BIOMECHANICS OF DYSFUNCTION AND INJURY MANAGEMENT FOR THE CERVICAL SPINE Darryl Frederick Sim Bachelor of Mechanical Engineering ( Hons ) / Bachelor of Business (Marketing) This thesis is submitted in accordance with of the regulations for the degree of Doctor of Philosophy School of Mechanical, Manufacturing and Medical Engineering Faculty of Built Environment and Engineering and Centre for Rehabilitation Science and Engineering Queensland University of Technology Brisbane, Queensland, Australia 2004
Transcript
BIOMECHANICS OF DYSFUNCTION
AND INJURY MANAGEMENT FOR
THE CERVICAL SPINE
Darryl Frederick Sim
Bachelor of Mechanical Engineering ( Hons ) / Bachelor of Business (Marketing)
This thesis is submitted in accordance with of the regulations for
the degree of Doctor of Philosophy
School of Mechanical, Manufacturing and Medical Engineering Faculty of Built Environment and Engineering
and Centre for Rehabilitation Science and Engineering
6.2 IMPLICATIONS FOR MUSCLE FUNCTION TESTING 119 AND REHABILITATION
6.3 FUTURE RESEARCH 121
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APPENDIX 1 Algorithms for moving axes (Cardan angles) 123 APPENDIX 2 PBU response assuming ideal gas relationship 125 APPENDIX 3 MADYMO 5.4 Hill type muscle model 127 APPENDIX 4 Tekscan Flexiforce sensor technical literature 132 APPENDIX 5 Labview front panel and block diagram for 136
Figure 1.1 Concept map of cervical spine injury diagnosis and 4 management.
Figure 2.1 Path of a multi-segment muscle in initial and flexed 13 positions. Only one part of the semispinalis capitis is shown to clarify muscle curvature. The intermediate sliding points are attached to the vertebrae. (van der Horst, Thunnissen et al. 1997)
Figure 2.2 Model prior to, and after, the inclusion of the upper 19 torso and skin surface.
Figure 2.3 Flexed and extended poses showing the continuity of the 20 skin surface.
Figure 2.4 Tree structure of rigid body system representing the 22 upper torso and neck model. (Body numbers in brackets)
Figure 2.5 Muscle force-length curves showing the difference 26 between active and prolonged spasm functions.
Figure 2.6 Summary of the influence of the particular dysfunctions 38 on the ROM about the primary and secondary axes of rotation.
Figure 3.1 Equipment set-up for clinical ROM evaluation. 44 Figure 3.2 Orientation of source relative to body. 45 Figure 3.3 Transformation between source and display angles. 47 Figure 3.4 Upper cervical rotation from flexed starting position. 50 Figure 3.5 Upper cervical rotation from neutral starting position. 50 Figure 3.6 Comparison of groups during active extension showing 54
the mean and standard deviation of the ROM (Cardan angles).
Figure 3.7 Comparison of groups during active extension showing 54
the mean and standard deviation of the ROM (Pearcy representation at the point of maximum extension).
Figure 3.8 Comparison of groups during active right lateral flexion 55 showing the mean and standard deviation of the ROM (Cardan angles).
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Figure 3.9 Comparison of groups during active right lateral flexion 55 showing the mean and standard deviation of the ROM
(Pearcy representation at the point of maximum right lateral flexion).
Figure 3.10 Comparison of groups during active left axial twist 56 showing the mean and standard deviation of the ROM
(Cardan angles).
Figure 3.11 Comparison of groups during active left axial twist 56 showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum right axial twist).
Figure 3.12 Comparison of groups during active right rotation 57 showing the mean and standard deviation of the ROM (Cardan angles).
Figure 3.13 Comparison of groups during active right rotation 57 showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum right axial twist).
Figure 3.14 Sample ROM trace showing differing points of maximum 59 Rotation during one complete axial twist cycle.
Figure 3.15 Sample ROM trace showing aberrant motion patterns. 65 Figure 3.16 Determination of the correlation between the difference 66
in reported maximum and the timing of the maximum rotations.
Figure 4.1 The STABILIZER pressure biofeedback unit 70
(Chattanooga Group Inc) used during the cranio-cervical flexion test and for neck muscle rehabilitation.
Figure 4.2 The distribution of the inflated size of the PBU at 72 20 mm Hg air pressure during the resting phase of the C-CF test.
Figure 4.3 Relationship between the inflated size of the PBU and 73 the contained air volume.
Figure 4.4 The PBU as it is used during the cranio-cervical flexion 74 test.
Figure 4.5 Orientation of the head-neck model for the cranio- 74 cervical flexion test simulation.
Figure 4.6 Typical PBU force-compression results for the three 77 bags tested.
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Figure 4.7 Overall PBU response for the 20 - 30 mm Hg pressure 79 range with the slope indicating the stiffness relating to the initial inflated size of the pressure bag.
Figure 4.8 Output from simulated PBU for particular muscle 80 group activations.
Figure 4.9 Snapshots of the motion resulting from the activation 82 of the deep neck flexor muscle group.
Figure 4.10 Displacement of the head contact point accompanying 82 deep neck flexor activation.
Figure 4.11 Head flexion accompanying activation of the deep 82 neck flexor muscle group.
Figure 4.12 Snapshots of the motion of the head accompanying 83 the activation of the extensor muscle group.
Figure 4.13 Displacement of the head contact point accompanying 83 the extensor muscle group activation.
Figure 4.14 Head flexion accompanying the extensor muscle group 83 activation.
Figure 4.15 Snapshots of the motion accompanying the activation 84 of the sternocleidomastoid muscles.
Figure 4.16 Displacement of the head point of contact accompanying 84 superficial flexor muscle activation.
Figure 4.17 Head flexion accompanying the superficial flexor muscle 84 activation.
Figure 4.18 Force between the head and headrest during muscle 85 activation.
Figure 4.19 Comparison of PBU pressure response with deep flexor 86 muscle group activation for different initial inflations.
Figure 4.20 Comparison of the displacement of the point of contact 86 for different initial PBU inflations.
Figure 4.21 Comparison of head flexion during the activation of the 87 deep flexor muscles with different PBU inflations.
Figure 4.22 Force characteristics of the PBU relevant to the C-CF 89 test.
Figure 4.23 Depression of the PBU required to generate the 90 10mm Hg pressure rise required during the C-CF test.
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Figure 5.1 FlexiforceTM Sensor Model A101 (Tekscan 2002) 96 Figure 5.2 Example of sensor excitation circuit (Tekscan 2002) 96 Figure 5.3 Force-plate configuration. 97 Figure 5.4 Flow diagram of the force and motion data analysis 99
and display.
Figure 5.5 Layout of the force sensors with the neutral point of 100 the movement axes aligned with the centroid of the triangle.
Figure 5.6 Sensor calibration curves after permanent mounting. 102 Figure 5.7 Sensor calibration curves for direct load application. 102 Figure 5.8 Discrepancies between the input and output Y-axis 103
displacements.
Figure 5.9 Discrepancies between the input and output Y-axis 104 displacements for the stiffer top-plate.
Figure 5.10 Effect of the output of sensor 1 on the Y-axis 104 displacement error.
Figure 5.11 Effect of the output of sensor 2 on the Y-axis 105 displacement error.
Figure 5.12 Effect of the output of sensor 3 on the Y-axis 105 displacement error.
Figure 5.13 Discrepancies between the input and output Y-axis 106 displacements after correcting the sensor 1 output.
Figure 5.14 Comparison of displayed and applied loads following 107 force-plate
Figure 5.15 Resting position prior to the cranio-cervical flexion test. 108 Figure 5.16 Gentle roll of the head as required by the cranio- 108
cervical flexion exercise.
Figure 5.17 Maximal flexion without any head lift. 109 Figure 5.18 Maximal extension used to test the output from the 109
forceplate. Figure 5.19 Influence of skull shape on point of contact. Panes A1 113
and A2 depict a rounded posterior skull profile and the resulting motion, whereas B1 and B2 depict a flatter profile. The blue arrow shows resting point of contact and red arrow shows contact point after head roll.
Figure A3.1 Pressure – Volume relationship for an ideal gas. 126
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LIST of TABLES
Table 2.1 Flexor muscles in the model (left and right). 16 Table 2.2 Extensor muscles in the model (left and right). 16 Table 2.3 Factorial experiment design for joint stiffness evaluation. 24 Table 2.4 Segmental rotations accompanying the primary actions. 28
(Results in degrees)
Table 2.5 Change in ROM resulting from factorial experimentation 30 applying combinations of unilateral zygapophysial joint stiffness. (Results in degrees)
Table 2.6 Change in ROM resulting from factorial experimentation 31 applying combinations of bilateral zygapophysial joint stiffness. (Results in degrees)
Table 2.7 Change in cervical ROM due to reduced disc stiffness. 32 (Results in degrees)
Table 2.8 Changes in ROM with muscle spasm. (Results in degrees) 34 Table 2.9 Results of altered alar ligament stiffness. 35
(Results in degrees)
Table 2.10 Change in ROM resulting from factorial experimentation 36 applying combinations of zygapophysial joint stiffness. (Results in degrees)
Table 3.1 Stratification of symptomatic population 48 Table 3.2 One-way ANOVA p values from stratified sample, 51
Cardan angles.
Table 3.3 One-way ANOVA p values from stratified sample, 52 Pearcy representation.
Table 3.4 One-way ANOVA p values from stratified sample, 52 Pearcy representation at the point of maximum primary rotation.
Table 3.5 Upper cervical rotation analysis: Comparison of groups 58 with particular symptoms.
Table 3.6 Stratified motion pattern data for extension and flexion 60 showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range.
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Table 3.7 Stratified motion pattern data for left and right lateral 60 flexion showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range.
Table 3.8 Stratified motion pattern data for the left and right 61 axial twist showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range..
Table 4.1 Force-compression relationship for PBU representation. 78
The units of force, F, and compression, x, are Newtons and millimetres respectively.
Table 4.2 Muscle activation - pressure response at different initial 91 inflations.
Table 5.1 Averaged force and movement during the C-CF action. 110 Table 5.2 Averaged force and movement during maximal flexion. 110 Table 5.3 Averaged force and movement during maximal extension. 110 Table 5.4 Effect of sensor spacing on measurement fluctuation. 112 Table 5.5 Comparison of reaction force between desired head roll 114
and maximal flexion.
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NOMENCLATURE
3D Three Dimensional
ALL Anterior Longitudinal Ligament
C-CF Cranio-Cervical Flexion
CL Capsular Ligament
COP Centre Of Pressure
FL Flavel Ligament
ISB International Society of Biomechanics
ISL Interspinous Ligament
JCS Joint Coordinate System
mmHg Millimetres Mercury (Pressure measurement)
ANOVA One-way Analysis Of Variation
PBU Pressure Biofeedback Unit
PLL Posterior Longitudinal Ligament
ROM Range Of Motion
SD Standard Deviation
SGI Silicon Graphics Inc.
WAD Whiplash Associated Disorder
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STATEMENT of AUTHORSHIP The work contained in this thesis has not been previously submitted for a degree
or diploma at any other higher education Institution. To the best of my knowledge
and belief, this thesis contains no material previously published or written by any
This manuscript would not be complete without acknowledgement of the
help and encouragement I have received during the years of academic pursuit that
preceded this document. Those that I must thank include family and friends,
colleagues who were similarly looking for the light at the end of the research
tunnel, and those who through their experience were able to shine some light
down the tunnel.
Firstly I must thank my wife and children who followed and supported me
while I took some seemingly rash steps outside of the ‘square’ and ventured away
from the workshop, through Engineering and eventually into the field of
Biomechanics. This journey has meant changes of home and school and has at
times stretched the finances but never the friendships, for which I am most
thankful.
The opportunity to enter biomechanical research came about through the
confidence that Professor Mark Pearcy and Professor John Evans, as Head of
Medical Engineering and Director of the Centre for Rehabilitation Science and
Engineering respectively, showed in me by accepting my application for
postgraduate studies and offering financial support through an APA scholarship
with a top-up through the Centre. I am thankful also for the help and
encouragement offered by both Mark and John in their role as co-supervisors.
I also acknowledge the assistance offered by Dr Timothy Barker, my
principal supervisor, who helped to keep the project on track during the
frustrations encountered through software licensing and access to the hardware
and software that were vital components of the project. I am grateful also for the
patience shown throughout my candidature, particularly during the concluding
stages.
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The Director, Dr Gwen Jull, and the team at the Whiplash Physical
Diagnostic Clinic, Physiotherapy Department, University of Queensland, must be
recognised for their contribution to this work through providing the clinical
perspective of the diagnosis of neck dysfunction and for giving me access to their
substantial research data-set. I enjoyed working part-time as part of this team
during my candidature and gained valuable insights into the ‘human’ side of the
neck injury diagnosis problem that encompassed more than I had originally
envisioned, coming from an engineering background.
Finally, thank you to the other ‘postgrads’ in the Medical Engineering group
for their companionship during my time at QUT. In particular I thank Justin for
his co-operation and assistance as we took up the challenge of learning and using
MADYMO together, albeit for much different purposes.
Introduction 1
Chapter 1
INTRODUCTION
The diagnosis and management of cervical spine injuries has attracted a
multi-disciplinary research effort from the Health, Allied Health and Scientific
professions as explanations are sought for persistent chronic symptoms. This
dissertation focuses on the biomechanical component of the cervical spine injury
diagnosis and rehabilitation management, this being one facet of establishing the
credibility of the manifested symptoms and the refinement of the diagnostic
process. Biomechanical analysis examines the internal forces and motions that
accompany external motion and provides a tool for investigating the relationship
between particular dysfunctions of the neck and their external manifestation.
This research is particularly relevant to the diagnosis of minor injuries that
arise typically from motor vehicle accidents and are classified as “whiplash
injuries”. Whiplash injuries arise from an acceleration-deceleration mechanism of
energy transfer to the neck during a collision, or some other mishap, (Scholten-
Peeters, Bekkering et al. 2002) and lead to long lasting symptoms in
approximately 25% of people who experience neck pain shortly after an accident
(Wallis, Lord et al. 1996; Brault, Siegmund et al. 1999). It is this group in
particular that would benefit from improved diagnostic processes and
rehabilitation management.
This chapter provides the background relating to neck injury diagnosis and
an outline of the research objectives and structure. The first section establishes the
relevance of biomechanics and how it can be applied to further the understanding
of injury diagnosis. Section 1.2 states the research objectives, Section 1.3 the
research strategy and Section 1.4 the thesis outline.
Introduction 2
1.1 BACKGROUND
In a review of biomechanical modelling, King (1984) stated that “the true
motivation for model formulation should be to help solve biomechanical problems
of clinical relevance”. This criterion was fundamental during the selection and
planning of this research and recent suggestions made by Dr Hugh Anton (1999),
the Chair of the injury diagnosis session of the World Congress on Whiplash-
Associated Disorders, which solicited rigorous evaluation of clinical diagnostic
procedures further directed this study. He also emphasised that while insurers and
payers have a vested interest in supporting research, priority must be given to
rehabilitation issues that are important to the person with a Whiplash Associated
Disorder (WAD).
Whiplash injuries are archetypical of the minor cervical spine injuries that
constitute the broader field addressed by this research, but receive the majority of
exposure because of the controversy generated by critics who do not accept the
credibility of this injury. Whiplash associated disorders have been the subject of
much debate, from their definition through to diagnosis and treatment, and
comment and criticism invariably follow any publication relating to this topic.
The Quebec Task Force (Spitzer, Skovron et al. 1995) made a concerted effort to
define whiplash and develop management plans. The conclusion from this task
force was that whiplash injuries result in "temporary discomfort," are "usually
self-limited," and have a "favorable prognosis," and that the "pain resulting from
whiplash injuries is not harmful." This report was found wanting when subjected
to critical evaluation (Freeman, Croft et al. 1998) and other formal studies refute
conjecture that symptoms are perpetrated or exaggerated for financial gain
(Bogduk and Yoganandan 2001). The disorder however is difficult to define and
diagnose because of the wide range of symptoms and requires a multi-parametric
diagnostic procedure that encompasses quality of life measures as well as physical
testing (Bono, Antonaci et al. 2000). In a review of current clinical practice
regarding whiplash associated disorders in the Netherlands, Scholten-Peeters et.
al. (2002) used a biopsychosocial model to encompass the dimensions of the
condition, but focussed on avoiding chronicity of the condition. This review
Introduction 3
further exposed the need for research leading to evidence based treatments for the
various chronic symptoms that develop following a whiplash injury.
Of the wide range of symptoms, chronic cervical spine pain syndromes may
be attributed to zygapophysial joints and intervertebral discs in about 50% of neck
pain cases following whiplash (Bogduk 1995). The diagnosis and treatment of
zygapophysial joint pain using diagnostic nerve blocking and radiofrequency
neurotomy have been shown to be reliable (McDonald, Lord et al. 1999), but
manual diagnosis by a trained manipulative therapist can be just as accurate in the
diagnosis of cervical zygapophysial syndromes (Jull, Bogduk et al. 1988). The
diagnosis of other cervical dysfunction syndromes, however, depends on current
clinical examination techniques because findings from plain film and magnetic
resonance imaging are typically normal after whiplash (Bogduk and Teasell
2000). Conclusive findings from clinical examination are hampered by the
“trained feel” and experience necessary to enable manual techniques to diagnose
these other spinal pain syndromes. Real progress in this area relies on research
that makes the extraction and interpretation of data more objective, and training to
improve the intra-clinician and inter-clinician reliability of testing procedures.
In an extensive review of biomechanical research into minor cervical
injuries covering seventy-nine publications, and spanning the past forty years,
Bogduk and Yoganandan (2001) found that the research had focused primarily on
the root of the whiplash controversy and had provided insights into how and
where the injuries occur. These insights have strengthened the credibility of
injuries associated with “whiplash” and its acceptance as a legitimate consequence
of low velocity impacts, but just as important is the accurate description and
localisation of the dysfunction. Mathematical modelling and computer simulation
provide tools for the further investigation of the biomechanical relationship
between localised injury and the clinical diagnosis suggested through palpation,
joint range of motion testing and muscle function/control evaluation. Objective
description of the dysfunction through measurable quantities would allow more
rational diagnosis and rehabilitation planning.
The concept map (Figure 1.1) graphically represents the fit of the proposed
biomechanical modelling into the larger picture of the clinical diagnosis and
Introduction 4
management of cervical spine injuries. Mobility, control and pain were identified
as the major elements of the clinical assessment of neck dysfunction and these
were subdivided to identify the components that could direct the modelling in this
research. While the various components are shown as separate entities to simplify
the diagram, it is recognised that they are interrelated and clinical decisions would
need to encompass all aspects, with weighting applied to the factors according to
the particular case in question
.
Kinesthetic awareness
Voluntary movement
CONTROL
Observation Imaging
CLINICAL DIAGNOSIS Manual examination
Guarding Evidence Measurement
PAIN
MOBILITY
Range of motion
Inter-segmental motion
Response Feel
MODELLING Strength Mobility
Neural control
Muscle function
Joint properties
Anatomicaldetail
Surgery Pain Management
INJURY MANAGEMENT
Exercise Manipulation
Figure 1.1 Concept map of cervical spine injury diagnosis and management.
