Mathematical Modelling of Muscle Recruitment And
MATHEMATICAL
MODELLING OF MUSCLE
RECRUITMENT AND
FUNCTION IN THE LUMBAR
SPINE
MICHELLE L GATTON BSc Hons
Submitted for the award of degree of Do ctor of Philosophy in the
Centre for Rehabilitation Science and Engineering Scho ol of
Mechanical Manufacturing and Medical Engineering Queensland
University of Technology
September
Keywords
lumbar spine anatomical mo del spinal mo del lumbar spine muscle moments
muscle force iii
Abstract
Low back pain is an increasing problem in industrialised countries and although
it is a ma jor so cio economic problem in terms of medical costs and lost pro duc
tivity relatively little is known ab out the pro cesses underlying the development
of the condition This is in part due to the complex interactions between b one
muscle nerves and other soft tissues of the spine and the fact that direct obser
vation and or measurementofthehuman spine is not p ossible using non invasive
techniques
Biomechanical mo dels have b een used extensively to estimate the forces and mo
ments exp erienced by the spine These mo dels provide a means of estimating the
internal parameters which can not be measured directly However application
of most of the mo dels currently available is restricted to tasks resembling those
for which the mo del w as designed due to the simpli ed representation of the
anatomy
The aim of this research was to develop a biomechanical mo del to investigate
the changes in forces and moments which are induced by muscle injury In
order to accurately simulate muscle injuries a detailed quasi static three dimen
sional mo del representing the anatomy of the lumbar spine was develop ed This
mo del includes the nine ma jor force generating muscles of the region erector
spinae comprising the longissimus thoracis and ilio costalis lumb orum multi
dus quadratus lumb orum latissimus dorsi psoas ma jor rectus ab dominis v
transverse ab dominis internal oblique and external oblique as well as the thora
columbar fascia through whichthetransverse ab dominis and parts of the internal
oblique and latissimus dorsi muscles attach to the spine The muscles included
in the mo del have been represented using muscle fascicles each having their
own force generating characteristics and lines of action
Particular attention has b een paid to ensuring the muscle lines of action are
anatomically realistic particularly for muscles which have broad attachments
e g internal and external obliques muscles which attach to the spine via the
thoracolumbar fascia e g transverse ab dominis and muscles whose paths are
altered bybony constraints such as the rib cage e g ilio costalis lumb orum pars
thoracis and parts of the longissimus thoracis pars thoracis In this endeavour
a separate sub mo del which accounts for the shap e of the torso by mo delling
it as a series of ellipses has been develop ed to mo del the lines of action of the
oblique muscles Likewise a separate sub mo del of the thoracolumbar fascia has
also been develop ed which accounts for the middle and p osterior layers of the
fascia and ensures that the line of action of the p osterior layer is related to the
size and shap e of the erector spinae m uscle
Published muscle activation data are used to enable the mo del to predict the
maximum forces and moments that may be generated by the muscles These
predictions are validated against published exp erimental studies rep orting max
imum isometric momentsforavariety of exertions The mo del p erforms well for
exion extension and lateral bend exertions but underpredicts the axial twist
moments that may be develop ed This discrepancy is most likely the result of
di erences between the exp erimental metho dology and the mo delled task
The application of the mo del is illustrated using examples of muscle injuries
created by surgical pro cedures The three examples used represent a p osterior
surgical approach to the spine an anterior approach to the spine and uni lateral
total hip replacement surgery Although the three examples simulate di erent
muscle injuries all demonstrate the pro duction of signi cant asymmetrical mo
ments and or reduced joint compression following surgical intervention This
result has implications for patient rehabilitation and the p otential for further
injury to the spine
The development and application of the mo del has highlighted a number of ar
eas where current knowlegde is de cient These include muscle activation levels
for tasks in p ostures other than upright standing changes in spinal kinematics
following surgical pro cedures such as spinal fusion or xation and a general lack
of understanding of how the b o dy adjusts to muscle injuries with resp ect to mus
cle activation patterns and levels rate of recovery from temp orary injuries and
comp ensatory actions by other muscles Thus the comprehensive and innovative
anatomical mo del which has b een develop ed not only provides atoolto predict
the forces and moments exp erienced by the intervertebral joints of the spine but
also highlights areas where further clinical research is required
Contents
Keywords iii
Abstract v
Table of Contents ix
List of Tables xv
List of Figures xix
List of Abbreviations xxv
Statement of Originality xxvii
Acknowledgements xxix
Intro duction
A Review of Past Mo delling of the Lumbar Spine
Electromyographic Mo dels
Mo dels by McGill and co workers
Mo dels by Granata and co workers
Cholewicki and McGill whole spine mo del
Optimisation Mo dels
Choice of ob jective functions
Mo dels by Schultz and co w orkers ix
Mo dels by Ladin and co workers
Mo dels by Gracovetsky Farfan and co workers
Mo dels by Stokes and Gardner Morse
Hybrid mo dels
Mo dels using Neural Networks
Anatomical Mo dels
Concluding Remarks
Anatomy and biomechanics of the lumbar spine
Muscular anatomyofthe lumbar spine
Muscle co ordinate data
Physiological cross sectional area
Muscle force
Length tension relationship
Active tension
Passive tension
Kinematics of the lumbar spine
Range of motion
Movement within the range of motion
Instantaneous centres of rotation
D mo del of the lumbar spine
Mo del Assumptions
Co ordinate system
Mo del input
Upright stance
Muscle Activation
Mo del structure
Change of basis calculations
Aligning the spine in the required p osition
Muscle lines of action
Output moment calculations
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
Longissimus thoracis pars thoracis
Fascicles attac hing to the ribs
Psoas ma jor muscle insertion on the femur
Ab dominal obliques
Torso mo del
Bending the torso
Application of metho dology
TLF
Anatomy of the TLF
Mo delling the TLF
Lines of action for the p osterior layer
Lines of action for the middle layer
Altering the p osture of the spine
Calculation of moments
mo del Application of the
Results and Validation
Comp onents of the mo del
Fascicles attaching to the ribs
Ab dominal obliques
TLF
Results from the entire mo del
Upright stance
Alternative p ostures
Validation of the mo del
Application of the mo del
Posterior lumbar surgery
Impairment of ab dominal muscles
Total Hip Replacement surgery
Conclusion
Conclusions and directions for further research
APPENDICES
A A study to compare PCSA and CSA values for the psoas ma jor
muscle
B Investigation of spinal kinematics during exion
C Co ordinates representing the ribs and vertebrae of the Visible
Man
C Posterior margin of the lumbar vertebrae
C Ribs to
D Determining lo cal co ordinate systems and lo cations of the IARs
from the spinal anatomy of the Visible Man
D Setting up an orthogonal basis on the vertebral body
D Basis vectors for the spine of the Visible Man
D Determining the lo cation of ICRs
E A comparison of techniques for mo delling the oblique muscle
lines of action
E Discussion
F Moments predicted by the TLF mo del
G Mo del output for individual muscle fascicles in upright stance
H Moments ab out a normal spine in a variety of p ostures
I Changes in forces and moments ab out a spine after p osterior
surgery
Bibliography
List of Tables
Muscles included in the anatomical mo dels prop osed by various
authors
Functional muscle groupings as prop osed by di erent authors
Data sources for each of the muscles crossing the lumbar spine
Muscle attachment co ordinates for muscles crossing the lumbar
spine as obtained from the Visible Man
Muscle attachment co ordinates for muscles crossing the lumbar
spine as derived from Stokes and Gardner Morse
Average values for the voluntary range of motion of each joint of
the lumbar spine for exion plus extension lateral b end and axial
twist as rep orted by White and Panjabi
Prop ortion of total motion allo cated to each intervertebral joint
in the lumbar spine
Positions of the ICRs within the spine of the Visible Man and the
vectors relating the p ositions of adjacent ICRs
Data required as input into the mo del
Details of studies providing information on spinal alignment in
upright stance and the weighted mean of these studies
Results from studies rep orting muscle activation levels during max
stance imum isometric exertions in upright
Maximum rotation allowable b efore adjacent transverse slices of
the mo delled torso intersect
Muscle fascicles which require changes to their line of action due
to it passing anterior to the rep orted ribinvarious exed p ostures xv
Data on the attachmentpoints for each of the bres of the oblique
muscles rep orted by Stokes and Gardner Morse and the
predicted z values
Parameter values for the torsos which b est t the data rep orted
in Table
Mo del output for the predicted maximum moments achievable in
the upright stance for a variety of exertions
Maximum muscle strains predicted by the mo del in a variety of
p ostures
Details of studies rep orting mean maximum moments generated
by volunteers under isometric conditions
con dence intervals for the mean maximum moments ob
tained exp erimentally from the studies outlined in Table
bounds on the sample for the maximum moments obtained
exp erimentally from the studies outlined in Table
Predicted maximum moments develop ed by the muscles during
exion and extension exertions assuming di erent optimal muscle
lengths
Predicted maximum moments develop ed by the muscles during
lateral bend and axial twist exertions assuming di erent optimal
muscle lengths
Angles of the oblique muscle bres and the correction factors re
quired to convert the rep orted PCSA values to male only PCSA
values adjusted for scan angle
Mo del predictions using adjusted PCSA values for the external
and internal obliques
Muscles whose function is disabled during p osterior lumbar surgery
at various spinal levels
Maximum forces exp erienced by the intervertebral joints following
surgery in the upright stance p osterior spinal
Simulated scenarios representing temp orary and p ermanent im
pairment of the left rectus ab dominis and external oblique follow
ing anterior lumbar interb o dy fusion
C Data p oints representing the base of the right spinous pro cess near
the vertebral body
C Data p oints representing the positionsofribs to
E Data on the attachment points for the left side of the body for
each of the vectors rep orted by Stokes and Gardner Morse
the predicted z values and rep orted PCSAs
E Parameter values for the torsos whic h b est t the data rep orted
by Stokes et al
E Comparison of the lengths of the comp onentvectors using straight
lines and the torso mo del
E Predicted lines of action for the left side of the torso using a
straight line approach and the torso mo del
E Predicted maximum moments able to be pro duced by the left
oblique muscles in upright stance
E Predicted maximum moments able to be generated by the left
internal oblique muscle in a variety of p ostures assuming a straight
line of action and using the torso mo del
G Mo del output for the predicted maximum moments achievable in
upright stance for individual muscle fascicles during a maximal
exion exertion
G Mo del output for the predicted maximum moments achievable in
upright stance for individual muscle fascicles during a maximal
extension exertion
G Mo del output for the predicted maximum moments achievable in
upright stance for individual muscle fascicles during a maximal
left lateral b end exertion
G Mo del output for the predicted maximum moments achievable in
upright stance for individual muscle fascicles during a maximal
left axial twist exertion
List of Figures
Muscles of the back p osterior view highlighting the erector spinae
and quadratus lumb orum
Muscles of the back p osterior view highlighting the latissimus
dorsi
Muscles lo cated on the anterior of the trunk which exert an e ect
of the lumbar spine
Muscles of the lumbar spine and hip anterior view right side
only highlighting the psoas ma jor
Schematic illustration of the fascicles used to represent the multi
dus muscle
Schematic illustration of the fascicles used to represent the longis
simus thoracis muscle
Schematic illustration of the fascicles used to represent the ilio
costalist lumb orum muscle
Length tension curve for passive active and total tension
Co ordinate system used in the mo del
General steps involved in calculating the maximum moments that
maybe develop ed by muscles of the lumbar spine
Angles de ning the rotation of the vertebra
Flow diagram illustrating the steps required to ensure fascicles
of the longissimus thoracis pars thoracis do not move in front of
vertebrae
Flow diagram illustrating the steps required to ensure fascicles
which attach to the ribs remain p osterior to the ribs during spinal
rotation xix
Schematic representation of the parameters in the torso mo del
Schematic illustrating the general structure of the TLF as seen
in a transverse slice
Schematic illustrating the comp onents of the left TLF
Schematic illustrating the vectors used in the calculation of the
lateral raphe for the left side from L to L
Scans used to estimate the line of action for the p osterior and
middle layers of the TLF
Di erences in the shap e of the erector spinae muscle b etween living
sub jects and cadaveric sp ecimens
The shap e and p osition of the lines representing the internal and
external obliques obtained from the torso mo del
Comparison of the erector spinae b order as determined by image
pro cessing to ols and the mo delled muscle b order
Contribution of muscles to the primary moment generated during
exion extension and lateral b end exertions
Contribution of muscles to axial twist moment during maximal
axial twist exertions
Moments generated ab out L L by a maximum exion exertion
in various p ostures
Moments generated ab out L L by a maximum extension exer
tion in various p ostures
Moments generated ab out L L by amaximum left lateral b end
exertion in various p ostures
Moments generated ab out L L by a maximum left axial twist
exertion in various p ostures
Contribution from each of the ma jor agonist and antagonist mus
cles to the exion moment predicted ab out L L during exion
exertions in avariety of p ostures
Comparison of predicted moments to the sample b ounds for
exp erimentally derived moments
Comparison of predicted moments to exp erimentally derived
sample b ounds for left axial twist exertions
Normalised muscle activation levels for a varietyofmuscles as re
ported by Jorgensen and Marras for sub maximal extension
e orts
Mean muscle activitylevels rep orted by McGill during iso
metric maximal axial twist exertions in three p ostures
Comparison of predicted moments using a variety of maximum
muscle intensities to exp erimentally derived sample b ounds
Predicted changes in extension moments pro duced during a max
imal extension exertion in upright stance after p osterior surgery
at various spinal levels
Predicted changes in the maximum moments and forces able to b e
generated by the muscles ab out L L during a maximal extension
exertion avarietyof p ostures following p osterior spinal surgery
Maximum moments that may be generated by the muscles dur
ing maximal exion exertions in a spine with reduced ab dominal
muscle function and an intact spine
Maximum moments that may b e generated bythemuscles during
a maximal extension exertion in a spine with reduced ab dominal
muscle function and an intact spine
Maximum moments that may be generated by the muscles dur
ing maximal left and right lateral bend exertions in a spine with
