motion are needed to distinguish between individuals with
and without LBP (irrespective of acute or chronic designation).
One metric commonly used to quantify dynamic coordination is continuous relative
phase (CRP), which in brief summary extends calculation of joint (or segment) angle alone to
also account for instantaneous velocity. The relative phase between instantaneous angle and
velocity in an angle-velocity phase plane, is calculated per equation (1.1),
(1.1)
where ϕ is phase angle, ω is joint (or segment) angular velocity, and θ is joint (or segment) angle.
Continuous relative phase between two joints (or segments) for a portion of motion is calculated
by subtracting the two respective phase angles across the time duration of interest. In depth
details on potential clinical uses for CRP in biomechanics are provided by (Hamill et al., 1999;
Seay et al., 2011), with an example application to characterize walking stability detailed by
(Hamill et al., 1999).
Between-stride standard deviation of CRP has been frequently applied as a metric to
quantify dynamic stability of body segment coordination. One study calculated CRP for subjects
with/without nonspecific LBP (n=6), walking on an increasing-speed treadmill (0.17m/s start, to
1.5m/s finish) to investigate whether trunk-pelvis dynamic stability was associated with LBP
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(Selles et al., 2001). In the transverse plane, pain-free individuals were found to have primarily
in-phase coordination between trunk and pelvis at slow speeds, and to transition to anti-phase at
faster speeds above ~1.0m/s. Anti-phase and in-phase coordination modes between the trunk
and pelvis are shown in Figure 2.1. In contrast, persons with LBP had decreased CRP variability
at high speeds relative to no-pain, suggesting more rigid control (increased stability) between the
segments with increasingly unstable walking conditions. The frontal plane was not investigated
in this study, and cause/effect for the transverse differences could not be determined.
A later study improved upon the former experimental design by including a wide range of
walking and running speeds (0.8m/s up to 3.8m/s), explicitly distinguishing all three anatomical
planes, and recruiting subjects for three conditions (n=14 each group): current-LBP (pain >4
months), resolved-LBP (pain-free >6 months), and no history of LBP (Seay et al., 2011).
Average, within-stride magnitude and variability at each speed were computed for each subject
group. In agreement with the earlier work, those with current-LBP relative to pain-free had
increased, dynamic trunk-pelvis stability (decreased CRP variability) in the transverse plane at
higher speeds. The same increased trunk-pelvis stability was also found in the frontal plane at
slow speeds (<2.8m/s). Both former studies interpreted primarily in-phase motion in either the
frontal or transverse planes (Figure 2.1), in combination with a corresponding increase in
dynamic stability (decrease in CRP variability), as a “guarded” gait strategy that indicated an
adaptation to, rather than a cause of, the current LBP.
Other, comparable work has suggested that interpreting between-stride standard deviation
in CRP as a measure of coordinative stability has limitations. In particular, authors demonstrated
that CRP variability is not sufficient to separate inter-subject variability from speed-induced
variability if multiphasic oscillations are present in the body segments being analyzed (Lamoth et
8
Figure 2.1 – Illustration of in-phase and anti-phase modes of trunk-pelvis coordination in the
frontal and transverse anatomical planes, adapted from (Seay et al., 2011).
al., 2002a). With respect to the commonly studied relative trunk-pelvis motion, tri-phasic pelvis
oscillations (transverse plane) have been found to develop in certain LBP-free individuals during
walking at moderate to high speeds, beginning around 1.0m/s (Lamoth et al., 2002a). As only
trunk-pelvis transverse plane motion was investigated in this work, whether or not similar multiphasic oscillations also develop in other segments/planes with increasing walking speed is
relatively unknown.
However, these findings do highlight the importance of measuring
coordinative stability with between-stride standard deviation of CRP only for slow walking
speeds (<~1.0m/s).
An alternative method to quantify dynamic stability of segmental coordination was
proposed by the same group (Lamoth et al., 2002b). Prior to calculating CRP, the raw pelvic and
thoracic segment oscillation signals were decomposed into component Fourier phases. Principle
frequencies were then identified, and used as filter cutoff frequencies, prior to the calculation of
9
CRP. The proposed CRFP method was applied to kinematic data collected on individuals with
and without LBP, walking at incremental speeds between 0.40 and 1.94m/s (Lamoth et al.,
2006b).
To confirm advantages of the developed CRFP method over traditional methods,
maximum minus minimum movement amplitudes (ROMs) of individual segments, and
traditional CRP, were also calculated. Average, within-stride magnitude and variability of both
segment ROMs, CRP, and CRFP were computed for each group-speed combination. Analyses
found that segmental ROMs were comparable in all anatomical planes between groups.
Transverse plane CRFP variability was decreased at faster walking speeds in persons with pain
relative to without, in agreement with earlier CRP work. However, average within-stride frontal
plane CRFP was more variable, particularly at higher speeds (anti-phase, Figure 2.1). Authors
suggested that individuals with LBP may compensate for more-tight transverse coordination with
less-tight frontal plane coordination. Less-tight frontal plane motion at higher speeds in the LBP
group slightly contradicts the findings of (Seay et al., 2011), who found a tighter coordination at
moderate speeds. These differences may potentially due to the aforementioned limitations of
CRP (versus CRFP) to differentiate speed-induced variability from inter-subject variability.
Slower walking speeds are generally preferred by individuals with LBP when asked to
walk at a self-selected pace. However, a cause/effect relationship of slow walking and currentLBP is not established, and may even vary between certain patient subgroups. One theory is that
slower walking results in less trunk-pelvis movement (i.e. more in-phase), resulting in less
aerobic exercise of stabilizing low back musculature and by extension a gradual loss of static
back endurance (SBE). Clinically, SBE is commonly used to characterize resistance of back
muscle extensors to fatigue (J. H. van Dieën et al., 2003), and is quantified by performing a test
of isometric opposition to a gradually increasing load imposed on the trunk, or through supine
10
leg raises. The effectiveness of diminished SBE as an LBP-identifier is generally associated
with knowledge that muscular fatigue can greatly inhibit muscular proprioception (Comerford
and Mottram, 2001). One study in particular showed that, in comparison to other frequently used
biomechanical measures for the low back, SBE deficiency longitudinally proved to be the most
accurate predictor of eventual LBP onset in originally LBP-free individuals (Luoto et al., 1995).
These findings highlight that a poor capacity to withstand repetitive, irregular loading increases
LBP susceptibility (even if magnitudes of the motion and loading are seemingly insignificant).
Broadly, muscular fatigue may be viewed as a biomechanical mechanism of LBP (rather than an
adaptation to LBP, see (Figure 1.1)
Motion of body segments, other than the trunk and pelvis, far removed from the lumbar
spine have also been investigated with respect to LBP. A review of walking with limited ankle
dorsiflexion (functional hallux limitus) illustrates how small changes in foot kinematics can
cause a cascade of biomechanical alterations throughout the body (Dananberg, 1993). When
ankle dorsiflexion is less than typical during the latter half of single-limb stance, increased
flexion compensations are made in the knee, hip, and lumbar spine to continue walking and
ensure toe clearance during swing. Flexing the trunk requires the curvature (lordosis) of the
lumbar spine to lessen, which orients passive spinal structures normally suited to cushion
compression loads in a more vulnerable orientation. For example, relative to higher lumbar joint
levels, the planes of facet contact in L4L5 and L5S1 are anatomically more frontal (versus
transverse), but upon lordosis straightening the typical IVD-facet load sharing is altered, and disc
compression is translated to more shear load along planes of facet contact (Dananberg, 1993;
Skrzypiec et al., 2013). Concurrently during this phase of gait (end of stance near toe off), hip
flexors are being recruited to initiate forward swing of the trailing limb, some of which are multi-
11
articular and span joints of the spine with origins on the anterior faces of the vertebral bodies
(e.g., psoas). The muscle path of the psoas allows potential contributions to intervertebral
compression, lateral bending, and axial twisting. Combined motion and loading of (lateral
bending + twisting + compression) has been shown to produce the greatest stresses/strains within
the disc relative to other combinations, suggestive of lumbar tissue injury and degeneration
through repetitive application (Schmidt et al., 2007). Thus, even seemingly negligible alterations
in lower-extremity biomechanics during walking can have substantial biomechanical effects at
the low back, which could potentially be associated with accelerated development of
degenerative LBP.
In order to robustly evaluate potential associations between whole-body metrics and
biomechanical LBP, in vivo spinal kinetics during walking (joint contact and muscular forces)
have warranted investigation. Whole-body metrics of interest could include walking speed,
trunk-pelvis coordination, lower-extremity inertial effects, and limitations in lower-extremity
joint function.
However, direct measurement of in vivo spinal mechanics is not currently
possible in a purely clinical environment without advanced biomechanical measurement
capabilities. Thus, computational tools are also needed to estimate these in vivo quantities during
dynamic movements and have proven useful. To the author’s knowledge at this writing, only
four studies have investigated low back in vivo joint loads of able-bodied individuals during
walking by applying musculoskeletal modeling and simulation techniques (Callaghan et al.,
1999; Cappozzo and Gazzani, 1982; Khoo et al., 1995; Seay et al., 2008), only one of which
further investigated activities of individual muscles (Callaghan et al., 1999).
The work by Callaghan and colleagues measured three-dimensional lumbar spine
kinematics, surface electromyography (EMG) on several low back muscle groups, and ground
12
reactions forces for five healthy subjects walking at several different speeds, with and without
arm swing restrictions. Various views exist regarding the function of arm swing during walking.
The longest standing theory is that in-phase arm swing during walking is purely passive due to
thorax inertia (Elftman, 1939), while a review of more recent work reports numerous studies
(modeling and EMG) that have quantified muscle activities associated with dynamic, net
shoulder moments (Meyns et al., 2013).
Callaghan found that a combination of slow walking
with restricted arm swing produced the most constant spinal joint loading, while fast walking
with less arm restriction corresponded to phasic joint loading.
Shear loading in the
anterior/posterior direction was the only direction that was significantly correlated (positive,
p<0.0003) with walking speed. Increased arm swing decreased axial and lateral lumbar spine
motion, but also correlated with decreased activity in all measured (and modeled) lumbar muscle
groups (peaks). This latter finding suggests that individuals who limit arm motion during
walking (for whatever reason) may place elevated demand on trunk musculature.
Further
cause/effect implications of arm swing findings were not explored in depth, although further
studies have found that arm swing decreases angular momentum about the vertical axis, and by
extension, the vertical ground reaction force is also decreased, leading to a net decrease in
metabolic energy consumption (~8%) (Umberger, 2008). With respect to the increasingly phasic
loading with faster walking and free arm swing observed by Callaghan, more recent work
discusses potential IVD-health benefits from mechanical loading afforded by walking, and these
studies are reviewed in Section 2.1.3. In summary, Callaghan’s early attempt at modeling and
simulating in vivo lumbar spine biomechanics during walking provides valuable insight, and
demonstrated the value of computational modeling and simulation (reviewed in Section 2.3).
13
Thus, further computational investigations are warranted that both apply, and continue to verify
and validate, such methodologies.
The body of literature that reports associations between body segment kinematics during
walking and LBP provides a strong foundation for further work. The findings collectively
suggest that relative to LBP-free individuals, those with LBP have similar within-stride
segmental ROMs, tighter (in-phase) transverse trunk-pelvis coordination at all speeds, different
frontal trunk-pelvis coordination that may be dependent upon speed, and reduced ability to
withstand continuous application of even small, abnormal motions (decreased low back muscular
endurance). Also, seemingly negligible alterations in normal arm swing and lower-extremity
joint kinematics have been shown have potentially large alterations on internal low back
biomechanics, with further investigation required.
2.1.2. Muscle Function
Muscle activity in LBP patients during walking relative to healthy individuals, has also been
investigated. The motivating theory is that individuals with pain should exhibit an altered
muscle coordination strategy, regardless of whether the alterations are a cause or result of the
pain. Several muscle groups significant to the discussion of LBP are displayed in Figure 2.2. A
broad review of trunk muscle action in LBP subjects distinguishes two prominently supported
theories of LBP development in the literature; pain-spasm-pain, and pain-adaptation (J. H. van
Dieën et al., 2003).
The former model postulates that LBP reflexively initiates muscle
activations that aggravate the pain source, which cascades into a cycle. The pain-adaptation
model contrastingly postulates that LBP informs the nervous system how to alter muscle
function, such that spinal tissue damage is avoided or mitigated (Figure 1.1).
14
(a)
(b)
(c)
(d)
Figure 2.2 – Selected musculature of the hip, pelvis, and low back (captured with AnyBody
Modeling Software). Psoas (a), erector spinae (b), abdominal obliques (c), and quadratus
lumborum (d).
15
Neither of the two theories of LBP development has garnered majority support within the
biomechanics community, potentially due to the difficulty of collecting in vivo data needed to
assess low back biomechanics. Surface EMG has been the most frequently applied experimental
tool over the past several decades to measure low back muscle activity during dynamic
movement. However, interpreting EMG as a measure of true muscle activation level, even with
normalization procedures, is difficult. Further using EMG signals during dynamic activities to
ascertain functional roles (agonist, antagonist, or purely postural) is generally not advised
without supplemental biomechanical modeling. Lastly, the low back and abdomen relative to
other body locations often have elevated levels of soft tissue that decrease signal strength. The
close-knit structure of the muscles also increases potential for cross talk in surface measurement.
Deep musculature such as the multifidi and psoas usually require fine wire instrumentation. As a
result, the primary muscle groups discussed in the LBP literature are (in order of relative
frequency): erector spinae (or paraspinal, if assumed to include the multifidi), rectus abdominus,
and external/internal obliques (Figure 2.2).
A generalized, functional separation of trunk musculature into three groups has been
proposed: local stabilizers, which are permanently active at some low level to maintain posture,
global stabilizers, which (eccentrically) modulate and limit movement, and global mobilizers,
which initiate and drive movement (Comerford and Mottram, 2001). These classifications are
frequently used to aid in interpretation of significant group differences in measured surface
EMG, and to suggest support of either pain-adaptation or pain-spasm-pain. However, these
conclusions must be taken with understanding of the discussed limitations of surface EMG for
determining functional roles of muscle groups. Furthermore, for those patient groups with a
suspected mechanical pain origin, rather than degenerative, a more patient-specific approach
16
may be needed.
For example, a majority of the nonspecific, chronic LBP diagnosed for
individuals with a lower limb amputation is suspected to have a myofascial cause associated with
altered whole-body biomechanics (Kulkarni et al., 2005). A process for the development of
serious, chronic LBP through repetition of slightly altered movement strategies is provided by
Comerford and Mottram (2001).
Spinal stability is an important concept associated with LBP, to which the relative
contribution of passive spinal structures (disc, facet, ligaments) versus active musculature has
been debated. Stability has numerous meanings in biomechanics, but with respect to the spinal
literature, refers to the capacity under normal physiological loads to maintain normal patterns of
vertebral motion that do not cause large deformity or onset of pain (Panjabi, 2003). Spinal
stability has been proposed to be the sum of contributions from (1) the passive spinal column
lending intrinsic stability, (2) the surrounding musculature lending dynamic stability, and (3) the
neurologic control system modulating the muscular recruitment (Panjabi, 1992). One study
adopting this framework, attempted to quantity the relative contributions of items (1) and (2) to
stability during spinal movements about the spinal neutral posture (a range where passive
contributions can be assumed negligible) (J. van Dieën et al., 2003). Matched LBP and pain-free
control subjects (n=16) performed the motions while EMG amplitudes of various trunk muscle
groups was recorded. Data were used to compute relative functional activation ratios during the
motion. An EMG-driven computer model was used to estimate ratios of agonist/antagonist
contributions to the measured total torque moment, also measured by cabled load cell. The most
significant difference was a larger contribution of the lumbar erector spinae to the total torque
moment, relative to the thoracic erector spinae contribution, in individuals with LBP.
In
Comerford’s framework (Comerford and Mottram, 2001), the lumbar erector spinae are
17
classified as local stabilizers, and the thoracic as global mobilizers. Notably, even though
muscular recruitment differences were observed, the LBP subjects did not report any LBP onset
during the small, slow movements. Thus, findings suggested that in the absence of large passive
contributions, certain stabilizing lumbar spine segmental musculature do contribute to total
spinal stability (corroborating (Panjabi, 1992)), and that alterations in normal levels of
contributions are (at least in some individuals) neuromuscular adaptations to, rather than direct
causes of, LBP.
A later study investigated whether passive soft tissue damage (qualified by diagnosed
ligamentous damage) affected total lumbar spine stability and low back muscle recruitment
strategy during motion. Twenty patients with passive-damage LBP, 20 LBP-free individuals, and
12 patients with nonspecific LBP performed a slow forward flexion task around the neutral
lumbar spine posture (Silfies et al., 2005). Surface EMG of five bilateral trunk muscle groups
were recorded and normalized to sub-maximal isometric standing, to estimate percent activity.