Introduction 5
Pain associated with neck movement is the primary indicator of some
underlying dysfunction and is the usual precursor to clinical intervention. The
challenges faced by clinicians are that the measurement of pain is quite subjective,
and the painful site may not be indicative of localised injury because of pain
referral mechanisms of the body. Evidence suggests that reliance on pain
provocation alone may lead to false positive joint dysfunction diagnoses but tissue
stiffness and abnormal joint motion provide further cues to assist a manipulative
therapist during treatment (Jull, Treleaven et al. 1994). In trying to find other cues
to assist diagnosis, biomechanical modelling of particular dysfunctions was
foreseen as a means of correlating movement patterns with the guarding strategies
associated with neck pain arising from particular structures.
The reduced mobility of the neck is the most obvious consequence of
strategies employed to avoid the onset of pain from pathological structures and
cervical range of motion has been shown to discriminate between asymptomatic
and whiplash subjects (Osterbauer, Long et al. 1996; Dall'Alba, Sterling et al.
2001). Range of motion can be accurately and reliably measured in three
dimensions, but of interest to biomechanists and clinicians alike is the
characterisation and interpretation of the angles of rotation in terms of the
anatomical frame of reference (Wu 2002). A particular application for the
biomechanical model of the neck foreseen in the early stages of this research was
the investigation of range of motion testing to determine if any relationship could
be established between the range of motion and particular dysfunctions of the
neck. The envisaged modelling also provided a means of evaluating the
contributions of particular dysfunctions at the intersegmental level.
Assessment of the control of head movement and voluntary recruitment of
particular muscle groups is another facet of neck injury diagnosis. A deficit in
neck muscle control may be evident through a loss of kinaesthetic awareness
because of a disturbance of the proprioceptive feedback from the muscles (Revel,
Andre-Deshays et al. 1991; Heikkila and Wenngren 1998) or inhibition of
particular muscle groups following injury (Jull 2000; Sterling, Jull et al. 2001).
The integral part that the muscles play in the motion and support of the head on
Introduction 6
the neck predetermined the selection of a model that included the major muscle
groups of the neck.
The two-way arrows between the clinical diagnosis, injury management and
modelling blocks indicate the iterative nature of progress in this area. The
definition and validation of a clinically relevant model would require input from
data and experience gathered both during diagnosis and injury management, and
the outcomes of the modelling could then be incorporated into clinical practice.
While this map largely summarises the focal points of this study, some of the
components identified in the figure were subsequently outside of the scope of this
project and remain the subject of future research.
1.2 RESEARCH OBJECTIVE
The motivation for this research arose from the perceived contribution that
biomechanical modelling and analysis could make to the diagnosis of minor
injuries of the cervical spine. The refinement and development of clinical
diagnostic tools and procedures relies on an understanding of how the internal
forces and motions are manifested. A detailed biomechanical model of the human
neck provided a unique opportunity to investigate particular dysfunctions that are
hidden in vivo.
1.2.1 Objective
The objective of this research was to improve the reliability of information
gained through clinical examination of minor neck injuries by using
biomechanical principles and a clinically relevant biomechanical model of the
human neck. Qualifying this objective was the expectation that the modelling and
analysis would help to correlate the measurable quantities with particular
dysfunctions in the neck so that the testing procedures can be ratified and refined.
This research, however, can only have an impact on those parts of the multi-
faceted diagnostic approach that involves force, motion and interaction between
structures.
Introduction 7
1.3 RESEARCH STRATEGY
The strategy adopted for this work was first to review the current clinical
diagnostic procedure and the collection and interpretation of data in terms of the
contribution that the field of biomechanics could offer. A suitable model of the
human neck was then identified and adapted to be clinically relevant to further the
knowledge and progression of cervical injury diagnosis and rehabilitation
management.
Since significant research and modelling of the human neck had already
been performed, it was preferable to adapt a current model for this research. The
model had to include sufficient anatomical detail to study the dysfunction of
particular structures, and provide suitable output for comparison with clinically
measurable parameters.
Facet joint stiffness, discal shear and muscle spasm were identified as the
primary dysfunctions accompanying cervicogenic pain (Corrigan and Maitland
1998). These symptoms are currently diagnosed through manual examination by
trained manipulative physiotherapists but a correlation between the symptoms and
manifested overall head-neck range of motion (ROM) was expected. To
investigate the effect that these injuries had on range and pattern of motion,
parametric changes were made to the model. The results were then compared with
the deficits in motion demonstrated clinically to determine the efficacy of ROM
testing.
Deficits in deep neck muscle control have also been demonstrated clinically
following minor injury (Jull 2000; Davis 2001), and rehabilitation of these
muscles requires an exercise that specifically targets the affected muscles. Deficits
in the activation of the deep neck flexor muscles and particular exercises to
address their rehabilitation have also been investigated for cervical headache
treatment (Jull, Barrett et al. 1999). Since similar muscle dysfunction occurs with
whiplash associated disorders, the biomechanics of the pressure bio-feedback
device that was adapted to assist with cervical spine muscle rehabilitation was
evaluated as a component of this thesis. The cervical spine model was used to
Introduction 8
study the action resulting from active control of the deep neck flexor muscles and
to correlate this activity with the output of the feedback device. An alternative
device was also developed to determine the feasibility of using the ground
reaction force and / or the motion of the point of contact between the head and the
headrest to provide feedback during the rehabilitation exercise.
1.4 THESIS OUTLINE
Since range of motion testing is one of the basic tenets of clinical
examination, Chapter 2 addresses the initial modifications to the cervical spine
model that were necessary to investigate ROM testing. This chapter firstly
presents a description of the modified de Jager detailed head/neck model (de Jager
1996; van der Horst, Thunnissen et al. 1997) and the MADYMO software that
was used as the development platform, and then the parametric changes that were
made to simulate particular dysfunctions. The next chapter provides the results of
the re-evaluation of available clinical ROM data for comparison with the
modelling output. Several methods of interpreting three-dimensional motion are in
common use but this section shows that the variability between people masks the
expected effects of particular dysfunctions. Chapter 4 details the biomechanical
modelling of the cranio-cervical flexion (C-CF) test that is used clinically to
determine the level of control of the muscles that lie close to the anterior face of
the cervical vertebrae. Also, described in Chapter 5 is the development of an
alternative instrument to aid in the rehabilitation of these muscles by providing
feedback to guide the prescribed exercises. The final chapter concludes the thesis
by summarising the implications of the research to theory and to practice.
Model Selection and Adaptation 9
Chapter 2
MODEL SELECTION AND ADAPTATION
Biomechanical simulation of cervical spine range of motion testing was
undertaken to assist in the interpretation of the relationship between particular
structural dysfunctions and their external manifestation, an investigation almost
impossible given only in vivo testing. Biomechanics was appropriate for this
study, being a field of science that applies the principles of physics and mechanics
to the interaction of bodies within biological systems, and simulation provides an
experimental environment for the physical or mathematical representation of real
world systems. In this study, the investigation of the inter-segmental forces and
motion patterns during simulated clinical range of motion assessment was directed
toward testing the correlation between specific cervical dysfunctions and
clinically measurable parameters. The aim of the study was to assist in the rational
assessment of clinical procedure and rehabilitation planning.
The attributes of the cervical spine model of particular importance to the
diagnosis of neck injury or dysfunction were the anatomical detail, joint
properties, muscle function and muscle control. Altering the parameters defining
these attributes specifically to simulate soft tissue injury or abnormal muscle
activation facilitated the investigation of diagnostic methods, with ROM testing
the focus of this chapter. This parametric analysis of cervical dysfunction using a
biofidelic model aimed to provide a foundation for diagnostic procedure
evaluation and refinement, thus complementing and extending current knowledge
obtained through clinical experience and research.
Model Selection and Adaptation 10
2.1 BACKGROUND
The initial task during this component of the study was to review the
available biomechanical modelling techniques and the simulation tools available
so that a suitable basis could be chosen for this study.
2.1.1 Types of Biomechanical Neck Models
Three types of models have been developed to describe the dynamic
behaviour of the head-neck complex. These can be classified as two pivot models,
discrete parameter models and finite element models (de Jager 1996). Each type
of model has been developed and validated for a particular purpose, although
mostly for impact loading situations.
The two pivot models represent the head and torso as rigid bodies connected
by a link with a pivot at each end. These models lump the mechanical behaviour
of the neck into the properties assigned to the pivots and have been shown to
adequately describe the motion of the head relative to the torso in an impact
situation (Bosio and Bowman 1986; Seeman, Muzzy et al. 1986; Thunnissen,
Wismans et al. 1995). These models however lack the anatomical detail necessary
to answer questions of clinically relevance.
Discrete parameter models include more anatomical detail, representing the
vertebrae also as rigid bodies and simulate the soft tissues using mass-less spring-
damper elements. This method is relevant for spinal modelling because the spine
is essentially comprised of a series of solid bodies (vertebrae) connected by non-
linear spring-damper systems (ligaments, discs, joints, muscles). The clinical
assessment of spinal function requires the evaluation of inter-segmental mobility
and range of motion, and these values can be obtained from the rigid body
response to an applied motion or applied force. This type of model has been
applied to a range of biomechanical problems and, among others, has been used
for automotive impact loading simulation (de Jager 1996; Happee, Hoofman et al.
1998), investigation of the influence of muscle tone and reflex activity (Peng,
Hain et al. 1996; van der Horst, Thunnissen et al. 1997; Keshner, Statler et al.
1997) and whole body vibration analysis (Fritz 1997).
Model Selection and Adaptation 11
Finite element models allow for highly detailed representation of geometry
and material behaviour of cervical spine structures. Each structural component, or
part thereof, can be modelled using numerous deformable elements with the
mechanical characteristics of the particular tissues being modelled. Finite element
models have been applied, amongst others, to: examine the effect of injury and
surgically inserted devices on cervical spine mobility (Clausen 1996; Maurel,
Lavaste et al. 1997); simulate the synovial fluid medium in the facet joints
(Kumaresan, Yoganandan et al. 1998); study the flow of material between the
head and spinal cavity during head impact (Hosey 1981); test the effect of seating
parameters on head and neck loads during impact (Chhor 1995; Kleinberger
1998). The difficulties with this method is in finding realistic property
descriptions for the many components of the cervical spine, especially when
considering that the geometrical and mechanical properties of anatomical
structures vary according to the age, health and injury history of an individual.
2.1.2 Computer Simulation
Computer simulation packages have been developed to provide graphical
input and output support for both rigid body dynamics and finite element
methods. These simulation packages vary depending on their intended use, but for
this research the MADYMO package (TNO, The Netherlands) that combined both
multi-body and finite element method techniques was most useful. The
availability of a previously developed detailed head/neck model using the
MADYMO platform (de Jager 1996; van der Horst, Thunnissen et al. 1997) also
influenced this choice. The multi-body techniques allow fast segmental and whole
model motion analysis, and the finite element component allows detailed
modelling of structural components. The MADYMO software package was
developed primarily to complement existing crash test procedures for the
evaluation of occupant safety and vehicle compliance. The program has graphical
input and output support from several third party pre and post processor programs.
MADYMO consists of a number of modules that perform components of the
overall response. The multi-body module calculates the contribution of the inertia
Model Selection and Adaptation 12
of the rigid bodies to the equations of motion. Other modules calculate the
contribution of specific force elements such as springs, dampers, seat belts and
other structural components that may be represented as finite element models
(Wismans 1995).
Other packages such as the Software for Interactive Musculo-skeletal
Modeling (Musculographics Inc.), Working Model (MSC Software) and
Matlab(The MathWorks) also provide the graphical environment and analysis
tools for the development and analysis of musculo-skeletal models. Since the
objective of this study was not to fully develop a detailed neck model, these other
modelling tools were not further explored following the licensing of MADYMO.
2.2 OBJECTIVE
The objective of this component of the study was to adapt the detailed neck
model for ROM simulation to investigate the effect of particular injuries. The
study aimed to test the discriminatory power of ROM testing by comparing the
3-D motion when specific parameters were changed in the model.
2.3 MODEL DESCRIPTION
The MADYMO 5.4 crash test simulation package used for this research
provided the tools for the dynamic evaluation of rigid bodies and finite element
models in three dimensions. Predefined and validated data-sets representing the
physical crash test dummies are provided for the user to include in simulations.
The range of these data-sets is being progressively expanded to include human
body models, however none were directly applicable to this research.
The detailed head-neck model, available as a research tool from TNO (The
Netherlands), included rigid body representation for the head and vertebrae (C1
through to T1), linear visco-elastic intervertebral discs, frictionless facet
(zygapophysial) joints, nonlinear visco-elastic ligaments and multi-segment
contractile Hill-type muscles representing the major extensor and flexor muscle
groups. The segmentation of the muscles, with frictionless attachment points to
Model Selection and Adaptation 13
the vertebral bodies between the points of muscle origin and insertion, ensured
more physiological lines of action particularly during flexion and side bending
(van der Horst, Thunnissen et al. 1997). Figure 2.1 shows the configuration of the
model, with the vertebral bodies represented by simple geometric shapes,
ligaments as tension only line elements and muscles (only one shown) as
segmented constant volume ellipsoids. The specification of the parameters
defining the geometry, joint stiffness, displacement–load characteristics of the
ligaments, centres of rotation, and the active and passive muscle characteristics
was based on available data and values used by other researchers (de Jager 1996).
This model had been validated with human volunteer responses to frontal and
lateral impact at several intensities.
This figure is not available online. Please consult the hardcopy thesis
available at the QUT Library.
Figure 2.1 Path of a multi-segment muscle in initial and flexed positions. Only one part of the semispinalis capitis is shown to clarify muscle curvature. The intermediate sliding points are attached to the vertebrae (van der Horst, Thunnissen et al. 1997).
Model Selection and Adaptation 14
2.3.1 Model Components
The rigid body system representing the human neck was composed of nine
bodies in a single branch, from T1, through the seven cervical vertebral bodies, to
the head. The rigid bodies are defined by their mass, the moments of inertia, the
location of the centre of gravity and the location of the joint relative to the
preceding body. These values are used to solve the equations of motion of the
system when subjected to an external perturbation. For impact simulation, a short
duration (0.2 secs) acceleration pulse was applied to the joint between the model
and inertial space to represent the transfer of force from the upper body to the
neck and head. Other external forces and torques were applied during this research
to simulate clinical procedures. The rigid body system was bracket jointed to
inertial space and all other joints were free to translate or rotate, although
constraints between the vertebral bodies were defined using visco-elastic
representations of the discs and ligaments, and contact between facet joints.
Ellipsoids are associated with the rigid bodies for visualisation, and to allow
the definition of contact interactions. The vertebrae are represented by ellipsoids
for the vertebral body, transverse and spinous processes, and inferior and superior
facets. The head has ellipsoids for the skull, jaw, eyes, nose and mouth.
The intervertebral discs are modelled using Cardan restraints, which are
parallel connections of linear elastic springs and linear viscous dampers for each
of the six degrees of freedom (rotation and translation about three orthogonal
axes).
The ligaments in the model, the anterior longitudinal ligament (ALL), the
posterior longitudinal ligament (PLL), the flavel ligament (FL), the interspinous
ligament (ISL) and the capsular ligaments (CL) are modelled as straight line
Kelvin (series connected spring / damper) elements. The ligaments are tension
only elements described using non-linear force-strain curves with a constant
damping coefficient. The transverse ligament and tectorial membrane in the upper
cervical spine are modelled using belt elements that are equivalent to multi-
segment Kelvin elements.
Model Selection and Adaptation 15
Contact interactions between bodies within a system, or with bodies of
another system can be specified using either force/displacement or
stress/displacement characteristics, with the latter taking account of the area in
contact. Surfaces are required for the definition of contact interactions between
bodies. Regular surfaces can be defined using ellipsoids, cylinders, spheres and
planes whereas facet surfaces, either triangular or quadrangular, allow for a more
general description of a surface. An almost rigid, frictionless contact between the
zygapophysial joint ellipsoids was used to approximate the synovial joint
behaviour. As part of the adaptation of the model for clinical simulation, a facet
surface was used to model the skin on the neck to allow the application of external
forces (Section 2.4.2).
Body actuators are provided in MADYMO to apply concentrated forces or
torques on bodies and were used to apply torque to the rigid body representing the
head during ROM simulation, in much the same way as passive ROM is tested
clinically. Actuators can be controlled through a signal from a motion sensor
within the system, or from an external source.
Joint and body sensors are output devices to track the motion of selected
points on the joints and rigid bodies during model activation. The output from a
sensor can be modified using summers, transformers and controllers to activate
muscles or actuators to simulate neural feedback or reflex action.
The muscles are represented as multi-segment elements, with some muscles
broken into several parts to account for different points of attachment of the
muscle group. There are 122 muscle elements defined, Tables 2.1 and 2.2, with a
total of 616 muscle segments. Gravity was neglected during activation of the
model in the upright position to simplify the activation of the muscles. Muscle
activity was initially set at zero, but in reality the neck muscles would need to be
slightly activated in the neutral position to hold the head upright.
Model Selection and Adaptation 16
Table 2.1 Cervical flexor muscles in the model (left and right).
extension characteristics and muscle activation. Specific injuries were inflicted on
the model and the external evidence of the injury was determined in terms of the
ROM about the primary axes.
2.4.5.1 Structural Dysfunction
Zygapophysial joint damage has been reported as the most common source
of pain in patients with on-going whiplash associated disorders (Bogduk and Lord
1998). Physical examination reveals reduced or blocked motion of the joints
where pain is provoked (Corrigan and Maitland 1998), therefore joint dysfunction
was modelled by constraining the motion of specific joints. The manifested
stiffness could be related to changes in the mechanics of the joint, or splinting
from muscle spasm across the joint as a protective mechanism. Modelling the
muscular splinting across individual joints was not possible using the muscles
available in the neck model because a sophisticated muscle recruitment strategy
would be required to maintain equilibrium during the imposed head motions. An
adequate simulation of a combination of physical symptoms causing joint stiffness
was achieved by changing the joint stiffness parameters for the particular joint
under investigation. For each joint dysfunction combination, a 5Nm torque was
applied to the head to simulate the passive ROM testing of the primary actions:
flexion/extension; left and right lateral flexion; left and right axial twist. The
torque was increased linearly from zero, with the cut-off chosen to coincide with
the maximum physiological ROM about the axis under consideration. A similar
criteria for determining the torque applied during whole cervical spine flexibility
experimentation was used by Panjabi et al. (2001) and Nightingale et al (2002)
who found that approximately 3.5 Nm was needed for their particular set-ups.
Three sites of dysfunction were chosen and a factorial experimentation
procedure was used to represent the various combinations of upper and lower
symptoms. Table 2.3 shows the sites and combinations used to assess the
contribution of particular sites of stiffness. Runs 8 and 16 represented the
Model Selection and Adaptation 24
asymptomatic state of the model and the ROM output of these runs was used as
the baseline against which the ROM for all other symptomatic states was
compared. Increasing the joint stiffness by a factor of ten, which was not chosen
to represent any particular level of injury but rather to determine the influence of a
gross change in the stiffness, simulated the “stiff” state of the particular joints
affected by the change. It should be noted at this point that each particular set of
parameters produces one result.
Table 2.3 Factorial experiment design for joint stiffness evaluation.