reduced ab dominal muscle function and an intact spine
Maximum moments that may b e generated bythemuscles during
maximal left and right axial twist exertions in a spine with reduced
ab dominal muscle function and an intact spine
Prop ortion of agonist momentwhich can b e attributed to provid
ing stability during maximal extension exertions under the simu
lated scenarios
Moments generated by the muscles during a maximal extension
exertion in an intact spine and one which has had the right psoas
ma jor muscle deactivated
Forces generated by the muscles during a maximal extension ex
ertion in an intact spine and one which has had the right psoas
ma jor muscle deactivated
F Maximum exion extension moments pro duced by the TLF in
upright stance using erector spinae characteristics from three in
dividuals and and
F Net moments ab out the ICRs pro duced by the TLF in a variety
of p ostures
H Moments generated ab out L L by a maximum exion exertion
in various p ostures
H Moments generated ab out L L by a maximum exion exertion
in various p ostures
H Moments generated ab out L L by a maximum exion exertion
in various p ostures
H Moments generated ab out L L by a maximum exion exertion
in various p ostures
H Moments generated ab out L S by a maximum exion exertion
in various p ostures
H Moments generated ab out L L by a maximum extension exer
tion in various p ostures
H Moments generated ab out L L by a maximum extension exer
tion in various p ostures
H Moments generated ab out L L by a maximum extension exer
tion in various p ostures
H Moments generated ab out L L by a maximum extension exer
tion in various p ostures
by a maximum extension exer H Moments generated ab out L S
tion in various p ostures
H Moments generated ab out L L by amaximum left lateral b end
exertion in various p ostures
H Moments generated ab out L L by amaximum left lateral b end
exertion in various p ostures
H Moments generated ab out L L by amaximum left lateral b end
exertion in various p ostures
H Moments generated ab out L L by amaximum left lateral b end
exertion in various p ostures
H Moments generated ab out L S by a maximum left lateral bend
exertion in various p ostures
H Moments generated ab out L L by a maximum left axial twist
exertion in various p ostures
H Moments generated ab out L L by a maximum left axial twist
exertion in various p ostures
H Moments generated ab out L L by a maximum left axial twist
exertion in various p ostures
H Moments generated ab out L L by a maximum left axial twist
exertion in various p ostures
H Moments generated ab out L S by a maximum left axial twist
exertion in various p ostures
I Predicted changes in the maximum moments and forces able to b e
generated by the muscles ab out L L during a maximal extension
exertion in a variety of p ostures following p osterior spinal surgery
I Predicted changes in the maximum moments and forces able to b e
generated by the muscles ab out L L during a maximal extension
exertion in a variety of p ostures following p osterior surgery
I Predicted changes in the maximum moments and forces able to b e
generated by the muscles ab out L L during a maximal extension
exertion in a variety of p ostures following p osterior surgery
I Predicted changes in the maximum moments and forces able to b e
generated by the muscles ab out L S during a maximal extension
exertion in a variety of p ostures following p osterior surgery
List of Abbreviations
ANN Arti cal neural networks
CI Con dence interval
CSA Cross sectional area
EMG Electromyography
IAR Instanteous axis of rotation
ICR Instanteous centre of rotation
IVD Intervertebral disc
MVC Maximum voluntary contraction
PCSA Physiological cross sectional area
SD Standard deviation
SE Standard error
THR Total hip replacement xxv
Statement of Originality
The work contained in this thesis has not b een previously submitted for a
degree or diploma at any other higher education institution To the best of my
knowledge and b elief the thesis contains no material previously published or
written by another p erson except where due reference is made
Signed
Date xxvii
Acknowledgments
I wish to express my sincere gratitude to the many p eople at QUT who have
help ed and guided me during the last few years
Prof Mark Pearcy and Dr Graeme Pettet my sup ervisors for their as
sistance and supp ort and their willingness to take on the challenge of a
multi disciplinary pro ject which stepp ed outside their past research inter
ests
Prof John Evans and Dr Timothy Barker for their valuable comments
and suggestions on various asp ects of my pro ject
The sta and p ostgraduate students within the Sc ho ol of Mechanical Man
ufacturing and Medical Engineering for making my time so enjoyable A
sp ecial thanks go es to Mick and Kurt for making me laugh during the
endless hours of program debugging
I would also like to express a very sp ecial thanks to Wayne and my parents for
their supp ort and encouragement Their fortitude and encouragement particu
larly during the last few months has help ed motivate me to nish so I can start
to enjoy my nights and weekends again
This research was conducted with nancial supp ort from an APAscholarship a
QUT Vice Chancellor s scholarship and additional funding from the Centre for
QUT Rehabilitation Science and Engineering xxix
Chapter
Intro duction
The human body is a complex combination of organs which integrate and co or
dinate to allow us to function and survive as individuals Although the human
body has b een the ob ject of scienti c interest for hundreds of years it is still
a relatively p o orly understo o d machine There are many illnesses and medical
conditions that still remain a mystery even though they may a ect large numbers
of p eople Scientists and clinicians do not know how or why these conditions
develop let alone how to treat or cure them One such condition is low back
pain LBP
In western so ciety the incidence of LBP has continually increased over the last
few decades to the p oint where the condition is now imp osing a signi cant so cio
economic burden on so ciety There are many causes of LBP from degenerative
or ruptured intervertebral discs to fractured endplates to compression of nerve
ro ots However there are many p eople who exp erience LBP for which no clinical
explanation can b e identi ed This problem has lead to many researchers invest
ing much time and money into the hunt for p otential causes of the condition
With technological advances in medical imaging and other equipment e g ne
wire EMG electro des subminiature pressure transducers and pressure sensitive
Intro duction
radio transducers researchers have been able to investigate a range of param
eters in an e ort to identify di erences between people who exp erience LBP
and those who do not At the same time there is considerable exp erimental
work b eing conducted to determine the structural prop erties of the vertebrae
intervertebral joints and discs and the mechanical limits of these structures
One of the problems exp erienced when dealing with the spine is that forces
strains and stresses exp erienced by the various comp onents cannot be directly
measured unless inv asive techniques are used Hence we may know what the
mechanical limits are of the various comp onents but we cannot measure how
close the forces strains or stresses exp erienced in vivo come to these limits This
has made it necessary to use metho ds other than direct measurement to predict
the b ehaviour in vivo metho ds such as biomechanical mo delling
Biomechanical mo dels use mathematical equations to describ e the behaviour
of the comp onents included In the case of the lumbar spine biomechanical
mo dels have b een used mainly to address ergonomic issues such as estimating the
compressive and shear forces exp erienced by the intervertebral joints during the
p erformance of di erent tasks and providing information on safe lifting loads
and techniques However there are many other p otential uses for biomechanical
mo dels outside this ergonomic niche
One area which has received relatively little attention is the impact of muscle
injury on the biomechanics of the spine Muscles are the only active force gen
erating comp onents and they can be injured like any other structure It is of
interest to know what biomechanical changes result from muscle injury and how
the b o dy adjusts to these changes given that the spinal muscles are fundamental
in the overall movement and stability of the spine
Of particular interest in this research are the biomec hanical changes intro duced
by muscle injury resulting from surgical intervention As the number of p eople
exp eriencing LBP increases so to do es the incidence of spinal surgery This has
lead to the development of new surgical techniques and instrumentation At the
same time the emphasis in rehabilitation has b een on getting the patient up
and moving as so on as p ossible These developments have left clinicians with
manychoices in the treatment of patients But what are the side e ects of these
treatments in terms of the biomechanical changes induced Is the conservation
of some muscles more imp ortantthan others when spinal stabilityand strength
are considered How do es the spinal system adjust to the changes imp osed
These are only a few of the questions which arise when considering the impact
of induced muscle injury Understanding these issues will help clinicians provide
the b est overall treatment for their patients and highlight areas where further
investigation is needed
The primary aim of this thesis was to develop a quasi static mathematical or
biomechanical mo del of the lumbar spine whichcontains enough detail to enable
it to b e used to investigate the biomechanical changes which result from muscle
injury This requires a full three dimensional representation of all the active
force generating comp onents of the lumbar region To date most of the mo dels
used to represent the lumbar region of the spine haveo versimpli ed the anatomy
such that they are not suitable for the intended purp ose A review of these
past mo dels is contained in Chapter This review covers all the ma jor typ es
of mo dels and concentrates on the anatomical representation of the muscles A
discussion of the anatomy and biomechanics of the lumbar spine relevant to the
development of the mo del is then presented Chapter This includes details of
muscle attachmentpoints the force generating capacityofthemuscles measures
of muscle area and the kinematics of the spine
Chapter describ es the metho dology develop ed to predict the maximum mo
ments that may be dev elop ed by the muscles ab out the intervertebral joints
Intro duction
This chapter includes a discussion of the assumptions made and the data re
quired to implement the mo del Emphasis has b een placed on ensuring the
muscle lines of action are anatomically realistic particularly for muscles which
have broad attachments e g the ab dominal oblique muscles or attach to the
spine via the thoracolumbar fascia TLF This is an area which many previous
mo dels have overlo oked
The results obtained from the application of the mo del to a normal spine using
published muscle activation levels are presented in Chapter These results are
validated by comparing the predicted values to published maximum moments
rep orted from exp erimental studies During discussion of the results particular
reference is made to the applicabilityand reliabilityof the input data used and
the assumptions made in b oth the mo del and exp erimental studies
Following validation the mo del is applied to simulate three surgical scenarios
Chapter These examples represent typical muscle injuries resulting from a
p osterior approach to the spine an anterior approach to the spine and uni lateral
total hip replacement surgery Although di erent muscle injuries are simulated
in these examples all three demonstrate similar changes with some interesting
results
Finally Chapter reviews the development and application of the mo del high
lighting the novel techniques develop ed This chapter also highlights areas where
further development of the mo del could occur and potential uses for the mo del
ranging from ergonomic applications to surgical applications to the development
of new surgerical instrumentation
Chapter
A Review of Past Mo delling of
the Lumbar Spine
Many mathematical mo dels of the lumbar spine havebeendevelop ed over the last
years The ma jority of these mo dels have b een used to predict compressiveor
shear forces acting on the intervertebral joints of the lumbar spine and all share
one common feature eachmust consist of an anatomical mo del of the spine and
a means of distributing force to the comp onents in this anatomical mo del
An anatomical mo del of the spine includes the muscles and ligaments which con
tribute to the moments generated within the spine the lines of action of these
muscles or ligaments the attachmentpoints or momentarmsofeach comp onent
and other structures such as the thoracolumbar fascia TLF and or interverte
bral discs Such anatomical mo dels can encompass the entire lumbar spine or
just the anatom ywhich crosses the region of interest
There are four main metho ds which are commonly used to allo cate force to the
numerous comp onents of an anatomical mo del electromyography EMG op
timisation combined EMG optimisation techniques and neural networks The
evolution of these techniques stems from the anatomical mo del b eing indeter
A Review of Past Mo delling of the Lumbar Spine
minate since there are usually more muscles in the mo del than equilibrium
conditions Each of the four classes of mo dels are discussed in detail b elow
Electromyographic Mo dels
EMG driven mo dels use electromyographic data to help allo cate force to the vari
ous anatomical comp onents The advantages of this technique include the ability
to incorp orate realistic muscle activation patterns including antagonist muscle
activity and account for individual variation between sub jects However the
technique is heavily relianton data which must be available in every p osture to
b e mo delled This data is b oth costly and time consuming to collect EMG data
for deep muscles is also sparse whic h means that muscle activation patterns for
these muscles must b e estimated from the activation of surface muscles Sp eci c
details of some EMG driven mo dels are given below
Mo dels by McGill and co workers
Stuart McGill and co workers are the dominant researchers driving the develop
ment of EMG mo dels of the lumbar spine Their mo dels McGill and Norman
McGill McGill of the lumbar spine represent a cross section at
the L L level and consist of two parts alinked segment mo del which uses the
dynamic load in the hands to estimate the reaction forces and moments ab out
mo del in which reac each axis corresp onding to the L L joint and a spinal
tion moments obtained from the linked segment mo del are partitioned between
muscles ligaments and discs
McGill and Norman represent the anatomy of the lumbar spine by
muscles and ligaments Although muscles were included in the mo del of
these bilateral sacrospinalis L psoas L and latissimus dorsi L L L and
Electromyographic Mo dels
L were considered not to generate any momentaboutL L and were therefore
not included in the analysis The muscles included in the mo del are indicated
in Table The ligaments included were the anterior and p osterior longitudi
nal ligaments ligamentum avum articular ligament of the zygop ophysial joints
intertransverse ligament interspinous ligament supraspinous ligament and tho
racolumbar fascia
The thoracolumbar fascia TLF is assumed to b e attached to the latissimus dorsi
and is mo delled as describ ed by Bogduk and Macintosh in a caudolateral
direction Although no mathematical relationship is given for calculating the
momentcontributed by the TLF in the work by McGill and Norman the
relationship vaguely describ ed app ears to be the same as that detailed in later
work McGill and Norman In this later work the extensor moment due
to the TLF is calculated using
M r F cos
LD F LD F
where M is the extensor momentdue to tension in the TLF Nm
LD F
r is the moment arm of the fascia m
F is the force in the latissimus dorsi laminae to L N and
LD F
is the angle of the latissimus dorsi vector with resp ect to the midline