The two LBP subgroups (passive-damage LBP vs. nonspecific LBP) did not differ significantly
relative to one another in any computed, muscular activity parameters. Upon pooling the two
LBP subgroups together, a significant difference of greater activation in both the rectus
abdominus and external obliques was found in the LBP group, relative to LBP-free.
Furthermore, a significantly lower synergist activation ratio of (obliques / rectus abdominus) was
observed in the passive-damage LBP group relative to LBP-free. The former findings indicated
that individuals with LBP may over-activate trunk flexors, and also rely more heavily on the
rectus abdominus (multi-segmental global mobilizer) rather than the obliques (uni-segmental
local stabilizer) to perform flexion. These findings collectively suggest that abdominal muscles
may play a more crucial role in spinal stability than previously thought, and also that individuals
18
with LBP have altered functional goals at the muscular level in performing certain movements,
irrespective of LBP etiology.
Few studies exist that have quantified low back and abdominal muscle activity during
walking.
One study evaluated surface EMG data on five trunk muscles for 15 healthy
individuals walking at speeds between 0.6-1.7m/s (Anders et al., 2007). In general, mean muscle
activity correlated positively with walking speed. Obliqus externus activity pattern changed
from low continuous activity, to biphasic with increasing walking speed. Little interpretive
analysis was offered, although EMG-time data for all five muscle groups were explicitly
reported, providing baseline data for further work investigating the effects of LBP on muscle
activity during walking.
A further study investigated low back muscle activity during walking in subjects
with/without chronic, nonspecific LBP.
Kinematic and EMG data (erector spinae) were
measured on 22 individuals with LBP and 17 with no LBP walking on a treadmill (Lamoth et al.,
2006a). Biphasic lumbar erector spinae activity across the gait cycle was observed in both
groups, but instances of maximum activation were significantly earlier in LBP subjects relative
to LBP-free subjects. A biphasic pattern of lumbar erector spinae activity with maximum action
near heel strike and negligible action during swing is understood as the norm for LBP-free
subjects (Arendt-Nielsen et al., 1996; Lamoth et al., 2006b). In addition to timing differences,
those with LBP also had greater within-stride variability in erector spinae activation, relative to
LBP-free. Principle component analysis (PCA) of the total variance in lumbar erector spinae
activity was applied to confirm that a majority of the variance was due to LBP status, over other
potential sources of variability, including: walking velocity, stride length, age, and weight.
19
These findings support the concept of an anticipatory, guarded gait strategy for individuals with
LBP, through altered time-dependent usage of local stabilizing trunk musculature.
Two, notable works have investigated the effects of induced, acute low back pain on
muscle recruitment during walking. The first collected motion and EMG data on ten subjects
with LBP (nonspecific, chronic) and ten control subjects with no LBP walking at 1.1m/s
(Arendt-Nielsen et al., 1996). The ten control subjects additionally agreed to experimental
inducement of acute LBP via a single hypertonic saline injection.
Relative to LBP-free,
individuals with LBP exhibited a significant increase in EMG activity within the lumbar region
during the swing phase, where normally these muscle groups should be inactive. The amount of
activity increase correlated strongly with reported severity of pain. Upon inducement of LBP,
the control group also developed this same altered muscle activation strategy, as well as a
reduction in lumbar muscle activity during double stance, where lumbar muscle groups should be
highly active. These findings strongly suggest that pain of a purely mechanical, muscular origin
can affect motor coordination strategies within the lumbar region during walking, in support of a
biomechanical mechanisms LBP theory (Figure 1.1).
The second induced-LBP walking study investigated acute pain resulting from muscular
fatigue. Low back surface EMG was recorded on 16 individuals with no prior LBP during
treadmill walking, both before and after two hours of wearing a 25% body-weight waistcoat
(Anders et al., 2005). Analysis of the EMG data of four subjects that developed LBP during the
loading scenario, of pre-pain relative to pain-free, showed that both lumbar and abdominal
muscle groups had significant deviations from normal activity, prior even to any muscle fatigue.
In each case, the particular muscle differences were highly individualized; suggesting that future
20
work aimed at guiding biomechanical treatments for LBP based on muscle activity should be
subject-specific.
Muscle recruitment sequence between synergistic pairs of low back extensors has been
investigated in individuals with LBP. Activity of both the erector spinae and gluteus maximus
were recorded on 43 LBP-free subjects during trunk flexion and extension motions, before and
after two hours of standing (Nelson-Wong et al., 2012). Patient-rated LBP (visual scale) during
motion was used to classify each subject as either a pain or no-pain subject. In those that
reported high LBP levels during motion tasks following standing, a distinct muscle recruitment
sequence of lumbar erector spinae activation followed by gluteus maximus was observed (topdown), while the no-pain group exhibited the opposite sequence (bottom-up). Significantly in
unplanned retrospective analyses, the top-down pattern was observed in the trials of paindeveloping individuals prior to developing any pain, suggesting that irregular recruitment
strategies that correlate with elevated LBP susceptibility may be learned over time irrespective of
chronic LBP.
Further alterations in hip muscle recruitment have been associated with LBP
development and susceptibility. Twenty-three LBP-free individuals participated in a 2-hour
standing trial while hip and low back surface EMG were collected (Nelson-Wong et al., 2008).
In those individuals that reported onset of LBP during standing, bilateral co-activation of the
gluteus medius was found.
Co-activation of unilateral lumbar erector spinae and rectus
abdominus (or external obliques), which has previously proven effective as an identifier of LBPsusceptible individuals, was not different between groups. Results suggested that, at least for the
sampled patient group, elevated hip muscle co-activation (rather than trunk co-activation)
increased LBP susceptibility. Hip abductor function has received little attention in the LBP
21
literature, although inhibited activation of hip extensors (gluteus maximus) has been observed
within current LBP patients (Leinonen and Kankaanpää, 2000; Nelson-Wong et al., 2012).
In summary the collection of literature on altered muscle activity in patients with LBP
leads to numerous significant findings.
A functional separation (local stabilizers, global
mobilizers/stabilizers) has been suggested to facilitate identification of underlying biomechanical
effects of LBP. Spinal stability may have more contribution from active musculature than
historically thought. While the passive subsystem does contribute to total spinal stability, damage
to the passive tissue does not necessarily always cause altered neuromuscular strategies.
Evaluations of standing and slow movement tasks found that, relative to LBP-free individuals,
those with LBP potentially have: greater agonist/antagonist co-contraction, altered agonist
(concentric) load sharing, and inhibited hip extensor activity. Additional walking evaluations
found in LBP patients: a reduced tolerance to muscle fatigue, increased low back muscular
activity during swing, decreased during double-limb stance, and altered erector spinae activity
(earlier peak activation, greater between-stride variability).
2.1.3. Spinal Tissue Mechanisms
Irrespective of altered kinematics and neuromuscular strategies that may lead to LBP,
biomechanical pain is a tissue-level phenomenon.
The most prevalent anatomical and
physiological sources of LBP diagnosed through physician physical exams or medical imaging
include spinal stenosis, osteoarthritis of the zygapophysial joints (facet OA), spondylolithesis
(vertebral slippage), and damage to spinal ligaments and musculature. The intervertebral disc
can be a cause of many of the above maladies (rather than a source of pain itself) when the disc,
slips, or herniates, or narrows with time. The two most prominent etiologies of LBP warranting
surgical interventions are IVD degeneration and facet joint OA. While degenerative biology
22
composes a large section of the LBP literature, this section will focus on review of
biomechanical factors that may accelerate the degenerative timescale or cause tissue pain
directly.
The intervertebral disc is composed of an inner, soft nucleus pulpous surrounded by a
stiff matrix of collagen fibers arranged in the annulus fibrosis. The IVD contributes damping
primarily to superior/inferior (S/I) compression, followed contributions to anterior/posterior
(A/P) shear load carrying, and thus these two modes have been most frequently investigated with
respect to IVD degeneration. Upper limits for transverse A/P shear loading associated with
tissue failure within the lumbar spine have been developed based on a compilation of in vitro
cadaver and porcine studies of lumbar motion segments (Gallagher and Marras, 2012). For A/P
shear, 1000N is recommended as tolerable for infrequent exposure and 700N for repetitive
loading.
Degeneration of the intervertebral disc over time has traditionally been thought to be
driven by decreases in necessary nutrition. The small amount of nutrition that is needed (IVD is
primarily avascular) has been suggested to be received primarily through passive diffusion at the
vascular, cartilangeous endplates (Grunhagen et al., 2011). The former arrived at these findings
by approximating a diurnal, cyclical loading as a quasi-static finite element simulation, therefore
the potential for more dynamic, cyclical loading to affect transport of larger solutes throughout
the disc nucleus via forced fluid flow has not been ruled out (Ferguson et al., 2004). Whether or
not the increasingly in-phase trunk-pelvis coordination observed in individuals with LBP could
cause more static loading that mechanically inhibits disc health over long periods of time has not
been directly investigated in the literature.
23
The angle-ply composite structure of the intervertebral disc has led some investigators to
apply general lamination theory to estimate safe loading of the annulus fibrosis in principal
directions (Iatridis and Gwynn, 2004). A range of 8.0-10.3MPa in the fiber direction was
suggested to initiate collagen fiber failure and 0.4-1.0MPa to initiate shear delamination. An
average cross-sectional area for the IVD of 15.9cm2 (Sato et al., 1999) can be used to estimate a
potential force range for shear delamination of 640-1600N. This range is considerably wide,
although earlier cited estimates from in vitro work fall within the range: 700N (frequent) and
1000N (infrequent).
The two encapsulated, synovial facet joints of a spinal motion segment are essential
structural units, located posterior to the IVD. The two primary biomechanical functions of the
facet joints are to limit lumbar spine extension, and to constrain medial-lateral translations and
axial rotations within the plane of the IVD. The joints share considerable load with the IVD in
both the S/I and A/P directions; S/I suggested to be 3-25% depending on trunk flexion
(Kalichman and Hunter, 2007), and A/P 43-66% (Skrzypiec et al., 2013), both depending on
overall lumbar spine posture. The facets carry greatest joint contact loads when trunk extension
is combined with additional axial twisting or lateral bending. The anatomical orientation of the
facet joints with respect to the transverse and frontal planes also varies by lumbar joint level
(White and Panjabi, 1990).
The onset of facet OA in aging individuals is clinically viewed as a consequence of
unavoidable joint wear, that likely varies based upon patient-specific overall spinal morphology.
A more sagittal (vs. frontal) orientation of the joint and a history of IVD complications are two
potentially unavoidable factors found to correlate with accelerated facet OA (Kalichman and
Hunter, 2007).
IVD degeneration can narrow intervertebral spacing and decrease spinal
24
stiffness, which if present will alter the normal disc-facet load by placing increased force on the
facets. A dissection of 100+ cadaver motion segments with facet joint OA observed confounding
IVD degeneration to be present in a significant majority (Kalichman and Hunter, 2007), thus
supporting the theory. Lastly, the L4L5 joint relative to higher levels experiences a greater,
constant shearing force, due to weight of the body, lumbar lordosis curvature, and facet joint
orientation. The L4L5 joint is known to be the most prevalent site of facet OA relative to other
spinal levels (Fujiwara et al., 2000). Repetitive application of abnormal lumbar spine loading,
even of small magnitude associated with work environment, posture, or difficulties with
activities of daily living, have potential to accelerate OA development.
A contrasting viewpoint is that facet OA and IVD degeneration are completely separate
mechanisms. One study quantified relative levels of disc and facet damage in patients with
degenerative LBP using CT and MRI (Schwarzer et al., 1994). A combination of facet OA and
disc degeneration was uncommon in the subject pool of 92 patients. However, no longitudinal
analyses were performed to confirm that subjects with IVD degeneration did not eventually
develop facet OA if left untreated.
Evidence in the literature, along with understood
biomechanical function of the facets, more strongly supports that a degenerative mechanisms
between the IVD and facet joints are likely coupled in a majority of individuals, although which
drives the other is not established.
Measured structural parameters (e.g. stiffness, centers of rotation), kinematics, and total
joint contact loads in normal and degenerated conditions, from either in vitro or in vivo study are
useful for validation of computational work. However, due to the difficulty in maintaining in
vivo integrity in laboratory settings, these data are rare. One study reports in vivo disc pressure
in an LBP-free, non-degenerated individual during 29 different tasks of daily living, measured
25
via an implanted transducer in the L4L5 joint (Wilke et al. 1999). A sampling of the data for
activities most relevant to biomechanical LBP is presented in Table 2.1. Data were reported as
IVD pressures from a transducer, values in Newtons to represent contact forces may be more
useful. For numerous confounding factors, including that transducers only measure hydrostatic
pressure in the fluid nucleus, Force = Pressure*Area can lead to errors in contact force as high as
44%.
Therefore, a mean correction factor of 0.66 has been suggested, so that Force =
Pressure*Area*Correction Factor (Dreischarf et al., 2013).
Assuming a mean IVD cross
sectional area of 1800mm2 yields the values presented in the right hand column of Table 2.1.
Table 2.1 – In vivo disc pressure in the L4L5 joint measured during various activities. Pressure
data may be transformed to estimates of joint contact force by use of a correction factor (c=0.66)
suggested in the literature, and an average IVD cross sectional area of 1800mm2.
Pressure1 [MPa]
0.50
1.10
0.53-0.65
0.50-0.70
0.38-0.60
Activity
Relaxed, standing
Standing, bent forward
Walking
Climbing stairs (one at a time)
Walking down stairs (one at a time)
Force2 [%BW]
87
190
92-112
87-121
66-104
1
(Wilke et al 1999)
(Dreischarf 2013)
2
A similar study measured in vivo L4L5 pressures in healthy subjects and in LBP subjects
with pain specific to L4L5 (Sato et al., 1999). The LBP subject pool was further subdivided into
individuals with/without diagnosed L4L5 degeneration. Concurrent kinematics of the L4L5 joint
measured via radiographs were also collected. Subjects reoriented the trunk to eight instructed
positions of combined flexion/rotation/bending during testing. Quantitative pressures similar to
those in Table 2.1 were reported and may also be useful for validation of biomechanical spine
models that have confounding degeneration.
The matched subject design among the LBP
subgroups allowed isolation of IVD degeneration effects on resultant pressures and kinematics.
Significantly, but in agreement with earlier studies, magnitude of IVD pressure was seen to
26
decrease with increasing grade of disc degeneration (quantified via MRI).
The neighboring
facet joints were suspected to be compensating for this load difference in response to disc
narrowing, although this was not confirmed. Lastly, for any study investigating subject-specific
finite element models of the spine, and desiring to compare their pressure outcome metrics to
these or Wilke’s data, a robust method for computing a model-specific correction factor (rather
than cavg=0.66) is detailed in the literature (Dreischarf et al., 2013).
In vitro and in vivo tissue measurements of the facet joints are even less frequently
reported in the literature relative to the IVD. Physically accessing the small, encapsulated joints
to measure contact forces, without compromising true structural behavior, is far more difficult
than measuring fluid pressure in the IVD. An early study did present load ranges measured on a
cadaveric single functional spinal unit (FSU) with strain gauges on facet surfaces at the L1-L2
level, in various spinal postures (Schendel et al., 1993). However, quantitative results are likely
too limited for robust validation, as only a single FSU was considered, and all musculature and
passive ligaments were removed. Inclusion of physiologically realistic in vivo loading has been
shown to significantly affect computational modeling outcomes on spinal loading (see Section
2.4).
A majority of studies attempt to represent in vivo loading artificially; such as
experimentally with a pure compressive preload on the L1 body, and in finite element models
with a load in the direction directed along the lordosis (follower load).
A recent, more robust cadaveric study measured facet joint contact forces, IVD pressures,
and intervertebral kinematics in eight full S1-L1 spines, both with and without representative
frontal plane pelvic obliquity (Popovich et al., 2013). Results for facet contact force for various
loading scenarios are summarized in Table 2.2. Axial rotation produced greater loads than in
flexion/extension and lateral bending, but simulated pelvic obliquity with additional rotation
27
produced the greatest facet loads. Also, IVD pressures and facet contact force were negatively
correlated, further supporting the concept of passive structural load sharing, particularly for
combined load scenarios.
Table 2.2 – Total facet loads during tri-planar motions, measured on an S1-L1 cadaveric lumbar
spine with all musculature and ligamentous structures intact.
Facet Load1
[N]
Motion
Flexion
27±16
Extension
33±10
Ipsilateral bend
50±30
Axial rotation
95±26
Axial rotation + mild frontal pelvic obliquity
110±30
Axial rotation + large frontal pelvic obliquity
1
(Popovich et al., 2013)
124±30
A final topic relevant to low back pain in adults, and particularly individuals with a
lower-limb amputation, is adult onset, idiopathic scoliosis. Scoliosis is a lateral deviation of the
spine (in the frontal plane) from the normal straight alignment in the mid-sagittal plane, as
represented in Figure 2.3. Clinically, a frontal angle (Cobb angle) greater than 10o diagnoses
scoliosis (Hebela and Tortolani, 2009). Scoliosis alters the normal coupling between the three
anatomical rotations of the spine, and can also be a direct cause of chronic, nonspecific LBP if
untreated. While there are many conditions and diseases associated with scoliosis, the cause of
85-90% of cases are generally not established (White and Panjabi, 1990). However, frequently
observed and/or suspected etiologies of functional scoliosis are muscle fatigue, inhibited low
back proprioception (Yamada, 1971), and continuous application of altered activity in stabilizing
spinal musculature (White and Panjabi, 1990). Muscle groups most associated with scoliosis and
28
targeted in chiropractic treatment are the quadratus lumborum, external obliques, and iliopsoas
(Ferguson, 2014).