Factor Description States
A C0-1 Joint(1) stiffness 1 Stiff -1 Std B C2-3 Joint(2) stiffness 1 Stiff -1 Std C C4-6 Joint(3) stiffness 1 Stiff -1 Std D Flexion / extension 1 Flexion -1 Extension E Lateral flexion 1 Left -1 Right Only one applies per runF Axial twist 1 Left -1 Right
The joint rotation output, Table 2.4, was obtained to examine the
contribution of each segment to the overall ROM. The ROM about the axes of
flexion, lateral flexion and axial twist are shown for each of the motion segments
of the cervical spine model. The sign convention used during the ROM evaluation
was flexion (+ve), extension (-ve), left lateral flexion (+ve), right lateral flexion (-
ve), left axial twist (+ve), right axial twist (-ve). This sign convention allowed the
comparison of the results obtained from the ROM simulations to be compared
with data previously collected from a symptomatic population at the Whiplash
Physical Diagnostic Clinic, University of Queensland.
2.5.2 Primary Motion Analysis
Tables 2.5 and 2.6 summarise the contribution of particular factors, and
combinations of factors, to the differences in recorded ROM between the
asymptomatic state of the model and the simulations with zygapophysial joint
symptoms.
Model Selection and Adaptation 30
Table 2.5 Change in ROM resulting from factorial experimentation applying combinations of unilateral zygapophysial joint stiffness. The factors represented by A, B and C are C0-1 joint stiffness, C2-3 joint stiffness and C4-6 joint stiffness respectively. (Results in degrees)
Table 2.6 Change in ROM resulting from factorial experimentation applying combinations of bilateral zygapophysial joint stiffness. The factors represented by A, B and C are C0-1 joint stiffness, C2-3 joint stiffness and C4-6 joint stiffness respectively. (Results in degrees)
Table 2.7 Change in cervical ROM due to reduced disc stiffness. (Results in degrees) Flexion - 50% reduction in disc stiffness Flexion - 90% reduction in disc stiffness
The effect of the stiffness of the alar ligaments on the upper cervical ROM is
shown in Table 2.9. The results of both ligament stiffness and laxity are presented
with the values representing the variation from the asymptomatic case.
Table 2.10 summarises the contribution of particular factors, and
combinations of factors, to the differences in recorded ROM between the
asymptomatic model and the models with zygapophysial joint symptoms during
the upper cervical rotation test. The factors represented by A, B and C are C0-1
joint stiffness, C2-3 joint stiffness and C4-6 joint stiffness respectively, being the
same as those used for the primary motion analysis previously.
Table 2.9 Results of altered alar ligament stiffness. (Results in degrees)
Dysfunction Flexion /
ExtensionLateral Flexion Axial Twist
Lax left & right alar turning left 0.6 -0.2 0.2
Stiff left & right alar turning left -0.1 0.5 -0.5
Lax right alar turning left 0.3 -0.2 0.2
Lax right alar turning right 0.0 0.0 -2.0
Stiff right alar turning left -0.1 0.5 -0.5
Stiff right alar turning right -0.0 -0.0 -1.9
Model Selection and Adaptation 36
Table 2.10 Change in ROM resulting from factorial experimentation applying combinations of zygapophysial joint stiffness. The factors represented by A, B and C are C0-1 joint stiffness, C2-3 joint stiffness and C4-6 joint stiffness respectively. (Results in degrees)
Left upper cervical rotation unilateral joint stiffness A B C AB AC BC ABC
The segmental motion response of the model, Table 2.4, compared very
favourably with the normal kinematic data presented in a comprehensive review
by Bogduk and Mercer (2000) except for the axial rotation response of the C1-C2
or atlanto-axial joint. The axial rotation at this level was very restricted at 9°
compared to the reported physiological average of 43°(SD 5.5°). This poor axial
response is a result of the difficulties imposed during modelling the mechanics of
the upper cervical spine within the constraints of the MADYMO program. The
vertebral discs of the lower cervical spine can be sufficiently modelled using
Cardan restraints that constrain the motion in the six degrees of freedom, whereas
the upper spine mechanics rely much more on contact interactions and
ligamentous restraints.
The passive ROM test simulation results, apart from the abnormal muscle
activation, showed surprisingly little variation despite large changes in the
stiffness parameters. Zygapophysial joint hypo-mobility and reduced discal
stiffness produced at most 6° deviation from the asymptomatic baseline. In
contrast, the muscle spasm simulation caused almost full twist (67°) as the
secondary motion during primary flexion. Figure 2.6 summarises the overall
results of the ROM simulation data, showing the range of primary and secondary
rotations generated as a result of the parametric changes to the model. This graph
masks most of the data from which it was derived by showing only the maximum
deviations, but what is evident is that for joint stiffness and discal laxity, the effect
on the secondary rotations was generally less than the effect on the primary
rotations whereas the opposite occurred with abnormal muscle activation. The
significance of this result is that scrutiny of secondary rotation patterns will
provide little further information about particular dysfunctions apart from muscle
spasm, which would be evident from external palpation anyway.
Looking more closely at the factorial experimentation results, extension
generated the most deviation while the interaction between factors contributed
almost nothing to the aberration of motion for all actions. Extension demonstrated
the greatest secondary axis deviation (corresponding to unilateral lower joint
stiffness) and the greatest primary axis reduction with bilateral upper joint
Model Selection and Adaptation 38
stiffness when compared with all other actions. Flexion and extension were also
shown to be the most discriminatory actions in the simulations of reduced disc
stiffness and prolonged muscle spasm, producing the greatest deviations from the
asymptomatic model response.
Influence of particular dysfunctions
Model output
-60
-40
-20
0
20
40
60
80
Ang
le d
evia
tion
(Deg
rees
)
Figure 2.6 Summary of the influence of the particular dysfunctions on the ROM about the primary and secondary axes of rotation.
The results of the upper cervical rotation test simulations showed little
response to the changed joint and ligament stiffness. This outcome was
unexpected because it indicated that little relative displacement, and hence little
change in length of the ligaments, was occurring and prompted further
investigation of the intersegmental motion. Table 2.4 showed the asymptomatic
segmental motion during the upper cervical rotation simulation and allowed
Primary Secondary Primary
Primary
Secondary
Secondary
Joint Stiffness
Disc Stiffness
Muscle Spasm
Model Selection and Adaptation 39
comparison with the ROM during upright axial rotation. Although the overall
rotations were similar to the average demonstrated clinically, it was important to
remember that the C2-C1 segment was excessively restrictive. Rotation at the C2-
C1 joint was only approximately twice that of the lower spine segments, pointing
to referral of motion down the spine. Comparing the segmental ROM during the
upper cervical rotation test with the upright rotation response revealed a small
reduction in segmental rotation in the lower spine, reduced coupled motion in the
lower cervical spine but increased coupling in the upper segments. The axial twist
of the C0-C1 and C1-C2 joints was also greater during the upper cervical rotation
test, indicating that the applied torque was absorbed more in the upper levels.
Considering the limitations of the model, the minimal response to the parametric
changes may be more attributed to the stiffness of the upper segments of the
model than the ineffectiveness of the test to discriminate between particular
dysfunctions.
2.7 CONCLUSION
The selection and adaptation of the detailed head-neck model for this ROM
study was satisfying, however the overall results were not as enlightening as
expected. The modelling of particular dysfunctions of the neck failed to identify
any signature movement patterns that could be attributed to specific injuries. Also,
the relevance of the modelling results was further reduced considering that the
natural variation in range of motion could be in the order of ±20° for flexion /
extension, ±12° for lateral flexion and ±14° for rotation (Christensen and Nilsson
1998), which was greater than the deviations generated by the parametric changes
to the model.
The excessive resistance to twisting of the upper segments of the model was
the greatest limitation during the application of the model to ROM evaluation.
The segments did, however, respond acceptably during flexion, extension and
lateral flexion. Since the greatest deviations from the baseline response were
evident during flexion and extension, correction of the twist response of the upper
segments was not required for this study. This limitation of the model would need
Model Selection and Adaptation 40
to be addressed however before clinical biofidelity could be claimed for the
model.
The modelling of chronic muscle spasm effectively demonstrated the effects
of abnormal muscle activation but the real effects in vivo would be moderated
through compensatory activation of other muscles. This compensation would be
difficult to model given the many muscle recruitment strategies available and was
not attempted given the constraints of this project. Another muscle activation
problem that was more directly related to the aims of this research is the subject of
Chapter 5 of this thesis. In this component of the study, the model was applied to
assess the biomechanics of the cranio-cervical flexion test that is used clinically to
evaluate deep neck muscle activation.
Since the outcome of this investigation suggested that ROM testing could
not discriminate between particular injuries, a substantial collection of clinical
data from a symptomatic population gathered by the Whiplash Physical
Diagnostic Clinic, University of Queensland, was evaluated to test this
hypothesis. The next chapter is devoted to this evaluation of the clinical ROM
data.
Range of Motion Data Analysis 41
Chapter 3
RANGE OF MOTION DATA ANALYSIS
Range of motion testing is used clinically as a primary indicator of
dysfunction of the cervical spine. While the range of motion can be measured
accurately in three dimensions using precision potentiometers, electromagnetic,
ultrasonic or video-graphic techniques, interpretation of the output must provide
clinicians with objective results to be of diagnostic benefit. Different
mathematical representations of the three dimensional motion of the head and
neck have been applied to characterise the pattern of motion, but the primary
clinical consideration is whether the output can effectively classify or localise
particular dysfunctions. The natural variation between subjects tends to
statistically mask the effects of particular dysfunctions and because of this, range
of motion analysis has added little to cervical dysfunction diagnosis apart from
attributing loss of range to an overall dysfunction. This chapter provides a review
of current analysis and the evaluation of the range and pattern of motion exhibited
by sub-groups, based on locality of manifested symptoms, within a symptomatic
population.
Range of Motion Data Analysis 42
3.1 BACKGROUND
The three dimensional kinematics of cervical motion can be reliably
measured using a variety of tools, all of which achieve a similar output in terms of
the angular description of the motion of applied sensors or markers. These
systems encompass mechanisms incorporating precision potentiometers (Dvorak,
Antinnes et al. 1992), video-graphic systems using cameras to track reflective
markers (Pearcy, Gill et al. 1987), ultrasonic systems using microphones and
ultrasonic transmitters (Dvir and Prushansky 2000), and electromagnetic systems
that track the motion of coils in a magnetic field (Trott, Pearcy et al. 1996).
Differences in the methodology for assessing the accuracy and reliability of these
systems make direct comparison difficult (Dvir and Prushansky 2000) but all have
been shown to have clinically viable performance. The data evaluated in this
chapter had been gathered using the Polhemus 3-Space Fastrak (A Kaiser
Aerospace and Electronics Company, Vermont), an electromagnetic goniometer,
at the Whiplash Physical Diagnostic Clinic, University of Queensland, Australia.
Analysis of the clinical range of motion data has shown that a reduction in
the range of motion can discriminate between persistent whiplash subjects and
asymptomatic subjects (Dall'Alba, Sterling et al. 2001) but the question remained
whether more information could be extracted from the ROM data that could assist
in the diagnosis of particular cervical dysfunctions.
3.2 OBJECTIVES
The objective of this study was to reassess the ROM data collected from the
symptomatic population in terms of the subjects’ corresponding physical
symptoms to establish:
• If a correlation could be established between the manifested symptoms and the
displayed ROM.
• If the pattern of motion was significant in the discrimination of particular
injuries.
• If the method of data representation using successive Cardan angles, as used
by the Whiplash Physical Diagnostic Clinic, was the most appropriate.
Range of Motion Data Analysis 43
3.3 METHOD
This section describes both the data collection and the data interpretation
methods. The data collection segment encompasses the equipment set-up and the
conversion of the raw data output into rotations about the reference axes. The data
interpretation segment then describes the methods used to explore the questions
posed by the objectives mentioned in Section 3.2.
3.3.1 Data Collection
The sensor orientation output from the Fastrak can be chosen to be in
Cardan angles or as a direction cosine string. The angles of rotation defined by
Polhemus are roll, elevation and azimuth that correspond to the system X, Y and
Z-axes respectively. The Cardan angles calculated by the device software
correspond to successive rotations about the Z, Y and X axes in that order
(Polhemus). The alternative output in terms of a direction cosine string is,
however, more useful for subsequent post-processing. The Fastrak that was used
to collect the data presented in this chapter was configured to give the direction
cosine output string in the order of the x direction cosines of the sensors’ x y z-
axes, the y direction cosines of the sensor’s x y z axes, and the z direction cosines
of the sensor’s x y z axes (Polhemus). By constructing a 3x3 matrix row-wise
from these values, the columns then contain the x y z vectors in rotation matrix
format. Orientation output can be obtained by the Fastrak from up to four sensors
simultaneously, and mathematical manipulation of the rotation matrices allows the
orientation of the sensors in 3D-space to be expressed either relative to the source,
or relative to another sensor.
In the clinic, the source was firmly attached to the rear of a wooden chair,
and two sensors were attached to the head and neck of the subject. One sensor was
attached to the bony protuberance of the C7 vertebra and the other was fixed to an
adjustable headband that held the sensor in a central position on the forehead
(Figure 3.1). The cervical ROM was calculated from the motion of the sensor on
the forehead relative to the motion of the sensor on the posterior base of the neck.
Range of Motion Data Analysis 44
Figure 3.1 Equipment set-up for clinical ROM evaluation
Representing the direction cosine matrices that describe the orientation of
the head and C7 sensors relative to the source as SRH and SRC7 respectively, the
rotations could be analysed individually to obtain the rotations relative to the
source, or combined to obtain the rotation of the head sensor relative to the C7
sensor. The relative orientation matrix of the head with respect to the C7 sensor, C7RH, could be determined using the combined rotation matrix generated by using
matrix multiplication as shown:
C7RH = ( SRC7)T x SRH
C7RH = C7RS x SRH
Range of Motion Data Analysis 45
The rotations about the chosen axes could then be obtained by applying the same
3-D angle calculation algorithm to either the individual sensor orientation matrix,
to obtain sensor relative to source rotations, or the combined orientation matrix to
obtain sensor 1 relative to sensor 2 rotations.
Since the substantial bank of ROM data under consideration here had been
collected prior to the commencement of this research, the interpretation of the data
required an understanding of the physical orientation of the device relative to the
subject and the orientation of the axes about which the final rotations were quoted.
The alignment of the axes of the source was matched to the anatomical axes as
shown in Figure 3.2 below. The ROM data was expressed as successive Cardan
angles and since Cardan angles are sequence dependent, the order in which the
rotations were calculated and reported was also important. While the set-up did
not comply with the accepted biomechanical standard of X - forward, Y - vertical
and Z - rightward (Wu, 2002), the axis of the primary motion had been chosen to
be the primary angle of rotation to most accurately describe the motion (McGill,
Cholewicki et al. 1997). Using the orientation of the source as shown, the rotation
sequences associated with the primary motions were:
• Flexion-extension, rotation about Y, then Z and X.
• Lateral flexion, rotation about Z, then Y and X.
• Axial twist, rotation about X, then Z and Y.
Figure 3.2 Orientation of source relative to body.
Range of Motion Data Analysis 46
From a given rotation matrix, the angles of rotation could be either referred
to the fixed axes of the source or the moving axes of the receiver. The data set that
was available for analysis was based on the moving axis principle. The derivation
of the successive rotations about the moving frame requires post-multiplication of
the individual axial rotations, where RX(α) represents the rotation about the X-
axis, RY(γ) the rotations about the Y-axis and RZ(β) the rotation about the Z-axis.
The equivalent rotation matrices for the primary motions of flexion/extension,
lateral flexion and rotation could be represented respectively as:
A
BRYZ’X’’(γβα) = RY(γ) RZ(β) RX(α) A
BRZY’X’’(γβα) = RZ(γ) RY(β) RX(α) A
BRXZ’Y’’(γβα) = RX(γ) RZ(β) RY(α)
The algorithms used for extracting the respective Cardan angles, based on
those provided by the International Society of Biomechanics (ISB) through the
kinematics toolbox for Matlab are given in Appendix 1. The equivalent rotation
matrices presented in the Appendices are a subset of the 24 angle set conventions
that represent the complete range of ordered sets of rotations presented by Craig
(1989).
The order of rotation used during the calculation of the ROM was based on
the orientation of the source relative to the subject, however, the results were
displayed and recorded with reference to a different set of axes. The reference
frame that was used to display the output, and for data recording, used rotation
about X for flexion/extension with flexion positive, rotation about Y for lateral
flexion with left positive, and rotation about Z for axial twist with left positive.
This transformation of axes as shown in Figure 3.3, meant that: display X = -
source Y, display Y = - source Z, and display Z = source X.
Range of Motion Data Analysis 47
X
Y
Z X
Y
Z
Source orientation Display orientation
Figure 3.3 Transformation between source and display angles.
3.3.2 Data Analysis
The primary motions analysed in this section relate to the six actions of
flexion, extension, left and right lateral flexion and left and right axial twist. Data
relating to the upper cervical rotation test was also available for a subset of the
subjects.
3.3.2.1 Primary Motion Analysis
The ROM data, expressed in terms of Cardan angles, used in this study had
previously been collected from 340 subjects who presented with persistent
whiplash associated disorder at the Whiplash Physical Diagnostic Clinic,
University of Queensland, Australia. These subjects had not responded to
conservative treatment during a period of at least three months post-injury. Each
subject was examined by a postgraduate manipulative physiotherapist and the site,
or sites, of dysfunction were determined using pain provocation and passive
intervertebral motion testing. The results of the manual examination were used to
stratify the sample population into ten groups (Table 3.1). Symptoms provoked at
the C2-C3 joint and above were classified as upper cervical dysfunctions.
Range of Motion Data Analysis 48
Table 3.1 Stratification of symptomatic population
Group Count
Unilateral left upper (10)
Unilateral left lower (24)
Unilateral left upper & lower (32)
Unilateral right upper (14)
Unilateral right lower (23)
Unilateral right upper & lower (38)
Bilateral upper (14)
Bilateral lower (40)
Bilateral upper & lower (72)
Mixed (73)
Following stratification of the sample population, the original data was re-
examined and the rotations about the three axes during the six actions of flexion,
extension, left and right lateral flexion and left and right axial twist were
statistically and graphically compared in terms of their average value and standard
deviation about the mean.
To determine the effect of representing the angular displacements in terms
of Cardan angles, the original data was re-evaluated relative to the anatomical
reference frame in accordance with recent recommendations by the International
Society of Biomechanics (ISB) (Wu 2002). During the reanalysis of the ROM
from the raw data, further parameters were extracted from the ROM traces to
investigate the pattern of the motion. The method developed by Pearcy, Gill et al
(1987) to describe the ROM of the lower spine was used during the reanalysis
because this method obtained rotations about the anatomical axes to represent
flexion, lateral bending and axial twist and the angles were not sequence
dependent. This method satisfied the ISB requirements and also removed the
problems of interpretation associated with the “floating axis” of the Joint
Coordinate System (JCS) proposed by Grood and Suntay (1983).
Range of Motion Data Analysis 49
3.3.2.2 Upper Cervical Rotation Analysis
The structure of the upper cervical spine is markedly different from the
lower segments and it is at this level that the majority of axial twist is facilitated.