degrees b orum us are the us thoracis t ab dominis uscles Other ab dominis m Ilio costalis Ilio costalis Ilio costalis Pyramidalis Longissim rans Muscles Sacrospinalis Sacrospinalis Sacrospinalis Medialis spinalis T rans Medial spinalis represen Longissim T Ilio costalis lum to only Ilio used lum body the ectors Ilio v of thor of side ber Long lum one um n for the Long thor t authors F F F ES represen arious ets v F F F F k y Multif b brac in F F F F Psoas bers prop osed F F F F F F F Num Ext Obl t F F F F F F In Obl authors e anatomical mo dels F F F F F F F Ab Rectus the resp ectiv in F F F F the Quad y b included F F F F F F F Lat dorsi rep orted Muscles as if more than one et al et al uscles etsky etsky able v v T describ ed m ta et al ultz et al ultz et al h h Graco Sc Sc Mo del Graco McGill et al Gran Nussbaum et al ultif us Other Muscles Thoracic m Ext Obl External F Ilio lum Long lum Longissim F Ilio b orum thor ternal oblique F Long lum b orum par lum t Obl In F In Long thor us thoracis par thoracis F ES ued tin F Multif con Ilio lum Ilio costalis lum Long thor Longissim
F F Psoas able T Rectus Ab Rectus ab dominis Ext Obl t F In borum Obl ES Erector spinae b orum pars thoracis F F Ab Rectus Quad Multif Multi dus Quad Quadratus lum F Ilio thor Ilio costalis lum Lat dorsi us dorsi b orum Psoas Psoas ma jor es et al Lat dorsi Latissim Mo del Stok Nussbaum et al oblique thoracis pars lum
A Review of Past Mo delling of the Lumbar Spine
The kinematic p ortion of the mo del develop ed by McGill and Norman
is based on a D skeleton consisting of pelvis rib cage and lumbar vertebrae
th
scaled to the dimensions of the percentile male The amount of rotation
in any direction between the rib cage and pelvis was partitioned to the ve
th
lumbar vertebrae using R B where R is the rotation of the i vertebra
i i i
th
rad is the p ercentage of the total rotation attributed to the i vertebra
i
and B is the total lumbar rotation rad For exion rotation was partitioned
between vertebrae such that and
L L L L
L
Momentcontributions from passive comp onents such as ligaments and discs were
calculated prior to the muscle moments Disc moments were calculated using
M exp R where M is the moment due to b ending in the
d d
disc Nm and R is the amount of exion of L rad Equations develop ed by
Anderson Cha n Herrin and Matthews were used with some mo di ca
tions for pretension and cross sectional area to calculate the forces generated by
the ligaments
EMG data was used as a guide to partitioning total muscular moment into ap
propriate forces In order to do this the maximum force of the muscles at rest
length assumed to corresp ond to the length when the b o dy is relaxed in a fetal
p osition was estimated as the physiological cross sectional area multiplied by a
muscle stress that varied from Ncm McGill and Norman The
into the force equation by multi neural activation of muscles was incorp orated
EM G
plying the maximum force by the ratio where EM G is the EMG during
m
EM G
m
maximum voluntary isometric contraction and EMG is the EMG recorded dur
The term used to describ e the maximum force a muscle can pro duce p er unit area varies
between authors The terms muscle stress muscle gain and muscle intensityhave b een used
interchangeably to describ e this parameter
Ncm is the unit commonly used to describ e muscle intensity Ncm is equivalentto
Nmm or Nm or kPa
Electromyographic Mo dels
ing the task b eing mo delled
Since muscle length and contracting velo city a ect maximal muscle force the
active length tension relationship was mo delled by McGill and Norman
as a p ositive half sine wave with the zero crossing at and of the rest length
and the p eak corresp onding to the muscle rest length sin L L L is
the rest length of the muscle and L is the current length Instantaneous muscle
and ligament lengths were calculated using either a straight line b etween origin
and insertion or an arc or series of arcs The passive length tension relationship
was adapted from Woittiez Huijing Bo om and Rozendal and mo delled
as
L
F exp P
pec
L
where F is the passive force normalised to the maximum force
pec
p otential and
P is the maximum muscle force
To ensure that the sum of muscle ligament and disc moments were equal to
the reactive moment each muscle force was multiplied by a common gain or
error term This has the e ect of altering the momentvalue while retaining the
relative contributions from each muscle
The mo del was applied to a lifting task with data being collected from three
volunteer weight lifters Eachvolunteer completed three lifting tasks with varying
load and at varying sp eed EMG data was collected for the rectus ab dominis
external oblique internal oblique latissimus dorsi upp er erector spinae and
lower erector spinae muscles Since not all muscles mo delled had EMG data
several assumptions regarding muscle activation levels were made These were
that the transverse ab dominis and psoas behave the same as the internal
A Review of Past Mo delling of the Lumbar Spine
oblique the longissimus thoracis and ilio costalis lumb orum b ehave the same
as the upp er erector spinae and the multi dus sacrospinalis and quadratus
lumb orum b ehave the same as the lower erector spinae
Output from the mo del for the lifting tasks indicated that muscular sources
generated of the required moment while the disc supplied the remaining
The ligament system created no moment since the lifters adopted a at
backed p osture From this study McGill and Norman concluded that
intra ab dominal pressure do es not act to reduce spinal compression but instead
maintains the geometry of the ab dominals and that the TLF only contributes a
small amount of the moment generated Output also indicated that calculated
compression and shear at the L L disc were within physiological limits
The base mo del develop ed by McGill and Norman has b een applied with
some minor adjustments to lateral b ending tasks McGill The changes
intro duced to the mo del include
partitioning of lateral b end between lumbar vertebrae such that
L
and
L L L L
reducing the muscle stress to Ncm
adapting the generalised ligamen t stress strain relationship to account for
individual exibility
calculating disc moments as M where M is the moment due to
d d
lateral b ending of the disc Nm and is the amount of lateral b end rad
The value of was arbitrarily chosen
mo delling the rst half of the muscle length tension relationship as a pos
itive half sine wave with the zero crossing at of the rest length and
the peak at muscle rest length while the second half was represented as a
Electromyographic Mo dels
L
linear relationship of the form
L
allowing the mechanical fulcrum of the jointtochange with p osture
McGill do es not sp ecify how EMG data was applied to muscles for which
no EMG data exists however given the similarities with the base mo del McGill
and Norman it might b e assumed the same groupings of muscle activations
were used
Application of the mo del to a lateral b ending task indicated that the ligament
contribution was very small except at the extreme ranges of bend Results also
show the mo del to adequately predict agonist antagonist co contraction It is no
surprise that muscles are the most imp ortant body tissue in generating lateral
b ending moments
A similar mo del to those discussed ab ove has also been develop ed to estimate
total torque during axial twist McGill This version of the mo del incor
p orates selected muscle slips with individual muscle forces being estimated
using
MS
F CSA K
m
MS
MEA
where F is the muscle force N
m
K is the maximum muscle intensity Ncm
CSA is the muscle cross sectional area cm
MS is the measured EMG signal and
MS is the maximum EMG signal observed
MEA
Moments were calculated from the D triple scalar pro duct of muscle force ab out
L L Application of the mo del predicted axial torques much lower than those
A Review of Past Mo delling of the Lumbar Spine
measured Nm predicted versus Nm measured with large amounts of an
tagonist muscle activity
The various mo dels by McGill and co workers account for many of the physio
logical factors a ecting force pro duction in muscles such as physiological cross
sectional area PCSA passive force generation and length tension relationships
An attempt has also been made to mo del the action of the TLF although this
is only in two dimensions
McGill and Norman and McGill acknowledge that maximum mus
cle force is a function of muscle length and mo del this relationship accordingly
However no attempt has b een made to adjust the maximum EMG signal used
for EMG normalisation in a similar way It would seem reasonable that if muscle
force varies with muscle length then maximum EMG signals would also vary
with muscle length This typ e of relationship would change the normalisation
of EMG data This concept is supp orted by Granata and Marras who
rep ort that muscle length and velo city e ect EMG values in a way not related
to muscle force
The mo del output app ears to pro duce physiologically acceptable estimates of
shear and compression across the L L joint However application of the mo del
by other researchers is limited by the availability of EMG data and the often
vague descriptions of the anatomy For instance the lines of action of some
muscles were mo delled using an arc or series of arcs but the exact muscles
mo delled in this way are not indicated Likewise the description of the lo cation
of the mechanical fulcrum ab out which moments are calculated is at b est vague
making it di cult for others to replicate the results of McGill and co workers
Electromyographic Mo dels
Mo dels by Granata and co workers
Granata and Marras intro duce a dynamic three dimensional mo del of the
lumb o sacral joint L S used to predict trunk moments and spinal loads during
static isokinetic and iso inertial lifting exertions The mo del contains muscle
equivalents and only accounts for active muscle forces by assuming that passive
muscle ligaments and discs do not generate moments The muscles included
in the mo del are indicated in Table The mo del was designed to simulate
a lifting exertion corresp onding to trunk extension from degrees exion to
upright
The muscle cross sectional areas used in the mo del are calculated as a function
of trunk depth and breadth as are the muscle moment arms EMG values were
used to assist with estimating muscle force namely
EM G t
j
Force g Ar ea F Vel F Ang
j j j j
EM G Ang Asmtr y
maxj
where Force is the force generated by muscle j N
j
g is the muscle force per unit area Ncm
EM G t is the time dep endent EMG signal level of muscle j
j
EM G Ang Asmtr y is the myo electric maxima for muscle j
maxj
as a function of trunk b ending angle Ang and asymmetry
Asmtr y
Ar ea is the cross sectional area of muscle j cm
j
F Vel is the EMG velo cit y Vel artifact of muscle j and
j
F Ang isthe relationship b etween tensile force and the length
j
of muscle j related to EMG
Granata and Marras state that muscle force per unit area i e gain
A Review of Past Mo delling of the Lumbar Spine
is highly variable b etween sub jects based on sub ject conditioning training and
natural ability To overcome this problem the gain was allowed to vary be
tween sub jects and was calculated by comparing the measured moment ab out
the b ending axis with the predicted moment generated by the muscle forces in
a series of calibration tests Gain was adjusted to achieve agreement between
the two values Once a sub ject gain had b een calculated this value remained
constan t in the mo del Gain values were accepted as b eing realistic if they were
within the range Ncm
Mo del validation was conducted by comparing the calculated gain values for
sub jects to physiological values and comparing mo delled and measured moments
Results indicate that gain values were within the physiological range with a
mean and standard deviation of Ncm and Ncm resp ectively predicted
values ranged from Ncm Co e cients of regression were used to compare
mo delled and measured moments on a p oint by p oint basis for static
isokinetic and iso inertial trials sub jects by exertions Granata and
Marras rep ort that over of trials p erformed with an R value greater
than concluding that the EMG assisted mo del is an excellent predictor of
trunk extension moment
The allo cation of di erent gain values to sub jects app ears to add to the in
dividualisation of the mo del However one must question the accuracy of the
muscle areas used since several studies have failed to show acceptable accuracy
in predicting muscle area from anthrop ometric parameters McGill Patt and
Norman Reid Costigan and Comrie
There would app ear to be an inconsistency in the rep orted value of individ
ual sub ject gains Granata and Marras state that for mo del adequacy
checking the predicted gain level must fall within the physiological range
Ncm Insp ection of the normalised distribution of calculated gains indi
Electromyographic Mo dels
cates that there were sub jects whose gain values were estimated to be
Ncm The authors fail to comment on this p oint Furthermore the descrip
tion of the technique used to compare the calculated and measured moments is
vague making it di cult to comment on its appropriateness for validation The
authors draw attention to the high R values and conclude that the mo del must
b e p erforming well A closer examination of the distribution of R values reveals
that while most of the values are over approximately of isokinetic tests
with a velo cityof s had R values of zero leading one to conclude that the
mo del only p erforms as well as rep orted under certain conditions
The mo del by Granata and Marras intro duces some go o d ideas but gen
erally the mo del structure is to o simple for use outside the designated task and
range of motion This simplicity results from the fact that the mo del only in
cludes a small number of muscles and assumes xed muscle vector directions
and that the moments are attributed totally to active muscle force The ex
p erimental comp onent of the study is p o orly detailed e g number of sub jects
sub ject characteristics number of tasks p erformed etc and some of the results
are di cult to interpret without knowing the exact exp erimental pro cedure
In later work Granata and Marras used a similar mo del to that previously
outlined to examine features of free dynamic lifting Signi cant di erences in
mo del structure compared with the previous mo del Granata and Marras
include
muscle force b eing calculated as
EM G t
j
Force Gain Ar ea F Vel F Leng th
j j j j
EM G
maxj
where
F Leng th Leng th Leng th Leng th
j j j j
F Vel Vel Vel
j j j
A Review of Past Mo delling of the Lumbar Spine
muscle origin and insertion points being allowed to move with the p osi
tion of the trunk with vectors between origin and insertion b eing used to
represent the muscle lines of action
In this mo del Granata and Marras calculate moments generated by isoki
netic and free lifts by male sub jects The authors state that separate lift
ing exertions were conducted The description of the exp erimental metho dology
sp eci es that there were sub jects who lifted loads of and kg at isoki
netic trunk angular velo cities and s as well as free dynamically
slow medium and fast lift rates Granata and Marras However this
only amounts to exertions sub jects loads lift sp eeds making it
di cult to ascertain how exertions were obtained
Mo del v alidation was achieved by examination of the calculated gain values
R values and the average absolute error AAE The authors suggest that all
three of these validation techniques lead to the conclusion that the mo del suc
cessfully predicts moments and muscle co contraction Sub ject gain values for
the dynamic exertions were SD Ncm in the sagittal plane and
SD Ncm in the lateral plane Although the authors suggest these values
fall within the physiological range the large standard deviation accompanying
the mean results in con dence intervals for the mean extending beyond the ac
range of Ncm ceptable
As with the previous mo del Granata and Marras this mo del and asso
ciated exp erimental validation is di cult to understand and analyse critically
due to the lack of sp eci c detail and missing information Although the two
mo dels are similar in a number of ways the authors have not referenced the