Figure 2.3 – Representation of a scoliotic, spinal deformity (childrenshospital.org)
Collective findings from literature investigating spinal tissues provide guidance for
further investigations into biomechanical mechanisms that may contribute to degeneration.
Combined motion and loading (lateral bending + axial rotation + compression) appears to place
passive structures that contribute to spinal stability (IVD and facet) at greatest risk for
accelerated degeneration. Frontal plane pelvic obliquity in particular was suggested to
significantly alter facet-IVD load sharing. Also, proper interpretation of in vitro or in vivo
experimental data to validate biomechanical spine models is crucial.
29
2.2.
Individuals with a Lower-Limb Amputation
A recent epidemiological survey within the United States recorded 1.6 million people
were living with limb loss in 2005, with estimated increases to 2.2 million by 2020, and 3.6
million by 2050 (Ziegler-Graham et al., 2008). The projected growth is due to the anticipated
increasing prevalence of dysvascular and diabetic conditions in aging adults, together accounting
for just over half of all amputations (Ziegler-Graham et al., 2008).
The remainder of
amputations are due to trauma (~45%), and cancer (<2%). Diabetes remains the leading cause of
amputation in the United States, although the number of traumatic amputations in 2010-2011 due
to combat-related injuries was significantly greater relative to the previous decade (Krueger et
al., 2012), and is also anticipated to increase. Irrespective of amputation cause, individuals with
a lower-limb amputation are susceptible to a range of chronic, secondary conditions including:
poor mental health, phantom limb pain, abnormal pain in both the residual and intact legs,
greater prevalence of knee osteoarthritis (Burke et al., 1978), and persistent, bothersome LBP
(Ehde et al., 2001; Ephraim et al., 2005; Kulkarni et al., 2005; van der Schans et al., 2002).
Within the general population, the growing sub-group of individuals with lower-limb
amputation has proven a distinct, elevated prevalence of LBP. Results of a comparative survey
incorporating traumatic lower-limb amputees both with and without LBP, found that not only is
LBP a prominent secondary disability of lower-limb amputees, but that individuals view that
pain as equal to or worse than all other pain conditions affiliated with the residual limb (Kulkarni
et al., 2005). Similarly, a 2004 national survey of quality of life in individuals with a lower-limb
amputation recorded that 62% of respondents reported experiencing persistent, bothersome
(chronic) LBP regardless of time since amputation (Ephraim et al., 2005).
30
The most frequent etiologies of LBP diagnosed in individuals with a lower-limb
amputation are not made clear in reports. As a start, the work by Kulkarni and colleagues
performed medical imaging diagnostics on a subset of patients that reported LBP, thus allowing
characterization of concomitant degeneration. No significant correlation was found between
amount of tissue degeneration quantified by medical imaging, and patient-reported severity of
reported LBP. Even though perceived pain severity can be highly dependent upon the patient,
these findings do suggest that a majority of individuals with a lower-limb amputation and
secondary LBP, likely suffer from biomechanical LBP, rather than degenerative pain sources
(Figure 1.1). In particular, the likelihood of muscular pain (myofascial) was further suggested,
due to collective patient descriptions of the pain sensation (Kulkarni et al., 2005). Investigations
of bone and joint changes in individuals with a lower-limb amputation also found no apparent
correlation between LBP and low back degenerative changes (Burke et al., 1978), although did
find a large prevalence of scoliosis (40-60%). Neither work used computed tomography as the
particular imaging mode to characterize disc and facet degeneration; the former used MRI, and
the latter used x-ray. This raises some concern whether level of degeneration was characterized
adequately. Images from MRI and x-ray are frequently criticized in their capacity to expose disc
and facet degeneration (Kalichman and Hunter, 2007).
Nonetheless, former etiological investigations in combination with numerous reports of
altered whole-body biomechanics in individuals with a lower-limb amputation, seem to strongly
suggest pain due to biomechanical mechanisms (Figure 1.1), and the type of biomechanical LBP
pathway presented by (Comerford and Mottram, 2001).
An encouraging aspect of this
conclusion is that, relative to degenerative LBP, biomechanical LBP (and scoliosis) can
potentially be treated with therapeutic and rehabilitative interventions to motion and posture
31
habits, versus more costly and high-risk methods involving injected nerve blocks and surgery.
Identification of whole-body, biomechanical alterations in individuals with a lower-limb
amputation, reported in the literature, is first needed.
Walking mechanics have been studied in subject pools with both transfemoral (TFA) and
transtibial (TTA) amputations. Transfemoral amputation refers to amputation between the hip
and the knee (or, across the femur). Transtibial amputation refers to amputation between the
knee and ankle. An epidemiological study of lower-limb amputation trends in the US suggested
that between 1988 and 1996, 39% of lower-limb amputee respondents (excluding toe) were
transfemoral, 42% were transtibial, and the remainder were foot, ankle, or specialized type
(Dillingham et al., 2002). Relative to TTA, individuals with TFA have been suggested to have
even greater susceptibility to LBP, and severity of secondary disabilities (Kulkarni et al., 2005;
Smith et al., 1999). In contrast, other work quantifying secondary disabilities within TFA and
TTA individuals found no statistical between-group difference of LBP prevalence (Hammarlund
et al., 2011).
Both TTA and TFA amputation removes muscle groups that contribute to walking
mechanics and are critical for body support, forward propulsion, swing initiation and
mediolateral balance. As a result, walking of individuals with a lower-limb amputation in
comparison to able-bodied has been characterized by numerous muscle compensations
(Silverman et al., 2008), altered whole-body dynamics (Silverman and Neptune, 2011),
asymmetrical coordination between body-segments (Devan et al., 2014), and a slower preferred
walking speed (Kulkarni et al., 2005). These altered biomechanics of individuals with a lowerlimb amputation relative to able-bodied individuals, are similar to previously reviewed
biomechanical differences between able-bodied individuals with and without LBP during
32
walking, such as: irregular coordination between pelvis and trunk (frontal and transverse), shifted
phase and erratic activations of the erector spinae, abnormal swing versus stance muscle
recruitment, and altered agonist/antagonist synergist ratios in the trunk-pelvis body region.
A
review in 2011 compiled all literature prior to time of writing that involved individuals with a
lower-limb amputation, and distinguished each study based on spatiotemporal and/or
physiological parameter examined (Sagawa et al., 2011).
A key finding was that of 122
parameters with potential usefulness in gait analyses (Benedetti et al., 1998), 78 had yet to be
investigated in individuals with a lower-limb amputation.
Motion of the lower lumbar spine during walking has been compared between TFA
individuals with and without LBP (occurring after amputation). Kinematic data were measured
on individuals with TFA+no-LBP (n=8), TFA+LBP (n=8), and non-amputees with no LBP
(n=6), walking at self-selected speeds (Morgenroth et al. 2010). Average self-selected walking
speed (~1.0m/s) was not significantly different between groups. Relative to the TFA+no-LBP
group, those with TFA+LBP had a greater within-stride transverse plane lumbar spine ROM. No
group differences were found in the frontal or sagittal planes. In a further pooled TFA versus
non-amputee comparison, those with TFA had a greater within-stride lumbar spine sagittal
ROM, suggesting a reduced lumbar lordosis. Finite element analysis of the L4L5 FSU
(representing all passive structures), has separately been applied to show that of the three
possible tri-planar trunk motions, posterolateral IVD strain and pressure were most sensitive to
base transverse rotation supplemented with additional frontal and/or sagittal bending (Schmidt et
al., 2007). The facet joints do carry large load in axial rotation, but not within the ROM studied
by Morgenroth. Additionally, reduced sagittal lordotic angle during gait has been suggested to
place the passive spinal tissues in a more vulnerable pose to resist spinal compression generated
33
near toe off (Dananberg, 1993). The particular biomechanical differences between pooled TFA
and able-bodied individuals, and also between TFA+no-LBP and TFA+LBP, have potential to be
associated with accelerated degenerative mechanisms.
Altered muscle recruitment in individuals with a lower-limb amputation, relative to ablebodied individuals, during walking has also been investigated. The collective literature suggests:
greater residual/intact limb hip extensor moments during early stance (Grumillier et al., 2008;
Silverman et al., 2008), elevated residual limb gluteus maximus activity during early/mid
residual limb stance (Winter and Sienko, 1988), elevated residual limb vasti/hamstring activity
during early residual-limb stance (Fey et al., 2010), and greater residual-limb hip flexor power
near residual limb toe off (Sadeghi et al., 2001). Notably, the review article of amputation
literature in 2011 found that of 26 amputation studies that report EMG data, all were isolated to
the lower extremities. Thus, no EMG data or findings with respect to altered activity of trunk
musculature in individuals with a lower-limb amputation during walking are reported in the
literature.
Irrespective the lack of existing low back EMG data, known biomechanical couplings
between the lumbar spine and lower extremities provide a basis for developing theories of
biomechanical LBP during walking of individuals with a lower limb amputation. In particular,
the potential for slight limitations in normal ankle function to affect other joint angles (knee, hip,
lumbar spine) via a chain of biomechanical compensations was reviewed previously (Dananberg,
1993). In individuals with lower-limb amputation, the ankle joint along with all spanning
musculature is completely removed. Thus, confounding biomechanical cascades propagating
from lower joints to the low back should be more severe. For example, elevated hip flexion
power in response to the missing ankle plantarflexors (Sadeghi et al., 2001) could involve the
34
psoas major, which originates on anterolateral faces of the vertebral bodies (Figure 2.2). The
psoas can generate significant lumbar spine compression when bilaterally activated, and slight
lateral flexion when unilaterally activated (see Figure 2.2). Elevated levels of spinal load with
the lumbar spine in a potentially vulnerable pose (reduced lordosis), has potential to be
associated with development of LBP (Dananberg, 1993). Additionally, lateral asymmetry in the
psoas muscle groups (intact hypertrophy, residual atrophy) has been observed in certain
individuals with TFA (Kulkarni et al., 2005), indicating asymmetrical reliance on the intact limb
psoas to perform hip flexion, and potentially less reliance on the residual side, where other hip
flexors may be producing increased hip flexor power.
Relative to able-bodied, individuals with a lower-limb amputation have altered spatiotemporal walking parameters. In particular, a slower self-selected walking speed (Hafner et al.,
2002; Kulkarni et al., 2005), and smaller ground reaction forces on the residual limb relative to
intact (Kulkarni et al., 2005), and in both limbs relative to able-bodied (Silverman and Neptune,
2011). A slower speed with lesser impulsive forces on the lower extremities has been associated
with a more guarded gait strategy and greater demands to maintain balance (particularly in the
frontal plane). Walking speed has been found to be the most frequently investigated gait metric
in pre-2011 amputee studies; however, nearly all focused on potential causative factors of slower
gait, rather than considering potential negligible affects of slower walking on other
biomechanics.
Associations between walking speed and trunk and pelvis kinematics during walking in
individuals with lower-limb amputation has been studied on a limited basis. One study measured
trunk-pelvis kinematics in individuals with TFA (n=27) across stride cycles of various speeds
(Goujon-Pillet et al., 2008). Results showed that mean trunk-pelvis transverse CRP during
35
strides was significantly lower in TFA relative to able-bodied, indicating an in-phase
coordination (Figure 2.1, Figure 1.1), strongly correlated with a decreased walking speed.
Frontal plane pelvic obliquity during stance was also significantly different between groups, with
greater inferior tilt towards the stance limb in individuals with TFA. A further similar study with
nearly identical design additionally computed variability of CRP to quantify dynamic movement
stability, and included TFA with/without LBP (Russell et al., 2013). In direct contrast to the
former work, mean CRP was not significantly different between able-bodied and pooled TFA in
the transverse plane, but was in the frontal (increased) and sagittal (lesser) (former work did not
compute CRP for frontal and sagittal). Variability in CRP was not different in any group
comparisons, nor did TFA with/without LBP differ in any metrics. Results of these two studies
in combination suggest that, irrespective of LBP ailment, lower-limb amputation results in
altered trunk-pelvis kinematics that are similar to those of able-bodied individuals with LBP.
Leg length discrepancy (LLD) in individuals with a lower-limb amputation has been
investigated with respect to secondary LBP.
Slight LLD is common even in able-bodied
individuals, and has been suggested to increase LBP susceptibility with greater discrepancy
(Gailey et al., 2008), although opinions vary. How LLD contributes to LBP in individuals with a
lower-limb amputation is not established, although altering length of the prosthetic pylon is
common clinical practice to attempt treatment for secondary LBP. Several case studies have
confirmed that LLD alteration was effective in decreasing (or eliminating) LBP for certain
individuals (Illes and Maola, 2012; Morgenroth and Shakir, 2009). Biomechanically, increasing
LLD can affect lateral tilting of the pelvis and frontal plane bending of the spine (Lee and
Turner-Smith 2003). Abnormal pelvic posture is a known risk factor for general, mechanical
LBP (Becker and Stumbo, 2013; Popovich et al., 2013). Greater medial/lateral impulsive ground
36
reaction force has also been observed in individuals with a lower-limb amputation, and has been
associated with LLD and/or attempts to alleviate residual limb pain (Kulkarni et al., 2005).
In summary, altered biomechanics during walking of individuals with a lower-limb
amputation are apparent.
Several differences are similar to those observed in able-bodied
individuals with LBP, relative to LBP-free, including: tighter transverse plane trunk-pelvis
coordination, greater overall trunk and pelvis transverse ROM, altered muscle recruitment
strategies, and a slower self-selected walking speed.
The few studies that have compared
walking of individuals with lower-limb amputation with/without secondary LBP, have found no
significant differences in segmental kinematics. However, forces in the low back (joint contact,
muscle group effort) that are known to be primary metrics associated with spinal stability, tissue
degeneration, and LBP, have not been explicitly investigated in individuals with a lower-limb
amputation. Limitations in clinical and laboratory means to measure such quantities in vivo
during dynamic movement have led to the lack of investigation in this area. Intriguing alternative
tools that can supplement experimental methods are reviewed in Section 2.3.
2.3.
Musculoskeletal Modeling and Simulation
Computational
modeling
and
rigid-body dynamic
simulation
of
the
human
musculoskeletal system has seen increasing development and application over the past several
decades.
Broadly, the methods involve application of an interconnected system of rigid
segments with anthropometry, mass/inertia, muscle anatomy, and muscle actuation properties
estimated to approximate in vitro and in vivo anatomy and physiology of the human body.
Experimentally
collected
data
including
motion
capture,
ground
reaction
forces,
electromyography, and medical imaging can be leveraged improve confidence in solutions, and
also to perform subject-specific studies. While several levels of complexity and formulation exist
37
and will be reviewed, generating a muscle-driven simulation refers to estimating a full set of
muscle forces capable of reproducing (in an inverse sense), or driving (in a forward sense), an
observed movement. Joint kinetics including reactions and powers may be of clinical or research
interest, and are also computed in this framework. Given the breadth of methods that have been
developed, a challenging task is the selection of appropriate modeling and simulation methods to
answer the research question. This section first reviews relevant background, advantages, and
disadvantages of the most common formulations (inverse/forward/hybrid dynamics), followed by
identification of critical methodological aspects involved with simulation of walking, the
complex spinal anatomy, and individuals with a lower-limb amputation.
The primary advantage of musculoskeletal simulation in contrast to purely experimental
laboratory methods is the ability to estimate unknown biomechanical parameters that may be
costly, difficult, or impossible to measure in vitro/vivo.
The basis of any muscle-driven
simulation is the dynamic equations of motion for a multi-articulated system. These relations can
generally be written as shown in equation (2.1),
C ,
where
,
e t
,
(2.1)
) are generalized system position, velocity, and acceleration respectively, M(q) a
collection of mass and inertial terms,
coriolis and centrifugal effects, G(q) gravitational
effects, R(q) a collection of muscular moment arms, FM individual muscle forces, and Fext any
applied external forces (Zajac et al., 2002). Inspection of equation (2.1) reveals the complexity
that any one muscle may affect the acceleration and power of any body segment, even those far
removed from the muscle itself. This phenomenon is referred to as dynamic coupling, and is a
consequence of a non-diagonal mass matrix upon inversion of equation (2.1).
38
Simulation frameworks are distinguished by the unknown and known quantities in
solution of equation (2.1). An inverse dynamic framework assumes motion
,
) and external
forces are known, and computes the necessary internal forces to achieve that motion. A forward
dynamic framework determines internal muscle forces through EMG-driven or optimization
methods, and proceeds to simulate resulting dynamic motion and external forces due to these
internal forces. Both methods have unique complexities, advantages, and disadvantages.