The function of this segment can be assessed clinically using the upper cervical
rotation test in which the subject is placed in full flexion, and remains fully flexed
during the axial twist of the head. This position helps to isolate the upper spine by
structurally blocking rotation in the lower segments. The 3-D motion analysis of
this test had previously been disregarded by researchers at the Whiplash Physical
Diagnostic Clinic, University of Queensland, because the data collection protocol
specified the start point as the point of full flexion. This resulted in axes of
rotation that were not initially aligned with the anatomical axes and therefore
didn’t reflect the true axial rotation as desired. These motion artefacts, particularly
rotation about the Y-axis (lateral flexion), have also been reported by other
biomechanists (Feipel, Rondelet et al. 1999; Feipel, Salvia et al. 2001; Hof,
Koerhuis et al. 2001). A sample trace of the reported rotations following a flexed
starting position is shown in Figure 3.4. Transformation of the recorded
orientation matrix to represent a neutral starting position was achieved by pre-
multiplying the direction cosine orientation matrix by the orientation matrix
representing full flexion for the same subject. Figure 3.5 shows the resultant
angles for the same motion and same subject as shown in Figure 3.4 using the
corrected starting orientation. The flexion-lateral bending-axial twist Cardan
sequence was used initially during this analysis to minimise the cross-talk effects
(Hof, Koerhuis et al. 2001) and the results were very similar to the angles
calculated using the Pearcy method.
Range of Motion Data Analysis 50
Upper Cervical Rotation - Flexed Start
-40-30-20-10
010203040
Time
Rota
tion
(Deg
rees
)
X RotationY RotationZ Rotation
Figure 3.4 Upper cervical rotation from flexed starting position representing three complete cycles.
Upper Cervical Rotation - Neutral Start
-100
1020304050
Time
Rot
atio
n (D
egre
es)
X RotationY RotationZ Rotation
Figure 3.5 Upper cervical rotation from neutral starting position representing three complete cycles.
Range of Motion Data Analysis 51
3.4 RESULTS
3.4.1 Primary Motion Analysis
The mean 3-D rotations and standard deviation about the mean were
calculated for each stratified group and a one-way analysis of variation (ANOVA)
comparison was used to test whether real differences existed between groups. The
original ROM data-set contained the averaged maximum Cardan angles about the
three primary axes for three consecutive movements. These maximum rotations
were extracted by selecting the maximum rotation about each axis in the time
period corresponding to one complete action from the neutral position and back
again. During the reanalysis of the original data in terms of rotations about the
anatomic axes (Pearcy Method), the maximum rotations about each axis during
the complete cycle were again selected. The timing of the maximum rotations
about each axis was also extracted to provide more information about the
movement. Also, for each action, the orientations about all axes were recorded at
the end of range, this being the point of maximum rotation about the primary axis
of rotation for the particular action. The results of the ANOVA for each of these
data-sets, the original and the reanalysed data, are shown in Tables 3.2, 3.3 and
3.4. The ‘p’ values presented in the tables indicate the probability that the
differences between the ROM manifested by the stratified groups are due to
chance, with 1.0 corresponding to pure chance.
Table 3.2 One-way ANOVA p values from stratified sample, Cardan angles.
X Y Z Axis Action
Flexion 0.62 0.57 0.97
Extension 0.15 0.66 0.93
Left lateral flexion 0.27 0.46 0.34
Right lateral flexion 0.73 0.21 0.27
Left axial twist 0.77 0.58 0.17
Right axial twist 0.18 0.62 0.59
Range of Motion Data Analysis 52
Table 3.3 One-way ANOVA p values from stratified sample, Pearcy representation.
X Y Z Axis Action
Flexion 0.73 0.40 0.75
Extension 0.18 0.91 0.95
Left lateral flexion 0.30 0.56 0.44
Right lateral flexion 0.67 0.43 0.25
Left axial twist 0.52 0.67 0.48
Right axial twist 0.81 0.40 0.40
Table 3.4 One-way ANOVA p values from stratified sample, Pearcy representation at the end of range.
X Y Z Axis Action
Flexion 0.78 0.42 0.79
Extension 0.16 0.85 0.90
Left lateral flexion 0.32 0.65 0.30
Right lateral flexion 0.37 0.43 0.15
Left axial twist 0.76 0.75 0.53
Right axial twist 0.65 0.60 0.40
The ANOVA results show that at best there was still a 15% probability that
the differences in means were due to chance when the probability of rejecting a
true hypothesis (alpha value) was set at 5%. With the hope of finding some
correlation between the site of dysfunction and the manifested ROM that may
have been masked by the statistical evaluation, the ROM data associated with the
actions that showed less than 20% probability of being due to chance alone was
further explored. The cervical spine motions in this category were extension, right
lateral flexion, left axial twist and right axial twist. Following the reanalysis of the
Range of Motion Data Analysis 53
data to determine the rotations in terms of the anatomic axes, the difference was
most evident when the rotations were recorded at the end of range (Table 3.4),
therefore these were shown in the following comparisons. Graphical
representations of the average values and standard deviation about the mean for
the different groups performing the significant actions are presented in Figures 3.6
to 3.13 below. The results from both the original Cardan angle and Pearcy
calculation methods are shown for visual comparison. For each of the active
movements, the stratified groups were shown such that; bars 1 to 10 correspond to
the rotations about the X-axis (flexion / extension), bars 11 to 20 correspond to
rotations about the Y-axis (lateral flexion), and bars 21 to 30 correspond to
rotations about the Z-axis (axial twist). The groups as discussed previously in
Section 3.3.2.1, were stratified according to the site of the manifested symptoms:
1 Unilateral left upper
2 Unilateral left lower
3 Unilateral left upper & lower
4 Unilateral right upper
5 Unilateral right lower
6 Unilateral right upper & lower
7 Bilateral upper
8 Bilateral lower
9 Bilateral upper & lower
10 Mixed
Range of Motion Data Analysis 54
Extension ROM - Stratified Sampling of Symptomatic Population
-60
-50
-40
-30
-20
-10
0
101 11 21
RO
M (D
egre
es)
Figure 3.6 Comparison of groups during active extension showing the mean and standard deviation of the ROM (Cardan angles).
Figure 3.7 Comparison of groups during active extension showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum extension).
Extension ROM - Stratified Sampling of Symptomatic Population
-60
-50
-40
-30
-20
-10
0
101 11 21
RO
M (D
egre
es)
Range of Motion Data Analysis 55
Right Lateral Flexion ROM - Stratified Sampling of Symptomatic Population
-50
-40
-30
-20
-10
0
101 11 21
RO
M (D
egre
es)
Figure 3.8 Comparison of groups during active right lateral flexion showing the mean and standard deviation of the ROM (Cardan angles).
Right Lateral Flexion ROM - Stratified Sampling of Symptomatic Population
-50
-40
-30
-20
-10
0
101 11 21
RO
M (D
egre
es)
Figure 3.9 Comparison of groups during active right lateral flexion showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum right lateral flexion).
Range of Motion Data Analysis 56
Left Rotation ROM - Stratified Sampling of Symptomatic Population
-10
0
10
20
30
40
50
60
70
1 11 21
RO
M (D
egre
es)
Figure 3.10 Comparison of groups during active left axial twist showing the mean and standard deviation of the ROM (Cardan angles).
Left Rotation ROM - Stratified Sampling of Symptomatic Population
-10
0
10
20
30
40
50
60
70
1 11 21
RO
M (D
egre
es)
Figure 3.11 Comparison of groups during active left axial twist showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum right axial twist).
Range of Motion Data Analysis 57
Right Rotation ROM - Stratified Sampling of Symptomatic Population
-70-60-50
-40-30-20-10
01020
1 11 21
RO
M (D
egre
es)
Figure 3.12 Comparison of groups during active right rotation showing the mean and standard deviation of the ROM (Cardan angles).
Right Rotation ROM - Stratified Sampling of Symptomatic Population
-70
-60
-50
-40
-30
-20
-10
0
101 11 21
RO
M (D
egre
es)
Figure 3.13 Comparison of groups during active right rotation showing the mean and standard deviation of the ROM (Pearcy representation at the point of maximum right axial twist).
Range of Motion Data Analysis 58
3.4.2 Upper Cervical Rotation Analysis
A summary of the ROM exhibited by groups of subjects manifesting
particular sites of dysfunction is shown in Table 3.5. The values shown represent
the average rotations in degrees about the X, Y and Z-axes that initially represent
flexion, lateral flexion and axial twist respectively. The sign convention adopted
for the clinical data was to assign positive values to flexion, left lateral flexion and
left axial twist. These rotations were calculated following correction for a neutral
starting position as described in section 3.3.2.2
Table 3.5 Upper cervical rotation analysis: Comparison of groups with particular symptoms.
Count X Y Z
Upper left symptoms - rotation to left 7 -2.5 -11.6 22.8
Upper left symptoms - rotation to right 7 -2.3 6.1 -32.3
Upper right symptoms – rotation to left 14 -1.7 -6.4 26.7
Upper right symptoms – rotation to right 14 -3.3 6.3 -27.6
Upper bilateral symptoms - rotation to left 28 -1.9 -11.0 25.7
Upper bilateral symptoms - rotation to right 28 -1.8 10.6 -28.5
No upper symptoms - rotation to left 15 -1.2 -9.1 25.0
No upper symptoms - rotation to right 15 -2.9 8.5 -29.8
Mixed symptoms - rotation to left 43 -1.4 -6.2 25.4
Mixed symptoms - rotation to right 43 -1.2 4.6 -29.6
Asymptomatic - rotation to left 92 -4.9 -6.8 34.4
Asymptomatic - rotation to right 92 -4.6 6.4 -37.3
3.4.3 Pattern of Motion Analysis
Further information about the pattern of motion during the active
movements was obtained by considering the point at which the maximum rotation
about each axis occurred. Figure 3.14 depicts a smooth axial twist (Z being the
primary axis of rotation) and shows that the maximum rotations about each axis
occur at different points during the motion.
Range of Motion Data Analysis 59
Figure 3.14 Sample ROM trace showing differing points of maximum rotation during one complete axial twist cycle.
The primary axis of rotation was selected for each activity and the time to
reach the maximum point of the secondary angles was expressed as a percentage
of the time to reach the maximum primary angle. The timing columns in the
Tables 3.6 to 3.8 below show these values, with positive percentages indicating
that the secondary maximum occurred after the primary maximum.
Another interpretation of the pattern of motion extracted during this analysis
was the value of the secondary rotations at the end of range, this being the point of
maximum primary rotation. Tables 3.6 to 3.8 also show the difference, in degrees,
between the recorded maximum secondary rotations for the complete movement
cycle and the value of the secondary rotations at the point of maximum primary
rotation (X, Y & Z axis difference columns). A sign convention was established
for these columns by recognising that for each movement cycle, the maximum
rotation about any axis (Rmax) would be greater than, or equal to, the rotation at
the end of range about the primary axis (Rmp). This meant that if Rmp was positive,
due to the chosen sign convention, the difference was shown as negative by
computing Rmp – Rmax. If Rmp was negative, the difference was shown as negative
by computing Rmax – Rmp. Positive values in these columns arise from Rmp and
Rmax being of opposite sign, which results from aberrant motion patterns as
discussed in section 3.5.2. This data was derived during the reanalysis of the raw
data files.
Smooth motion during axial rotation
-70-60-50-40-30-20-10
010
Time
Rot
atio
n (D
egre
es)
X RotationsY RotationsZ Rotations
Range of Motion Data Analysis 60
Table 3.6 Stratified motion pattern data for extension and flexion showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range.
Extension – X primary axis Flexion – X primary axis
Group Y axis
difference Z axis
difference Y axis timing
Z axis timing
Y axis difference
Z axis difference
Y axis timing
Z axis timing
1 0.3 -1.1 -0.4 -3.9 -1.0 -0.3 8.2 2.1
2 -0.6 -0.1 3.2 5.4 -0.4 -0.6 3.6 3.8
3 -0.3 0.2 10.6 2.7 0.3 -0.1 5.2 0.9
4 -0.4 -0.6 -0.4 -1.0 0.6 -0.6 4.9 2.7
5 -0.5 -0.2 -1.2 5.3 0.6 -0.1 2.3 2.9
6 -0.7 -0.2 1.9 9.4 -0.4 -0.7 2.1 6.6
7 -0.4 0.3 4.9 4.2 -0.2 -0.3 1.8 3.2
8 -0.5 0.5 6.4 4.5 -0.3 -0.9 4.2 2.4
9 -0.2 0.2 5.9 12.5 -0.1 -0.4 5.5 2.6
10 -0.1 -0.3 8.5 10.1 -0.2 -0.3 1.5 3.9
Table 3.7 Stratified motion pattern data for left and right lateral flexion showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range.
Left lateral flexion – Y primary axis Right lateral flexion – Y primary axis
Group X axis
difference Z axis
difference X axis timing
Z axis timing
X axis difference
Z axis difference
X axis timing
Z axis timing
1 0.5 -1.1 2.1 4.6 0.9 -0.7 2.9 3.2
2 -0.9 -0.9 3.6 4.1 -0.1 -0.1 4.0 -2.0
3 0.9 -0.1 9.3 1.5 -0.5 -0.5 7.8 3.3
4 0.3 1.5 9.1 11.2 -0.6 -1.0 6.1 8.5
5 1.0 0.6 4.5 4.9 1.1 0.5 10.2 8.4
6 1.3 -0.4 9.3 5.2 -0.4 -0.7 4.1 5.2
7 0.1 0.8 4.7 7.4 -0.3 -0.2 10.3 7.4
8 0.4 -0.2 4.0 6.8 0.2 -0.9 4.1 5.3
9 0.9 -0.2 7.2 4.4 0.1 -0.1 9.0 8.3
10 1.0 -0.0 7.9 7.3 0.6 0.4 7.0 5.7
Range of Motion Data Analysis 61
Table 3.8 Stratified motion pattern data for the left and right axial twist showing the difference in rotation about the secondary axes (degrees) and timing of the maximum secondary rotations (%) when comparing complete cycle maximums with the values recorded at the end of the primary range.
Left axial twist – Z primary axis Right axial twist – Z primary axis
Group X axis
difference Y axis
difference X axis timing
Y axis timing
X axis difference
Y axis difference
X axis timing
Y axis timing
1 -1.0 -0.7 6.0 -2.2 -1.1 1.2 6.4 -5.7
2 -0.1 -0.3 1.1 -3.2 -0.3 1.1 6.9 -2.8
3 0.1 0.1 4.3 0.0 -0.1 -0.2 10.0 1.7
4 -2.2 0.4 7.9 -1.4 0.4 -0.3 6.8 3.8
5 -0.5 -0.1 1.3 -1.5 -1.0 0.1 7.5 0.0
6 -0.5 -0.6 7.1 -0.3 -0.6 -0.4 11.2 -0.2
7 -1.1 0.0 9.6 0.4 -0.1 0.5 -0.3 -6.6
8 0.1 -0.6 1.6 -1.7 0.2 -0.2 8.6 -1.5
9 0.1 -0.1 4.8 -2.6 -0.2 -0.6 4.3 -2.4
10 -0.2 -0.2 5.2 -1.6 0.1 -0.7 8.2 -0.5
3.5 DISCUSSION
3.5.1 Primary Motion Analysis
The number of subjects in each group ranged from 10 to 73, with the greater
numbers being in groups manifesting multiple sites of dysfunction. This disparity
reduces the accuracy of the statistical analysis but is significant in revealing the
distribution of chronic symptoms amongst the sample “whiplash” population
considered during this research. While other data was not available to determine
the external validity of the observations, and remembering that the stratification of
the population relied on the diagnostic skill of the Manipulative Therapist,
analysis of the distribution yielded:
• Upper cervical symptoms, occurring alone, were manifested least frequently
with similar numbers of left, right and bilateral sites of dysfunction.
Range of Motion Data Analysis 62
• Unilateral lower symptoms were equally manifested on the left and right and
were twice as common as upper cervical symptoms.
• Bilateral lower symptoms occurred approximately three times as frequently as
bilateral upper symptoms.
• Unilateral symptoms alone were manifested about half as often as bilateral
symptoms.
• The majority of subjects exhibited mixed or multiple sites of dysfunction.
The results of the ANOVA calculations showed that for the most part, the
ROM about any of the three axes was not significantly different between groups
manifesting different symptoms. The outcomes warranting further investigation
were: the rotation about the X-axis during extension; rotation about the Z-axis for
right lateral flexion; rotation about Z-axis during left axial twist and rotation about
the X-axis for right axial twist. The probability of the difference in mean rotations
about these particular axes being due to chance was less than 20% using either of
the calculation methods. This lenient cut-off was chosen in the hope that further
investigation would highlight otherwise hidden differences between the
symptomatic groups.
For extension, the probability of relevant differences in mean rotations
about the X-axis was similar using both of the calculation methods. During
extension, rotation about the X-axis describes the primary motion. Figures 3.6 and
3.7 show that the group with only unilateral right upper symptoms exhibited the
maximum extension (41°), while the group with mixed symptoms exhibited the
minimum extension (32°). Considering the anatomical near symmetry about the
sagittal plane, the perturbation of ROM in extension would be expected to be
similar for left and right-sided symptoms. The corresponding left sided
symptomatic groups both demonstrated 35° of extension, which weakened any
predictions based on the right-sided observations. Also, both of the right-sided
groups were represented by small numbers of subjects, 10 and 19 respectively,
further reducing the significance of the result.
The next motion considered was right lateral flexion. The primary axis of
rotation for this action was the Y-axis, but the real difference appeared to exist
Range of Motion Data Analysis 63
with respect to the twist axis (ANOVA p value, 0.15). Figure 3.9 shows that while
there was approximately 6 degrees difference between the maximum and
minimum rotations about the Z-axis, this difference was no more than one
standard deviation from the mean of the individual groups. It is worth noting at
this point, the difference in the reported secondary rotations between the different
angle calculation methods, while the primary angles are very similar in all cases.
Figure 3.8 shows the results using the Cardan angle representation for the same
right lateral flexion motion. For this action the Cardan secondary rotations show a
smaller variation, visually confirming the results of the ANOVA, Table 3.3,
which indicated a higher probability that the results were due to chance.
The next motion considered was left axial twist. The primary axis of
rotation for this action was the Z-axis, about which a real difference appeared to
exist when using the Cardan angle representation (ANOVA p value, 0.17). The
group with unilateral right upper symptoms exhibited the maximum ROM (56°)
again. Since the upper cervical spine primarily facilitates head rotation, a
dysfunction such as joint laxity may allow a greater contralateral ROM as in this
case, but this response was not mirrored during right rotation. During right
rotation the maximum ROM (55°) was again attributed to the unilateral right
upper group. These results would indicate that the small sample size reflected the
ROM of a more mobile group, rather than offering a signature to a particular
dysfunction. Observing that this group demonstrated the maximum primary
rotation for all actions further substantiated the cervical spine mobility of this
group.
The rotations about the X-axis (a secondary motion during axial twist) also
appeared significant (ANOVA p value, 0.18) during right axial twist, again using
the Cardan angles. These conjoint motions could be expected to reflect the pattern
of motion associated with a particular localised injury. While the average rotations
about the X-axis ranged from 3 to 8 degrees, this range was similar to one
standard deviation within the groups during this action so no real significance
could be attributed. Also the coupled rotations would be expected to be similar
between ipsilateral injury / action groups, and contralateral injury / action groups,
but this wasn’t the case for the examined population. Comparing the results of
Range of Motion Data Analysis 64
left-sided symptoms during left axial twist with right-sided symptoms during right
axial twist revealed no particular features. Similarly the comparison of right-sided
symptoms during left axial twist with left-sided symptoms during right axial twist
was inconclusive.