earlier work in the later mo del s description or discussed di erences in the mo del
structures These di erences include changing the myo electric maxima used in
The myo electric maxima is measured using the EMG pro cess and is equivalent to the
Electromyographic Mo dels
the force equation from b eing a function of trunk b ending angle and asymmetry
to a single myo electric maxima collected during maximum voluntary contraction
MVC e orts and changes to the length and angle functions used in the force
calculation
Marras and Granata applied the mo del previously develop ed Granata
and Marras with some minor mo di cations to investigate spinal loading
during lateral b ending The mo di cations intro duced include
adjustment of the velo city mo dulation such that
Vel
j
e for Vel
j
F Vel
j
for Vel
j
trunk angle being adjusted to be the angle between L S and T Lat
eral spine curvature resulting from rotation of each vertebral segment was
not accounted for so a correction factor was needed to adjust for over
prediction of angle and velo city Marras and Granata
The mo del was applied to tasks in whichtwelvemalevolunteers p erformed static
and isokinetic lateral exertions while carrying weights in their hands Mo del
validitywas p erformed using the same criteria as Granata and Marras
Results indicate that there was signi cant agonistic and antagonistic muscle ac
tivity during the tasks It was concluded by the authors that the mo del p erformed
well under the exp erimental conditions as de ned bytheaverage gain value
low AAE and high R values average of Predicted spinal loads Ncm
were found to increase with load lifted and also with rate of lateral b ending while
coactivation was observed to increase signi cantly as lateral velo city increased
The authors conclude that any analysis which neglects antagonistic muscle ac
maximum EMG signal
A Review of Past Mo delling of the Lumbar Spine
tivity will signi cantly underestimate spinal loads This is the same conclusion
reached in previous work
The same comments regarding this work can be made as for the previous work
since they are primarily based on the same mo del Marras and Granata
state that the mo del used the same muscle insertion data describ ed in Granata
and Marras however there is no muscle insertion data in this previous
pap er except for a statement that the physiological cross sectional area origin
and insertion of eachmuscle is calculated as a function of sub ject anthrop ometry
including trunk depth and breadth Marras and Granata Once again
there w ould app ear to be a lack of clarity in the rep orting of the metho dology
Cholewicki and McGill whole spine mo del
Cholewicki and McGill develop ed a dimensional dynamic mo del which
encompassed all joints of the lumbar spine to investigate the stability of the
lumbar spine The mo del is an extension of the segmental mo dels previously
develop ed McGill and Norman McGill but has b een mo di ed to in
corp orate the anatomyover the entire length of the lumbar spine Ninetymuscle
fascicles were included in the mo del which had degrees of freedom To allow
dynamic mo delling it was assumed that each intervertebral joint contributes a
constan t prop ortion of the total rotation angle b etween S and T in all three di
rections Three dimensional rotations were obtained by rotating in the sequence
Z X then Y where X Y and Z corresp ond to the orthopaedic axes of lateral
b ending axial twist and exion extension resp ectively Moments contributed by
passive tissues such as discs and ligaments were estimated as one lump ed passive
tissue force based on the passive sti ness and coupled rotations Moments were
calculated as
Electromyographic Mo dels
b
xj j j
M a e
xj xj j j
b
yj j j
M a e
yj yj j j
b
zj j j
a e for lateral b end twist
zj
M
zj
b b
zj j j zi
a e e for exion
zj
where M is the moment ab out axis h of joint j
hj
is a coupling co e cient set between Nm rad and Nm rad
are the angles of rotation ab out the X Yand Z axis
j j j
resp ectively at joint j rad and
a b are magnitude and shap e co e cients ab out axis i of joint j
ij ij
Muscle force was partitioned between the muscle fascicles using EMG data
Since EMG data were not av ailable for all muscles in the mo del muscle fasci
cles were group ed according to anatomical and functional similarities The psoas
ma jor was assumed to b ehave the same as the internal obliques while the quadra
tus lumb orum was assumed to b ehave like the lower erector spinae Maximum
isometric muscle stress was assumed to b e Ncm
The analysis conducted was primarily related to investigating spinal stability
using a stability index derived by the authors Results from this analysis indicate
that passive tissues play a crucial role in stabilising the spine during tasks which
place little demand on muscular forces In particular instabilitywas asso ciated
with neutral p ostures where the multi dus and lumbar erector spinae muscles
had near zero force at the mid lumbar levels L L Stability app eared to
increase during demanding tasks as de ned by the joint compression force The
authors suggest that the activity of the short intrinsic muscles that span only
one or two joints are necessary to maintain stability of the whole lumbar spine
A Review of Past Mo delling of the Lumbar Spine
This mo del assumes that there is no joint translation with only rotation ab out
the disc centroid allowed This is in direct con ict with the movement seen on
radiographs where translation can in some sub jects be quite large
Cholewicki and McGill s mo del helps shed some light on the function of
the smaller muscles of the back However the assumptions used to mo del the
kinematics are almost certainly to o simplistic
Optimisation Mo dels
In biomechanical mo dels optimisation is used as a numerical solution to the
problem of indeterminacy Numerical optimisation is the pro cess of allo cating
muscle forces such that the allo cation minimises or maximises some ob jective
function sub ject to given constraints Mathematically optimisation mo dels can
be expressed in the generalised form
minimise x
such that Ax b
x
i
x U
i i
where x is the ob jective function x is the force in muscle i U is the up
i i
per bound on the force in muscle i and Ax b are the moment equilibrium
conditions
Optimisation mo dels require no exp erimental data in their formulation and are
to almost any task These typ es of mo dels are most com therefore applicable
monly criticised for their arbitrary choice of ob jective function their inabilityto
account for individual variabilityinmuscle recruitment patterns and their failure
Optimisation Mo dels
to predict co contraction of antagonist muscles adequately
Choice of ob jective functions
One of the main criticisms of optimisation mo delling is the choice of ob jec
tive function Although any ob jective function can be devised Crowninshield
and Brand stress the imp ortance of using an ob jective function based on
known physiological principles where a physiological criterion is de ned as one
which requires no arbitrary upp er limits on individual muscle force Some of
the ob jective functions whichhave b een prop osed are brie y summarised b elow
Sum of squared muscle stresses The ob jective function is minimise x
P
x A where A is the cross sectional area of muscle i
i i i
Sumofcubed muscle stresses This ob jective function develop ed byCrown
P
inshield and Brand minimises the function x x A
i i
Crowninshield and Brand suggest this ob jective function will max
imise endurance and as such will only suit mo dels of activities in which
endurance is of imp ortance e g casual walking
Minimum compression This ob jective function was develop ed by Schultz
P
and Andersson and minimises x c x where c represents
i i i
uscle the contribution to spinal compression force p er newton of force in m
i This ob jective function e ectively cho oses the muscles with the longest
moment arms since these pro duce the least compressive load per unit of
moment
Minimum stress compression The ob jective function develop ed by Bean
Cha n and Schultz involves two steps the rst is to determine the
vector of upp er b ounds U by nding the minimum stress suchthat
min
A Review of Past Mo delling of the Lumbar Spine
equations to have solutions when U A The second
i min i
P
i i
step is to minimise x x sub ject to to where is
i
th i
the caudo cranial comp onent of the unit force vector of the i muscle
points in the rostral direction
Eigenvector synergy model This metho d of estimating muscle force is
based on the eigenvectors corresp onding to the nonzero eigenvalues of
T
A A According to Gielen and vanZuylen these eigenvectors rep
resent synergies that pro duce moments ab out the spine This approach
is quite detailed containing steps and it is recommended that readers
refer to the original work of Gielen and vanZuylen for the precise
metho dology
Least squares concept This mo del was develop ed by Han Go el and Kumar
and p enalises the departure of the actual stress from an optimum
h i
P
n
F
n
i
surface The ob jective function is minimise x where S
i
A
i
F is the force in muscle i S is the p ermissible stress intensityinmuscle i
i i
and n or
Ob jective functions can be either linear or nonlinear in nature Mathematical
analysis reveals that the optimum solution in a linear formulation always lies at a
corner p oint of the feasible region that is at the intersection of the constraints
while non linear formulations can haveanoptimum solution anywhere within the
feasible region This di erence has b een recognised by several authors including
Pedersen Brand Cheng and Arora and Hughes Bean and Cha n
who conclude that linear functions are likely to preclude or minimise the pos
sibility for antagonistic activity Crowninshield and Brand also suggest
that a non linear ob jective function will predict lower individual stresses and a
higher number of active muscles when compared to linear ob jective functions
Optimisation Mo dels
Various authors haveinvestigated how the choiceofobjective function impacts on
mo del output Schultz and Andersson suggest that the choice of ob jective
function is not very imp ortant during maximal exertions but in submaximal
e orts di erent ob jective functions can yield signi cantly di erent estimates of
muscle tension Supp orting this Hughes concludes that the choice of
ob jective function can signi cantly a ect the magnitude of spinal compression
force predictions while Hughes Cha n Lavender and Andersson suggest
that di erences in mo del output are dep endent on the tasks analysed
Several authors have rep orted studies which use the same anatomical mo del to
compare mo del predictions resulting from di erent ob jective functions Sch ultz
Hadersp eck Warwick and Portillo conducted a study in whichfourobjec
tive functions were compared using the and muscle mo dels develop ed
by the same authors see Section The four optimisation schemes consid
ered were approximate minimisation of the maximum required muscle stress
along with minimisation of spinal compression as describ ed in Section
minimum compression with an upp er limit of Ncm on muscle stress
minimum sum of the squared muscle stresses and minimum sum of the cub ed
muscle stresses Schultz et al rep ort the b est overall correlation b etween
mo del predictions and EMG data were obtained using the rst optimisation
scheme for all three anatomical mo dels
Hughes et al compared the output from di erent optimisation mo dels
with EMG data for two isometric tasks frontal loading and constant moment
trials Each task was mo delled using ob jective functions the minimum
sum of squared muscle stresses the minimum sum of cub ed muscle stresses
minimum stress compression and the eigenvector synergy mo del Mo del re
sults for the L L cutting plane were compared with EMG data collected for the
erector spinae rectus ab dominis external oblique and latissimus dorsi muscles
A Review of Past Mo delling of the Lumbar Spine
The free body analysis ab ove the cutting plane of L L consisted of mus
cles left and right erector spinae rectus ab dominis internal oblique external
oblique and latissimus dorsi with muscle moment arms and cross sectional areas
as given by Tracy Gibson Szypryt Rutherford and Corlett and lines of
action as describ ed byDumas Poulin Roy Gagnon and Jovanovic Mo d
els were evaluated by a qualitative comparison of mo del predictions and EMG
values and a statistical analysis of the constant moment trial which identi ed
inconsistencies in the mo del predictions and exp erimental results Results indi
cate that the ob jective function which minimised the sum of the cub ed muscle
stresses was the only mo del to pro duce output consistent with the EMG data
analysed However even this mo del had problems predicting the activity of the
latissimus dorsi muscle during the constant moment trial
In a later study Hughes compared the output from optimisation mo d
els with resp ect to spinal compression during p ostures exp erienced in the work
place The comp onents of the free body mo del were as describ ed in Hughes et
al for the L L cutting plane with the four ob jective functions inves
tigated being minimum spinal compression with maximum muscle stress of
Ncm minimum stress compression minimum sum of the squared
muscle stresses and minimum sum of the cub ed muscle stresses Spinal com
pression values from each mo del were compared for p ostures videotap ed from
an industrial workplace The ma jority of these p ostures involved asymmetric
lifting and pulling This study did not compare mo del results with exp erimental
data instead investigating the di erences in mo del output caused by the use
of di erent ob jective functions Results indicate that predictions from the min
imum stress compression mo del were signi cantly larger for anterior p osterior
AP shear compression and resultant force than output from the other three
mo dels P Hughes also found that for some tasks no feasible so
lution existed for the minimum compression mo del since their imp osed limit of
Optimisation Mo dels
Ncm on individual muscle stress was exceeded Results indicated that none
of the mo dels predicted co contraction
The study by Hughes app ears to have overlo oked several factors the
most imp ortant b eing the free body or anatomical mo del not changing muscle
moment arms and lines of action with changing p osture Additionally the data
used to represent muscle area was the cross sectional area recorded from MRI
scans which may di er from PCSA
Each of the ob jective functions used in this study was develop ed and tested by the
original authors using isometric trials thereby eliminating the numerous issues
asso ciated with changing p osture The application of the optimisation schemes
to a xed anatomical mo del to investigate di erent p ostures is a ma jor downfall
and could e ect some of the conclusions reached For instance Hughes
found that in several cases no feasible solution was available for the minimum
compression mo del due to the maximum limit of Ncm for muscle stress
b eing exceeded and that this was a ma jor problem with the mo del However the
stress limit of Ncm should apply to muscles at their rest lengths Given the
form of the length tension relationship for muscles see Section it would b e
exp ected that maximum muscle force and hence the stress limit would increase
for lengths greater than the rest length Although the p ostures examined by
Hughes are not sp eci ed it would be reasonable to assume that in some
p ostures the muscle length for some muscles exceeds the rest length thereby
enabling stresses to b e greater than Ncm The omission of this detail from
the anatomical mo del mayhave resulted in the exclusion of p erfectly acceptable
p ostures from the analysis and the nding that the usefulness of the minimum
compression mo del is seriously limited Hughes also suggested that none of
the ob jective functions predict co contraction This nding is not consistent with
the results of other authors Bean et al Crowninshield and Brand
A Review of Past Mo delling of the Lumbar Spine
and may also be related to the lack of consideration of anatomical geometry in
the p ostures analysed
Mo dels by Schultz and co workers
Alb ert Schultz and co workers pro duced some of the earliest segmental optimi