The solution of equation (2.1) can be computed without considering individual muscles,
and this is termed inverse dynamic analysis. The traditional Newton-Euler equations of motion
are iteratively solved along the chain of each segment in model, using known external forces and
discretely-derived joint kinematics
,
). Inverse kinematics may be a pre-requisite step, in
which laboratory measurements of experimental kinematic marker data are used to calculate
model joint angles (q) that best reproduce the motion. A least-squares optimization to minimize
the distance between virtual body markers and processed motion-capture data of optical skinmounted markers across the motion is typically sufficient to simulate whole-body walking,
although more robust methods may be warranted for joint-specific investigation, such as for
detailed knee study (Andersen et al., 2010a).
Due to error propagation from experimental sources (noise, skin artifact) nonphysiological, external forces and moments (residuals) are required between simulated ground
and the attached, proximal segment (usually the pelvis) to satisfy the dynamic equations of
motion. Methods have been developed to reduce the magnitude of the non-physiological forces,
such as a residual elimination algorithm (REA) (Thelen and Anderson, 2006) or a residual
reduction algorithm (RRA) (Delp et al., 2007). In broad summary, the mass properties of the
trunk or pelvis segment can be adjusted and the inverse kinematics solution slightly altered to
39
minimize residual forces and moments. Inverse dynamic methods are computationally efficient
and are implemented in numerous software packages, but terminate at the prediction of joint
intersegmental force. Inverse dynamics has proven useful in clinical settings to investigate
altered biomechanics during pathologic gait. However as a descriptive rather than predictive
approach, results must be interpreted carefully. Supplementing estimated joint torques with
concurrently measured EMG to form clinical conclusions of individual muscle function is not
recommended, due to unaccounted for dynamic coupling.
Therefore, extended methods exist to estimate individual muscle forces corresponding to
an inverse dynamics solution. When many muscles are added to the system, an over-determinate
system with more muscles than degrees of freedom is created. Static optimization techniques are
one means to resolve the redundancy problem (Tsirakos, 1997).
A nonlinear, constrained
optimization problem is typically formulated as,
minimize G(FM)
subject to (equation (2.1)
(2.2)
0 < aM < 1.0
where aM represent muscular activations, and the constraint enforces that muscles can only pull,
not push (Erdemir et al., 2007). To arrive at individual muscle force estimations across the
movement, the optimization problem is iteratively solved at each time step. The G(FM) function
is an objective criterion that should be chosen to represent a meaningful approximation of a
physiologically-based goal that is relevant to the movement being studied.
Various physiologic movement criteria have been proposed in the literature for certain
movements and sub-systems of the body. A comprehensive review is provided by (Tsirakos,
1997). For walking, common choices include minimizations of metabolic cost (Umberger,
40
2010), or polynomial functions of muscle activations. An accepted common objective function
for lower extremity walking has been the minimization of the sum of cubed muscle stresses
(current force normalized by cross-sectional area), which effectively minimizes muscular fatigue,
and has produced activation predictions that compare well with concurrent EMG during walking
(Crowninshield and Brand, 1981). Numerous functions have been used in spinal simulation; one
study compared minimization of cubed muscle stress, squared muscle stress, total joint
compression, and eigenvector synergy (a proposed measure of spinal stability) and found cubed
muscle stress to produce predictions in best agreement with measured EMG (Hughes and
Chaffin, 1994). Without adequate EMG for validation, confidence in solution is generally
limited by this step, where the unknown goals of the complex central nervous system are
essentially surmised. Furthermore, selection of an appropriate motor task is increasingly difficult
for individuals with pathology or pain, as an altered muscle recruitment goal is usually apparent,
such as in LBP (Arendt-Nielsen et al., 1996), and in individuals with a lower-limb amputation
(Fey et al., 2010). Nonetheless, static optimization approaches have proven useful in clinical
applications, such as in developing design inputs for total knee replacements (Andriacchi et al.,
1997).
Limitations of static optimization approaches have been suggested. Firstly, inverse
dynamics based static optimization is known to underestimate the total joint contact force, as
muscle co-contraction about a joint is generally not a system state found to be optimal by the
most popular objective criteria (Tsirakos, 1997). This is particularly significant with respect to
spine modeling, as significant flexor/extensor co-contraction has been observed experimentally
during demanding flexion/extension tasks (Granata et al., 2005), and also in individuals with
LBP (Hall et al., 2009). Secondly, muscular activation dynamics are difficult to include in the
41
framework, as the overall solution is independent of time. However, exceptions do exist that
have approximated activation dynamics in static optimization (Happee, 1994). Thirdly, forward
simulation of gait has been applied to show that intrinsic force-length-velocity properties are key
contributors to body support and stability during walking (Gerritsen et al., 1998).
These
phenomena are also difficult to include in the inverse framework and are often neglected in favor
of simple muscle models, although again, exceptions do exist that have successfully
approximated the three-element Hill muscle model in an inverse framework (Damsgaard et al.,
2006).
Static optimization has several prominent advantages relative to other methods. A
distinction between the joint intersegmental (or, resultant) and the total joint contact force must
be established. Joint intersegmental forces are caused by segmental accelerations and external
forces (i.g. GRF), and are those computed by iterative application of the Newton-Euler equations
in inverse dynamics. The joint intersegmental force underestimates the total joint contact force,
which additionally accounts for compressive forces due to spanning musculature and passive
structures (ligaments, cartilage). Static optimization accounts for the effect of muscles, and also
any passive structures modeled, thus obtaining a better estimate of total joint contact force.
Lastly, relative to forward approaches, static optimization is more computationally efficient, as
multiple integrations of the system equations are not required.
Forward dynamic optimization methods of simulation are different from inverse
dynamics based static optimization in several key areas. Firstly, equation (2.1) is rearranged to
solve for acceleration as a function of applied forces. By defining initial conditions of muscle
excitations and various constraints on system parameters, the equation can be integrated to
compute the resultant motion (Pandy, 2001). Development of forward dynamic methods for
42
musculoskeletal simulation began at the same time as static optimization, however forward
dynamics was most hindered by computational limitations, and thus inverse dynamic based static
optimization has seen more application. In contrast to static optimization, forward dynamics is
time-dependent, and thus both intrinsic muscle properties and activation dynamics are easily
incorporated into solution schemes (Erdemir et al., 2007). Also, the solution is less prone to
propagation of experimental measurement error, although possibly at the expense of less strict
kinematic tracking. Significantly, the forward dynamic versus inverse static methods have been
shown to produce highly similar estimations of both muscle forces and total joint contact forces
in the simulation of normal walking (Anderson and Pandy 2001). The authors also proposed that
if a study aims only to estimate muscle forces and associated joint contact forces, the use of the
computationally more demanding forward dynamic optimization is not currently justified.
Regardless, with continually increasing computational power, forward dynamics
continues to grow in popularity due to several unique analyses afforded through the problem
formulation. For example, forward optimal tracking has been applied to investigate individual
contributions of the biarticular gastrocnemius and uniarticular soleus to body support, forward
progression, and the hip intersegmental force during walking (Neptune et al., 2001; Zajac et al.,
2003). This category of analyses (induced acceleration analysis, IAA) is not possible in an
inverse static optimization framework. Contribution of individual muscles to segmental power
can also be elucidated with dynamic optimization. A single computed muscle power represents
the net power delivered and received to/from every segment in the system by the muscle, and can
be useful to assess muscle coordination principles (Zajac et al., 2002). Forward techniques
using optimal control comprise a further class of musculoskeletal simulations, and require only
initial muscle conditions with no experimental data. A primary benefit of optimal control is that
43
the entire motion is included in the optimization, thus, task-based optimization criteria can be
enforced, such as “move the trunk as smooth as possible” (Menegaldo et al., 2003). A more in
depth review of optimal control simulation is provided by (Pandy, 2001).
Hybrid inverse/forward approaches have also been developed and seek a middle ground
between the unique analyses afforded by through dynamic optimization, and the low
computational demand of static optimization.
One example is computed muscle control,
developed by (Thelen et al., 2003). In brief summary, computed joint kinematics are tracked
during a single forward dynamic optimization simulation solution of equation (2.1), minimizing
error between experimental and predicted joint angles. At each time step, a static optimization
solution is obtained to resolve muscle redundancy.
Computed muscle control has proven
particularly useful in the study of high pace and dynamic movements, and is also implemented
open source simulation software (Delp et al., 2007).
To generate muscle-driven simulations, a musculoskeletal model of the necessary
portions of the body must first be soundly constructed. A developing trend in the modeling
community is to share generic, whole-body models. Thus, detailed models with substantial
preliminary validation have been developed for several musculoskeletal sub-systems, and can be
modified with relatively minimal effort to serve the researcher’s purpose, such as subjectspecific simulation. This sharing process greatly accelerates biomechanical modeling research,
and also increases confidence within the clinical and industry communities in simulation as a
viable tool. Available lower extremity models differ primarily in the modeled musculature and
in some cases, accompanying software package. One example is the LowerLimb2010 model,
provided for free with OpenSim software and developed by (Arnold et al., 2010). The model
parameters (muscle anatomy, muscle composition) are compiled from 21 cadavers to represent
44
44 Hill-type muscles. A contrasting example is the TwenteLowerExtremity model, packaged
with the AnyBody Modeling System. In contrast to LowerLimb2010, all muscular and joint
parameters for this model were taken from a single, consistent donor dataset (Klein Horsman,
2007). As the AnyBody Modeling System is principally an inverse dynamics based static
optimization platform, increased muscle detail is represented, including 55 muscle groups
separated into 159 separate actuators. Lastly, in either model, joint definitions are approximated
to lesser degrees of freedom than in vivo, as is common practice in the whole-body simulation
literature.
Available models of the lumbar spine are much less prevalent in terms of generic
availability. Early spine simulation studies developed simple EMG-assisted inverted pendulum
models (Granata and Marras, 1993), and link-segment models of the low back including up to 66
muscle fascicles, to predict lumbar muscle forces (Kong et al., 1998). The most current and
detailed, generic spine models available also exist in implementations of OpenSim and AnyBody
(Christophy et al., 2012b; de Zee et al., 2007). Both models include the five lumbar vertebrae,
and resolve the individual kinematics as a function of net trunk-pelvis motion. In contrast to the
OpenSim models, the AnyBody low back model is integrated with the comprehensive
TwenteLowerExtremity model, allowing whole-body studies of human movement that include
the lumbar spine, and thus potentially investigations of low back biomechanics during walking.
Representations of passive IVD joint stiffness in both models are simple, linear approximations.
More robust, six-degree of freedom nonlinear stiffness models for use in rigid-body dynamic
studies have recently been proposed (Christophy et al., 2012a).
Computational modeling and simulation has been applied on several occasions to
investigate the altered biomechanics of individuals with a lower-limb amputation during
45
walking. In each case, findings have provided valuable information that may otherwise have
been unattainable using only traditional experimental methods. The primary focus has been
lower extremity alterations, thus an even smaller selection of these works have investigated low
back biomechanics. Only one study exists at the time of this writing that estimates in vivo low
back biomechanics of individuals with lower-limb amputation during walking. The subject pool
included 20 individuals with TTA, 20 TFA, and 20 non-amputees (Hendershot and Wolf, 2013).
Three dimensional kinematics and ground reaction forces were measured, walking overground at
a self-selected speed (average~1.35m/s). Intersegmental forces and moments in the L5S1 joint
were computed using both top-down and bottom-up inverse dynamics, and timing and magnitude
of peak forces/moments during stance of each limb were extracted. Comparing sets of results
between the top-down and bottom-up inverse dynamic approaches showed the two methods were
equivalent. Several significant differences in peak forces during the gait cycle were found
between individuals with lower-limb amputation, relative to non-amputees. The strongest group
differences were a greater maximum anterior force, and a lesser minimum posterior force, during
residual swing, and also a greater maximum lateral force during residual stance. The strength of
the difference increased for higher level of amputation (TFA vs TTA). As muscles were not
included in the analysis, the intersegmental joint forces/moments may have underestimated the
shape and magnitude of total joint contact forces/moments, due to the unaccounted for effects of
whole-body musculature (Zajac et al., 2002).
Also, subject parameters of age, time since
amputation, prosthesis type, and self-selected walking speed may be associated with low back
biomechanics, but potential effects of these parameters on the estimated metrics were not
investigated.
46
Another study used forward dynamic tracking simulation (sagittal plane only) to
investigate if contributions from energy storage and return prostheses (ESAR) and various
muscular compensations could produce normal, symmetric gait in unilateral TTA (Zmitrewicz et
al., 2007). Simulation results suggested that the prosthesis did contribute positively to trunk
support, but had slight, net negative contributions to forward propulsion and swing initiation. To
achieve symmetric gait, increased contributions to forward propulsion were required from the
residual limb rectus femoris and gluteus maximus during residual stance, and from the intact
limb soleus, gluteus maximus, and rectus femoris during early intact stance. Also, both the
residual and intact limb psoas had to deliver increased energy to the respective limb to initiate
swing. Since the simulation suggested a symmetric gait is physiologically attainable, but a
majority of individuals with TTA still walk with asymmetric gait, muscle atrophy and inhibited
sensory feedback may be more primary determinants of their gait strategy than previously
thought.
A further study applied forward dynamic simulations of TTA and non-amputee walking
to quantify contributions of the prosthesis, and of any muscular compensations, to numerous
whole-body gait parameters (Silverman and Neptune 2012). Averaged experimental data for
both individuals with TTA and non-amputees were supplied as the optimal tracking targets for
simulations. Simulation results suggested that the passive TTA prostheses did contribute to both
body support and residual limb braking in the absence of the ankle muscles, but did not
completely replace the function of the gastrocnemius to deliver energy to the residual limb for
swing initiation. Contributions of the rectus femoris and vasti to braking were reduced in
compensation of the elevated braking contribution from the prosthesis. Such compensations
47
have potential to be associated with LBP through dynamic coupling and unintended
biomechanical cascades that propagate to the low back.
In summary, the choice of framework and underlying modeling assumptions selected for
a study should be based on the specific research question being investigated, type of analyses
planned, and availability of experimental data. Both forward and inverse frameworks have
unique advantages and limitations, but have proven utility in developing unique findings
unattainable in experimental walking analyses alone. Further work investigating the associations
between altered walking strategies and low back biomechanics is motivated by these previous
successes.
2.4.
Finite Element Analysis of the Spine
Musculoskeletal dynamic simulation can estimate total joint reaction forces and rigid-body
dynamics. However, with respect to the passive tissues of the spine, distributions among facet
joints, the IVD, and ligaments are of interest. Finite element analysis of the spine allows such
investigations. Combination of the two methods in a multi-scale sense is of primary interest to
this work. To facilitate further discussion, a diagram of an anatomical FSU and a corresponding
finite element model is provided in Figure 2.4.
Tools for scientific investigations of the tissue-level low back biomechanics that address
the issues of in vitro and in vivo study are needed. The finite element method (FEM), originally
developed for civil and aeronautical structural applications, has first applications in
biomechanics reported as early as 1979 by Miller. The number of biomechanical and medical
studies published each year reporting FEM use has grown geometrically since initiation in the
80’s to approximately 1400 in 2009 (Erdemir et al., 2012). This growth is primarily because
FEM analyses overcome many limitations of in vitro and in vivo studies, but also because
48
relative to other discrete methods, FE robustly handles the complexities of nonlinear living tissue
and contact conditions.
(a)
(b)
Figure 2.4 - Anatomical FSU (a) compared to a representative finite element model (b).
Image (a) adapted from ilo.org
With respect to the spine, FEM is particularly well-suited to represent the spine’s wide
range of material properties, including nonlinear behavior of the IVD, complex bone geometry,
and articulation of the facet joints. Other structural constituents of the spine include bony
vertebral bodies, stabilizing elastic ligaments, and detailed musculature. With respect to tissue
level causes of LBP in individuals with a lower limb amputation, a brief review of FEM methods
that have been used to model spinal anatomy and degeneration is warranted. Recent uses of
musculoskeletal simulation in combination with FEM of the spine in a multi-scale sense are also
reviewed.
The IVD is a frequently addressed spinal component in terms of orthopedic surgery and
implantation and thus has an extensive backing in current FEM literature.
The level of
complexity used to model the disc varies with the specific research question. The IVD has been
modeled as a single component nearly as frequently as it has been a constituent of the larger
49
spinal assembly. The IVD in vivo is known to exhibit material inhomogeneity, anisotropy, and
porosity (Jones and Wilcox, 2008). Studies concerned with the dynamic response of the IVD
(e.g. design of total disc replacements) have developed methods to model stress relaxation,
creep, and viscoelastic effects. One study systematically compared results from three popular
FEM methods to model the IVD, to experimentally measured annulus fibrosis response (Yin and
Elliott, 2005). Compared methods included modeling of individual fibers within a homogenous
ground material, approximating a fiber-reinforced strain energy model, and a multi-scale
homogenization model of repeated volume elements.