Since the analysis of the available ROM data proved inconclusive as far as
discriminating between particular injuries, alternative methods of representing the
3-D range and pattern of motion were investigated (Section 3.5.3).
3.5.2 Upper Cervical Rotation Analysis
The data available for this analysis again resulted in some small sample
sizes for particular groups, in particular those manifesting only upper left sided
symptoms (7 out of 107). All symptomatic groups however manifested similar
ROM, and followed the same pattern as the asymptomatic control population. The
observations of note were:
• Axial twist to the left was less than axial twist to the right, with the most
marked difference (9.5°) corresponding to upper left symptoms.
• Coupled rotations about the Y-axis (lateral flexion) were opposite in sign to
the primary axial twist with the greatest coupling accompanying bilateral
upper symptoms (-11° with left axial twist and 10.5° with right axial twist).
3.5.3 Pattern of Motion
The pattern of motion showed some differences between groups but
couldn’t be reliably used to discriminate between particular injuries, however the
influence of actions not part of the primary movement on the reporting of coupled
motions was highlighted. A positive difference between the recorded maximum
rotation and the value corresponding with the end of range rotation occurred in 40
of the 120 secondary rotations reported in Tables 3.6 to 3.8, which indicates that
in one third of cases, the recorded maximum secondary rotations for the whole
time period of the action were not a measure of coupled motion but reflect part of
the action either preceding or following the principal motion. Figure 3.15 shows a
Range of Motion Data Analysis 65
sample of aberrant lateral flexion motion where the primary rotation occurs about
the Y-axis. At the end of range, point of maximum Y rotation, both secondary
coupled rotations are positive whereas the maximums for the whole time period
would be recorded as negative.
The timing of the maximum secondary rotations compared with the primary
rotation also provides an indicator of the smoothness/aberration of the motion
without the need to visualise the trace. Smooth head motion about a primary axis
producing almost pure flexion/extension, lateral flexion or axial twist is typically
characterised by minimal deviation in the timing of the maximum rotations.
Figure 3.15 Sample ROM trace showing aberrant motion patterns.
A scatter plot was used to test the correlation between the differences in
reported maximums and the points at which the secondary rotations occurred
relative to the maximum primary rotation. Figure 3.16 shows the results for
extension, which were typical of the results for all of the actions. The scatter of
the data points showed that no correlation was evident, however the greatest
concentration was in the quadrant that corresponded with a reduction in reported
secondary rotations, and maximum secondary rotations that followed the
maximum primary rotation.
Aberrant motion during lateral flexion
-30
-20
-10
0
10
Time
Rot
atio
n (D
egre
es)
X RotationsY RotationsZ Rotations
Range of Motion Data Analysis 66
Figure 3.16 Determination of the correlation between the difference in reported maximum and the timing of the maximum rotations.
3.5.4 Data Representation
The original data collected using the Cardanic moving axis principle
precluded the interpretation of the rotations about the secondary axes in terms of
the anatomical reference frame. This limitation is often disregarded or overlooked
when describing motion clinically, so a method of representing the angles with
respect to the anatomical reference frame was considered to be most desirable.
Fixed axis Cardan angles could have been used to achieve this anatomical
association through deriving the equivalent rotation matrix by subsequent pre-
multiplication of individual axial rotations. This is in contrast to the moving axis
principle that uses post-multiplication of the individual axial rotations. This
method, however, is also sequence dependent and requires careful handling of the
orientation data to ensure that the primary movement is extracted first.
The method described by Pearcy et al (1987) that was used during the re-
analysis satisfied recent ISB recommendations, and because the reported angles
are not dependent on the sequence of analysis, direct comparisons can be made
between the primary and secondary angles of rotation for any of the physiological
Pattern of Motion Analysis - Extension
-5.0
0.0
5.0
10.0
15.0
-1.5 -1.0 -0.5 0.0 0.5 1.0
Average difference in reported maximums (Degrees)
Aver
age
timin
g of
max
imum
ro
tatio
ns (%
)
Y RotationZ Rotation
Range of Motion Data Analysis 67
head motions. All subsequent re-analysis and discussion of data in this thesis has
been based on this method.
3.5.4.1 Other Methods
Other methods of defining 3-D motion data have been proposed and were
considered during the selection of the analysis method.
A method that modelled the joints as overlapping cylinders had been
recently proposed for spinal motion definition (Crawford, Yamaguchi et al. 1999).
This analysis yielded three angles; the tilt angle, tilt azimuth angle and twist angle
that describe the relationship of the upper body with respect to the lower body.
While this method produces a stable and unambiguous representation of joint
motion, overall range of cervical motion may be oversimplified by considering it
as one joint.
An alternative method of characterising head motion represented the motion
in terms of an instantaneous axis about, and along which, a rigid body can be
thought to be moving at any point in time (Woltring, Long et al. 1994). This
method has been shown to discriminate between whiplash and asymptomatic
subjects but couldn’t be used as a measure of movement concentration. This
limitation rendered this technique of little benefit in the diagnosis of specific
injuries.
3.6 CONCLUSION
The results of this evaluation of clinical ROM data add weight to the
conclusions from Chapter 2 (the modelling of ROM testing) that range of motion
testing doesn’t expose any correlation between particular dysfunctions and their
external manifestation. The anatomical complexity of the human neck, the
potential for a diverse range of injuries, both in site and severity, and the body’s
protective mechanisms all combine to mask the root of the dysfunction.
Restricted ROM about the principal axes was evident during all of the
primary motions (flexion/extension, lateral flexion, axial twist) and during upper
cervical rotation for all of the symptomatic subjects but the rotations about the
Range of Motion Data Analysis 68
secondary axes were not significantly different. The stratification of the
symptomatic population based on the site of the manifested symptoms also failed
to show significant differences between groups based on their exhibited 3-D
ROM.
The reanalysis of the ROM data to investigate the pattern of motion also
proved ineffective in the discrimination of particular injuries, however the results
showed that substantial differences in coupled motion might be reported if
aberrant motion patterns are present. An improvement in accuracy of the reported
coupled rotations was achieved by recording the rotations about the three
anatomical axes at the end of range, this being the point in time of the maximum
primary rotation. A measure of the aberration in the movement pattern can be
obtained by also recording the timing of the maximum secondary rotations and
comparing these with the timing of the maximum primary rotation.
The method of data interpretation and reporting is also an important aspect
of ROM discussion. Successive Cardan angles are widely used and provide an
accurate description of the 3-D motion if the order of analysis is matched to the
primary motion and reported along with the results. Clinically, however, the
motion is often discussed with reference to the anatomical axes associated with
flexion / extension, lateral flexion and axial twist, which is not technically correct
when using Cardan angles. A non-sequence dependent method of analysis with
rotations referred to the anatomical axes (Pearcy Method) was chosen for the
reanalysis of the ROM data in this study, allowing direct comparison of both
primary and secondary rotations during any of the physiological activities.
Accepting that the consideration of the three dimensional nature of the
cervical spine motion may add little to the specific diagnosis of the dysfunction,
the assessment of the range of motion exhibited by symptomatic subjects will,
however, remain a valuable clinical tool, initially to determine the level of
movement restriction and then to monitor the progress during the treatment
(Wang, Olson et al, 2003). A simple manual goniometer would be sufficient for
this component of the clinical evaluation since consideration of the smaller
secondary rotations is not effectual.
Deep Neck Muscle Testing and Rehabilitation 69
Chapter 4
DEEP NECK MUSCLE TESTING AND REHABILITATION
Slow recovery following a minor neck injury, typically “whiplash”, has been
shown clinically to be associated with a deficit in cervical muscle function and
control (Sterling, Jull et al, 2003; Nederland, Hermens et al, 2003). The problem
confronting clinicians is how to demonstrate this deficit reliably, particularly
deficits of the deep muscles that cannot be monitored non-invasively. The
demonstration of the deficit and provision of feedback during rehabilitation have
been addressed clinically by using a pressure bio-feedback unit and the purpose of
this study was to evaluate the biomechanics of this clinical procedure. The value
of the cervical spine model as an instrument during this evaluation became
apparent during the adaptation of the model to simulate the ROM testing as
described in the Chapter 2.
Deep Neck Muscle Testing and Rehabilitation 70
4.1 BACKGROUND
The cranio-cervical flexion (C-CF) test has been developed for the clinical
assessment of cervical muscle function and control, particularly the deep flexor
group. The function of these deep neck flexor muscles has been found to be
significantly inferior in those suffering cervical headache (Jull, Barrett et al. 1999)
and/or whiplash associated disorders (Jull 2000). The use of the STABILIZER
pressure biofeedback unit (PBU), Figure 4.1, has been fundamental during the
development of the C-CF test and for the training of subjects during neck muscle
rehabilitation. The PBU is comprised of a segmented bladder and a hand-piece
that includes an air pump and pressure dial that is calibrated in millimeters
mercury (mmHg). The bladder is folded and clipped together for the C-CF test,
and is placed under the upper part of the neck with the subject lying supine with
their head in a neutral position. The bag is initially inflated with air to a pressure
of 20mmHg and the subject is trained to increase the pressure in the bag, in staged
increments of 2mmHg up to 30mmHg, by gently rolling their head to reduce the
cervical lordosis.
This figure is not available online. Please consult the hardcopy thesis
available at the QUT Library.
Figure 4.1 The STABILIZER pressure biofeedback unit (Chattanooga Group Inc) used during the cranio-cervical flexion test and for neck muscle rehabilitation.
Deep Neck Muscle Testing and Rehabilitation 71
Anthropometric differences between subjects, however, require variation of
the inflation of the PBU to establish the starting pressure. The effect of this
variation on the operation and calibration of the device is addressed in this study.
The operation of the bag can be analysed using basic fluid mechanics,
considering that air at normal temperature and pressures can be treated as an ideal
gas (Massey 1979). After inflation the bag can be considered as a closed system
with a fixed mass of gas in an adiabatic environment (no heat transfer) because,
during the operation of the device, the limited time in contact with the skin and
the temperature differential between the skin and the air in the bag would not
produce significant heat transfer. In these conditions the pressure (P) and volume
(V) of a gas are directly related, meaning that at any state of compression the
product of pressure and volume is constant. For two states representing initial
inflation (P1, V1) and a subsequent state of compression (P2, V2),
P1V1 = P2V2
Manipulation of this relationship reveals that the output, in terms of a set
pressure increase, is dependent on the initial volume and is not linearly dependent
on the reduction in volume (Appendix 2).
4.2 OBJECTIVE
The primary objective of this component of the study was to use an
adaptation of the cervical spine model to simulate the C-CF test, and thereby to
examine the correlation between specific neck muscle activation and external
measures. Within this study was an investigation of the effect of the variability of
the PBU properties on the outcome of the C-CF test. This required an analysis of
the response of the PBU to applied forces so that the input parameters of the
model of the feed-back unit could be defined.
Deep Neck Muscle Testing and Rehabilitation 72
4.3 METHOD
Modelling this test had two components. Firstly the characteristics of the
pressure biofeedback unit (PBU) were established so that the bag could be
represented in the overall simulation of the C-CF test. Then the cervical spine
model, that had been adapted for the ROM evaluation in Chapter 2, was orientated
in the supine position and the muscles were activated to replicate the testing
procedure.
4.3.1 PBU Characteristic Evaluation
Since the initial volume of air in the PBU was expected to affect the output
(Section 4.1) the inflated size of the bag was measured during the testing of 35
consecutive subjects at the Whiplash Clinic, University of Queensland, to
determine the working range. To measure the inflated size, the bag was taken
from under the neck following the test and placed between the parallel plates of a
bench vice and compressed until the pressure was restored to 20mm Hg as it was
during the resting stages of the test. The inflated size of the bag ranged from
21.5mm to 53.5mm, as measured between the faces of the plates on the vice. The
average inflated size of the bag was 40mm, with the distribution shown in Figure
4.2.
PBU Inflated Size at Rest
02468
1012
0-25 25-30 30-35 35-40 40-45 45-50 50-55
Inflated size (mm)
Freq
uenc
y
Figure 4.2 The distribution of the inflated size of the PBU at 20 mm Hg air pressure during the resting phase of the C-CF test.
Deep Neck Muscle Testing and Rehabilitation 73
The relationship between the inflated size and the volume of air contained
by the PBU is shown in Figure 4.3, although the inflated size of the bag was used
as the control variable during the subsequent testing of the bag characteristics.
The data points correspond to full pumps of the inflator (the bulb below the dial in
Figure 4.1), with the volume measured by the displacement of water from an
inverted graduated cylinder. This non-linear relationship can be attributed to the
construction of the PBU bag which results in a much more rounded profile as the
inflation increases.
PBU Inflated Size - Volume Relationship
150
200
250
300
350
400
20 25 30 35 40 45 50 55 60
Inflated size (mm)
Air
volu
me
(ml)
Figure 4.3 Relationship between the inflated size of the PBU and the contained air volume.
The force-displacement characteristics of the PBU were required for the
definition of the contact interactions between the bag and the posterior surface of
the neck in the simulation of the C-CF test. To establish the relationship between
the amount of compression and the resistance offered by the bag, which equalled
the force required to compress it, a Hounsfield compression-testing machine was
used to measure the force applied as the bag was compressed between a pair of
parallel surfaces.
Deep Neck Muscle Testing and Rehabilitation 74
Figure 4.4 The PBU as it is used during the cranio-cervical flexion test.
Figure 4.5 Orientation of the head-neck model to simulate the cranio-cervical flexion test simulation.
Deep Neck Muscle Testing and Rehabilitation 75
A series of tests were performed starting at 20mm plate separation through to
55mm to obtain the bag characteristics across the whole range of the inflated
sizes. For each test the bag was placed between the plates and initially inflated to
20mmHg. The bag was then compressed, measuring the force exerted and relative
displacement of the constraining surfaces as the pressure in the bag was
incrementally increased. Each test was repeated three times, and three different
bags were used to assess the variability between units.
4.3.2 C-CF Test Modelling
To simulate the C-CF test, as depicted in Figure 4.4, the cervical spine
model was orientated to represent the supine position and a representative
biofeedback unit, for force / displacement output, was placed under the posterior
surface of the neck (Figure 4.5). An ellipsoid was used to represent the PBU in the
model because this allowed the contact interaction function, between the bag and
posterior neck surface, to be matched to the values previously determined from
the compression testing of the PBU.
MADYMO had an air-bag simulation module that was investigated for the
PBU simulation but the output proved very difficult to stabilise. Since the air-bag
module uses finite element methods, the output was sensitive to the size of the
elements, the mechanical properties of the bag material and the parameters
relating to gas dynamics, therefore the simpler surface-to-surface contact
interaction method was used.
Three muscle groups; the deep flexors, superficial flexors and extensors,
were selectively activated to compare the output from the simulated PBU. The
muscle attachments points in the model were based on detailed anatomy texts and
the muscle force was directly related to the respective physiologic cross-sectional
areas (de Jager 1996). The deep flexor group was composed of the longus colli
and longus capitus muscles. The longus colli muscle was represented as seven
bundles with origins at the T1 level and insertions at C6, C5, C4, C3, C2, C1 and
skull. All bundles had a maximum contractile force of 12N. The longus capitus
muscle was represented by four bundles inserting on the skull with origins at C6,
Deep Neck Muscle Testing and Rehabilitation 76
C5, C4 and C3 levels. Each of these bundles had a maximum contractile force of
25N. The sternocleidomastoid (SCM) muscle was used to represent the superficial
flexors. This muscle was defined as two bundles to represent the sterno and
clavicular origins and both inserted on the skull. These bundles had a maximum
contractile force of 185 N each. The longissimus cervicus muscle was used to
represent the extensors. This muscle had six bundles with origins at the T2 level
and insertions at C7, C6, C5, C4, C3 and C2. These bundles all had a maximum
contractile force of 12N apart from the T2-C7 bundle that had a maximum
contractile force of 24N.
Activation of particular muscle groups was effected by changing the active
state parameter (A) in the contractile force (FCE) relationship of the Hill muscle
model:
FCE = A FmaxfH(vr)fL(lr)
where: Fmax is the force exerted by the muscle at maximal isometric contraction
fH(vr) is the force-velocity relationship
fL(lr) is the force-length relationship
The active state parameter could be varied from 0, rest state, to 1
corresponding to full activation. A full explanation of the muscle model from the
MADYMO manual is included in Appendix 3.
The simulations were repeated after halving the curvature of the spine to
assess the effect of the initial lordosis (spinal curvature) on the measurable output.
Halving the angles between the vertebral bodies, and adjusting the position of the
contacting faces of the zygapophysial joints to restore the original orientation
between them, reduced the curvature of the spine to half of the original. The axes
about which the intervertebral stiffness was defined were adjusted to match the
new orientation of the bodies to restore the same resting stiffness as was specified
in the base model. To achieve the neutral resting position, the headrest was
lowered by 8mm and the vertical position of the PBU was adjusted to again
achieve a starting pressure of 20mm Hg.
Deep Neck Muscle Testing and Rehabilitation 77
Since clinically the subjects are instructed to gently roll their head, the
output from the C-CF test model specifying the movement of the centre of
pressure and flexion of the head were also monitored to assess the biofidelity of
the model.
4.4 RESULTS
This section presents the results firstly of the technical evaluation of the
PBU and then the results of the C-CF simulation. The properties of the PBU, as
detailed in section 4.4.1, were used to set the parameters in the model of the
pressure bag in the C-CF test simulation.
4.4.1 Evaluation of PBU
The force / compression results of the three trials for each PBU were plotted
together to obtain the characteristics of each bag for the range of initial inflations
from 20mm to 55mm. The same procedure was used to test three bags. The results
obtained when the bag was inflated to 40mm (Figure 4.6) were typical.
PBU Force - Compression Relationship. 40 mm Inflated size
14161820222426
0 0.5 1 1.5
Compression (mm)
Forc
e (N
)
Bag 1Bag 2Bag 3
Figure 4.6 Typical PBU force-compression results for the three bags tested.
Deep Neck Muscle Testing and Rehabilitation 78
Table 4.1 Force-compression relationship for PBU representation. The units of force, F, and compression, x, are Newtons and millimetres respectively.
PBU 1, 2 & 3 Overall
Relationship R2 Relationship R2
20mm inflation
F = 18.43x + 23.97 0.92 F = 19.91x + 23.33 0.99 F = 19.01x + 23.57 0.96 F = 18.96x + 23.34 0.99
25mm inflation
F = 15.49x + 21.61 0.99 F = 13.79x + 21.66 0.97 F = 14.71x + 21.41 0.97 F = 15.09x + 20.87 0.98
30mm inflation
F = 11.29x + 19.95 0.96 F = 11.49x + 19.58 0.99 F = 11.42x + 19.53 0.97 F = 11.41x + 19.08 0.99
35mm inflation
F = 9.48x + 17.36 0.99 F = 8.73x + 17.26 0.99 F = 8.96x + 17.18 0.98 F = 8.74x + 16.90 0.99
40mm inflation
F = 7.28x + 15.73 0.99 F = 6.82x + 15.24 0.99 F = 6.89x + 15.49 0.98 F = 6.62x + 15.47 0.99
45mm inflation
F = 5.43x + 13.42 0.99 F = 5.19x + 13.27 0.99 F = 5.26x + 13.19 0.98 F = 5.07x + 12.95 0.99
50mm inflation
F = 3.99x + 11.38 0.99 F = 4.03x + 11.68 0.99 F = 3.99x + 11.32 0.97 F = 3.94x + 10.92 0.99
55mm inflation
F = 3.07x + 9.97 0.97 F = 3.11x + 9.81 0.99 F = 3.07x + 9.65 0.96 F = 2.97x + 9.25 0.99
Deep Neck Muscle Testing and Rehabilitation 79
The force / compression characteristics of the bags could be approximated as
a linear relationship over the normal operating pressure range of 20 – 30mmHg.