sation mo dels The mo dels develop ed by this group involve balancing the forces
and moments generated by isometric contractions with the internal loads gener
ated by the muscles Schultz and Andersson Schultz The mo dels of
Schultz and co workers assume that the spinal segment of interest resists com
pression lateral shear and interp oser anterior p osterior shear but has no
signi cant moment resistance in the upright p osition Internal loads are calcu
lated using a linear programming approach with the ob jective function b eing the
minimisation of the maximum required muscle contraction force p er unit area of
muscle cross section stress and the minimisation of spinal compression This
ob jective function is calculated by setting a maximum muscle stress and deter
mining a solution If no solution is achievable then the maximum allowable stress
is increased and the pro cedure rep eated
The anatomical mo dels used represent a cross section of the lumbar spine at the
L level and involves either or muscles The muscles represented in
the and muscle mo dels Schultz and Andersson Sc hultz et al
are indicated in Table The muscle mo del Schultz et al is a sim
pli cation of the muscle mo del such that the psoas and quadratus lumb orum
muscles were deleted and the three groups of erector spinae muscles combined
into one equivalent All muscles are depicted as circles with the centroids and ar
eas adjusted for sub ject trunk width and depth Intra ab dominal pressure IAP
was also included in the mo dels
The mo dels are static in nature but can represent some dynamic situations under
Optimisation Mo dels
the sp eci c conditions outlined by Schultz If motion is truly dynamic
the mo dels can b e adjusted to incorp orate the inertial moments and forces
Schultz Andersson Ortengren Hadersp eck and Nachemson validate the
calculation of internal forces by the muscle mo del using EMG intradiscal
pressure and intra ab dominal pressure measured on volunteers p erforming a
variety of isometric tasks in standing and seated p ostures Intradiscal pressure
was measured by a subminiature pressure transducer built into the tip of anee
dle whichwas inserted p osteroloaterally into the centre of the third lumbar disc
while IAP was measured by a pressure sensitive radio transducer swallowed by
the sub ject Results indicate go o d correlation between predicted spinal com
pression and measured intradiscal pressure with a correlation co e cient of
Good correlation was also found between the measured EMG signals and pre
dicted contraction force for the erector spinae muscle r while a p o orer
correlation was rep orted for the anterior muscles correlation co e cients range
from to However one might question the muscle activity data obtained
from this study due to the invasive nature even though the authors stated that
they tried to avoid p ostures in whic h the con guration of the spine might be
unduly in uenced by the presence of the pressure measuring needle or in which
the sub jects might b e excessively uncomfortable b ecause of the needle Schultz
et al
In a later study Schultz et al compared the results of the and
muscle mo dels The study rep orted that the predicted muscle contraction
forces compared well with exp erimentally measured EMG data with correlation
co e cients of or ab ove for all but twisting moments It was also rep orted
that none of the correlation co e cients dep ended signi cantly on the mo del used
This is no surprise since EMG data was only collected for the erector spinae
rectus ab dominis and internal and external oblique muscles and only correlations
A Review of Past Mo delling of the Lumbar Spine
between the predicted values and measured EMG were rep orted Additionally
the internal force predictions made using the or muscle mo dels in which
the erector spinae groups were combined into one were roughly the sum of the
previously distributed forces After reviewing the metho dology it is easy to see
why this may be the case
The equilibrium constraints consist of a number of terms which can be broadly
represented by y R R where y is the muscle centroid lo cation in the j direction
l r
and R and R are the unknown muscle in the left and rightmuscles resp ectively
l r
Considering the situation where two muscles are combined and represented by
one equivalentmuscle the single equivalentisgiven a cross sectional area equal
to the sum of the comp onent areas and a centroid lo cation corresp onding to this
combination As an example assume that muscles and are to be combined
and represented by muscle In the equilibrium constraints of the mo del this
equates to the original terms y R R y R R b eing represented by
r l r l
the single term y R R If the combined centroid lo cation is in the middle
r l
y y
and the forces in muscle and are of the previous lo cations y
roughly equivalent R R R R then the term in the equilibrium
r r r l
equation b ecomes
y R r R l y y R R y R R
r l r l
y R R y R R R R
r l r l r l
y R R
r l
Hence the single equivalent muscle has a force which is approximately twice
that of muscle A similar approach can b e used for more than twomuscles and
for muscles of unequal size
Additional validation of the muscle mo del was rep orted by Zetterb erg et al
with ne wire monop olar electro des b eing used to measure muscle elec
Optimisation Mo dels
trical activity in the multi dus longissimus p ortion of erector spinae rectus
ab dominis external obliques and internal obliques Results pro duce go o d cor
relations between the measured and predicted muscle behaviour for the erector
spinae and rectus ab dominis muscles but only correlation co e cients between
and for the oblique muscles This is in agreement with past results based
on surface electro de studies Schultz et al The authors suggest that the
function of antagonist muscles needs to be reviewed in further mo delling work
by changing the ob jective function used
The mo dels develop ed bySch ultz and co workersusedataonmuscle size and p o
sition obtained from anatomical drawings adjusted for trunk depth and width
As mentioned in Section the accuracy of this metho d is questionable and
relies heavily on the accuracy of the muscle placement in the original drawings
Additionally the direction of the muscles are xed which is anatomically unreal
istic in altered p ostures
Marras used the muscle mo del develop ed by Schultz and Andersson
in an attempt to predict muscle activities during controlled isokinetic
motion This typ e of analysis was addressed by Schultz and Andersson
but the mo del was never trialled on suc h data The only di erences intro duced to
the mo del by Marras were an upp er b ound on muscle force and maximum
contraction intensity and an ob jective function which minimises compression
Exp erimental data was based on sagittally symmetric isometric and isokinetic
back lift maximum exertions by sub jects around the L S joint EMG
activity was monitored via ne wire electro des implanted in the right and left
latissimus dorsi erector spinae external oblique internal oblique and rectus
ab dominis IAP was also measured via a catheter transducer inserted into the
stomach via the nasal passage
One of the problems Marras rep orted with the mo del was that for sagit
A Review of Past Mo delling of the Lumbar Spine
tally symmetric lifts all bar three of the constraint equations b ecome redundant
Hence a linear ob jective function will at most predict activemuscles those with
the longest moment arms For the tasks p erformed the muscles predicted to be
active were the latissimus dorsi and the right and left erector spinae with the
activity of the latissimus dorsi b eing overpredicted by to and the activity
of the erector spinae b eing underpredicted by approximately The mo del
also overpredicted IAP by ab out Hence the muscle mo del of Schultz and
Andersson as applied by Marras did not predict muscle activity
well for the isokinetic tasks p erformed
One imp ortant point which has been acknowledged by Marras is the
lack of consideration given to the change in maximum muscle force in relation
to changing muscle length This point was overlo oked by setting a maximum
muscle force based on the relationship CSA Ncm The cross sectional
areas CSA used by Marras were obtained from CT scans at the L
level It is unlikely that these CSA values have been corrected for scan angle
since the images were obtained from a book of computer tomography pictures
This will result in the CSAs b eing overestimated for muscles which do not run
p erp endicular to the scan plane resulting in an overestimation of the maximum
muscle force Additionally the mo del was applied to the L S joint but muscle
information was collected at the L level It would also app ear that Marras
used the same muscle directions as Schultz and Andersson even
though the mo del was applied to a di erent spinal level
The ob jective function used bySchultz approximately minimises the mus
cle contraction intensity and the spinal compression force Work by Bean et al
formally computes this ob jective function by using a double linear pro
gramming metho d The rst stage of this metho d is to minimise maximum
muscle intensity The second stage then uses the optimal muscle intensity cal
Optimisation Mo dels
culated in stage to minimise the sum of the muscle forces This second step
e ectively minimises spinal compression Bean et al suggest this metho d
is sup erior to earlier schemes due to the instability of solutions as intensityvalues
change slightly This new metho d is applied to the muscle mo del previously
describ ed Although no comparative data is provided the authors rep ort that
the results compare well to the EMG measurements presented by Schultz and
Andersson
Further work bySchultz intro duces several mo di cations to the mo del of
Bean et al These include intro ducing spine motion segment passive resis
tances to moments allowance for muscle contraction intensities larger than the
initially calculated values allowance for ab dominal pressure without prescribing
what that pressure is and inclusion of the transverse ab dominis muscle These
mo di cations are included in the mo del via the constraint equations used in the
double linear programming metho d Inclusion of the transverse ab dominis cre
ates a muscle mo del with constraints This mo del is more complex than
earlier versions due to the incorp oration of more anatomical reality
Mo dels by Ladin and co workers
Work by Ladin Murthy and De Luca and Ladin Murthy and De Luca
intro duced a novel application for mo del output The mo del of the L
cross section incorp orates muscles bilateral pairs and minimises the spinal
compression due to muscle forces only Anatomical data was based on that
rep orted bySchultz et al with only isometric contractions in the upright
stance b eing considered Muscle stresses were constrained to b e p ositive and no
larger than a set maximum which was determined by continually increasing the
level until a solution for the system was achieved
The authors develop ed muscle activity surfaces for each muscle bychanging the
A Review of Past Mo delling of the Lumbar Spine
arm p osition and load weight and p osition These surfaces describ e the force
in the muscle for a mesh of external exion and lateral b ending moments Each
of these curves contains a zone referred to as the switching curve This curve
indicates when a muscle b ecomes active These on o predictions of muscle
activation were validated against EMG data for the rectus ab dominis medial
external oblique and multi dus muscles on eight male sub jects p erforming six
tasks The success rate of the on o prediction of muscle activity ranged from
for contralateral muscles and for ipsilateral muscles
It is suggested by Ladin et al and Ladin et al that the switch
curves provide a means of representing a functional grouping of muscles that
are similarly activated by integrating lo cation orientation and cross sectional
area These groupings are erector spinae group ilio costalis multi dus and
longissimus and latissimus dorsi quadratus lumb orum and psoas lateral
p ortions of the oblique muscles medial p ortions of the oblique muscles and
the rectus ab dominis The order of recruitment for increasing lateral b ending
moment for a given exion moment is as listed ab ove e g group activates
b efore group b efore group etc
Validity of the mo del output was tested by Ladin and Ne who designed
an exercise which follows an isoforce curve as predicted by the mo del The
rationale b ehind this work was that if a muscle develops a constant force output
then the corresp onding EMG signal should b e relatively constant Results show
there to be go o d correlation between the time of change of the predicted force
and the EMG signal with the mo del p erforming b etter for the contralateral
muscles when compared to the ipsilateral muscles
Ladin et al suggest that the switchcurves can b e used in the development
of low back exercises However there are several p oints which should b e addressed
or investigated further b efore the mo del output is applied to this task First
Optimisation Mo dels
the mo del has a fairly low success rate of predicting on o muscle activities
for ipsilateral muscles ab out during the tasks for which it is designed
Further investigation would b e needed for other isometric and non isometric tasks
to extend the application of the mo del Additionally only three muscles were
involved in the EMG validation This should b e extended to include more of the
muscles included in the mo del The second point which needs to be considered
is the fact that only one spinal level is mo delled It is unknown whether spinal
segments ab ove and b elow the segment under review are in equilibrium using
the calculated muscle forces This issue arises in all segmental mo dels since the
muscles included in the mo dels span more than just the level of interest Finally
the form of the ob jective function in the optimisation is an arbitrary choice
which tends to equilibrate the stress level across all muscles that participate in
load sharing The e ect the choice of this ob jective function has on the results
is unknown A sensitivity analysis of the switch curves using di erent ob jective
functions may address this issue
Mo dels by Gracovetsky Farfan and co workers
Initial work by Gracovetsky Farfan and Lamy involved developing a two
dimensional mathematical mo del of the lumbar spine in which muscle and
ve ligament forces were mo delled across the ve lumbar vertebrae A static
weight lifting task was simulated and it was assumed that each of the muscles
was active at each vertebral level Table lists the muscles included in this
mo del The ob jective function utilised was a minimal stress mo del of the form
given in Equation The axis of rotation was also considered to be variable
and was determined from the optimisation
A Review of Past Mo delling of the Lumbar Spine
X
S min
i
i
X
where S S l X X Se Lig i
i ij ij i j i
j
S is the shear created by muscle j at intervertebral joint i
ij
l is the lever arm of muscle j at intervertebral joint i
ij
X is the force generated by muscle j per unit area j
j
X is the displacementofthe centre of rotation for joint
m
m m
Se is the contribution of external load to shear at joint i and
i
Lig i is the pull of the TLF at intervertebral joint i
In total Gracovetsky et al had variables sub ject to equality con
straints consisting of moment equations and an equation for the psoas muscle
and inequality constraints corresp onding to limits on biological tissues
Mo del results indicate that the muscles app ear to work in groups and that the
p ositions of the centres of rotation do not change until the ligaments become
active
The work by Gracovetsky et al was the rst rep orted mo del of it s typ e
and was a large step towards understanding the mechanics of the spine The
mo del makes many assumptions regarding the anatomy of the spine and func
tion of the muscles The biggest drawback of the modelisthat it is only in two
dimensions Gracovetsky et al mo del the spine in a variety of p ositions
inclination They state that in the from upright to approximately degrees
particular weight lifting example studied the rst degrees of forward b ending
Optimisation Mo dels
is provided by exion of the spine while the remaining is provided by rotation of