The three methods approximated
experimentally measured annulus fibrosis properties equally well, and results suggested that any
of the three would be adequate for use in FEM studies of disc degeneration.
Studies incorporating multiple IVD’s into a complete L1-L5 lumbar spine have used
other models. Constitutive relations, such as the isotropic, incompressible hyperelastic MooneyRivlin material law, supplemented with in vitro cadaveric parameters are common (Schmidt et
al., 2007). The former study was able to approximate intradiscular pressures, fiber strains, and
shear strains that compared well with previously reported in vitro values. The greatest
stress/strain in the annulus was observed postereolaterally, elevated localized levels of which are
known to correlate with disc prolapse.
The geometry of the IVD is commonly simplified as axisymmetric in the sagittal plane
with flat inferior/superior surfaces. Segmentation analysis of medical image data to achieve a
more physiologically accurate shape is currently the state of the art (Jones and Wilcox, 2008).
The prior work by Schmidt reconstructed the IVD volume geometry from 0.49mm resolution CT
scan data. Current practice may be summarized as distinguishing between the nucleus, annulus
ground material (various sub-compartments), and annulus collagen fibers, using a combination
50
of the documented methods for material definitions and medical images to develop volume
geometry.
The bony vertebrae superior and inferior to an IVD are additional, significant
components of any spinal FEM model. The vertebral bodies exhibit variable bone density
throughout the volume and a slight, quantifiable elastic response.
Relative to the IVD,
representing the complex geometry accurately is perhaps the most significant challenge to this
component, and is much more crucial to resulting analyses since the geometry defines facet
joints and insertion points for numerous ligaments.
Development of methods to reliably
reproduce vertebral geometry from medical data has resulted primarily from studies that simulate
vertebral fracture and failure, where detailed response of the geometry constitutes the entirety of
analyses. Methods range in complexity from manually distinguishing between cancellous and
cortical density levels throughout the volume via sections of distinct elastic moduli, to automatic
distribution of inhomogeneous material properties based on image analysis (Jones and Wilcox,
2008). Automatic assignment of material properties via image analysis is done by correlating a
range of Young’s modulus to the range observed in a density parameter (e.g. CT Hounsfield
units) of a medical image, which distinguishes between bone regions. Image-analysis has been
suggested to result in a more realistic, total stiffness of the vertebral unit.
The finite elements used to construct the internal volume and external surfaces can vary.
Eight or twelve node brick elements appear most common in construction of bone volume (Jones
and Wilcox, 2008). As with prior modeling decisions, the required level of complexity in the
vertebral representation depends upon the research question being investigated. For example, in
analyzing soft tissue mechanics of a functional spinal unit (FSU) under low cyclical loading,
strains are likely orders of magnitude larger in the soft tissue than in the bone, and a reasonable
51
assumption may be to approximate the bones as rigid shells. Lastly, if vertebrae have been
imaged individually in vitro, accurate re-alignment of multiple computerized vertebrae into
original anatomical position (lordosis angle) remains a significant task.
Approximation of facet joint articulation and connective ligaments are additional
comple ities when modeling two or more SU’s.
apid development of multi-level lumbar
spine models only picked up in the last ten years (Jones and Wilcox, 2008). Therefore, methods
to model facets and ligaments are less frequently documented than for the IVD and vertebral
body. Experimental observations of spinal ligaments (flavum, intertransverse, interspinous,
supraspinous, capsular, etc.) have revealed nonlinear behavior, thus point-to-point non-linear
elastic elements connecting nodes of adjacent vertebral bodies, are common (Kurutz, 2010). For
example, the black elements depicted in Figure 2.4 are of this type.
Modeling facet articulation has been done using a broader range of methods. A
combination of an additional cartilage layer between inferior/superior articular processes,
variable-stiffness gap elements, and low-magnitude friction have all been applied in practice
(Jones and Wilcox, 2008). One different approach appears in a finite element study of facet load
transmission at the L2-L3 level due to axial compression (Teo et al., 2003).
To reduce
computational cost, the curved facet surfaces were discretized into 2D planar elements
coincident with underlying continuum solid elements, allowing sliding, surface contact with a
dynamically changing contact area. Frictionless, variable stiffness articular cartilage of 0.2mm
was also included on each surface.
The study produced results that compared well with
experimentally measured facet contact force during compression, although results were highly
sensitive to the simplified surface geometry in the presence of sagittal motion. Other authors
have confirmed this method as adequate for spinal compression studies, but inadequate when
52
predicting A/P sagittal shear or distribution of compressive stress, and thus suggest a supplement
to the method to include curvature effects (Holzapfel and Stadler, 2006). If possible, realistic in
vivo facet morphology should be preserved.
When modeling two or more SU’s, appropriate boundary and loading conditions to
represent physiological loading become increasingly complex. The L5 joint is separated by one
IVD from the relatively larger sacrum in vivo, and a fixed kinematic boundary condition applied
to the inferior endplate of the L5 vertebral body reasonably approximates this connection
(Kurutz, 2010). Idealized moments and force vectors are then applied to the most superior
endplate of the segment chain in the simplest loading case. This method can be augmented by
application of a load following lumbar spine lordosis angle (follower load), as an approximation
of physiological muscle action. Attempts have been made to fully replace the idealized forces
and drive the model individual muscle forces applied at anatomically relevant locations along the
lumbar spine (Rohlmann et al., 2006). The former study applied a follower load and idealized
moment to a lumbar spine FE model with defined muscle fascicle attachments, observing
resulting forces in the muscle elements. In comparison to current optimization methods, this
study is limited in that no physiologically based criterion was used to distribute muscle forces in
a meaningful way.
Current multi-scale methods instead use rigid-body musculoskeletal simulation and
optimization to first determine muscle force profiles corresponding to an observed movement.
After ensuring direct correspondence between models, individual muscle forces are subsequently
applied as finite element boundary conditions. This framework was first attempted almost a
decade ago (Kong et al., 1998), by determining finite element boundary conditions through
minimizing squared muscle stress in inverse dynamic static optimization of a muscle-actuated,
53
rigid-body model of the thorax.
Most recent applications of combined finite element and
musculoskeletal simulation include analysis of: hip implant loads during stand-to-sit (Kunze et
al., 2012), stresses in a femur during walking (Wagner and Divringi, 2010), cervical spine tissue
mechanics in response to neck rotation (Toosizadeh and Haghpanahi, 2011), stresses in a
vertebral body due to static lifting of a heavy object (Wong et al., 2011), and stresses in the IVD
due to trunk posture (Gadomski et al., 2011; Zhu et al., 2013).
A key consideration in multi-scale modeling is to limit error propagation due to exchange
of information between the finite element and rigid body model. With respect to the spine, a
source of such error may arise from applying muscle forces determined via a rigid body analysis
that uses fixed centers of intervertebral rotation (CORs), to a model with non-constant CORs and
elastic vertebral bodies. One study tested eight total combinations of elastic/rigid vertebrae,
fixed/variable CORs, and elastic/non-elastic posterior elements in a finite element spine model,
while applying muscle loads from inverse dynamics (Zhu et al., 2013). A maximum
disagreement of 2o between finite element and inverse dynamic predictions of intervertebral
rotation (IVR) was observed in the worst case (corresponding to 20o trunk flexion). A case with
non-fixed CORs, rigid vertebral bodies, and elastic posterior elements produced IVR predictions
within 0.5o. These findings are greatly beneficial to the developing area of multi-scale finite
element and musculoskeletal simulation.
An expansive and necessary body of work detailed in the literature, which supplements
developed biomechanical finite element models, are corresponding verification and validation
studies. In regards to modeling, verification questions whether the underlying theory is being
solved correctly.
In contrast, validation questions whether the selected theory adequately
represents the real phenomena being modeled. In terms of FEM, model verification is verified
54
by how accurately the discretized equations approximate the analytical equations. When using
commercial FE software, code verification is provided in the documentation as a reference,
however researchers must still show that final mesh resolution produces a converged solution.
Validation must be done against in vivo or in vitro measurements after producing results, in order
to make any valid clinical recommendations. Indirect validation by comparing finite element
results to results of other, comparable finite element studies that did validate against an
experiment is also an accepted method, although is not the ideal approach. Also, uncertainties in
material and boundary condition definitions for spinal finite element models typically warrant
sensitivity studies of primary outcome metrics to these input parameters (Jones and Wilcox,
2008).
Application of FEM to the study of spinal function is clearly an established area of work.
The strengths of FEM in representing the dynamic behavior of the spine serve well the
requirements of a tissue-level investigation of mechanical LBP mechanisms. Driving finite
element analyses with muscle loads determined though rigid-body musculoskeletal simulation is
has a short history, and maintaining model correspondence remains a current challenge.
However application of methods to investigate low back loading during gait, and to investigate
pain mechanisms of a patient population with altered gait (individuals with a lower limb
amputation) would both be novel developments.
2.5.
Summary
Collective literature findings provided motivation for an investigation of low back
biomechanics in individuals with a lower limb amputation during walking, via application of
musculoskeletal modeling and finite element simulations.
Based on discussions of LBP
mechanisms, quantities of trunk-pelvis relative kinematics, muscle forces in the low back, and
55
total joint contact force were identified as metrics that could be readily compared with previous
literature and clinical findings (see Sections 2.1.1, 2.1.2, and 2.1.3 respectively). Simulation
literature suggested that a static optimization framework would be sufficient to reliably estimate
these three metrics (Anderson and Pandy, 2001). Lastly the work performed and explained in
the following chapters established baseline data, biomechanical models, and simulation tools to
be part of a computational workflow with potential to be applied clinically in diagnoses and
rehabilitation of patients with biomechanical LBP (Figure 1.2).
56
3.CHAPTER 3
LOW BACK KINEMATICS, MUSCLE FORCES, AND JOINT CONTACT FORCES
DURING WALKING OF INDIVIDUALS WITH TRANSTIBIAL AMPUTATION
A paper to be submitted to the Journal of Gait & Posture
Adam J. Yoder1,2, Anthony J. Petrella, and Anne K. Silverman3
3.1.
Abstract
Individuals with a unilateral, below-knee amputation (TTA) have an increased
susceptibility to chronic low back pain (LBP) relative to able-bodied individuals.
While
individuals with TTA have numerous alterations in lower extremity body segment dynamics,
muscle recruitment, and joint kinetics during walking, a definitive cause of increased LBP
susceptibility has not been established. Thus, the purpose of this work was to compare dynamic
low back biomechanics during walking between individuals with and without unilateral, TTA
using computational modeling and simulation. Experimental walking data were used to scale a
generic, muscle-actuated whole body model with additional detail in the L1-L5 lumbar, and to
simulate gait with concurrent estimates of dynamic internal low back biomechanics.
Results showed several group differences in computed low back metrics during particular
phases of the gait cycle. Most significant in individuals with an amputation was greater lateral
range of axial trunk rotation near toe off of the residual limb was also found concurrently with
greater force in residual-side erector spinae and psoas. Repetition of such abnormal trunk motion
________________________
1
Graduate student, Associate Professor, and Assistant Professor, respectively, in the Department
of Mechanical Engineering, Colorado School of Mines.
2
Primary researcher and author
3
Author for correspondence
57
towards the residual-side during residual single limb stance, concurrently with greater intact-side
trunk muscle forces and a greater L4L5 lumbar joint contact force. A greater biomechanics over
time has potential to cause deficiencies in muscular endurance, strength asymmetries, inhibited
proprioception, and myofascial pain, each associated with increased susceptibility to chronic,
biomechanical LBP and other secondary musculoskeletal disorders.
3.2.
Introduction
Individuals with unilateral lower limb amputation have a greater prevalence of low back
pain (LBP) relative to the general population (Ephraim et al., 2005; Kulkarni et al., 2005). The
cause of this greater prevalence is not well-understood, but is thought to be a result of
biomechanical differences in the low back in contrast to potential degenerative etiologies (Burke
et al., 1978; Kulkarni et al., 2005).
Relative to non-amputees, individuals with transtibial
amputation (TTA) walk with altered body segment kinematics (Hendershot and Wolf, 2013;
Michaud et al., 2000; Rueda et al., 2013), lower extremity joint kinetics (Sadeghi et al., 2001;
Silverman et al., 2008), and dynamic muscle recruitment (Winter and Sienko, 1988). Many of
these reported biomechanical changes have potential to be associated with development of
secondary pain conditions. Asymmetric motion between the trunk and pelvis during walking of
individuals with a lower limb amputation (Hendershot and Wolf, 2013; Michaud et al., 2000;
Rueda et al., 2013), has been highlighted as a potential whole-body biomechanical factor that
contributes to development of biomechanical LBP (Devan et al., 2014).
Biomechanical evaluation of individuals with a lower limb amputation have focused
largely on lower extremity dynamics, and thus few studies reported findings of altered low back
biomechanics in individuals with a lower limb amputation. Reduced relative motion between the
trunk and pelvis in the transverse plane has been observed in individuals with TFA and no LBP,
58
relative to non-amputees (Goujon-Pillet et al., 2008). Individuals with TFA and concurrent
secondary LBP have greater overall trunk and pelvis ROM in the transverse plane during
walking, relative to TFA with no LBP (Morgenroth et al., 2010). Even fewer findings exist
regarding altered low back biomechanics in individuals with TTA, although relative to nonamputees, inhibited trunk proprioception (Hendershot and Nussbaum, 2013) and reduced
frontal/sagittal trunk stiffness have been found (Hendershot et al., 2013) in response to standing
perturbations.
Several biomechanical differences between individuals with and without an amputation
are similar to biomechanical differences between able-bodied individuals with and without LBP.
Tighter transverse trunk-pelvis coordination has been found in combination with more variable
frontal coordination in able-bodied individuals with LBP relative to LBP-free (Lamoth et al.,
2006b). Reduced low back proprioception resulting from muscular fatigue (Gandevia, 1994),
and decreased static trunk extensor endurance (Luoto et al., 1995) have also been associated with
increased susceptibility to biomechanical LBP in able-bodied individuals.
Further characterization of dynamic, in vivo low back biomechanics in individuals with
TTA during walking is needed to understand how LBP develops in this population. Dynamic
lumbar joint forces in individuals with and without a lower limb amputation during walking is
has only recently been explored (Hendershot and Wolf, 2013), although dynamic muscle
recruitment also plays a large role in biomechanical LBP development (Comerford and Mottram,
2001; Sato et al., 1999).
However, quantifying muscle and joint contact forces in vivo,
particularly during dynamic motions such as walking, is challenging. Whole-body
musculoskeletal modeling and simulation has proven utility in estimating biomechanical
parameters that may be difficult, costly, or impossible to quantify in vivo during dynamic
59
movement, including estimates of joint contact forces and forces produced by individual muscles
(Anderson and Pandy, 2001; Andriacchi et al., 1997; Sasaki and Neptune, 2010; Zajac et al.,
2003).
Thus, the purpose of this study was to compare low back kinematics, net lumbar joint
contact forces, and forces within primary low back muscle groups between individuals with and
without TTA during walking using computational modeling techniques. Based on known wholebody alterations reported in previous work, the hypothesis was that the three estimated low back
metrics would be different between groups, during particular discrete phases of the gait cycle.
3.3.
Methods
Walking mechanics of six individuals with unilateral, traumatic TTA and six able-bodied
individuals were selected from a larger, previously-collected dataset (Fey et al., 2010; Silverman
et al., 2008). Group characteristics of the selected participants are provided in Table 3.1. Each
individual with TTA wore their own passive prosthesis, with alignment and fit confirmed by a
prosthetist prior to data collection. All participants were skilled walkers and were free of
secondary musculoskeletal disorders and pain. The data collection protocol was approved by the
local Institutional Review Board and all participants provided informed consent prior to
participation.
The experimental protocol has been previously described in detail (Fey et al., 2010;
Silverman et al., 2008). Briefly, an eight-camera motion capture system (Vicon, Oxford Metrics)
was used to record three-dimensional kinematics of the lower limbs, pelvis and thorax (120Hz)
during overground walking. Muscle electromyography data were also recorded (1200Hz) via
surface electrodes (Motion Labs Inc.) on eight intact lower extremity muscle groups, including
the gluteus maximus (GMAX), gluteus medius (GMED), biceps femoris long head (BF), rectus
60
femoris (RF), vastus
lateralis, soleus, medial gastrocnemius, and tibialis anterior.
Electromyographic data were not collected from the soleus, gastrocnemius, and tibialis anterior
of the residual limb of people with TTA. Four concealed force plates (AMTI Inc.) embedded in a
10m walkway were used to record ground reaction forces (1200Hz). Trials that fell within
0.90±0.10m/s, and that contained three consecutive force plate hits containing a residual limb
gait cycle, were selected for inclusion in this work.
Table 3.1 – Mean (SD) of participant characteristics.