The linear regression equations representing the force-compression data and the
correlation coefficients (R2) for the individual bags are shown in Table 4.1. In
these equations the force, F, was measured in Newtons and the compression, x,
was measured in millimetres. The force-compression characteristics of the three
bags were not statistically different so the results were combined to obtain an
average force-compression relationship, which is also shown in Table 4.1. Figure
4.7 shows the combined results graphically, with the slope of the line indicating
the stiffness of the bag. These relationships were used as inputs for the contact
interaction between the PBU and the posterior neck surface in the model.
Figure 4.7 Overall PBU response for the 20 - 30 mm Hg pressure range with the slope indicating the stiffness relating to the initial inflated size of the pressure bag.
PBU Forc
1520
25
30
3540
Forc
e (N
)
Deep Neck Muscle Testing and Rehabilitation 80
PBU Pressure Output
0102030405060
0 20 40 60 80 100
Muscle activation (%)
Pres
sure
(mm
Hg)
Deep flexorsExtensorsSuperf. flexors
Figure 4.8 Output from simulated PBU for particular muscle group activations.
Deep Neck Muscle Testing and Rehabilitation 81
4.4.2 C-CF Test Modelling
The response of the C-CF test model to particular muscle group activation
was firstly determined using the PBU force/compression relationship
corresponding to the average inflation of 40mm (Section 4.3.1). The model of the
neck and head was allowed to settle against the headrest under the influence of
gravity and the position of the simulated PBU was adjusted vertically such that
the initial contact interaction between the bag and the posterior surface of the neck
generated a 20mmHg pressure output. The muscles were then steadily activated
up to 100 % of their peak contractile force. Figure 4.8 shows the PBU pressure
output in terms of the muscle activation.
To further understand the pressure output, the motion of the initial point of
contact (point of maximum contact force) between the posterior surface of the
head and the headrest was tracked during each muscle group activation
simulation. Figure 4.9 shows snapshots of the motion resulting from the activation
of the deep neck flexor muscles, starting from the zero position, prior to the
application of gravity. The second shot captures the resting position in which the
output of the simulated PBU corresponded with the 20mmHg starting pressure.
The final shot shows the results of 100% muscle activation. Figure 4.10 shows a
trace of the displacement of the initial point of contact between the head and the
headrest during the muscle activation with the level of activation shown on the
graph. Positive values for horizontal and vertical motion of the head correspond to
movement toward the upper torso and away from the headrest respectively. Figure
4.11 describes the same action in terms of the head flexion response, where
flexion is positive and extension negative.
Deep Neck Muscle Testing and Rehabilitation 82
Zero position Settled position
100% muscle activation
Figure 4.9 Snapshots of the motion resulting from the activation of the deep neck flexor muscle group.
Displacement of contact point with DNF activation
0%
20%40%
60%80%
100%
-8-6-4-2024
-8 -6 -4 -2 0 2
X Displacement (mm)
Y D
ispl
acem
ent (
mm
)
Figure 4.10 Displacement of the head contact point accompanying deep neck flexor activation.
Figure 4.11 Head flexion accompanying activation of the deep neck flexor muscle group.
Head flexion with activation of DNF muscles
0
2
4
6
8
0 20 40 60 80 100
Muscle activation (%)
Flex
ion
(Deg
rees
)
Y
X
Deep Neck Muscle Testing and Rehabilitation 83
Similarly, snapshots of the motion of the head and the graphical description
of the motion generated through the activation of the extensor muscle group are
shown in Figures 4.12 through to 4.14. The two snapshots in this case are the
resting and final positions after full muscle activation. These shots demonstrate
that the extensors produce little external response.
Settled position 100% muscle activation
Figure 4.12 Snapshots of the motion of the head accompanying the activation of the extensor muscle group.
Figure 4.13 Displacement of the head contact point accompanying the extensor muscle group activation.
Figure 4.14 Head flexion accompanying the extensor muscle group activation.
Displacement of contact point with extensor activation
100%70%40%20%0%
-5.7
-5.6
-5.5
1 1.2 1.4 1.6
X Displacement (mm)
Y D
ispl
acem
ent (
mm
)
Head flexion with extensor muscle activation
-0.1
0
0.1
0.2
0.3
0 20 40 60 80 100
Muscle activation (%)
Flex
ion
(Deg
rees
)
Deep Neck Muscle Testing and Rehabilitation 84
The effect of activating the sternocleidomastoid muscles is shown in Figures
4.15 through to 4.17. The snapshots from the simulation show that initially head
extension occurs and then the neck is flexed as the line of action of the muscle
force changes.
Settled position 80% muscle activation
100% muscle activation
Figure 4.15 Snapshots of the motion accompanying the activation of the sternocleidomastoid muscles.
Displacement of contact point with superficial flexor activation
0% 20% 40%80%
100%
-100
1020304050
0 5 10 15 20 25
X Displacement (mm)
Y D
ispl
acem
ent (
mm
)
Figure 4.16 Displacement of the head point of contact accompanying superficial flexor muscle activation.
Figure 4.17 Head flexion accompanying the superficial flexor muscle activation.
Head flexion with sternocleidomastoid activation
-20
-15
-10
-5
0
0 20 40 60 80 100
Muscle activation (%)
Flex
ion
(Deg
rees
)
Deep Neck Muscle Testing and Rehabilitation 85
To complete the information retrieved from the simulation, Figure 4.18
shows the force between the head and the headrest as the particular muscle groups
were activated.
Force on headrest
0
10
20
30
40
0 20 40 60 80 100
Muscle activation (%)
Forc
e (N
)
Deep flexorsExtensorsSuperf. flexors
Figure 4.18 Force between the head and headrest during muscle activation.
Having established that the deep flexor muscle group activation produced
the action requested clinically, the simulation of the C-CF test was further
extended to investigate the effect of the initial PBU inflation on the outcome of
the test. The functions determined experimentally, section 4.4.1, were used to
specify the contact interactions between the PBU and the neck surface. During
this series of C-CF test simulations, the head was again allowed to settle against
the headrest under the influence of gravity and the vertical position of the PBU
was adjusted such that the initial compression generated a 20mmHg pressure
output. The deep flexor muscles were then steadily activated up to 100 % of their
peak contractile force, however attention was directed toward the clinical
operating pressure range of 20 – 30mmHg. Three states represented by 25mm,
40mm and 50mm initial inflated size of the PBU were modelled. The case with
the PBU removed was also considered. Figure 4.19 shows the pressure output
from the simulated PBU for the three initial inflations.
Deep Neck Muscle Testing and Rehabilitation 86
Figure 4.19 Comparison of PBU pressure response with deep flexor muscle group activation for different initial inflations.
Figure 4.20 Comparison of the displacement of the point of contact for different initial PBU inflations.
Influence of inflation on the displacement of the contact point
0%10%
20%
30% 40%
0%
10%
40%
30%
20%
-6.5 -6
-5.5 -5
-4.5 -4
-3.5 -3
-4 -3 -2 -1 0 1 2 3 4
X Displacement (mm)
Y D
ispl
acem
ent (
mm
)
No PBU 25 mm40 mm50 mm
Effect of inflation on pressure output
20
25
30
35
0 10 20 30 40
Muscle activation (%)
Pres
sure
(mm
Hg)
25 mm40 mm50 mm
Deep Neck Muscle Testing and Rehabilitation 87
A comparison of the displacement of the point of contact between the head
and the headrest for the different PBU inflation states as the deep flexors are
activated is shown in Figure 4.20. The starting point is different in each case
because the force exerted by the PBU on the neck surface is determined by the
inflated size (Figure 4.7), and this affects the settled position. The level of muscle
activation is the same for each state and shown as points on the line.
Figure 4.21 shows the head flexion response during the simulated C-CF test
for the particular initial inflation states of the PBU.
Comparison of head flexion with different PBU inflations
-4-20246
0 10 20 30 40
Muscle activation (%)
Flex
ion
(Deg
rees
)
No PBU25 mm40 mm50 mm
Figure 4.21 Comparison of head flexion during the activation of the deep flexor muscles with different PBU inflations.
Deep Neck Muscle Testing and Rehabilitation 88
4.5 DISCUSSION
4.5.1 PBU Characteristics
The data obtained from the compression testing of the PBU bags
demonstrated consistency of results both during successive trials using the same
bag and between PBUs. In comparison with the overall values obtained by
combining the data, the stiffness values varied by a maximum of 6.2% and the
initial force varied by a maximum of 4.2%. This variation could be attributed to
the compartmental construction of the bag. Figure 4.1 shows the bag as three
connected compartments that are clipped together to form a “sandwich” for the
C-CF test. The folding process may restrict the flow of air between compartments
and the orientation of each layer may be slightly different during each trial of the
bag. The linear regression correlation coefficients (R2) were all close to 1
indicating that the force-compression relationship could be reasonably
approximated as linear for the operating pressure range of the PBU.
The compression test, that was used to obtain the PBU characteristics for
input into the pressure bag simulation, demonstrated clearly that the stiffness of
the PBU was dependent on the initial volume of air in the bag. The bag was the
stiffest at the low inflations, 19.1 N/mm at 20mm inflation, and softest at large
inflations, 3.1 N/mm at 55mm inflation, where the inflation was measured by
constraining the bag between parallel plates. The stiffness at the average inflation
of 40mm was 6.9 N/mm. In terms of the operation of the bag, the stiffness
determines the amount that the bag must be compressed to generate a set increase
in pressure. Clinically, the compression is caused by flattening the curvature of
the neck and the anthropometry of the subject determines the required initial
inflation. Therefore, subjects with a greater natural curvature must generate a
greater reduction of curvature to achieve the goal PBU pressures.
Another significant characteristic of the PBU is the force exerted by the bag
on its constraints at the starting pressure of 20mmHg. At low inflations the force
is much greater, being 23.6N at 20mm inflation, compared with 9.7N at 55mm
inflation. The force exerted at the average inflation of 40mm was 15.5N. This
characteristic is demonstrated in Figure 4.22, and is related to the inflated shape of
Deep Neck Muscle Testing and Rehabilitation 89
the bag and the relationship: Force = Pressure x Area. The shape of the inflated
bag becomes more rounded as the enclosed volume of air increases and therefore
the area in contact with the constraints becomes smaller for the same internal
pressure in the bag. This characteristic impacts on how comfortable the bag feels
under the neck during the test because the higher forces associated with the low
bag inflation may provoke pain in subjects experiencing tenderness in the area
where the PBU contacts the neck.
Another characteristic of the PBU is that at low initial inflations, the
depression (compressive distance) required to generate an air pressure of
30mmHg was minimal but the increase in force required to generate the pressure
increase was the greatest (Figure 4.23). Conversely at larger inflations the
depression required increased significantly but the additional force required to
generate the increase in pressure decreased. These observations highlight that the
PBU does not present a “level playing field” for either flexion feedback
(Depression) or muscle activation feedback (Force) across the range of inflations
required clinically.
PBU Force Characteristics
05
10152025303540
20 30 40 50 60
Inflated size (mm)
Forc
e (N
)
Force at 30mm HgForce at 20mm HgIncrease in Force
Figure 4.22 Force characteristics of the PBU relevant to the C-CF test.
Deep Neck Muscle Testing and Rehabilitation 90
PBU Depression Characteristics
0.0
0.5
1.0
1.5
2.0
2.5
20 30 40 50 60
Inflated size (mm)
Dep
ress
ion
(mm
)
Figure 4.23 Depression of the PBU required to generate the 10mm Hg pressure rise required during the C-CF test.
4.5.2 C-CF Test Simulation
The interpretation of the results of the C-CF test simulations must be made
in light of the muscle groups chosen to represent the deep and superficial flexors
and the extensors. Physiologically, these muscle groups would not be recruited in
isolation. Figure 4.8 showed that activation of the deep flexor group produced the
greatest rise in pressure of the PBU, with 100% activation producing almost
30mmHg pressure rise. This pressure rise was accompanied with a steady flexion
action (Figure 4.11) and minimal lifting of the head (Figure 4.10). Activation of
the SCMs produced an immediate reduction in PBU pressure because the spine
was firstly forced into extension until the head had rolled enough to alter the line
of action of the muscle force causing head lift. Activation of the extensors
produced some increase in the PBU pressure but this was accompanied with very
little flexion or head motion. The reduction of the curvature of the spine was also
accompanied by an increase in the force between the head and headrest (Figure
4.18) as would be expected of a retraction action.
Deep Neck Muscle Testing and Rehabilitation 91
The investigation of the PBU characteristics showed significant differences
relative to the initial inflation so three levels were chosen to represent the inflation
range; 25mm and 50mm initial inflations representing the endpoints of the tested
population and 40mm inflation being the average. The simulated PBU was also
removed to provide a baseline for the determination of the effect of the PBU.
Figure 4.8 showed that the maximum muscle activation required to achieve a
30mmHg pressure output from the PBU was just less than 40% of the maximum
contraction so attention was focused on this part of the simulation for the
comparison of PBU properties.
The deep flexor muscle activation required to generate 30mmHg of air
pressure in the PBU (Table 4.2) was similar for 25mm and 40mm initial inflations
but the highly inflated state required the greatest activation. Looking at the results
in terms of muscle activation, the same muscle activation produced 2.4 and
3.2mm Hg greater air pressure rise for the 40mm and 25mm initial inflation cases
respectively compared to the 50mm inflation case.
Table 4.2 Muscle activation - pressure response at different initial inflations.
Inflation
(mm) Pressure (mmHg)
Activation (%)
25 30 29
40 30 31
50 30 38.5
25 33.2 38.5
40 32.4 38.5
50 30.0 38.5
Deep Neck Muscle Testing and Rehabilitation 92
While these results could be taken to indicate that avoiding the high inflation
states produces a stable PBU response, the head contact point displacement
(Figure 4.20) and head flexion responses (Figure 4.21) at the lower inflations were
quite different. The starting displacements represent the settling of the head into
the headrest under the influence of gravity before muscle activation. The initial
settling was greatest for the case without the PBU as would be expected because
there was no support for the neck. The vertical displacement of the contact point
between the head and headrest was similar for all PBU inflations, however the
horizontal displacements manifested distinct differences. These results are more
easily interpreted when the flexion response is considered concurrently. The
stiffness of the PBU at 25mm inflation caused an initial extension of the neck
because of the high contact force at the starting PBU pressure of 20mmHg. This
extension brought the point of contact of the head toward the upper torso (+ve).
The flexion following muscle activation then produced a slide in the negative
direction. The amount of slide produced was similar; 2.0mm, 1.8mm and 2.2mm
for 25mm, 40mm and 50mm inflations respectively. The horizontal displacement
was greatest without the PBU, 3.4mm, this being accompanied by the greatest
flexion.
The alterations to the model to reduce the curvature of the spine by half of
its original amount produced only small variations in the overall response. The
most significant change was the increase in muscle activation required to achieve
30mmHg air pressure in the PBU, 1.3%, for the 50mm inflation case, which
reflected only a small change in the muscle line of action. These results indicate
that the anthropometry of the neck, which determines the initial inflation of the
PBU, has much more influence on the output than the spinal curvature.
Deep Neck Muscle Testing and Rehabilitation 93
4.6 CONCLUSION
Modelling the C-CF test provided confirmation of the efficacy of using the
PBU to provide feedback relating to the activation of the deep flexor muscles in
the neck. Activation of this muscle group produced a deflection of the bag that in
turn produced a measurable increase in the contained air pressure. However,
investigation of the properties of the PBU identified significant differences in the
stiffness of the bag for the different levels of inflation that are required during the
clinical use of this equipment. The differences in measurable output from the PBU
must be accounted for if comparisons are to be made between subjects and effort
must be made to standardise the inflation of the PBU during the initial set-up of
the test.
The simulation of the C-CF test identified that the motion of the point of
pressure of the head on the headrest, and the force at this point of contact during
the activation of the deep flexor muscle group could provide an alternative source
of measurable output that could be used as feedback during neck muscle
rehabilitation. The feasibility of using this type of motion feedback to guide the
correct action to target the deep muscles specifically, and the development of this
alternative is the subject of the next chapter.
Force and Motion Feedback Device 94
Chapter 5
FORCE AND MOTION FEEDBACK DEVICE
The prescription and execution of an exercise routine to target specific muscle
groups requires a reliable feedback mechanism to guide the desired action. This
study of an alternative device to the pressure bio-feedback unit, as investigated in
Chapter 4, is part of the circular interaction between modelling, clinical diagnosis
and injury management as envisaged in Chapter 1. Modelling of the cranio-
cervical flexion (C-CF) exercise suggested that the motion of the point of contact
between the head and a headrest, and the reaction force supporting the head, could
provide alternative sources of feedback for exercise guidance, so this possibility
was assessed.
Force and Motion Feedback Device 95
5.1 BACKGROUND
The study of force and motion during human activity is the basis of
biomechanics and accurate and reliable instrumentation has been developed but at
a cost that often prohibits general clinical usage. Force plates are widely used for
gait and sway analysis to investigate ground reaction forces and the movement of
the centre of pressure, however the smallest of this range is too large ( ≅ 400mm x
600mm x 35mm ) for use in cervical dysfunction diagnosis and rehabilitation. The
cost of these devices ( ≅ $10 000 ) also prohibits general use so a small, low cost
alternative was required to provide simple feedback to guide the correct action
during the prescribed neck exercise.
5.2 OBJECTIVE
The objective of this component of the project was to investigate the
feasibility of an alternative feedback device that used the motion and forces at the
point of contact between the head and headrest to guide the desired action.
5.3 DESIGN AND CALIBRATION
The initial designing of this feedback device involved the selection of force
sensors and the sizing of the force plate needed to gather the force and motion
data. The software support for the interpretation and visualisation of the data was
then developed so that the device could firstly be calibrated, and then used to
monitor the action during the C-CF test, previously described in Chapter 4.
5.3.1 Selection of Force Sensors
The selection of the force sensors for this application was constrained
primarily by the need to produce a very slim-line force plate that could be placed
under the head without upsetting the natural resting posture of the neck while
lying supine on a firm surface. Tekscan produced an ultra-thin (0.127mm) force
sensing resistor, FlexiforceTM Sensor (Specifications, Appendix 4), that was
Force and Motion Feedback Device 96
appropriate for this application. The A101 sensor is 14mm wide and 203mm long
with a 9.53mm diameter active sensing area at the end of the strip (Figure 5.1).
This figure is not available online. Please consult the hardcopy thesis
available at the QUT Library.
Figure 5.1 FlexiforceTM Sensor Model A101 (Tekscan 2002)
The FlexiforceTM single element sensors were incorporated into a force-to-
voltage circuit (Figure 5.2) and the output voltage was then calibrated in terms of
applied mass. These sensors are available in five standard force ranges up to a
maximum of 4448N, with the 0 - 111N range being chosen for this application.
This figure is not available online. Please consult the hardcopy thesis
available at the QUT Library.