the p elvis However the metho d of allo cating inclination to the various inter
vertebral joints is not mentioned although one of the conclusions made was that
muscle activation dep ended on inclination Although the centres of rotation were
determined by optimisation each p osition was restricted to remain within the
disc area and not deviate more than inches from the centre of the disc No
vertical deviation was allowed This restriction on the centre of rotation has b een
sup erseded by the later work of Pearcy and Bogduk who rep orted that in
many cases the instantaneous axis of rotation is lo cated within the sup erior part
of the lower vertebra of the joint
One of the ma jor assumptions made by Gracovetsky et al was that the
activation of the psoas was a function of the compression at the L disc This
assumption arose as a means of maintaining spinal stability for deviations from
the sagittal plane Gracovetsky et al explain that the psoas is a prime
candidate for such reinforcement since the psoas is the only muscle that is
attached to the discs at all levels except p ossibly for L The psoas activation
was assumed to be given by X C where C is the compression at
psoas
L This is a gross o versimpli cation of the function of the psoas muscle which
may pro duce misleading mo del results
Gracovetsky Farfan and co workers prop osed an amended mo del of the spine
in a series of three pap ers Gracovetsky Farfan and Lamy Gracovetsky
Farfan and Helleur Gracovetsky and Farfan This mo del included a
very detailed representation of the anatomy of the spine based on the hyp othesis
that stress is minimised and equalised across all intervertebral joints One of
the strengths of this mo del is the anatomical detail included see Table for
muscles included The mo del describ es the velumbar vertebrae and asso ciated
discs with the p elvis acting as a base and thorax and head treated as a solid
A Review of Past Mo delling of the Lumbar Spine
blo ck with xed centre of gravity Muscles having a diverse area of attachment
were divided into strands with each strand having a limited attachment area
This is similar to the concept of muscle fascicles which are discussed further in
Chapter The centre of rotation is assumed to be on the bisector of the disc
one third of the distance from the p osterior edge with movement restricted to
the sagittal plane Muscles are group ed into seven groups such that all muscles
within the group have the same activity The muscle groupings used were
an erector spinae group consisting of the medialis spinalis ilio costalis lumb orum
and sacrospinalis multi dus latissimus dorsi quadratus lumb orum
psoas rectus ab dominis and external obliques internal obliques transverse
ab dominis
The p osterior ligamentous system of the spine was divided into two comp onents
the TLF and the midline ligaments the supraspinous interspinous and capsular
ligaments the ligamentum avum and p osterior longitudinal ligament lump ed
together The TLF was used to represent the ab dominal mechanism by attach
ing to the spinous pro cesses of the vertebrae the ribs and lateral margin of the
p elvis and the transverse ab dominis and internal oblique muscles This attach
ment to the ab dominal musculature generates a longitudinal tension whenever
the ab dominals are active representing the mechanical conversion of lateral pull
into longitudinal tension Gracovetsky et al This feature acts to extend
the spine by bringing the L and L spinous pro cesses together and induces com
pression but no shear at that joint In comparison the midline ligaments cannot
b e activated unless the spine is exed su ciently and generate compressiveand
shear forces Gracovetsky et al use this representation of the fascia to ex
plain the presence of intra ab dominal pressure such that the pressurisation acts
to ensure the prop er shap e of the fascia and supp ort the ho op tension gener
ated bythemuscles Furthermore the authors suggest that the intra ab dominal
pressure cannot exceed arterial blo o d pressure
Optimisation Mo dels
The allo cation of force was determined by minimising and equalising the muscle
stress at all intervertebral joints This was achieved using the ob jective function
minimise C shear C Comp C mid C grp C grp
where shear is the square of the euclidean norm SEN of the shear vector
at each joint
Comp is the SEN of the compression vector at each joint
Mid is the SEN of the midline ligamentvector at each joint
grp isthe SEN of the muscle vectors for groups to at
each joint
grp is the SEN of the muscle group at each joint and
C C C C C are constants
This ob jective function makes the assumption that the central nervous system
can measure stress and co ordinate the muscle activity so as to adjust muscle and
ligament tensions to obtain minimum stress The mo del was implemented for a
dead lift by a champion weight lifter since it is assumed that such an athlete
has acquired the skill to utilise his spinal mechanism to its maximum capability
Gracovetsky et al
Few analytical results are presented to validate the prop osed mo del although
the authors claim the mo del explains a wide variety of observed exp erimental
data including EMG resp onses muscle relaxation at full exion intra ab dominal
pressure intradiscal pressure and maximum muscular extension moment Gra
covetsky and Farfan conclude that during a maximum lift the muscles
ligaments and bones are stressed at two thirds of their ultimate strength and
that they obtain these values simultaneously
A Review of Past Mo delling of the Lumbar Spine
Although this work contains some interesting concepts and acknowledges the
imp ortance of anatomic reality itisdisappointing that the lack of mathematical
detail and validation of results restricts its application by other authors
Mo dels by Stokes and Gardner Morse
Stokes and Gardner Morse develop ed a three dimensional mo del of the
lumbar spine to analyse muscle recruitment and loading at all of the lumbar
joints simultaneously The mo del included the ve lumbar vertebrae and two
rigid bodies representing the thorax and sacrum p elvis The motion segments
in the mo del were represented as either b eams or ball and so cket joints with
each of these alternatives having di erent sti ness prop erties and b eing analysed
separately It should b e noted that in the b eam mo del the ends of the b eam were
connected to the vertebral body centres while in the ball and so cket mo del
the joint for movement is midway between the vertebral body centres Hence
neither mo del incorp orates information ab out the actual p osition of the centre
of rotation The mo del represented a spine in a neutral standing p osition and it
was assumed that there were no forces or moments due to b o dyweight or elastic
stresses Linear programming was used to optimise the system which contained
muscle forces Table and displacements at each vertebra or forces
between each pair of vertebrae The ob jective function maximised the external
loading when moments were individually applied at the vertebral b o dy centre of
T The moments considered were extension exion lateral b ending and axial
torque Muscles were constrained to have forces in the range zero to kPa and
were assumed to take a straight line from origin to insertion Further constraints
were made restricting the displacement of the centre of the intervertebral body
to less than mm and in the sagittal plane and mm and in other planes
The single joint intervertebral muscles intertransversii and rotatores the in
Optimisation Mo dels
ternal and external obliques transverse ab dominal and quadratus lumb orum
muscles were omitted from the mo del The e ects of intra ab dominal pressure
were also ignored
Results suggest that for both joint alternatives considered many muscles were
not active in maximum e ort conditions The ball and so cket mo del showed
a great deal of antagonistic muscle activity for nonsagittal plane e orts while
antagonistic muscle activity in the b eam mo del was dramatically less The mo del
by Stokes and Gardner Morse requires simultaneous equilibrium at all
joints with the result that the maximum e orts rep orted are less than those
rep orted for mo dels which do not have this criteria e g segmental mo dels It
was rep orted that this simultaneous equilibrium requirement limited the number
of active muscles and the degree of activation which could be achieved and
that maximum contraction of all muscles would be inappropriate This mo del
addresses the equilibrium problems asso ciated with segmental mo dels but omits
some ma jor muscles e g internal and external obliques It also oversimpli es
the anatomy by assuming a straight line of action between muscle origin and
insertion
In more recentwork Stokes and Gardner Morse a intro duce the concept of
amulti criteria ob jective function which combines information ab out spine stabil
ity displacement and force This typ e of ob jective function allows muscle forces
to be allo cated after consideration of a number of factors thought to in uence
the allo cation pro cess but intro duces the problem of weighting the imp ortance
of each comp onent This typ e of combined ob jective function acknowledges that
the central nervous system probably uses a numb er of parameters in the recruit
ment of spinal muscles thus improving the anatomical reality of the optimisation
pro cess
A Review of Past Mo delling of the Lumbar Spine
Hybrid mo dels
Cholewicki and McGill prop osed a hybrid mo del which incorp orates fea
tures of EMG mo delling and also optimisation The mo del called EMG assisted
optimisation involves adjusting the force predictions from an EMG mo del so as
to satisfy the three moment equilibrium constraints simultaneously This is done
by adjusting a gain value for each muscle such that it is optimised around
Mathematically the optimisation can be expressed as
n
X
minimise M g
i i
i
n
X
sub ject to g M M
i xi x
i
n
X
g M M
i yi y
i
n
X
g M M
i zi z
i
g
i
where n is the number of muscle fascicles
g is the gain for muscle i Nm
i
M is the estimated moment from the EMG mo del generated by
i
q
muscle i Nm M M M
xi yi zi
M M M are the estimated moments generated by muscle i ab out
xi yi zi
the X Y Z joint axes resp ectively Nm
Cholewicki et al apply this metho dology to isometric exertions in an
upright standing p osture using an anatomical mo del comprising of muscle
fascicles and ligamentous comp onents Although fascicles were included
only of these crossed the level of interest L L meaning only these
Mo dels using Neural Networks
muscles were included in the mo del The anatomical mo del is similar to that
prop osed by McGill and although Cholewicki et al illustrated
this metho d using isometric exertions the technique could be applied to the
results of any EMG mo del Results suggest that the output is highly correlated
with output from EMG mo dels and represents EMG data well The similarity
between EMG mo del output and hybrid mo del output rep orted by Cholewicki
et al is no surprise since the adjustments to EMG predicted moments are
optimised ab out thereby ensuring that changes to predicted moments from
EMG mo dels are small
The hybrid mo del app ears to b e an improvementover the EMG mo del however
it still faces many of the same problems as the EMG mo dels including not b eing
able to predict b eyond the EMG data set the mo delling of passive tissue elements
and the costly acquisition of data
Mo dels using Neural Networks
A recent development in the area of spinal mo delling is the use of arti cial
neural networks ANN as an alternative to optimisation or EMG Supp orters
of ANN cite problems with the choice of ob jective function in optimisation and
the dep endence on EMG data in EMG mo dels as reasons for the use of ANN
Nussbaum Cha n and Martin a
Nussbaum et al a prop osed the rst ANN mo del using a three layer fully
connected feed forward network arc hitecture Four input units corresp onding
to the magnitudes of applied right lateral left lateral exion and extension mo
ments were incorp orated with eight output units corresp onding to the bilateral
erector spinae rectus ab dominis external oblique and latissimus dorsi muscles
Table Information obtained from the output units corresp onds to the
A Review of Past Mo delling of the Lumbar Spine
normalised EMG signals for each muscle which may be interpreted as muscle
activation levels The use of a logistic sigmoidal function in the output layer en
sures that the network output is b etween and The network was trained and
tested on exp erimental data from Lavender Tsuang Hafezi Andersson Cha n
and Hughes b which consisted of moment orientation EMG signals ob
tained from sub jects resisting a static moment applied to the L L motion
segment The mo del was trained on approximately one quarter of the data us
ing a back propagation metho d in which the total sum of squares was used as a
measure of error
Output from the testing stage of the ANN mo del was linearly regressed with
recorded EMG values as was output from the optimisation mo dels of Bean et
al and Crowninshield and Brand Assessment of the p erformance
of the ANN mo del was made by comparing the co e cients of determination ob
tained from the regression mo dels The authors rep ort b etter correlation with
measured EMG values using the ANN mo del than with either optimisation mo del
for all muscles with the exception of the left erector spinae The rep orted R
values from the ANN mo del are approximately for the erector spinae rectus
ab dominis and external oblique muscles and for the latissimus dorsi mus
cle Hence the authors suggest that if input patterns are regular consistent
and well b ehaved then a network mo del given su cient size and training will
generate very accurate predictions for novel data within the same parameter
space of the training set Nussbaum et al a
Additional validation was undertaken by Nussbaum and Cha n b who
regressed the ANN mo del output with EMG data rep orted by Seroussi and Pop e
Hughes and Lavender et al b The co e cients of deter
mination for the regressions range from to for all muscles excluding
the latissimus dorsi Hence it would app ear that the ANN output compares
Mo dels using Neural Networks
favourably with EMG data from sources other than that it was trained on Nuss
baum and Cha n b also compare the ANN output to the results from the
optimisation mo del prop osed by Crowninshield and Brand Unlike the
comparison made by Nussbaum et al a Nussbaum and Cha n b
regress the compression forces predicted by the ANN and optimisation mo dels
for loading conditions Results suggest that the gradient of the line of b est t
was not signi cantly di erent from one P
Nussbaum and Cha n b also assessed the accuracy of the ANN mo del
output in relation to correctly identifying the activity state of a muscle that is
whether the muscle is on or o This is a comparable test to that conducted
by Ladin et al using their switching curves The ANN mo del achieved
correct predictions of active on and silent o states with approximately
success The authors suggest this success rate would increase to if
the latissimus dorsi muscle predictions are ignored and that this success rate
is sup erior to that rep orted by Ladin et al esp ecially since Ladin et al
ignored the latissimus dorsi muscle and did not apply extension moments
which would have elicited more oblique muscle activity something optimisation
mo dels generally have di culty predicting
Several points need to be considered when assessing the mo del and testing pro
cedures used by Nussbaum et al a The rst is the inclusion of only four
uscles in the mo del It would app ear that these four muscles were chosen m
b ecause EMG data existed for them The mo del structure creates a mapping
function to match EMG patterns for the muscles based on externally applied
moments The mo del do es not consider the equilibrium conditions of the applied
moments This may be one reason why the results t the data well Further to
this the wayinwhich the ANN mo del was compared to the optimisation mo dels
by Nussbaum et al a is interesting To allow comparison output from
A Review of Past Mo delling of the Lumbar Spine
the optimisation mo dels was normalised using the maximum force potential of