Age
[years]
Height
[cm]
Weight
[kg]
Time Since
Amputation
[years]
Prosthesis
Gender
(male/female)
Non-amputee
(n=6)
35.3
(12.6)
176.2
(6.6)
71.9
(15.2)
-
-
5/1
TTA (n=6)
43.7
(7.7)
173.7
(9.4)
90.9
(14.7)
5.0
(1.4)
4 SACH/
2 ESAR
5/1
3.3.1. Musculoskeletal Model
A generic whole-body model was used to represent each participant and investigate low
back biomechanics (AnyBody Modeling System v6.0, Model Repository v1.6, Aalborg,
Denmark, Figure 3.1). The lower extremity model has been validated for prediction of muscle
activity during gait, and has previously been applied to study gait of individuals with a transtibial
amputation (Voinescu et al., 2012). Each leg had seven degrees of freedom (DOF) and 55
muscle groups (163 fascicles). All lower extremity muscles were modeled as three-element Hill
actuators, with muscular properties (e.g., physiological cross-sectional area, optimal fiber/tendon
length, pennation angle) and anatomical paths based on a single, consistent donor dataset (Klein
Horsman et al., 2007). A version of the model with unilateral, transtibial amputation was created
61
(Figure 3.1) by replacing ankle musculature on the amputated side with passive ankle
dorsi/plantarflexion and inversion/eversion reaction torques. Mass and inertial properties of the
prosthetic shank were adjusted to represent an amputation (Mattes et al., 2000). To account for
effects of lower extremity ligaments and passive structures during gait, passive torques were
added at the knee, as an exponential function of knee joint angle (Audu, 1985).
Figure 3.1 - Whole-body musculoskeletal model. The prosthesis is represented by removed
ankle musculature and an adjusted shank center of mass location. Marker-based segment frames
for HAT and pelvis with respect to the laboratory global reference are shown.
The low back portion of the whole-body model contained five lumbar joints between S1
and T12, each with three DOF and fixed centers of rotation (de Zee et al., 2007). The model has
previously been validated for prediction of lumbar joint contact forces, against in vivo data
(Rasmussen et al., 2009). All segments superior to the L1-T12 joint were represented as a single
lumped-mass head-arms-torso (HAT) segment. The five individual intervertebral rotations were
constrained as a function of total, relative rotation between the HAT and pelvis segments. Eight
62
primary muscle groups (erector spinae, multifidi, semispinalis, quadratus lumborum, abdominal
obliques, transversus, rectus abdominus, origins of psoas major) were modeled with 188
fascicles (de Zee et al., 2007; Hansen et al., 2006). The walking speed simulated in this work
caused small ranges of lumbar segmental motion and negligible dynamic effects, thus inertial
properties of the vertebrae were assumed negligible and muscles were modeled as single force
elements with physiological cross-sectional area as input. Intra-abdominal pressure was modeled
as a variable extension moment on the spine, computed as a function of abdominal volume (de
Zee et al., 2007). Reactions due to passive spinal structures were modeled by linear reaction
torques at the five lumbar joints, with properties based on average, in vitro measurements of
intact spinal stiffness (Bisschop et al., 2013).
3.3.2. Simulation Framework
The modified generic model was scaled to each participant’s anthropometry by
optimizing model parameters (segment lengths, virtual marker set) to best fit an experimental
static standing trial, similar to Anderson et al. (2010). Total tendon-fiber length was scaled with
the body segments, and individual segment masses were computed as a percentage of total
measured body mass (Winter, 2009). Joint angles that best reproduced the gait cycle were
estimated using least-squares optimization between virtual and experimental markers across the
motion (Andersen et al., 2009), with optimal segment lengths and virtual marker locations fixed
from each subject’s static standing trial.
Inverse kinematic solutions and processed ground reaction forces were input into a static
optimization muscle recruitment simplex algorithm to compute total joint contact forces and
corresponding individual muscle excitations across the gait cycle. A fatigue-based movement
criteria previously validated for walking (Ackermann and van den Bogert, 2010), minimized the
63
sum of cubed muscle activations subject to dynamic equilibrium and physiological constraints on
muscle activity. Lower bound activity constraints were developed using EMG measured on
lower extremity muscle groups. Raw data were demeaned, rectified, and high pass filtered
(20Hz). RMS envelopes were computed and low-pass filtered (6Hz) to obtain smooth estimates
of excitation. To estimate activation, envelopes were uniformly shifted forward in time 15ms to
account for first-order activation/deactivation dynamics (Zajac, 1989) that were not included in
the muscle models. Following a preliminary analysis, residual forces and moments applied
between pelvis and ground were reduced by slightly increasing/decreasing the total mass
assigned to the HAT segment. The muscle recruitment algorithm was then applied to the
adjusted model.
3.3.3. Data Analysis
Primary outcome metrics included HAT-pelvis relative rotation, computed using an Euler
Z-Y-X rotation sequence (sagittal bending - transverse rotation - frontal bending) of HAT
relative to pelvis (Figure 1). Total joint contact force between the L4 and L5 vertebral segments
due to all spanning musculature was resolved along each of the three anatomical directions (force
on the L4 body w.r.t to L5). Modeled muscle fascicles were collected into four primary low
back muscle groups (erector spinae, psoas major, internal+external obliques, quadratus
lumborum), and total forces within muscle groups were computed by summing all fascicle
forces.
Time series of the primary outcome metrics extracted from the model (trunk-pelvis
relative angles, L4L5 joint contact forces, low back muscle forces) were time-normalized to 0100% of the gait cycle. Average and range values of each outcome metric during four discrete
phases of gait were computed for each individual: residual single-limb stance (~15-50%),
64
residual swing (~65-100%), and both double support phases (~0-15%,~50-65%). TTA and nonamputee outcome metrics were compared using two-sample unpaired t-tests (α 0.05) between
groups, testing for significant differences in average or range values for each outcome metric
within each phase of gait.
3.4.
Results
Across all simulations, gait cycle marker tracking errors within inverse kinematic solutions
were low, with all below 2.0cm and a study RMS-gait cycle average of 9.7mm. Residual forces
and moments were also low, with RMS averages across the gait cycle of 3.1, 3.5 and 5.7%BW
for anterior/posterior, medial/lateral, superior/inferior forces respectively, and 2.2, 3.3 and
0.8%BW-m for frontal, sagittal, transverse moments, respectively. In review of simulated muscle
activity, contractile force production of those lower extremity muscles with constrained activity
showed excellent qualitative agreement with raw, filtered EMG signals.
3.4.1. Trunk-Pelvis Kinematics and Low Back Joint Contact Force
Three primary kinematic differences were observed in the frontal and transverse planes
(Figure 3.2, Table 3.2). Individuals with TTA had greater lateral bending toward the residual
limb during residual single-limb stance (p=0.006) and second double-limb support (p=0.005),
and also had a greater range of transverse rotation during both double-limb support phases
(p=0.003,0.029).
In general, low back joint contact forces were similar between groups in all three
directions (Figure 3.2, Table 3.2). Individuals with TTA had a greater average L4L5 joint
contact force in the superior/inferior direction during residual single-limb stance (p=0.022). In
addition, the range of superior/inferior force during second double-limb support and residual
limb swing in individuals with TTA approached significance (p<0.10).
65
Figure 3.2 - Group average results for trunk-pelvis relative angle (left), and L4L5 joint contact
force (right), throughout the gait cycle. Significant group differences (p<0.05) in either average
(AVG) or range (RNG) during discrete phases of gait are distinguished (*).
66
Table 3.2 - Group mean (SD) of outcome metrics that were significantly different (*), or that
approached significance, in average (AVG) or range (RNG) during a phase (PHS) of gait. Phases
correspond to ipsilateral (residual) limb stance (ST), swing (SW), and first/second doublesupport limb (DS1,DS2).
Metric
TrunkPelvis Angle
Frontal Bending
Transverse Rotation
Superior/Inferior
Ipsilateral
Joint
Contact
Force
DOF/Muscle
Erector Spinae
Psoas Major
Obliques
Contralateral
Low Back
Muscles
Erector Spinae
Psoas Major
Quadratus
Lumborum
Obliques
PHS QTY
ST AVG
DS2 AVG
DS1 RNG
DS2 RNG
TTA
Non-amputee
[deg., %BW] [deg., %BW]
p-value
3.8(1.8)
0.0(2.8)
3.3(1.1)
3.1(1.7)
0.6(1.8)
-4.0(1.4)
1.4(0.8)
1.4(0.4)
0.006*
0.005*
0.003*
0.029*
ST
DS2
SW
DS1
DS2
SW
SW
DS1
DS2
SW
DS1
ST
ST
AVG
RNG
RNG
RNG
RNG
RNG
RNG
RNG
RNG
AVG
RNG
AVG
AVG
88.4(5.7)
32.7(11.3)
60.2(19.0)
18.6(8.1)
37.4(21.9)
38.7(13.7)
16.6(7.9)
13.6(6.8)
16.1(4.0)
14.7(2.4)
31.2(16.1)
22.1(7.4)
10.8(3.5)
81.3(5.0)
22.3(11.8)
45.4(8.9)
11.4(6.1)
16.4(9.8)
24.8(9.6)
8.8(1.6)
9.3(3.2)
9.4(3.5)
12.1(3.6)
15.9(10.4)
16.5(4.0)
7.6(3.5)
0.022*
0.075
0.057
0.055
0.029*
0.034*
0.029*
0.096
0.006*
0.085
0.041*
0.066
0.072
DS1
RNG
4.8(1.6)
2.1(1.2)
0.003*
DS1 RNG
ST AVG
13.0(2.7)
18.0(3.9)
9.6(3.7)
11.6(3.1)
0.049
0.005*
67
3.4.2. Low Back Muscle Forces
There were several differences in muscle forces between groups (Figure 3.3, Table 3.2).
On the ipsilateral (residual limb) side, individuals with TTA had a greater range of force within
the erector spinae (p=0.029) and obliques (p=0.006) during second double-limb support. During
residual limb swing, the ipsilateral erector spinae (p=0.034) and psoas major (p=0.029) also had
a greater range of force production. On the contralateral side, individuals with TTA had a
greater range of force within the erector spinae (p=0.041) and quadratus lumborum (p=0.003)
during the first double-limb support phase. Also on the contralateral side, individuals with TTA
had greater average force within the obliques during residual limb stance (p=0.005).
3.5.
Discussion
The purpose of this study was to compare low back kinematics, net lumbar joint contact
forces, and forces within primary low back muscle groups between individuals with and without
a transtibial amputation during walking. Numerous significant differences in these metrics
between groups were found, and most occurred concurrently during specific phases of gait.
Kinematic and joint contact force results were consistent with results from comparable
modeling studies that have investigated low back kinetics during walking (Callaghan et al.,
1999; Hendershot and Wolf, 2013; Khoo et al., 1995).
In addition, a range for in vivo
intervertebral reaction force during gait was estimated from reported in vivo L4L5 intervertebral
pressures measured during walking (Wilke et al., 1999), by using a mean suggested correction
factor of 0.66 for transforming between intervertebral pressures and contact force (Dreischarf et
al., 2013). This yielded 91-112%BW, which supported simulated group average resultant L4L5
joint contact forces, of 91%BW (TTA) and 87%BW (non-amputee) across the gait cycle.
68
Figure 3.3 – Group average results for cumulative force within ipsilateral (top) and contralateral (bottom) low back muscle groups
throughout the gait cycle. Significant group differences (p<0.05) in either average (AVG) or range (RNG) during discrete phases of
gait are distinguished (*).
69
Individuals with TTA had greater lateral bending toward the residual limb throughout
residual limb stance (Figure 3.2, Table 3.2).
Similar results for frontal-plane bending were
found in previous walking analyses of both transfemoral (Jaegers et al., 1995) and transtibial
individuals (Michaud et al., 2000; Rueda et al., 2013). Prior authors suggested that greater
lateral bending may be a mechanism to compensate for weak or missing hip abductors on the
residual limb. However, even small lateral displacements of the trunk mass, that accounts for
over half of total body weight, could place elevated demands on contralateral musculature
(primarily paraspinals, obliques, quadratus lumborum) to maintain trunk posture and dynamic
balance during walking. The most significant muscular difference in results of this work was a
greater concurrent force from the contralateral obliques in individuals with TTA (Figure 3.3).
This finding supports speculative hypotheses of previous work that found similar kinematic
differences, but did not model musculature (Hendershot and Wolf, 2013; Rueda et al., 2013).
Repetitive elevated muscle forces over time, may be associated with mechanical LBP, through
fatigue of abdominals and resulting strength asymmetries between trunk flexors/extensors
(Comerford and Mottram, 2001).
Elevated activity of the external obliques in combination with normal levels of the erector
spinae, has been observed in able-bodied individuals with LBP (relative to LBP-free) performing
trunk sagittal flexion (Silfies et al., 2005). Such an asymmetrical recruitment strategy has
potential to affect lumbar spine loading. The single group difference in joint contact force also
occurred concurrently during residual stance, as a greater superior/inferior force in individuals
with TTA (roughly 8%BW difference between groups, Table 3.2). A combined motion and
loading scenario of (lateral bending + axial rotation + superior/inferior compression), relative to
single-DOF motions and loadings, has experimentally been found to cause the greatest structural
70
stresses on passive soft tissues in cadaveric work during simulated pelvic obliquity (Popovich et
al., 2013).
Individuals with TTA also had concurrent, greater ranges of force within residual-side
erector spinae and psoas, near toe off of the residual limb. Also near residual limb toe off, a
greater range of superior/inferior force in individuals with TTA near residual limb toe off
approached significance (p=0.057, Figure 3.2, Table 3.2). Greater residual limb hip flexor
moments and powers near residual toe off have previously been observed in individuals with
unilateral TTA (Sadeghi et al., 2001). The psoas can provide a hip flexion moment, spine
compression, and spinal lateral bending, however increased force output to initiate swing in
compensation of missing ankle musculature has potential to increase load on facet joints and the
IVD beyond normal levels (Dananberg, 1993).
Potential explanations for the elevated range of force from the intact-side erector spinae
and quadratus lumborum following residual heel strike, in individuals with TTA, are less clear
(Figure 3.3). Both muscles are capable of generating frontal plane moments away from the
residual limb. Similar to the supposed concentric function of the contralateral obliques during
residual stance, these muscles may be responsible for eccentrically modulating trunk motion as
both lateral flexion and axial rotation increase towards the residual limb, more rapidly in
individuals with TTA (Table 3.2).
Decreased, bilaterally-asymmetric frontal
plane trunk
stiffness has been found in individuals with unilateral, lower limb amputation when responding
to standing perturbations (Hendershot et al., 2013).
Trunk stiffness is known to have
dynamically changing, relative contributions from active trunk musculature and passive
structures, based on posture and type of motion. Asymmetry in bi-lateral psoas muscle tone has
been found in medical imaging of certain individuals with a lower limb amputation (Kulkarni et
71
al., 2005). These hip asymmetries, and other potential differences in deeper, stabilizing trunk
musculature, were highlighted as potential causes of the decreased and asymmetrical trunk
stiffness. Here, the asymmetrical usage of contra/ipsilateral oblique musculature during
respective stance phases may also affect dynamic trunk stiffness.
Later in the gait cycle, the significantly greater range of force within residual-side
obliques (DS2, 6.7%BW difference, Table 3.2) may be driving the more rapid, axial rotation of
the HAT back towards the intact limb during residual pre-swing. Previous work that measured,
average trunk-pelvis relative ROM in the transverse plane during walking of individuals with
TFA, both with/without LBP, observed no significant differences relative to LBP-free ablebodied controls (Morgenroth et al., 2010). The lack of significant differences observed by
Morgenroth (2010) agrees with the findings of this work, where trunk-pelvis transverse ROM
was similar between LBP-free individuals with and without TTA, throughout all four phases of
gait.
The numerous muscular differences found in this study have potential to be associated
with development of musculoskeletal spinal disorders.
An previous observation made in
physical examination of individuals with lower limb amputation (n=42) was a distinct prevalence
(43%) of scoliosis in medical examination of individuals with unilateral, lower limb amputation
(Burke et al., 1978). Adult onset, idiopathic functional scoliosis is associated with muscle
fatigue and abnormal recruitment of particular muscle groups (quadratus lumborum, psoas,
external oblique), and is commonly associated with confounding chronic, nonspecific LBP. The
apparent, altered muscular recruitment of individuals with TTA also supports a previous
hypothesis that a majority of LBP in individuals with lower limb amputation is myofascial,
rather than degenerative (Kulkarni et al., 2005).
72
A particular, comparable modeling study (Hendershot and Wolf, 2013) applied inverse
dynamics to estimate intersegmental forces and moments in the low back and suggested
additional, potential differences in low back biomechanics of individuals with a lower limb
amputation (20 TTA, 20 TFA). Differences in peak L5S1 forces in individuals with transtibial
amputation relative to able-bodied individuals, were suggested: greater anterior force and lesser
posterior force during residual swing, and greater lateral force during residual stance. In results
of this study, anterior/posterior forces were consistently directed anteriorly throughout the gait
cycle (Figure 1), and did not differ in average value between groups. Differences in findings
may due to a combination of differences in methodology and recruited subject pool.