Figure 5.2 Example of sensor excitation circuit (Tekscan 2002)
Force and Motion Feedback Device 97
5.3.2 Force Plate Design
A triangular sensor arrangement was selected because of the stability of a
tripod support and to reduce the accuracy required during manufacture and
assembly of the force plate. Since the sensors are ultra thin, small variations in the
mounting height or small deformations of the baseplate could unload a sensor in a
four cornered configuration. A triangular configuration also minimises the
channels required for data collection.
The top and bottom plates were made from 4mm thick Perspex and shaped
to provide support for the sensor lead connections (Figure 5.3). The sensors were
spaced equilaterally 170mm apart as this suited the sensor length and provided
enough working area between the sensors for this application. To accommodate
some bending of the top-plate during use, the sensors were mounted on raised
pads on the bottom plate and rubber pads were used to transfer the load to the
sensors from the top plate.
Figure 5.3 Force-plate configuration.
Force and Motion Feedback Device 98
5.3.3 Software Development
Software was required to convert the input, three channels of voltage data,
into the required output, being the movement of the point of contact between the
head and the force-plate, and the total force. LabVIEW 5.1 (National Instruments,
USA) was used to develop a virtual instrument for the data acquisition, analysis
and display. LabVIEW provides a graphical programming environment for the
assembling of software objects (virtual instruments) and allows the development
of interactive front panel control and display blocks.
Figure 5.4 shows the flow diagram for the analysis and display of the data.
The actual LabVIEW block diagram and front panel that implements these steps
and provides the visual feedback are shown in Appendix 5. The voltage output
from each sensor was sampled at approximately 15 Hz and the signals converted
from analogue to digital for subsequent processing. The location of the point of
contact and the total force was calculated for each sample and then the output was
smoothed by calculating a moving average across three consecutive
measurements. Since feedback was required relative to the resting position of the
head, the initial (resting) position of the point of contact and the reaction force
was subtracted from all subsequent values to show the deviation away from the
zero position of the display.
5.3.3.1 Position Calculation
The position of the point of contact was calculated by resolving the forces
about the centroid of the triangle enclosed by the sensors. The centroid of a
triangle lies on a line from the apex to the centre of the base and at the point two
thirds of the distance from the apex to the base (Figure 5.5). The x-position was
determined by resolving forces about the Y-axis, resulting in the formula:
321
32 )(85FFF
FFx++−
= [mm]
Force and Motion Feedback Device 99
The y-position was determined by resolving forces about the X-axis, resulting in:
321
132 98)(49FFF
FFFy++−+
= [mm]
where F1 , F2 and F3 are the forces at the respective sensors.
3 Voltage channels
A/D Conversion
Convert to force
Add forces
Calculate mo ving average
Star t data collection Store starting
values Subtract
starting values
Display force deviation
Calculate X & Y
Calculate moving average
Subtract starting values
Display X & Y deviation
Store values
Yes
Collec tion finished
W rite to file End
Yes
Figure 5.4 Flow diagram of the force and motion data analysis and display.
Force and Motion Feedback Device 100
X
Y
(x,y) F
1
2 3
85mm 85mm
49mm
98mm
Figure 5.5 Layout of the force sensors with the neutral point of the movement axes aligned with the centroid of the triangle.
To provide feedback about the head motion, an X-Y display showed the
deviation of the point of contact to guide the sliding action required by the C-CF
exercise. A three bar output was devised to guide the targeted distal slide. Red
bars each side of a central green bar indicated where the contact position was in
relation to the specified target position.
5.3.3.2 Reaction Force Feedback
The total force applied to the plate was found by summing the forces
recorded by the three sensors and a graded colour indicator was used as feedback
for the reaction force. The indicator was set to register as green in the resting
position, changing to red if the force increased due to retraction and blue if the
force decreased due to head lift or excessive head flexion during the prescribed
action.
Force and Motion Feedback Device 101
5.3.4 Calibration
The technical information accompanying the FlexiforceTM sensors
(Appendix 4) specifies a linear relationship between the force applied and the
voltage output but the actual response was expected to be dependant on the
mounting of the sensors, especially on non-rigid materials.
5.3.4.1 Sensor Mounting
A compliant layer was required to allow for the deformation of the top-plate
and a range of thicknesses was tested to determine the effect on the output.
Insertion rubber with a compressive strength of approximately 3.5 MPa was used
during trials 1, 2 and 3 with thicknesses of 1.2mm, 2.4mm and 3.6mm
respectively. Soft eraser rubber was used for trials 4 and 5 with respective
thicknesses of 5mm and 10mm. In all cases, the rubber layer was cut from a sheet
using an 8mm diameter wad punch and placed centrally on the sensing surface.
This comparative study was performed by applying a range of loads, from
0.5kg to 9kg, to the centroid of the sensor layout and recording the voltage output
from each sensor. The load – voltage relationship was determined for each sensor
by attributing one third of the load to each support. From this preliminary testing,
a 2.4mm thickness of insertion rubber was chosen for the permanent mounting of
the sensors. While the overall linear correlation was similar for all insertion
thicknesses (Appendix 6) the thinnest layer displayed a greater deviation at the
higher loads. After gluing, the calibration process was repeated, with the results
shown in Figure 5.6.
Force and Motion Feedback Device 102
Sensor 1 Calibrat ion
y = 0.4098x - 0.0207R2 = 0.9735
0.0
0.5
1.0
1.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Sensor 2 Calibrat ion
y = 0.4593x - 0.0916R2 = 0.9852
0.0
0.5
1.0
1.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Sensor 3 Calibrat ion
y = 0.5775x - 0.0479R2 = 0.9893
0.0
0.5
1.0
1.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Figure 5.6 Sensor calibration curves after permanent mounting.
Since the results above were considerably different from the results prior to
gluing, the sensors were loaded individually by placing the load directly above the
sensor to investigate the effect of the top plate deformation (Figure 5.7).
Sensor 1,Load - Voltage Relat ionship
y = 0.754x - 0.4954R2 = 0.9626
00.5
11.5
22.5
33.5
0 1 2 3 4 5
L o a d (kg )
Sensor 2, Load - Voltage Relat ionship
y = 0.6415x - 0.4186R2 = 0.9673
00.5
11.5
22.5
33.5
0 1 2 3 4 5
L o a d (kg )
Sensor 3, Load -Voltage Relat ionship
y = 0.7369x - 0.3494R2 = 0.9786
00.5
11.5
22.5
33.5
0 1 2 3 4 5
L o a d (kg )
Figure 5.7 Sensor calibration curves for direct load application.
5.3.4.2 Centre of Pressure Calibration
After the initial calibration, the movement of the centre of pressure (COP)
was assessed by comparing the displacement output with a known input for a
range of applied loads. The action being assessed by the C-CF test is a slide in the
direction of the Y-axis (Figure 5.5), therefore the output was determined for
deviations of 30mm each side of the zero point (centroid of sensor layout). The
initial results showed considerable errors (Figure 5.8) that were attributed to the
transfer of the load through the sensor mountings.
Force and Motion Feedback Device 103
Y Displacement Error
-15
-10
-5
0
5
10
15
20
0 1 2 3 4 5
Load (kg)
Y di
sp. e
rror
(mm
)
30 mm disp.20 mm disp.10 mm disp.-10 mm disp.-20 mm disp.-30 mm disp.
Figure 5.8 Discrepancies between the input and output Y-axis displacements.
These inaccuracies rendered the force-plate unserviceable for the
measurement of the movement of the centre of pressure so further
experimentation was conducted to try to improve the accuracy. The effect of the
deformation of the top-plate under load was investigated by doubling the
thickness of the top-plate. This in effect increased the bending stiffness eight-fold
since the bending stiffness is governed by the second moment of inertia, I, which
for a rectangular section equals:
12
3bd where b is the breadth and d is the depth of the section.
Doubling the depth, d, produces a 23 increase in the second moment of inertia, I .
The Y-axis displacement errors resulting from the stiff upper plate
investigation are shown in Figure 5.9. These results show greater deviation than
was evident with the original top-plate.
Force and Motion Feedback Device 104
Y Displacement error
-10-505
101520253035
0 1 2 3 4 5
Load (kg)
Y di
sp. e
rror
(mm
)30 mm disp.20 mm disp.10 mm disp.-10 mm disp.-20 mm disp.-30 mm disp.
Figure 5.9 Discrepancies between the input and output Y-axis displacements for the stiffer top-plate.
Finding that the stiffness of the top-plate had an adverse effect on the
accuracy of the device, further attempts were made to reduce the error by
determining the influence that each particular sensor had on the Y-axis deviation.
The contribution of individual sensors was visualised by plotting the error against
the output from each sensor (Figure 5.10 – 5.12).
Effect of F1 on Y displacement error
-15-10-505
10152025
0 0.5 1 1.5 2 2.5 3 3.5
F1 (kg)
Y di
sp. e
rror
(mm
)
Figure 5.10 Effect of the output of sensor 1 on the Y-axis displacement error.
Force and Motion Feedback Device 105
Effect of F2 on Y displacement error
-15-10-505
10152025
0 0.5 1 1.5 2 2.5
F2 (kg)
Y di
sp e
rror
(mm
)
Figure 5.11 Effect of the output of sensor 2 on the Y-axis displacement error.
Effect of F3 on Y displacement error
-15-10-505
10152025
0 0.5 1 1.5 2 2.5
F3 (kg)
Y di
sp e
rror
(mm
)
Figure 5.12 Effect of the output of sensor 3 on the Y-axis displacement error.
Figure 5.10 shows a trend toward greater error, although with less deviation,
as the output from sensor 1 increased. This trend was corrected by reducing the
slope of the linear relationship between the input voltage and the applied force,
which reduced the contribution from this sensor during the calculation of the Y-
displacement. The other sensors showed the same scatter at the lower force levels
but the error reduced as the force increased. After correcting the output from
Force and Motion Feedback Device 106
sensor one, the displacement error was tested again (Figure 5.13). This correction
improved the result, particularly in the mid-range, however ± 5mm on
measurements up to 30mm still indicates considerable inaccuracy. Also, since no
correlation was evident between the error and the actual displacement of the
centre of pressure, this inaccuracy must be attributed to the inconsistency of the
device more than to the calibration of the sensors.
Y Displacement Error
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
0 1 2 3 4 5
Load (kg)
Y di
sp. e
rror
30 mm disp.20 mm disp.10 mm disp.-10 mm disp.-20 mm disp.-30 mm disp.
Figure 5.13 Discrepancies between the input and output Y-axis displacements after correcting the sensor 1 output.
After altering the calibration of the sensors to achieve some improvement in
the centre of pressure output, the total load output was checked against the load
applied (Figure 5.14). The diagonal line represents perfect correlation between
input and output. The regression coefficient (R2) for the data about this line is
0.99, which means that the total load output from the force-plate could be used
with confidence.
Force and Motion Feedback Device 107
Forceplate Load - Displayed Load Relationship
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Load (kg)
Dis
play
ed L
oad
(kg)
Figure 5.14 Comparison of displayed and applied loads following force-plate calibration.
5.4 C-CF ACTION ASSESSMENT
While recognising that the force-plate could not accurately describe the
movement of the centre of pressure, the total force output results were sufficiently
satisfying to continue with the assessment of the feasibility of using the device to
provide feedback to guide the correct action during the C-CF exercise. Five
asymptomatic subjects were assessed to determine the variability between
subjects.
5.4.1 Force and Motion Deviation
The total ground reaction force was measured during the C-CF action, and
even though the motion of the centre of pressure output had proven to be
inaccurate, this measurement was also recorded as part of the variability analysis.
The range of both reaction force and movement of the COP were recorded so that
the effect of the variability of the device could be accounted for as part of the
Force and Motion Feedback Device 108
evaluation. The C-CF action was guided by instructions to gently roll the head
without lifting. Self-palpation of the superficial anterior neck muscles was used to
prevent the recruitment of the wrong muscle groups during the action. Figures
5.15 and 5.16 show the C-CF action resulting in a gentle roll of head without
superficial muscle activity.
Figure 5.15 Resting position prior to the cranio-cervical flexion test.
Figure 5.16 Gentle roll of the head as required by the cranio-cervical flexion exercise.
Force and Motion Feedback Device 109
Maximal flexion was achieved through recruiting these superficial muscles,
again without lifting the head off the force-plate (Figure 5.17). Maximal extension
was achieved by instructing the subjects to roll their head back as far as possible
(Figure 5.18). This action is not part of the C-CF action but was used to test the
response of the force-plate.
Figure 5.17 Maximal flexion without any head lift.
Figure 5.18 Maximal extension used to test the output from the force-plate.
Force and Motion Feedback Device 110
Table 5.1 Averaged force and movement during the C-CF action.
Subject Force Deviation (N)
Average (Range)
COP Deviation (mm)
Average (Range)
Flexion (degrees) Average
1 2.5 ( 2.2 - 2.7 ) 8.4 ( 8.1 - 8.7 ) 9
2 0.9 ( 0.7 - 1.1 ) 1.4 ( 1.3 - 1.6 ) 12
3 1.8 ( 1.7 - 2.0 ) -7.7 ( -8.0 - -7.4 ) 7
4 3.6 ( 3.1 - 4.2 ) -1.6 ( -2.9 - -0.6 ) 7
5 2.4 ( 2.4 - 2.9 ) 1.1 ( 0.9 - 1.4 ) 14
Table 5.2 Averaged force and movement during maximal flexion.
Subject Force Deviation (N)
Average (Range)
COP Deviation (mm)
Average (Range)
Flexion (degrees) Average
1 12.0 ( 10.7 - 12.9 ) 7.3 ( 6.7 - 8.1 ) 19
2 2.8 ( 2.6 - 3.2 ) -1.3 ( -2.3 - -0.6 ) 16
3 1.9 ( 1.1 - 3.0 ) -14.8 ( -15.4 - -13.6 ) 11
4 9.9 ( 8.7 - 11.8 ) -0.8 ( -2.8 - -1.0 ) 10
5 5.0 ( 4.6 - 5.5 ) 1.3 ( 1.2 - 1.6 ) 21
Table 5.3 Averaged force and movement during maximal extension.
Subject Force Deviation (N)
Average (Range)
COP Deviation (mm)
Average (Range)
Extension (degrees) Average
1 36.4 ( 35.0 - 38.2 ) -46.6 ( -46.9 - -46.2 ) 49
2 5.9 ( 4.3 - 7.4 ) -18.1 ( -18.5 - -17.4 ) 25
3 33.1 ( 32.9 - 33.2 ) -21.6 ( -21.8 - -21.4 ) 26
4 9.7 ( 7.2 - 11.7 ) 0.4 ( -0.3 - 1.4 ) 26
5 49.4 ( 43.8 - 53.4 ) -8.5 ( -8.7 - -8.2 ) 35
Force and Motion Feedback Device 111
Table 5.1 shows the results for the individual subjects during the same
gentle rolling action as prescribed during the C-CF test. Positive force values
indicate an increase in the reaction force. Positive COP deviation indicates
movement of the point of contact, between the head and the force-plate, away
from the lower body. The rotation of the head, flexion / extension, was measured
using a manual goniometer.
The initial results, above, seemed to indicate that the motion of the COP was
subject specific, with movement indicated in both positive and negative
directions. This was confirmed by considering the output corresponding to
maximal flexion (Table 5.2) and extension (Table 5.3).
5.5 DISCUSSION
5.5.1 Force-Plate Design
The COP motion results from the C-CF action assessment revealed that the
measurement area could be reduced for this application because the movement
range fell within ± 10mm from the resting position during the prescribed action.
The reduction in size of the force-plate however is constrained by the need for
stability and alignment under the head.
Reducing the size of the top-plate, and hence the sensor spacing, has an
impact on the stiffness of the top-plate for the same material thickness, and the
sensitivity of the sensors. Increasing the stiffness of the top-plate was shown
earlier to have little effect on the measurement error, although the reduced sensor
spacing should reduce the measurement fluctuation that would result from
instability in the output of the sensor. Since the calculation of the COP motion is
related to the physical dimensions of the sensor spacing (Section 5.3.3.1), smaller
spacings result in smaller fluctuations in the motion output for a given variation of
the sensor output. A 90mm sensor spacing was considered for comparison with
the original 170mm spacing. Table 5.4 shows the effect of a 5% variation of the
output of each sensor for both sensor spacings.
Force and Motion Feedback Device 112
Table 5.4 Effect of sensor spacing on measurement fluctuation.
170mm Spacing 90mm Spacing
Load (kg) Shift (mm) Shift (mm)
F1 F2 F3 X Y X Y
1.05 1 1 0.00 -1.61 0.00 -0.85
1 1.05 1 1.39 0.80 0.74 0.43
1 1 1.05 -1.39 0.80 -0.74 0.43
These results show that the shift caused by the sensor output variation is
related to the sensor spacing according to:
17090
170
90 =ShiftShift
Conversely, a given displacement produces a greater change in sensor output
when the sensors are closer together. The displacement calculations then rely
more on the linear approximation of the load – voltage output relationship, which
could lead to errors outweighing the gains achieved through the reduction in
centre of pressure measurement shift.
The transfer of load to the sensors through the sensor mounting was the most
probable source of error. The mountings were glued together to hold the device
together and to resist the shear forces generated during the prescribed sliding
action. Figures 5.6 and 5.7 indicate the difference ( up to 60% ) in the load-output
voltage relationship between central loading and loading directly over the sensor.
Elimination of the compliant layer to reduce this variability could be achieved by
placing the sensors between a rigid lower plate and linear bearings supporting the
upper plate. This modification however was not further explored when initial COP
motion results indicated that this measurement would be unsuitable for exercise
feedback.
Force and Motion Feedback Device 113
5.5.2 C-CF Action Assessment
The COP motion assessment produced unexpected results, with considerable
variation between subjects (from -7.7mm to 8.4mm deviation). A shift in the
positive Y direction was expected, coinciding with a slide of the point of contact
during the head rolling action. This expectation was tempered by the modelling
results which indicated only minimal movement ( 2mm ), however movement of
the COP in the negative direction was not anticipated. The variation in output
occurred even though the head flexion angle and self-palpation of the superficial
muscles indicated that the action was being performed correctly in each case. This
result could be attributed to the shape of the skull as demonstrated in Figure 5.19.
The skull shape was a variable that had not been considered during the design of
the feedback device.
Figure 5.19 Influence of skull shape on point of contact. Panes A1 and A2 depict a rounded posterior skull profile and the resulting motion, whereas B1 and B2 depict a flatter profile. The blue arrow shows resting point of contact and red arrow shows contact point after head roll.
A1 A2
B1 B2
Force and Motion Feedback Device 114
Figure 5.19 panes A1 and A2 show the movement of the point of contact
from the blue arrow to the red arrow as the head rolls forward when the posterior
profile of the skull is well rounded. If the posterior profile is flatter with
protrusion of the occipital bone, Figure 5.19 panes B1 and B2, the point of contact
moves in the opposite direction with the same head rolling motion.
The head extension action also demonstrated the variation in COP output (
from -47mm to 1mm ). The amount of extension achieved showed no correlation
with the COP motion output and the variation must again be attributed to skull
shape.
The deviation of the reaction force during the C-CF exercise ( 0.9N – 3.6N )
was much more consistent than the COP motion between subjects, although again
it could not be correlated with the amount of flexion. This lack of correlation
would prevent the device from being calibrated to provide feedback during staged
muscle recruitment, however the increase in reaction force during maximal
flexion ( Table 5.5 ) indicated that the reaction force could provide feedback to
prevent the recruitment of other muscle groups.