each muscle PCSA Ncm These values were used in a linear regression
against EMG data which was normalised using the maximal and resting val
ues for each muscle Hence the normalised EMG values show some individual
variability where as the normalisation of the optimisation results do es not One
further problem with the prop osed ANN mo del is the inability to include muscles
for which there is no EMG data this is particularly relevant for deep muscles of
the back such as the multi dus
A more complex ANN mo del containing four layers was prop osed by Nussbaum
Martin and Cha n This mo del has an input layer consisting of six units
representing the magnitudes of external static moments at L L a hidden layer
amuscle layer containing units see Table and an output layer consisting
of three units representing the reactive moments in each plane Although most
of the weights on the unit connections are trained the connections within the
muscle and output layers are calculated using
k
w S PCSA
k m max m
m
where S is the upp er limit of muscle stress Ncm
max
PCSA is the physiological cross sectional area of muscle unit m cm
m
k
is the moment generated ab out axis k by aunitforce in muscle m N
m
Within the muscle layer of the neural network inhibitory connections exist
These connections allow each muscle sends an inhibitory signal to itself and
to all other muscle units thereby intro ducing comp etition b etween muscles
It is claimed by the authors that this mo del which is trained by comparing in
put external moments to reactive moments can be develop ed without the use
Resting values were those measured while the sub ject was relaxed
Mo dels using Neural Networks
of EMG data However EMG data is used to calibrate the inhibitory parame
ters by matching muscle unit information to EMG data Results suggest that
there is little problem training the mo del to equilibrate the moments With the
mo del trained and the inhibitory factors calibrated an assessment of the mo del
was made by Nussbaum et al by comparing the predicted muscle acti
vations to EMG data It is suggested by the authors that realistic patterns of
muscle activitywere obtained only after inclusion of comp etition within and b e
tween muscles and that while the patterns of predicted muscle activity closely
matched exp erimental values there were frequent discrepancies in magnitudes
Nussbaum et al As with the previous mo del Nussbaum et al a
the ANN did not predict the activation of the latissimus dorsi well
This ANN mo del has a number of assumptions ab out the geometry of the in
cluded muscles In fact each of the comp onents in the connection terms linking
muscles with the output layer is sub ject to some uncertainty Although the value
k
for S and references for are given no mention is made of the source of
max
m
the PCSA values used with the authors stating that the PCSA values used were
mostly within of those presented by McGill Santaguida and Stevens
The authors suggest that electrical cross talk in the EMG data may explain
discrepancies in the regression of predicted and measured activity for the rec
tus ab dominis which had higher predicted values than measured and external
oblique which predicted lower than measured data However EMG techniques
havebeenwell do cumented with no other studies having this cross talk problem
Instead the problem may b e an artifact of the contribution of other muscles not
included in the mo del
The ANN mo del prop osed by Nussbaum et al app ears to give go o d results
suggesting that the use of neural networks may be a successful alternative to
optimisation or EMG mo dels However the impact of excluding the deep back
A Review of Past Mo delling of the Lumbar Spine
muscles and transverse ab dominis and the generalised anatomyof the included
muscles must b e considered The authors cite a lack of EMG data and anatomical
detail as reasons for excluding the other muscles and use the results of McGill
who suggests that other muscles have a relatively smaller contribution to
lumbar moments to justify the exclusion This hardly seems a go o d reason for
omitting several large muscles including the quadratus lumb orum
Anatomical Mo dels
All of the mo dels discussed previously in this Chapter di er in the anatomical
mo dels used Indeed trying to review and compare the muscles included in the
previous mo dels is a challenging task The mo dels rep orted by Gracovetsky et al
Gracovetsky et al and McGill and Norman incorp orate the
sacrospinalis muscle Table Anatomy texts Williams and Warwick
Hollinshead describ e the sacrospinalis as analogous to the erector spinae
muscle which consists of comp onents the ilio costalis longissimus and spinalis
Bogduk provides a more detailed description of the comp onents of the
lumbar erector spinae rep orting that it consists of the longissimus thoracis and
the ilio costalis lumborum Thus it might be reasonable to assume the mo dels
of Gracovetsky et al Gracovetsky et al and McGill and Norman
use the term sacrospinalis instead of erector spinae However all three
mo dels also include the ilio costalis and either the medialis spinalis Gracovetsky
et al Gracovetsky et al or the longissimus McGill and Norman
Given that these muscles are considered to b e comp onents of the erector
spinae it is not clear how both the erector spinae and its comp onents could be
included in the same mo del This makes interpretation di cult
The di erences observed in the mo dels reviewed include incorp orating di erent
Anatomical Mo dels
numb ers of muscles using di erent sources for PCSA values or using CSA
grouping muscles di erently with resp ect to activation and using values b etween
Ncm and Ncm for the maximum muscle intensity Much of the reason
for these di erences stems from a lack of detailed anatomical information for the
muscles of the lumbar spine However it is the anatomical mo del that forms
the basis on which EMG optimisation or ANN techniques are applied With
out a comprehensive anatomical mo del which re ects the complex anatomy of
the region the mo del will be de cient in some asp ect irresp ective of the force
allo cating technique used This p oint has b een acknowledged by several authors
McGill and Norman Nussbaum Cha n and Rechtien b Davis and
Mirka McGill and Norman suggest that using a mo del incorp orat
ing the detailed anatomy of the erector spinae muscle has the e ect of reducing
predicted spinal compression and shear and also changing the direction of the
shear when compared to a one muscle equivalent Nussbaum et al b
reinforces this nding by rep orting that predicted spinal shear and compressive
forces are sensitivetochanges in muscle lines of action particularly during asym
metric loading Nussbaum and Cha n a acknowledge the imp ortance of
the anatomical mo del underlying the muscle force predicting algorithm and pro
p osed an improved anatomical mo del The mo del concentrates on scaling and
deforming the mo delled anatomy to represent that of a particular sub ject in
a sp eci ed exed or bent p osture However the mo del do es not improve on
the muscular representation still using a single equivalent for each of the eight
muscles included with attachment points determined from anatomical texts
An investigation into the in uence of mo del complexity on outcomes was under
taken by van Die en In this study the minimum sum of cub ed stresses
was used as the ob jective function whichwas applied to three anatomical mo dels
each containing di erent assumptions regarding the anatomy or more precisely
the number of indep endent muscles included in the mo del The mo del was con
A Review of Past Mo delling of the Lumbar Spine
Table Functional muscle groupings as prop osed by di erent authors
These groups are used in biomechanical mo dels to reduce the amountof
input data assumptions required by assuming muscles in the same group
have the same activation levels No similarityinthe muscles included in each
group by each author is implied
Grp Gracovetsky et al McGill et al van Die en
I Medial spinalis Longissimus thoracis Longissimus thoracis
Ilio costalis lumborum Ilio costalis lumborum
Sacrospinalis
II Multi dus Multi dus Multi dus
Sacrospinalis
Quadratus lumborum
III Latissimus dorsi Latissimus dorsi Ilio costalis lumborum
IV Psoas Psoas Psoas ma jor
Transverse ab dominis
Internal oblique
V Rectus ab dominis Rectus ab dominis Rectus ab dominis
VI External obliques External obliques External obliques
Internal obliques
Transverse ab dominis
VI I Quadratus lumborum Internal obliques
Transverse ab dominis
structed around the L S joint with the full mo del containing muscle slips
The other two mo dels contained the same anatomical information but group ed
the activation of muscles into and groups These groups were chosen on
the basis of accepted anatomical de nition and re ect proximity common in
nervation and function relationships van Die en The resulting groups
of muscles are indicated in Table The latissimus dorsi and quadratus lumbo
rum muscles were not included in the mo del due to a lack of accurate anatomical
data Mo del output was compared with the EMG data rep orted byLavender et
al b and Lavender Tsuang Andersson Hafezi and Shin a for the
bar and thoracic parts of the longissimus thoracis muscles anterior parts of lum
the external oblique muscles and the left and right rectus ab dominis muscles
Concluding Remarks
Results indicate that activation patterns predicted by the full mo del were not
very di erent to activation patterns of group ed muscles and that the corresp on
dence b etween predicted activity and EMG data was satisfactory when compared
to previous studies In fact correlations between predicted activity and EMG
data were b etter with the exception of left rectus ab dominis than those rep orted
by Hughes et al and Nussbaum et al using the same ob jective
function but only a muscle mo del van Die en suggests the p o or corre
lation of left rectus ab dominis is related to the exclusion of the latissimus dorsi
from the mo del
This work shows that b etter correlations with EMG data can be obtained from
mo dels incorp orating accurate and detailed anatomy of spinal muscles This
study also suggests there is minimal loss of accuracy in constraining activation
levels to b e constant within sp eci ed anatomically derived muscle groups
The grouping of muscles into functional groups is an interesting p oint with di er
ent authors suggesting di erent groupings Table Gracovetsky and Farfan
develop ed muscle groups based on the hyp othesised action of the mus
cles while McGill and Norman use groups based on available EMG
data McGill and Norman give no indication of the reasoning b ehind the
allo cation of deep muscles to the surface muscles measured by EMG except for
the psoas which is assumed to function as a spinal stabiliser like the internal
oblique Neither of these groupings corresp ond to those prop osed by van Die en
nor those obtained from the results of the mo del by Ladin et al
Concluding Remarks
If a muscle is included in a mo del the line of action attachment p oints or mo
ment arms should b e anatomically realistic Today s medical imaging technology
A Review of Past Mo delling of the Lumbar Spine
sup ersedes the use of anatomical drawings to estimate muscle p osition and size
while detailed dissection studies provide the necessary data on attachment p oints
for some muscles Anatomical mo dels should include the capacitytochange mus
cle lines of action or moment arms when spinal p osture changes As mentioned
in the previous discussion of individual mo dels many mo dels do not contain this
feature
Two areas where past mo dels are lacking is in the mo delling of the lines of action
of the internal and external oblique muscles and the mo delling of the TLF
The oblique muscles wrap around the sides of the torso helping to maintain the
torso shap e No past mo dels havecontained any metho dology which attempts to
include this feature in calculating the muscle lines of action Several authors have
included a comp onent in the anatomical mo del to represent the TLF However
all past attempts to mo del this structure have b een in t wo dimensions and have
only included one of the layers of the fascia the p osterior layer Both of these
issues need to be considered further if anatomical mo dels and consequently
biomechanical mo dels are to improve their representation of the true anatomy
of the lumbar spine
A review of the anatomical information required to develop a detailed mo del of
the lumbar spine is presented in Chapter Various biomechanical prop erties
such as spinal kinematics and muscle force are also discussed These two com
anatomy and realistic biomechanics provide the basis for the ponents detailed
development of a fully three dimensional anatomical mo del of the lumbar spine
Chapter
Anatomy and biomechanics of
the lumbar spine
The lumbar spine is a complex combination of b one muscle ligament interver
tebral disc and fascia These comp onents provide supp ort and structure to the
spine facilitate movement and provide a means of attaching muscle to b one For
the purp oses of the mo del being develop ed the muscular comp onent is of pri
mary interest since this is the only active force generating comp onent Although
the other structures of the spine are able to resist moments and forces e g b one
and intervertebral discs or develop passive forces e g ligaments the mus
cles which cross the lumbar spine have the largest force generating capacity To
accurately mo del the in uence of the muscles on the spine numerous factors
need to be considered These include the lo cation of the attachment p oints of
the muscles the path the muscle takes b etween the attachment p oints the force
generated within the muscle the points ab out which the spinal segments rotate
and the range of motion of the spine Each of these areas except the muscle lines
of action which are discussed separately in Chapter are addressed in the re
mainder of this chapter This information provides the basis for the development
of a detailed anatomical mo del of the lumbar spine
Anatomy and biomechanics of the lumbar spine
Muscular anatomy of the lumbar spine
There are nine ma jor muscles which either attachtothelumbar spine or cross the
lumbar region of the torso These are the multi dus erector spinae consisting of
the longissimus thoracis and ilio costalis lumb orum quadratus lumb orum psoas
ma jor latissimus dorsi rectus ab dominis internal oblique external oblique and
transverse ab dominis Figures to illustrate the lo cation of these muscles
Mo at and Mottram Most of the muscles have multiple attachment
points across the spine For this reason each muscle is represented by fascicles
where a fascicle is de ned as a group of muscle bres which have a common
and discrete origin and insertion The number of fascicles used to represent
a muscle dep ends on the structure of the muscle The detailed information
required to de ne a muscle fascicle is only able to be obtained from dissection
studies of human cadavers Of the nine muscles which are asso ciated with the
lumbar spine ve have been the sub ject of detailed anatomical studies For
the remaining muscles quasi fascicles have b een develop ed by various authors
using alternative means Using the available information the nine muscles of the
lumbar region can b e represented by fascicles The only muscle for which the
use of fascicles is not appropriate is the transverse ab dominis since this muscle
has no direct attachment to the spine instead attaching via the TLF Figures
and are schematic representations of the approximate p ositions of
the fascicles of the multi dus longissimus thoracis and ilio costalis muscles
The ma jor advantage of representing the muscles by their comp onent fascicles is
that it allows a more accurate representation of the muscle in terms of its moment
generating capacity that is lines of action attachment p oints and cross sectional
areas It also provides a means of assessing the imp ortance of di erent parts of
the muscle in generating moments
Muscular anatomy of the lumbar spine
Figure Muscles of the back p osterior view with the erector spinae
and quadratus lumb orum highlighted in red Repro duced from Mo at and
Mottram
Anatomy and biomechanics of the lumbar spine