Intersegmental joint forces/moments from inverse dynamics underestimate total joint contact
forces/moments from muscle-driven simulations, due to the unaccounted for effects of wholebody musculature (Zajac et al., 2002). In addition relative to this work, the recruited subject pool
was notably younger with shorter time since amputation and faster self-selected walking speed of
~1.35m/s (Table 3.1). Collective differences between current and former findings suggest that
low back biomechanics in individuals with a lower limb amputation are affected by dynamic
muscle recruitment, age, time since amputation, and walking speed.
This study had several limitations. Firstly, inverse-dynamics based static optimization
does not facilitate quantification of individual muscular contributions to whole-body metrics,
such as total joint forces and moments.
Future work should apply a forward dynamics
framework that would enable decomposition of low back joint contact forces into individual
muscular contributions (e.g. Sasaki and Neptune, 2010). Secondly, while the upper extremity
experimental marker protocol was sufficient to quantify overall low back kinematics, future
work may consider using additional instrumentation with greater precision in measuring
73
dynamic, in vivo intervertebral kinematics, such as biplane fluoroscopy (Lin et al., 2014). Lastly,
concurrent low back surface EMG was not collected as part of the experimental protocol for
comparison against simulated low back muscle activity. However, lower extremity activations
agreed well with corresponding EMG prior even to applying optimization constraints. Thus,
there is reasonable confidence in low back muscular activity. Future work should supplement
experimental lower extremity protocols with low back surface EMG measurements to include
erector spinae, external obliques, and rectus abdominus.
Ultimately, this study identified abnormal, dynamic biomechanics internal to the low
back during walking in individuals with transtibial amputation. These findings contribute to a
long-term goal to identify biomechanical mechanisms that elevate LBP susceptibility in
individuals with a lower limb amputation, and ultimately to inform effective clinical
interventions to rehabilitate biomechanical LBP. As the subject pool for this study excluded
individuals with current LBP, the presented data can be leveraged as a baseline in future
investigations that may include individuals with LBP and additional group factors of potential
interest, such as time since amputation and prosthesis type. The utility of additional low back
biomechanical metrics, such as distribution of total forces among passive spinal structures, to
distinguish between individuals with/without a lower limb amputation and with/without
secondary low back pain should also be investigated.
74
4.CHAPTER 4
SIMULATION AND MODEL DETAILS
The generic, whole-body musculoskeletal model (Model Repository v1.6, AnyBody
Modeling System v6.0) described in Chapter 3 required further mortifications beyond the scope
of the manuscript. In depth details on these modeling and simulation components are discussed
in this chapter.
4.1.
Additional Musculoskeletal Model Background
The lower and upper extremity models are shown in Figure 4.1. The model named
“ oCap odel” in the AnyBody
odel
epository was used as the basis for this work.
Modifications to the shank portion of the lower extremity model to represent amputation are
shown, including: translation of the center of mass closer to the knee joint, reduction of the total
shank mass by 25%, and removal of all ankle-spanning musculature. Also, the virtual marker set
was reproduced on the AnyBody model to agree with the experimental protocol (Figure 4.1).
For both parts of the model, comprehensive definition of musculature existed in the
generic distribution of the repository model. A listing of the modeled muscle groups is provided
in Table 4.1 for the upper extremities and Table 4.2 for the lower extremities. Also, a full
reporting of individual subject parameters is provided in Table A.1 of Appendix A (expanding
on (Table 3.1).
4.2.
Simulation Settings & Parameter Optimization
For each subject simulation, experimental data files (.c3d) with kinematic and ground
reaction forces were imported directly into AnyBody.
Timing of gait events for each subject
were determined using automated event detection in Visual3D (Stanhope et al., 1990). For
inverse kinematics and dynamics simulations, time steps were set equivalent to number of frames
75
(a)
(b)
(c)
Figure 4.1 – The generic musculoskeletal model (MoCapModel, Model Repository v1.6,
AnyBody Modeling System v6.0). The lower back model (a) and lower extremity (b) are
paired together to allow whole-body simulation. The experimental marker set applied
virtually to the model (c).
76
Table 4.1 – Modeled lower extremity muscle groups in generic lower extremity model.
Musculature removed in the transtibial amputation version are shaded.
Lower Extremity Muscles
Adductor Brevis Proximal
Gluteus Medius Posterior
Adductor Brevis Mid
Gluteus Minimus Anterior
Adductor Brevis Distal
Gluteus Minimus Mid
Adductor Longus
Gluteus Minimus Posterior
Adductor Magnus Distal
Gracilis
Adductor Magnus Mid
Iliacus Lateralis
Adductor Magnus Proximal
Iliacus Mid
Biceps Femoris Caput. Longum Iliacus Medialis
Biceps Femoris Caput. Breve
Obturator Externus Inferior
Extensor Digitorum Longus
Obturator Externus Superior
Extensor Hallucis Longus
Obturator Internus
Flexor Digitorum Longus
Pectineus
Flexor Hallucis Longus
Peroneus Brevis
Gastrocnemius Lateralis
Peroneus Longus
Gastrocnemius Medialis
Peroneus Tertius
Gemellus Inferior
Piriformis
Gemellus Superior
Plantaris
Gluteus Maximus Superior
Popliteus
Gluteus Maximus Inferior
PsoasMinor
Gluteus Medius Anterior
Psoas Major
Quadratus Femoris
Rectus Femoris
Sartorius Proximal
Sartorius Distal
Semimembranosus
Semitendinosus
Soleus Medialis
Soleus Lateralis
Tensor Fasciae Latae
Tibialis Anterior
Tibialis Posterior Medialis
Tibialis Posterior Lateralis
Vastus Intermedius
Vastus Lateralis Inferior
Vastus Lateralis Superior
Vastus Medialis Inferior
Vastus Medialis Mid
Vastus Medialis Superior
Table 4.2 – Modeled trunk muscle groups. Number of fascicles per group represent divisions in
lines of action to represent muscle with large surface area.
Muscle Group
Rectus Abdominus
Transversus
Multifidus
Erector Spinae
Spinalis
Iliocostalis lumborum pars lumborum
Ilicostalis lumborum pars thoracis
Longissimus thoracis pars lumborum
Longissimus thoracis pars thoracis
Psoas Major
Quadratus Lumborum
Obliqus Externus
Obliqus Internus
Thoracic Multifidi
Semispinalis
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#Fascicles
1
5
19
3
4
5
8
12
10
5
6
6
10
8
between identified start and stop times, coinciding with initial and final ipsilateral heel strike.
For model parameter optimization trial runs, prior to inverse kinematics (both static standing and
gait trials, for each subject), time increments were set to one-sixth of the motion frames to
increase computational efficiency (Andersen et al., 2010b).
The model parameter optimization procedure applied in this work is unique to the
AnyBody Modeling System. An in-depth description of algorithm development is provided by
(Andersen et al., 2010b). Briefly, model parameters that the researcher may have low confidence
in can be optimized to obtain a robust inverse kinematic solution that improves dynamic
consistency of the model with the measured experimental data; for this work, relative location of
virtual motion markers within segment frames, and length of rigid body-segments. For motion
markers, any of the three translational degrees of freedom can be held fixed (in directions of high
confidence), or be optimized (in directions of least confidence). As an example, consider the left
iliac crest marker, shown in Figure 4.2. One may be reasonably confident that the crest is near
frontal-plane zero and at a fixed height superior from the anterior superior iliac spine marker.
However, the position within the frontal plane may be relatively less certain, due to unknown
amounts of soft tissue around the abdomen, with high variability between each individual.
Therefore, the marker can essentially be constrained along a line in the frontal plane, by fixing
the “X” and “Y” directions, and assigning “Z” to be optimized, as depicted in Figure 4.2. This
process is highly useful for shank and thigh cluster markers, where essentially no sense of
position relative to bone and joint axes are known with confidence, so all three directions can be
optimized (notice the large displacements in these markers before and after optimization, Figure
4.2). Desired segment lengths can also be optimized, and all were in the static standing trial.
Lastly, using this process only on the static standing trial to determine all subject parameters to
78
be held fixed for gait, mitigates to some degree potential errors from skin artifact during motion.
An example for a representative subject before and after parameter optimization is shown in
Figure 4.3.
(a)
(b)
Figure 4.2 –Optimization settings for the iliac crest marker, with green representing the degree of
freedom can change, and red representing a fixed condition.
Little guidance is offered by the AnyBody developers on specification of optimization
settings to optimize a virtual marker set (Andersen et al., 2010b).
Custom, standardized
optimization settings were developed based upon the experimental protocol, and applied
consistently across subjects. These settings are reported in Table C.1 of Appendix C. With
subject-specific, optimized parameters determined from the static trial, inverse kinematics
solutions were computed as described in the manuscript (Chapter 3). To additionally mitigate
error propagation in this step, tracking weights to apply during least-squares difference
optimization between virtual and experimental markers were assigned for all subjects as reported
in Table C.1 of Appendix C.
79
(a)
(b)
Figure 4.3 – Example of model parameters (a) before, and (b) after applying the optimization
sequence with the optimization settings reported in Table C.1 of Appendix C. For this
representative subject, notice in particular the shortening of the thigh and shank segments, and
the narrowing of the pelvis.
80
(a)
(b)
Figure 4.4 – Minimization of marker tracking errors to <20mm, for a representative subject.
Results from a static trial (a) indicate how far off markers remain after applied parameter
optimization. The relatively higher errors during the gait trial (b) indicate effects of skin artifact
and errors associated with modeling assumptions.
81
4.3.
Muscle Fiber and Tendon Calibration
The implementation of the three element Hill muscle model requires a defined length of
the tendon at which force begins to develop upon stretch (tendon slack length). These
parameters are defined in the generic model based on the cadaver dataset. However, tendon
slack length may also be assumed to vary per individual, and for this work a suggested
calibration process was applied to determine these slack lengths. This is done by, after subject
specific segment lengths have been optimized and fixed, making an assumption that each muscle
group should develop optimal force (or, moment about a joint) in a certain, functional joint
position. This calibration process is similar to methods proposed by Delp (1990), for
determining tendon slack lengths. Calibration poses and muscle groups calibrated in each pose
are defined in Appendix B.
4.4.
Joint Angle Conventions
Rotational kinematics between the trunk and pelvis segments were computed using an
Euler rotation sequence between two marker-based frames Figure 4.5. No clinically-meaningful,
anatomical reference frames are defined in the generic model, so custom frames were created
based on ISB recommendations (Wu et al., 2005, 2002). The pelvis frame was defined so that
the +Z axis ran from the right anterior-superior iliac spine to the left anterior-superior iliac spine,
+X axis point anterior along the line from midpoint of the left and right posterior superior iliac
spines to the midpoint of the left and right anterior-superior iliac spines, and the +Y axis normal
to the XZ plane and pointing superior. The thorax frame was defined so that the +Z axis ran
from the left acromion to the right acromion, +Y axis pointing superior along the line from the
midpoint of the iliac crests to the midpoint of the acromia, and +X axis normal to the ZY and
pointing anterior. Resulting Euler rotation sequence of the local thorax frame relative to the
82
fixed global pelvis was then defined as Z-Y-X for flexion(-)/extension(+), followed by
left(+)/right(-) axial rotation, followed by left(-)/right(+) lateral bending. As frames were based
on end-position of virtual markers, naturally occurring anatomic tilt or obliquity of the pelvis
could cause a static offset in the Euler angle. Therefore, angles during static trials were recorded
during the parameter optimization process, and later subtracted from gait angles to normalize
kinematics to quiet standing.
Figure 4.5 – Representation of frames created to measure thorax 3DOF rotation relative to pelvis.
Each frame is based on position of virtual markers in the model, rather than model anatomical
landmarks.
The L4L5 total joint contact forces were computed within the inverse-dynamics based
static optimization framework by resolving translational reaction forces at the 3DOF spherical
83
joint. The effects of all spanning musculature were implicitly accounted for when solving the
system equations (2.1). The joint coordinate system is shown in Figure 4.6. Joint contact forces
were computed with respect to the proximal segment frame (L5), as forces applied on the distal
segment (L4).
Figure 4.6 – Joint coordinate system in the L4L5 joint for measurement of total joint contact
force. Contact forces are measured with respect to the proximal L5 frame, as forces on the distal
L4 body. The red center indicates the estimated, constant center of intervertebral rotation.
4.5.
Lower Extremity EMG constraints
To develop the lower bound constraints from recorded lower-extremity EMG, a custom
MATLAB script was created. The open source MATLAB toolbox c3dserver was used to input
analog voltage data from c3d files. Raw signals (1200Hz) were sequentially demeaned, rectified,
and bi-directional high pass filtered at 20Hz. A moving RMS 80ms window (using convolution)
was then applied to the partially processed data to obtain an envelope. The envelope was bidirectional low pass filtered at 4Hz to obtain a smoothed envelope acceptable as a signal for
simulated activation. Lastly, the all envelopes (for all muscle groups, irrespective of fiber twitch
composition) was shifted forward in time 15ms (Zajac, 1989) to represent first-order activation
dynamics not accounted for in the static optimization framework. Results for a representative
84
subject’s contralateral gluteus medius are shown in Figure 4.7. Complete results for all subject
simulated muscle activations compared to original EMG signals are provided in Appendix D.
Smoothed and shifted envelopes were resampled for each subject to the necessary time
duration corresponding to the gait cycle simulation window. As a final step, each signal was
scaled to a realistic muscular activation on a 0.0-1.0 scale. To accomplish this, all static
optimization simulations were completed to obtain relative estimates of activity in the muscle
group with no constraints. As an initial guess, the maximum occurring voltage value in the gait
cycle window was normalized to the maximum observed value in the simulated results, unless
that value fell below 0.20, in which case 0.20 was used.
Within the AnyBody software,
constraints were applied using a parameterized beta spline function, and applied to all muscle
fascicles with the muscle group.
Figure 4.7 – Processing steps to compute EMG-based lower bound activation constraints, applied
to a representative contralateral gluteus medius signal.
85
5.CHAPTER 5
FINITE ELEMENT LUMBAR SPINE GEOMETERY
FOR MULTI-SCALE SIMULATION
Attempts to perform finite element simulation in combination with muscle-actuated, rigid
body dynamic simulation have previously been described in the literature, and have shown
potential to facilitate investigations of total joint contact force and moment distribution among
passive, structural tissues during realistic activities of daily living. A primary issue in the
development of these multi-scale simulations is disagreement in predicted kinematics between
the two simulations, due to a mismatch in model constituents. In particular, discrepancies in
geometry, and structural parameters (e.g. total passive joint stiffness), can lead to errors (Zhu et
al., 2013). Therefore, the purpose of this work was to explore subject-specific scaling of lumbar
spine muscle attachments to fit generalized, vertebral geometry for the finite element portion of a
multi-scale simulation framework.
5.1.
Methods & Results
A cadaver-based L1-L5 finite element model constructed from medical imaging data is
shown in Figure 5.1. This model was part of a previous
aster’s thesis in the Colorado School
of Mines Department of Mechanical Engineering, within the Computational Biomechanics
Group (Huls, 2010). The model contained all five vertebrae modeled as rigid shells, in addition
to facet cartilage at two joint levels, nonlinear ligaments at all levels, and four intervertebral
discs. The bone geometry (rigid, quadrilateral shell elements) was extracted and is shown in
comparison to the generic bone geometry in the AnyBody lumbar spine model (Figure 5.2). In
contrast to the cadaver-based geometry, the AnyBody geometry is based on a single sagittallysymmetric vertebrae, which is duplicated at all five vertebral levels.
86
(a)
(b)
Figure 5.1 – Cadaver-based L1-L5 finite element model used as the basis for multi-scale
simulation work (Huls, 2010), from lateral (a) and frontal (b) views.
(a)
(b)
Figure 5.2 – Bone geometry from the AnyBody model (a, brown) in comparison to the cadaver
bone mesh (b, blue). The red spheres in the AnyBody model distinguish approximated, constant
intervertebral joint centers.
87
Preliminary, qualitative comparisons of the two spinal geometries suggested significant
differences in overall size, along with morphological differences in facets, spinous processes,
and transverse processes (Figure 5.2). While such differences would be expected in comparison
of any two individuals’ spinal geometry, to establish model correspondence for multi-scale
simulation, one spine must be adjusted to agree geometrically with the other. In this case, the
AnyBody generic geometry has little physiological basis in comparison to the segmented,
cadaver-based geometry. Also, non-affine transformations are needed to achieve shape matching
in aspects other than uniform sizing, and application of such transforms (e.g. with skew) to the
cadaver mesh had high potential to create non-physiological contact planes in both the facet
joints and vertebral endplates. Therefore, adjustments were made to the AnyBody geometry to
match the detailed shape of the FE model derived from cadaveric image data.
The AnyBody Modeling System (v6.0, Aalborg, Denmark) was used to define and apply
geometry-fitting transformations. The AnyBody software implements functions of the open
source Visualization Toolkit to create and apply subject-specific, three-dimensional
transformations (www.vtk.org). Further information on the general use of this code package as a
means to apply medical-imaging based, subject-specific scaling to the AnyBody models is
openly available (anybodytech.com, Lesson 3). For this work, a sequence of three consecutive
transforms was developed and applied to adjust the generic AnyBody geometry and muscular
parameters (e.g. muscle path origins/insertions) to the cadaver geometry (Figure 5.4).