Table 5.5 Comparison of reaction force between desired head roll and maximal flexion.
Subject Force deviation during head roll (N)
Force deviation during maximal flexion (N)
Flexion increase (degrees)
1 2.5 12.0 10
2 0.9 2.8 4
3 1.8 1.9 4
4 3.6 9.9 3
5 2.7 5.0 7
Force and Motion Feedback Device 115
5.6 CONCLUSION
The results of the investigation of the motion and forces at the point of
contact between the head and headrest indicated that further development of any
similar device should be directed toward simply providing total reaction force
feedback. The deviation of the total reaction force from the resting value could
reliably guide the desired action by indicating the recruitment of other muscle
groups that either increase or decrease the total reaction force.
The motion of the centre of pressure was found to be subject specific,
depending on the posterior shape of the skull that determined the point of contact
during the head rolling action. An important outcome however is that the action
will feel different for different people, ranging from a slide to a roll of the head on
the headrest, and this must be accounted for by clinicians when guiding the
rehabilitation of the deep neck muscles. The training of self-palpation of the
anterior neck muscles to ensure that these muscles are not being recruited is
important to ensure that the correct action is performed.
Conclusion 116
Chapter 6
CONCLUSION
The diagnosis and treatment of chronic neck pain has been described as
difficult and frustrating for both the clinician and patient (Carette 1994). The
difficulty arises because the pain, which could arise from muscles, ligaments,
discs or joints in the neck, may be referred to another site. Typically lower
cervical segments may refer pain to the shoulder and upper limb, and upper
segment dysfunction may present as headache (Bogduk and Teasell 2000).
Frustration has developed through an underlying query as to the genuineness of
the symptoms manifested by those presenting for assessment. These difficulties
and frustrations provided the stimulus for the objective scrutiny of the
measurement and assessment of neck dysfunction in an effort to obviate the
stigma associated with chronic neck symptoms. The assessment of range of
motion, and the methods of testing and rehabilitating the function of the deep neck
muscles, were components of the bigger picture of clinical diagnosis and
management of cervical spine injuries that presented opportunities for further
biomechanical evaluation. This thesis examined these biomechanical aspects of
the clinical diagnosis of minor cervical spine injuries using a detailed
biomechanical model to simulate injuries to particular structures and to model
abnormal muscle activation. As indicated by the concept map in Chapter 1, the
observations and results arising from this research are only part of the cycle of
advancement in this area, and as information flows between the areas of clinical
diagnosis, injury management and modelling, further questions will be raised.
Conclusion 117
6.1 IMPLICATIONS FOR RANGE OF MOTION TESTING
Range of motion testing has been persistently applied during the clinical
assessment of cervical spine dysfunction, however little had been deduced from
the results apart from associating a loss of range with manifested physical
symptoms. While the range of motion can be accurately measured and recorded in
three dimensions, evaluation of the three dimensional nature of the motion was
found, in this study, to add little to the clinical diagnosis of neck dysfunctions.
As part of this research, biomechanical modelling of range of motion testing
was used in an attempt to understand better what to expect from the clinical data.
The aim of this biomechanical analysis was to use a biofidelic model of the
human neck to determine the correlation between particular injuries and their
external manifestation. The de Jager detailed head-neck model (de Jager 1996)
was chosen as the foundation for this research because it incorporated sufficient
anatomical detail and was supported by a powerful mathematical modelling
package, MADYMO, but the model required adaptation because it had been
developed for crash test simulations to investigate the response of the head and
neck to a short duration, high acceleration impulse. Passive range of motion
testing was simulated by applying a force to the head to generate the primary
motions of flexion/extension, lateral flexion and axial twisting, and parametric
changes were made to particular structures to simulate dysfunction of
zygapophysial joints, intervertebral discs, upper segment ligament integrity and
muscle control. The overall results, however, were not as enlightening as
expected, with only minimal variation in ROM accompanying gross changes in
structural properties, apart from muscle spasm that produced very aberrant motion
patterns.
Cervical spine range of motion data had been collected from more than three
hundred clients of the Whiplash Physical Diagnostic Clinic, University of
Queensland, prior to this study and this data was reanalysed to obtain more
information about the motion for comparison with the ROM test modelling
results. This clinical data revealed a more general reduction in range of motion
exhibited by symptomatic subjects than could be predicted by particular
perturbations of the model. Also, the natural variation in range of motion was
Conclusion 118
greater than the deviations generated by the parametric changes to the adapted
head-neck model. Further re-evaluation of the available clinical data, through
stratifying the symptomatic population into samples based on the site of the
manifested symptoms, failed to show significant differences between groups
based on their exhibited three dimensional range of motion. Also, reanalysis of the
range of motion data to investigate the pattern of motion (timing of maximum
rotations about the three primary axes) proved ineffective in the discrimination
between particular injuries. These results further confirmed the non-
discriminatory nature of range of motion testing, reinforcing the notion that the
scientific collection and interpretation of the three dimensional motion patterns
can not be justified clinically. Range of motion testing, however, has a place
clinically, initially to determine the level of movement restriction and then to
monitor the progress during treatment. This assessment though could be
performed sufficiently using a simple goniometer to measure the rotations about
the primary axis of rotation for the particular movement being tested.
Even though the description of the 3-D range of motion has limited use
clinically, the description of 3-D motion is significant biomechanically, and the
method of data interpretation and reporting is an important aspect of range of
motion discussion. The re-analysis of the available range of motion data from the
whiplash population indicated that substantial differences in coupled motion could
be reported if aberrant motion patterns were present. The aberrations in the
movement pattern may be associated with guarding strategies to avoid discomfort
or because the subject failed to follow the instructions given to produce the
required action. Consistent motion patterns associated with guarding may have
clinical significance, and may be distinguished through passive guidance of the
action, with resistance to performing the action when guided passively indicating
pain avoidance.
Improvements in the accuracy of the reported 3-D range of motion were
achieved by recording the rotations about the three anatomical axes at the end of
range, this being the point of maximum rotation in the direction of primary
motion. Also, since clinically the motion is discussed with reference to the
anatomical axes, the method of motion description presented by Pearcy et al
Conclusion 119
(1987) that is based on the joint coordinate system, a non-sequence dependent
method of analysis, is the preferred method and allows direct comparison of both
primary and secondary rotations during any of the physiological activities.
Reflecting on the components of clinical diagnosis shown on the concept
map (Figure 1.1), the main outcome from the modelling of range of motion testing
was showing that particular dysfunctions of the neck structures are masked by
interlinking of the components of cervical spine mobility, control and pain. Since
no relationship was found between specific dysfunctions and patterns of motion,
the control of head motion and the range of movement must be mediated by other
factors such as the presence or perception of pain.
6.2 IMPLICATIONS FOR MUSCLE FUNCTION TESTING AND REHABILITATION
The other component of the clinical assessment of minor neck injuries that
was identified for biomechanical evaluation was the cranio-cervical flexion
test. This test has additional importance because it is used to guide the
rehabilitation of the deep neck flexor group of muscles if a deficit in their control
is evident. The de Jager head-neck model was used again for this investigation
after some further adaptation. A surface was required to encompass the structures
and muscles of the neck so that the contact interaction between the posterior
surface of the neck and a simulated pressure bio-feedback unit could be specified.
The model was orientated in a supine position and the muscle groups were
selectively activated to determine the resulting movement of the head and the
output of the simulated pressure bag. Modelling the cranio-cervical flexion test
provided confirmation of the efficacy of using the pressure bio-feedback unit to
provide visual indication of the activation of the deep flexor muscles in the neck.
The results showed that it was only the activation of the longus colli – longus
capitus muscle groups, which lie close to the anterior surface of the cervical spine,
that produced a reduction in the cervical lordosis and a corresponding increase in
the pressure in the feed-back device.
Conclusion 120
Investigation of the properties of the pressure bio-feedback unit identified
significant differences in the stiffness of the bag for different levels of inflation.
Different levels of inflation are encountered clinically because of the
anthropometric differences between subjects, therefore standardisation of the
inflation of the PBU during the initial set-up of the test is necessary to improve
the reliability of the device. This standardisation is also important if comparisons
between subjects are to be reported. In the case of minimal curvature of the neck,
achieving the starting air pressure of 20mmHg in the bio-feedback unit may exert
enough force on the back of the neck to be uncomfortable for the subject. At the
other end of the scale, where the bio-feedback unit needs to be highly inflated,
very little starting force is exerted but the 10mmHg increase in enclosed air
pressure as required by the test protocol is difficult to achieve because of the
amount of compression required.
The motion of the point of pressure of the head on the headrest and the force
at this point of contact during the activation of the deep flexor muscle group
provided an alternative source of feedback that was investigated following the
identification of the calibration difficulties associated with the pressure bio-
feedback unit. A slimline force-plate was constructed using a triangular pattern of
Flexiforce® force sensing resistors (Tekscan) between perspex top and bottom
plates. Labview, which offers a graphical programming environment for virtual
instrumentation, was used to develop a program for the collection and display of
the total ground reaction force and movement of the centre of pressure data. The
motion of the centre of pressure was found to be subject specific, depending on
the posterior shape of the skull that determined the point of contact during the
head rolling action. Clinically, this result is important because the action that is
prescribed to target the deep flexor muscle group will feel different for different
people, ranging from a slide to a roll of the head on the headrest, and this must be
accounted for during the exercise training. The total ground reaction force output
however was more consistent between subjects and could be used to show that the
specified head roll was being performed with minimal retraction or head lift. The
deviation of the total reaction force from the resting value could reliably guide the
Conclusion 121
desired action by indicating the recruitment of other muscle groups that either
increased or decreased the total reaction force.
The biomechanical modelling of the cranio-cervical flexion test and the
experimentation associated with an alternative feedback device conducted during
this component of the overall study contributed, as proposed in the concept map
(Figure 1.1), to both the clinical diagnosis and injury management domains. The
modelling provided another dimension for the validation of existing devices and
the development of alternatives, and a platform was established for future
research.
6.3 FUTURE RESEARCH
The adaptation of the de Jager neck model, which transformed it from an
impact assessment tool to make it suitable for clinical research, has provided a
biomechanical modelling platform from which other clinical research questions
can be addressed. As experience is gained with the MADYMO modelling package
and the models that have been developed through it, the power and versatility of
the program becomes more apparent. Refinements and alterations would need to
be made to the model to satisfy particular research requirements but all could
piece together to extend the model’s clinical validity.
While the de Jager detailed head-neck model proved to be a sound basis for
this research, the excessive resistance to axial twisting of the upper cervical
segments of the model was the greatest limitation during the application of the
model to range of motion evaluation. The segments did, however, respond
acceptably during flexion, extension and lateral flexion and since the greatest
deviations from the baseline response were evident during flexion and extension,
correction of the axial twist response of the upper segments was not required for
this study. This limitation of the model would need to be addressed however
before clinical biofidelity could be claimed for the model.
Conclusion 122
Muscle activation was found to have the greatest effect on the deviation
from the asymptomatic range of motion and further research is needed to quantify
these effects. The modelling of chronic muscle spasm effectively demonstrated
the effects of abnormal muscle function but the real effects in vivo would be
moderated through compensatory activation of other muscles. This compensation
would be difficult to model given the many muscle recruitment strategies
available, however approximations to the response could be achieved through
muscle recruitment optimisation. Investigation of the disturbance of the
proprioceptive feedback from the muscles following injury could also have
clinical value.
Also, the results obtained from the small, low cost force-plate developed for
this study warrant further refinement of a similar device. The Flexiforce® force
sensors manifested a reasonably linear force – output response but the method of
mounting, using a glued compliant layer to accommodate the bending of the top
and bottom plates, reduced this linearity and amplified calibration differences
between sensors. Elimination of the anomalies associated with the mounting while
still allowing force transfer would need to be the focus of further development.
These sensors would have a wide application in the field of biomechanics and
offer a real alternative to other load cell devices.
As research continues in this field of the diagnosis and injury management
of cervical spine injuries, real progress will be made through the type of
multidisciplinary effort and iterative development by Biomechanists and
Therapists as experienced during this research.
Appendices 123
APPENDIX 1
Algorithms for moving axes (Cardan angles)
The algorithms used to determine the Cardan angles describing the 3-D
motion of the head were slightly different for each of the primary actions to
account for the order of analysis, given the same initial orientation output from the
Fastrak.
Flexion-Extension: A
BRYZ’X’’(βγα) = RY(β) RZ(γ) RX(α)
gama = asin(R(2,1)); %'assumption' that cos(gama)>0 % alphasin = asin(-R(2,3)/cos(gama)); alphacos = acos(R(2,2)/cos(gama)); if (alphacos>pi/2 & alphasin>0) alpha=pi-alphasin; end; if (alphacos>pi/2 & alphasin<0) alpha=-pi-alphasin; end; if (alphacos<=pi/2) alpha=alphasin; end; % betasin = asin(-R(3,1)/cos(gama)); betacos = acos(R(1,1)/cos(gama)); if (betacos>pi/2 & betasin>0) beta=pi-betasin; end; if (betacos>pi/2 & betasin<0) beta=-pi-betasin; end; if (betacos<=pi/2) beta=betasin; end; % dispXYZ =[-beta,-gama,alpha].*(180/pi);
Lateral Flexion: A
BRZY’X’’(γβα) = RZ(γ) RY(β) RX(α)
beta = asin(-R(3,1)); %'assumption' that cos(beta)>0 % alphasin = asin(R(3,2)/cos(beta)); alphacos = acos(R(3,3)/cos(beta)); if (alphacos>pi/2 & alphasin>0)
Appendices 124
alpha=pi-alphasin; end; if (alphacos>pi/2 & alphasin<0) alpha=-pi-alphasin; end; if (alphacos<=pi/2) alpha=alphasin; end; % gamasin = asin(R(2,1)/cos(beta)); gamacos = acos(R(1,1)/cos(beta)); if (gamacos>pi/2 & gamasin>0) gama=pi-gamasin; end; if (gamacos>pi/2 & gamasin<0) gama=-pi-gamasin; end; if (gamacos<=pi/2) gama=gamasin; end; % dispXYZ =[-beta,-gama,alpha].*(180/pi);
Rotation: A
BRXZ’Y’’ (αγβ) = RX(α) RZ(γ) RY(β)
gama = asin(-R(1,2)); %'assumption' that cos(gama)>0 % alphasin = asin(R(3,2)/cos(gama)); alphacos = acos(R(2,2)/cos(gama)); if (alphacos>pi/2 & alphasin>0) alpha=pi-alphasin; end; if (alphacos>pi/2 & alphasin<0) alpha=-pi-alphasin; end; if (alphacos<=pi/2) alpha=alphasin; end; % betasin = asin(R(1,3)/cos(gama)); betacos = acos(R(1,1)/cos(gama)); if (betacos>pi/2 & betasin>0) beta=pi-betasin; end; if (betacos>pi/2 & betasin<0) beta=-pi-betasin; end; if (betacos<=pi/2) beta=betasin; end; % dispXYZ =[-beta,-gama,alpha].*(180/pi);
Appendices 125
APPENDIX 2
PBU response assuming ideal gas relationships
Manipulation of the basic ideal gas law (P1V1 = P2V2) yields an equation to
calculate the change in volume (∆V), for a chosen initial pressure (P1) and
pressure increase (∆P), in terms of the initial volume of gas (V1). It should be
noted that as P1 increases to P2 , V1 must decrease to V2 to maintain equality,
therefore P2 = P1 + ∆P and V2 = V1 - ∆V .
11
11
11
11
1
12
1
2
111
12
11
22
11
2211
1
1
VPP
PV
VPP
PPPV
VPP
PV
VPPV
PVPVV
VVPVP
VPVP
VPVP
∆+
∆=∆⇔
∆+−∆+
=∆⇔
∆+
−=∆⇔
−=∆⇔
−=∆⇔
∆−=⇔
=⇔
=
This relationship is shown graphically, Figure A3.1, for the operating range of the
PBU from 20 - 30mmHg. P1 was set at 20mm Hg and ∆P was increased from 2 –
10mmHg to show the relationship between the change in pressure and the change
in volume.
Appendices 126
Pressure - Volume Response
5
10
1520
25
30
35
2 4 6 8 10
Change in Pressure (mm Hg)
Cha
nge
in V
olum
e(%
V1)
Figure A3.1 Pressure – Volume relationship for an ideal gas.
While this relationship is non-linear, a linear relationship would be a close
approximation over the considered range (R2 = 0.99). More important to the
operation and calibration of a PBU is that the change in volume required to
generate a chosen change in pressure is dependent on the initial volume of gas in
the PBU.
Appendices pp. 127-131
APPENDIX 3
MADYMO 5.4 – Hill type muscle model
Appendix 3 (pp. 127-131) is not available online. Please consult the hardcopy thesis
Available at the QUT Library.
Appendices pp. 132-135
APPENDIX 4
Tekscan FlexiForceTM Sensors technical literature ( www.tekscan.com/flexiforce/ )
Appendix 4 (pp. 132-135) is not available online. Please consult the hardcopy thesis
Available at the QUT Library.
Appendices 136
APPENDIX 5
Labview front panel and block diagram used to control the force-plate.
Appendices 137
Appendices 138
APPENDIX 6
Sensor load – output voltage relationships for various mounting layer thicknesses used for the selection of the sensor mounting material.
Trial 1 , Sensor 1, Load - Voltage Relat ionship
y = 1.0153x +0.0717 R2 = 0.9946
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 1 , Sensor 2, Load - Voltage Relat ionship
y = 0.8828x - 0.0299R2 = 0.996
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 1 , Sensor 3, Load - Voltage Relat ionship
y = 0.8324x + 0.0134R2 = 0.9936
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 2 , Sensor 1, Load - Voltage Relat ionship
y = 0.9345x + 0.0121R2 = 0.9919
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 2 , Sensor 2, Load - Voltage Relat ionship
y = 0.8129x + 0.0207R2 = 0.9957
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 2 , Sensor 3, Load - Voltage Relat ionship
y = 0.7989x - 0.0379R2 = 0.9954
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 3 , Sensor 1, Load - Voltage Relat ionship
y = 0.9193x + 0.0033R2 = 0.9944
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 3 , Sensor 2, Load - Voltage Relat ionship
y = 0.7346x + 0.0214R2 = 0.9942
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 3 , Sensor 3, Load - Voltage Relat ionship
y = 0.7488x - 0.0815R2 = 0.9964
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Appendices 139
Trial 4 , Sensor 1, Load - Voltage Relat ionship
y = 0.8558x + 0.0141R2 = 0.9935
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5
L o a d (kg )
Trial 4 , Sensor 2, Load - Voltage Relat ionship
y = 0.7795x - 0.0018R2 = 0.9884
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5
L o a d (kg )
Trial 4 , Sensor 3, Load / Voltage
y = 0.6944x - 0.004R2 = 0.9964
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5
L o a d (kg )
Trial 5 , Sensor 1, Load -Voltage Relat ionship
y = 0.5714x + 0.1255R2 = 0.9863
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 5 , Sensor 2, Load - Voltage Relat ionship
y = 0.6304x + 0.1023R2 = 0.9915
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Trial 5 , Sensor 3, Load - Voltage Relat ionship
y = 0.7213x + 0.017R2 = 0.9894
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
L o a d (kg )
Appendices 140
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