For step one, five paired landmarks were identified on each of the L1 superior endplates,
and on the L5 inferior endplates (Figure 5.3). These ten landmarks were used to define an affine,
rigid-body registration (similarity transform) that relocated the cadaver L1-L5 lumbar vertebrae
to the location of the generic AnyBody spine. Uniform sizing of the cadaver spine to the size of
88
the AnyBody spine was also allowed. The outcome of this step before and after performing the
transformation is shown in Figure 5.3, and also in Figure 5.4 in preparation for step two.
(a)
(b)
(c)
(d)
Figure 5.3 – Rigid-body similarity transform for initial alignment (step one). Paired landmark
selection on the superior endplate of L1 (a,b), and outcome of transformation (c,d).
89
Step 1
(a)
(b)
Step 2
(c)
(d)
Step 3
(e)
(f)
Figure 5.4 – Representation of three-step sequential transform process. Step one is after the
rigid-body similarity transform, step two is after the 25-landmark RBF transform, and step three
is after the 1500 auto-seeded landmark STL-based transform. In each image, red landmarks
correspond to the generic AnyBody vertebrae, and green landmarks to the cadaver-based
vertebrae.
90
For step two, a landmark-based nonlinear radial basis function (RBF) transformation was
performed to adjust shape of the AnyBody vertebrae to the cadaver geometry. Seventeen
landmarks were identified per vertebrae, focused around the transverse and spinous processes of
each vertebral level, where a majority of muscle origins/insertions are defined in the AnyBody
model. A representation of the complete, paired sets is shown in Figure 5.4.
For step three, a surface-based nonlinear RBF transformation was performed to further fit
the shape of matching anatomical regions to one another. This required geometries to be nearly
fit to one another through application of steps one and two.
The surface-based function
implemented in AnyBody automatically seeds a specified number of landmarks on the two
geometries, and uses closest-point calculations to determine landmark correspondence. A set of
1500 landmarks was used, and the outcome of the surface fit is shown in step three of Figure 5.4.
The implementation of subject-specific scaling functions within the AnyBody software
ultimately facilitates adjustment of musculoskeletal model parameters. In terms of a multi-scale
simulation
framework,
this
allows
semi-automated
adjustment
of
muscle
path
origins/insertions/via-points (nodes) to fit intended finite element geometry. In the generic
AnyBody lumbar model, the three-dimensional locations of muscle nodes are initially defined
with respect to the generic, sagittally-symmetric bone geometry. A representation of all muscle
nodes within the lumbar region is shown in Figure 5.5. To address the objective of this work, the
parameterized transformations were applied simultaneously to all three-dimensional lumbar
muscle nodes at each step of the three-step, bone-based transform process. The robustness of
this procedure to relocate muscle nodes to the cadaver geometry was assessed for the transverse
and spinous processes, as shown in Figure 5.6. The outcome for a representative transverse
process (L4 level) following application of each transform step is shown in Figure 5.7.
91
Figure 5.5 – Lumbar muscle nodes in the AnyBody model, compared to target cadaver geometry
(blue). All locations were initially defined with respect to the generic bone geometry (brown).
Figure 5.6 - Bone geometry from the generic model (brown) and cadaver (blue) aligned after step
one rigid-body registration. Anatomical regions of interest for muscle node relocation were the
spinous processes (top right) and transverse process (bottom right) at each vertebral level.
92
Step 1
Step 2
Step 3
(a)
(b)
(c)
Figure 5.7 - Comparison of transform methods, applied to AnyBody bone geometry (brown) and
muscle nodes (green), performed from left to right additively. From left, rigid body registration,
followed by four-landmark radial basis function, followed by automated 1500 landmark surfacebased fitting.
Overall, the muscle node relocation procedure was sufficient to move generic node
definitions to corresponding, relative locations on the cadaver geometry (Figure 5.7). However,
bi-lateral performance in the frontal plane was not comparable.
This was due to anatomical
variabilty with respect to the sagittal plane. As one example, the left L4 transverse process of the
cadaver spine was substantially different form the right transverse process (Figure 5.1). In view
of future multi-scale analyses (Figure 1.2), such intrasubject variability would complicate
baseline interpretation of outcome metrics by adding model-induced intrasubject variablity to
potential, gait strategy intersubject variability.
Therefore, baseline sagittaly-symmetric geometry was created using tools within
HyperMesh software (Altair Hyperworks, Troy, MI).
The L1-L5 vertebral geometry was first
split along an approximated, mid-saggital plane. Edges of non-uniformly split elements were
adjusted to lie on the resulting mid-saggital profile. The volume morphing tool in HyperMesh
was used to make anatomical adjustments representative of an average L1-L5 spine, based on
93
established guidelines from the anatomical literature (Pearcy and Bogduk, 1988; White and
Panjabi, 1990). Adjustments primarily included: shape and angle of the transverse process in
both the frontal and sagittal planes, and anterior/posterior depth of the vertebral bodies in the
frontal plane. The final, generalized bone geometry is shown in Figure 5.9.
Generalized facet cartilage was also created at all lumbar joint levels on the right side,
using the final bone geometry as a basis. Surface areas of the bone shell mesh to replace with
cartilage were visually identified based on established anatomical guidelines (White and Panjabi,
1990). The solid layer extrusion tool was used to generate three-dimensional element layers
(quadrilaterals) inward and outward from the bone surface (1.0mm each), as shown in Figure 5.8.
Any interference initially created by the outward extrusion was mitigated by translating facet
processes away from each other. The volume morphing tool was used to constrain translations to
a single plane that was an approximate normal of each facet contact surface. In this way, the
anatomically-intended contact behavior was preserved. Right side cartilage at all levels was also
mirrored with the bone geometry about the mid-sagittal plane.
(a)
(b)
Figure 5.8 – Representative facet cartilage created at each of the four joint levels.
94
(c)
(a)
(b)
(c)
(d)
Figure 5.9 - Creation of baseline, sagittally-symmetric spinal geometry. The raw, segmented
cadaver mesh is shown in blue (left), and the final, mirrored geometry is shown in green (right).
95
6.CHAPTER 6
GENERAL CONCLUSIONS
Ultimately, this body of work identified abnormal low back biomechanics during walking
of individuals with a unilateral transtibial amputation. Musculoskeletal modeling and simulation
facilitated estimation of in vivo biomechanical parameters that are currently infeasible to measure
in a laboratory setting. The findings of this work contribute to a goal within the biomechanical
research community to better understand mechanisms that contribute to the development of LBP
in individuals with a lower-limb amputation. Knowledge will be disseminated through submittal
of Chapter 3 as a manuscript to the journal of Gait & Posture (April 2014). Novel, spinal
geometry was also created to enable future, multi-scale finite element and rigid body dynamic
simulation. Lastly, the collective biomechanical data, models, and simulations from this thesis
work may serve as a baseline in future efforts to use computational tools as part of a patientspecific tool to aid in clinical rehabilitation of patients with biomechanical, musculoskeletal
disorders (Figure 1.2).
6.1.
Recommendations for Future Research
Collective literature findings provided the initial motivation for an investigation of low
back biomechanics in individuals with a lower-limb amputation. The three primary outcome
metrics were also chosen to facilitate comparisons with previous work and clinical data: trunkpelvis relative kinematics, muscle forces in the low back, and total joint contact force. Small
differences between groups were found in these particular three metrics; however, further
differences may exist in other biomechanical metrics. For example, a dynamic phase diagram
(e.g. trunk-pelvis angle versus hip angle) computed using motion capture data during walking
96
was recently shown to provide a visual description of asymmetric gait strategies between people
with/without unilateral hip (Landgraeber et al., 2014).
This is an example of a readily
interpretable, visual metric that may be useful as an initial patient classification in the diagnosis
of biomechanical disorders. Following initial diagnoses, a clinician could indicate a patient for
more in-depth, biomechanical evaluation through patient-specific modeling and simulation
(Figure 1.2). Also, the subject pool for this study excluded individuals with secondary LBP.
Future work should leverage this baseline data to investigate potential effects of additional intersubject parameters on low back biomechanics, such as: age, time since amputation, prosthesis
type, self-selected walking speed, static standing trunk-pelvis pose, and current LBP.
The current state of computational modeling and simulation in biomechanics is
characterized by tradeoffs between time required to develop robust, subject-specific simulations,
the computational costs required to run these simulations, and sample size. As computational
power continues to increase, these limitations will be mitigated. Future work should consider
applying a forward dynamics framework that would allow additional investigations, such as
induced acceleration analyses, segment power analyses, and joint contact force decompositions.
These analyses quantify individual muscular contributions to low back joint contact forces,
measures of low back dynamic stability, and trunk-pelvis kinematics. Lastly, in either a forward
or inverse simulation framework, the sensitivity of whole-body, biomechanical outcome metrics
to modeling assumptions and inverse kinematics/dynamics error propagation should be further
established.
A supplemented experimental data collection protocol could also benefit future work.
Novel tools with increased precision in kinematic measurement of dynamic, in vivo vertebral
body motion have recently been suggested. For example, bi-plane fluoroscopy can detect
97
millimeter-level precision of in vivo vertebral kinematics during motion (Lin et al., 2014). If
using whole-body marker motion capture, additional skin markers on the lumbar region and
upper extremities should be included, such as described by Armand et al, and Mason et al (both
2014) . Contributions to total body angular momentum from the arms during walking has been
found to be as large as 25%, relative to pelvis (2%), thorax (5%), and legs (60%) (Bruijn et al.,
2008).
As individuals with lower-limb amputation have altered regulation of whole-body
balance (Silverman and Neptune, 2011), accounting for the potential effects of arm swing in
dynamic simulation is important. Lastly, clinical measures of subject-specific muscle group
strengths and endurance, if collected could potentially be useful in making further subjectspecific model adjustments, such as representations of atrophy by adjustment of three-element
Hill muscle model parameters.
Future, multi-scale finite element and rigid-body dynamics simulation has potential to
enable investigations of total lumbar joint contact force and moment distribution among passive
soft tissues (intervertebral disc, facet joints, ligaments).
However, maintaining model
correspondence to avoid model-induced error propagation has been a challenge in past work
(Zhu et al., 2013).
Three-dimensional, spatial transformations facilitated subject-specific
adjustment of generic, lumbar muscle parameters to fit medical-imaging based anatomy, in this
work. Future work must investigate further challenges of dynamically communicating necessary
model parameters between software packages, such as: motion and load dependent estimates of
total intervertebral stiffness from finite element simulation, and dynamic muscle forces from
musculoskeletal gait simulation.
Lastly, collaborations between the biomechanical research and clinical communities, and
discussions of findings such as those presented in this work, will be crucial to future successes in
98
patient-specific rehabilitation and treatment (Figure 1.2). Input from people that work first-hand
treating and rehabilitating individuals with a lower limb amputation should become part of the
future methods development.
This type of cooperation should also lessen the challenge of
translating estimated, biomechanical parameters (joint contact forces/moments, forces within
muscle groups, trunk-pelvis coordination) to a targeted treatment plan.
99
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112
8. APPENDIX A
SUBJECT PARAMETERS
Table A.1 – Parameters of subjects selected for simulation.
Time from
Height Weight Amputation
Subject1 Age Gender (cm)
(kg)
(years)
Diagnosis Foot Type
NonAmp1 39
M
176.5
57.2
NonAmp2 55
M
172.7
65.8
NonAmp3 28
F
180.3
66.5
NonAmp4 43
M
167.6
97.1
NonAmp5 23
M
186.7
61.7
NonAmp6 24
M
173.4
83.5
TTA1
40
M
182.9
115.2
6
Trauma
ESAR
TTA2
37
M
179.1
94.8
5
Trauma
SACH
TTA3
39
F
157.5
79.8
5
Trauma
SACH
TTA4
46
M
167.6
85.7
4
Traumatic
SACH
TTA5
42
M
177.8
96.2
3
Traumatic
SACH
TTA6
58
M
177.2
73.5
7
Traumatic
ESAR
1
Prefi es “C” and “V” distinguish non-amputees, and “ ” distinguishes individuals with
unilateral, transtibial amputation.
113
9.APPENDIX B
HILL MUSCLE TENDON/FIBER CALIBRATION
The six calibration poses used to determine tendon slack length for each individual are
shown. Lower extremity joint angles defining the pose are also listed. Each subsequent pose
overwrites the results of the previous poses for any included muscles. Muscle groups calibrated
in each pose are listed under the corresponding image. Note that the visual behavior of the
muscles in these images is purely a graphical artifact of the GUI.
Knee = (-) extension (+) flexion
Ankle = (-) plantarflexion (+) dorsiflexion
Subtalar = (-) inversion (+) eversion
Hip Ad/Ab = (-) ad (+) ab
Hip ext/int = (-) int (+) ext
Hip flex/ext = (-) extension (+) flexion
114
Ankle = 0
Subtalar = 0
Knee = 0
Hip Ad/Ab = 0
Hip ext/int = 0
Hip flex/ext = 0
Ankle = 10
Subtalar = 0
Knee = 0
Ankle = -20
Subtalar = 0
Knee = -70
Hip Ad/Ab = 0
Hip ext/int = 0
Hip flex/ext = 0
Ankle = +10 Hip Ad/Ab = 0
Subtalar = -20 Hip ext/int = 10
Knee = -50
Hip flex/ext = -60
Ankle = -5
Subtalar = 0
Knee = -80
Hip Ad/Ab = -10
Hip ext/int = 0
Hip flex/ext = -50
Ankle = +10 Hip Ad/Ab = 0
Subtalar = 0 Hip ext/int = 0
Knee = 0
Hip flex/ext = -35
115
Hip Ad/Ab = 0
Hip ext/int = 0
Hip flex/ext = -50
10. APPENDIX C
PARAMETER OPTMIZATION AND MARKER TRACKING SETTINGS
Table C.1 – Settings applied in the AnyBody parameter optimization process, and inverse
kinematics solution
Marker
right anterior illiac spine
left anterior illiac spine
left posterior illiac spine
right posterior illiac spine
left illiac crest
right illiac crest
C7 vertebrae
left acromion
right acromion
left lateral malleoli
right lateral malleoli
right medial malleoli
left medial malleoli
right dorsal foot
right 5th metatarsal
right 1st metatarsal
right 2nd distal phalange
left dorsal foot
left 5th metatarsal
left 1st metatarsal
left 2nd distal phalange
right heel
left heel
right lateral knee
left lateral knee
right medial knee
left medial knee
right greater trochanter
left greater trochanter
* ALL SHANK/THIGH
CLUSTERS
Translational DOF
x
y
z
Off
Off
Off
Off
Off
Off
On
Off
Off
On
Off
Off
Off
Off
On
Off
Off
On
Off
Off
Off
Off
Off
On
Off
Off
On
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
On
On
On
Off
Off
On
Off
Off
On
Off
Off
Off
On
On
On
Off
Off
On
Off
Off
On
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
On
Off
Off
On
Off
Off
Off
Off
Off
Off
Off
Tracking Weight
Wx
Wy
Wz
15.0
15.0
15.0
15.0
15.0
15.0
5.0
5.0
5.0
5.0
5.0
5.0
1.0
5.0
1.0
1.0
5.0
1.0
10.0
10.0
10.0
5.0
5.0
1.0
5.0
5.0
1.0
1.0
1.0
5.0
1.0
1.0
5.0
7.0
1.0
7.0
7.0
1.0
7.0
1.0
1.0
1.0
1.0
5.0
1.0
1.0
5.0
1.0
1.0
1.0
5.0
1.0
1.0
1.0
1.0
5.0
1.0
1.0
5.0
1.0
1.0
1.0
5.0
5.0
1.0
5.0
5.0
1.0
5.0
10.0
1.0
10.0
10.0
1.0
10.0
10.0
1.0
10.0
10.0
1.0
10.0
1.0
1.0
1.0
1.0
1.0
1.0
On
1.0
On
116
On
1.0
1.0
11. APPENDIX D
LOWER EXTREMITY EMG VALIDATION
Each figure represents comparison of simulated lower extremity muscle activities against
the original raw EMG signals. The y-axes for each figure is plotted as force in Newtons, and xaxes are percent residual limb gait cycle. On a single muscle group subplot, each distinct curve
represents a separate modeled fascicle (e.g. muscles with large surface areas were modeled as
many fascicles). The titles are subject tags corresponding to Table A.1. Subplot titles are
formatted with (muscle group name)_(side); where “side” is either ipsilateral (IPSI) or
contralateral (CONT). Raw EMG signals are plotted in the shaded subplots directly below each
muscle group subplot.
117
NonAmp1
NonAmp2
118
NonAmp3
NonAmp4
119
NonAmp5
NonAmp6
120
TTA1
TTA2
121
TTA3
TTA4
122
TTA5
TTA6
123