Figure Muscles of the back p osterior view with the latissimus dorsi
highlighted in red Repro duced from Mo at and Mottram
Muscular anatomy of the lumbar spine
Figure Muscles lo cated on the anterior of the trunk which exert an
e ect of the lumbar spine The rectus ab dominis has been divided on the
rightto exp ose the underlying muscles The rectus ab dominis transverse
ab dominis external and internal oblique muscles are highlighted in red
Repro duced from Mo at and Mottram
Anatomy and biomechanics of the lumbar spine
Figure Muscles of the lumbar spine and hip anterior view rightside
only with the psoas ma jor highlighted in red Repro duced from Mo at and
Mottram
Muscular anatomy of the lumbar spine
Figure Schematic illustration of the fascicles used to represent the
multi dus muscle
Anatomy and biomechanics of the lumbar spine
a Longissimus thoracis pars thorasic
b Longissimus thoracis pars lumborum
Figure Schematic illustration of the fascicles used to represent the
longissimus thoracis muscle
Muscular anatomy of the lumbar spine
a Ilio costalis lumb orum pars thorasic
b Ilio costalis lumb orum pars lumb orum
Figure Schematic illustration of the fascicles used to represent the
ilio costalis lumb orum muscle
Anatomy and biomechanics of the lumbar spine
Muscle co ordinate data
Co ordinates for the attachment p oints of the various muscles crossing the lumbar
spine were obtained for each fascicle These co ordinates were derived using two
di erent techniques with b oth b eing based on the anatomical geometry of the Visible Man Visible Human Pro ject
National Library of Medicine Methesda
MD
Where detailed anatomical descriptions of the attachment p oints were available
the corresp onding D co ordinates were determined by lo cating the anatomically
describ ed point on a reconstruction of the skeleton of the Visible Man The
ANALYZE ware system Robb Hanson Karwoski Larson Workman and
soft
Stacy Robb and Hanson was used to build this reconstruction from
transverse CT images taken at mm intervals from the frozen cadaver This soft
ware was develop ed by Biomedical Imaging Resource at the Mayo Foundation
USA and provides a comprehensive image visualisation and analysis package
The original gray scale resolution of the CT images was reduced linearly from
bit to bit with the bone threshold set to at the new
scale The resulting le was pixels with physical dimensions of
mm Rendering of the data by ray casting provided an approxi
mation of the bony surface from which the D co ordinates of any point on the
skeleton could b e determined
For muscles where a detailed description of the anatomical p osition of the at
tachment points was not available the co ordinates were derived from those re
ported by Stokes and Gardner Morse b The attachment points rep orted
by Stokes and Gardner Morse b were originally obtained from the Vis
National Library of Man and Visible Woman Visible Human Pro ject
ible
Medicine Methesda MD but were scaled and rotated to t the geometry of
the average spine for their sample p opulation For use in the prop osed mo del
Muscular anatomy of the lumbar spine
the p oints were adjusted back to t the skeleton of the Visible Man This was
achieved by scaling and rotating the data by and resp ectively
Stokes p ersonal communication Table indicates the data sources
used to determine the co ordinates for each muscle while Tables and
provide the D co ordinates for each of the muscle fascicles
Table Data sources for each of the muscles crossing the lumbar spine
Muscle Data source Typ e of data
Multi dus Macintosh et al Anatomical
Bogduk Macintosh and Pearcy a Anatomical
y
Erector spinae Macintosh and Bogduk Anatomical
Bogduk et al a Anatomical
Psoas ma jor Bogduk Pearcy and Had eld b Anatomical
Latissimus dorsi Bogduk Johnson and Spalding Anatomical
Rectus ab dominis Stokes and Gardner Morse b Co ordinate
Quadratus lumb orum Stokes and Gardner Morse b Co ordinate
Internal obliques Stokes and Gardner Morse b Co ordinate
External obliques Stokes and Gardner Morse b Co ordinate
y
The erector spinae consists of the longissimus thoracis and the ilio costalis lumborum side erse mm t ertebra b elly righ Muscle length the hing rostral to for t reference v mm PCSA Man hmen ert S Ref v S S S S L L S S L S S Visible the ertebra for fascicles attac from SP spinous pro cess TP transv t hmen Co ordinates obtained attac as er ertebral b o dy w Lo spine VB v used as the reference v bar t on the sup erior endplate of the attac lum mamillary pro cess mamillary pro cess mamillary pro cess mamillary pro cess mamillary pro cess mamillary pro cess the S Anatomical L L sacrum sacrum sacrum S p osterior iliac spine L S p osterior iliac spine iliac crest terior p oin ert L Ref L v L L L L L L L L L L is left with L crossing k e uscles m t e to the most an for Co ordinates hmen terior and v is an attac j e co ordinates t Upp er hmen SP SP SP SP SP SP SP SP SP SP SP SP is rostral v attac i e shaft L Anatomical shaft L tip L tip L tip L tip L tip L tip L shaft L tip L tip L tip L v Muscle ert v Co ordinates are expressed in mm relativ Muscle b elly length is only indicated for fascicles with long tendons ascicle able m s Muscle F Multi dus m s m t m t m t m t m t m t m s m t m t m t T only Ref L pro cess mm b elly Muscle length mm PCSA ert S S S Ref v S L L S S L S S L S L S L L t hmen Co ordinates attac er w of sacrum of sacrum of sacrum Lo ued tin con SP SP SP SP SP SP SP SP SP Anatomical L sacrum paramedian paramedian L S sacrum L S sacrum L sacrum L dorsal surface of sacrum L paramedian L ert able Ref v L L L L L L L L L L L L L L L L L T t Co ordinates hmen attac thoracis Upp er pars SP SP SP SP SP SP SP SP rib rib thoracis th th Anatomical shaft L tip L tip L T T tip L T tip L T tip L T shaft L T tip L T us ascicle T T T T T T T Muscle F m s m t m t Longissim L m t L L m t L m t L m s L m t L mm b elly Muscle length mm PCSA ert Ref v S S S S S S S S S S S S S S S S S t hmen Co ordinates attac er w Lo ued tin con SP SP SP SP S Anatomical S sacrum sacrum ilium ilium ilium ilium ilium iliac crest iliac crest S S sacrum sacrum sacrum sacrum ert able L Ref v L L L L L L L L L L L L L L L L T t Co ordinates hmen attac b orum thoracis lum Upp er pars TP TP TP TP TP rib rib pars th th L L L L L rib rib rib b orum rib rib th th th thoracis th th Anatomical T T medial medial medial medial medial angle of angle of T T T lum us ascicle T T T T T Muscle F L L Longissim L L L L Ilio costalis IT IT L L L L mm b elly Muscle length mm PCSA ert Ref v S S S S S S S S S S S S S S S S S t hmen Co ordinates attac er w Lo ter ter ter ter ter ter ter ued han han han han han han han tin con Anatomical iliac crest iliac crest iliac crest iliac crest lesser tro c lesser tro c lesser tro c iliac crest lesser tro c iliac crest lesser tro c lesser tro c lesser tro c iliac crest iliac crest iliac crest iliac crest ert able Ref v L L L L L L L L L L L L L L L L L T t Co ordinates hmen borum TP TP TP attac lum of L of L of L to disc Upp er t rib rib rib pars ertebral disc ertebral disc ertebral disc TP TP TP TP rib rib rib th th th th th th L L L L terv terv terv in in in b orum VB adjacen L L L terior medial terior medial terior medial Anatomical angle of lateral lateral lateral L angle of L L L an angle of an an angle of angle of angle of lateral lum ma jor IVD IVD IVD VB L L L TP TP TP ascicle Muscle F IT i i i Psoas pL IT pL pL pL pL IT pL pL IT IT IT Ilio costalis i mm b elly Muscle length mm PCSA ert Ref v S S S S S t hmen Co ordinates attac er w Lo ter ter ter ter ued han han han han tin con rib Anatomical lesser tro c lesser tro c lesser tro c lesser tro c illium th ert able Ref v L L L L L T y t of the t Co ordinates hmen TP TP attac of L of L Upp er ttodisc ertebral disc terv in t the p osition of the fascicle at the heigh VB adjacen L terior medial terior medial umerus Anatomical an L L h an dorsi us IVD TP L VB TP ascicle co ordinates represen Muscle F pL pL pL pL Latissim Iliac y
Physiological cross sectional area
Table Muscle attachment co ordinates for muscles crossing the lumbar
spine as derived from the data rep orted by Stokes and Gardner Morse
for right side of body Co ordinates are expressed relativetothe most anterior
p ointon the sup erior endplate of the attachment reference vertebra Ref
vert ve i is rostral ve j is anterior and ve k is left with L used as
the reference vertebra for fascicles attaching rostral to L
Muscle Upp er attachment Lower attachment PCSA
Fascicle Co ordinates Ref Co ordinates Ref mm
vert vert
Rectus ab dominis
L S
Quadratus lumborum
QLT L S
QLL L S
QLL L S
QLL L S
QLL L S
External oblique
Ext L S
Ext L S
Ext L S
Ext L S
Ext L S
Ext L S
Internal oblique
Int L S
Int L S
Int L S
Int L S
Int L S
Physiological cross sectional area
A measure of muscle area which is related to muscle force is the physiological
muscle volume
and repre cross sectional area PCSA PCSA is calculated as
muscle length
sents an average cross sectional area of a muscle or fascicle
Anatomy and biomechanics of the lumbar spine
PCSA data is di cult to obtain with few studies rep orting such data Recently
there has b een a proliferation of studies rep orting muscle CSA obtained from var
ious typ es of medical imaging With the prevalence of CSA data it is b ecoming
increasingly common to see CSA used instead of PCSA to estimate maximum
muscle force Granata and Marras Han et al Marras Nussbaum
and Cha n a However CSA may not be equivalent to PCSA due to the
muscle morphology and the angle b etween the transverse plane of the muscle and
the plane used to image the muscle To investigate this issue further a study
was undertaken to ascertain if CSA values rep orted for the psoas ma jor muscle
could be adjusted to account for the scan angle using published data and to
assess the impact of doing this This study is rep orted fully in Gatton Pearcy
and Pettet a copy of which is contained in App endix A
The results from this study indicate that without adjustment rep orted CSA
values for the psoas ma jor muscle are larger than PCSA values This implies
that the use of CSA instead of PCSA data will result in an overestimate of the
force a muscle can pro duce When an attempt was made to adjust the published
CSA values to account for di erences in the transverse plane of the muscle and
scan plane it was discovered that the lack of information ab out scan angle
sub ject p osture etc in the imaging studies made the adjustment imp ossible in
many circumstances This severely limits the use of CSA values in mo dels of the
lumbar spine Interestingly comparison of published CSA values for the psoas
ma jor muscle from di erent studies reveal that the CSA di ers b etween male and
female sub jects with males having larger CSAs than females This highlights
the need to assess the appropriateness of muscle data relative to the intended
use of the mo del
Muscle force
Muscle force
Muscles are contractile materials The force which any particular muscle pro
duces at anygiven time is related to the physiologic prop erties of the muscle e g
size area architecture and its orientation It is well established that maximum
isometric muscle force is related to muscle PCSA Bogduk et al a Woittiez
et al Tsuang Novak Schipplein Hafezi Tra mow and Andersson
The generalised force area relationship can b e represented as F K PCSA
max
where K is the maximum muscle intensity force per unit area Estimates of
maximum muscle intensity have been made for several human muscles but to
date no value sp eci cally for the back or ab dominal muscles has been estab
lished However it is generally accepted that the value of K lies in the range
Ncm Bogduk et al b
There are several factors known to a ect the maximum force a muscle can pro
duce Two of these factors are the muscle length relative to its rest length and
the velo city of the contraction Since the mo del being develop ed is quasi static
in nature only the length tension relationship will b e discussed further
Length tension relationship
The maximum isometric force develop ed within a muscle dep ends up on the strain
of the m uscle The curve obtained by plotting muscle tension against strain is
known as the length tension curve and consists of two comp onents which rep
resent the anatomy and physiology of the muscle The rst comp onent is the
contractile muscle consisting of muscle bres arranged in a sp eci c architecture
This comp onentcontributes the active force in the muscle The second comp o
nent is the elastic tissue consisting of connective tissue and sarcolemma of the
muscle bres This contributes the passive force The total tension develop ed
Anatomy and biomechanics of the lumbar spine
within a muscle is the combined e ect of the active and passive forces
Active tension
A mathematical formulation for the active length tension curve was develop ed
by Kaufman An and Chao This formulation takes into account di ering
muscle architectures and successfully mo dels the asymmetry of the active length
tension relationship This mo del used the index of architecture i as de ned by
a
Woittiez et al to representmuscle architecture i is the mean bre length
a
at muscle optimum length divided bythemuscle optimum length Values for i
a
are by de nition less than or equal to one with values close to one representing
muscle bres acting along the direction of the muscle The mo del develop ed by
F
b
Kaufman et al calculates the normalised muscle tension F
a
F
max
using Equation The active length tension curve for muscles as describ ed by
Kaufman et al with i is illustrated in Figure
a
i
a
for i exp
a
i
a
b
F
a
exp ln for i
a
L L
where is the muscle strain
L
L is the instantaneous muscle b elly length
L is the length of the muscle b elly where F is achieved
max
optimum length and
i is the index of architecture
a
The optimal length of a muscle is the length at whichitcanachieve its maximum active
force
Muscle force
2.5
2 Passive Force Active Force 1.5 Total Force
1 Normalised muscle tension 0.5
0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Muscle strain
Figure Length tension curve for passive active and total tension when
i
a
The mo del describ ed in Equation captures manyofthemuscle characteristics
observed in vivo such as parallel muscle bres b eing able to maintain their force
for a greater distance than p ennate muscles Gareis Solomonow Baratta Best
and D Ambrosia tted this mo del to exp erimental data on nine cat muscles
with relatively go o d results b eing obtained for all but two muscles These two
muscles were found to b e grossly nonhomogeneous in architecture with resp ect
to optimal lengths and p ennation patterns
Some authors have used EMG data to develop a relationship between muscle
and Cha n use EMG data from ve male length and tension Raschke
sub jects to suggest that the length tension relationship for the erector spinae
muscle is linear However closer insp ection reveals that the exp eriment only
covered a range of muscle lengths from approximately to of the optimum
length This range corresp onds to a small section on the left increasing side of
Anatomy and biomechanics of the lumbar spine
the theoretical active length tension curve which may well be approximated by
a linear function
The active length tension curve provides an upp er limit to the force able to be
generated by amuscle at any particular length Physiologically it is p ossible for
a muscle to generate any active force under the sp eci ed maximum Hawkins
and Bey note that in the case of the rat tibialis anterior muscle the
length tension curve obtained exp erimentally follows the exp ected pattern even
though the total muscle force was b elow the exp ected maximum based on muscle
characteristics
Passive tension
The passive comp onent of the length tension curve is generally mo delled as an
exp onential function since it has a very slow increase with elongation b elow the
optimum length and a sharp increase with any elongation past the optimum
length Gareis et al Woittiez et al use Equation to mo del the
normalised passive force at muscle length n Figure illustrates this passive
length tension curve
F n F exp cos
fp
fp
where F n is the normalised passive force at muscle length n
fp
F is the passive force of b ers at the optimum length
fp
L L
is the muscle strain
L
L is the length of the muscle
L is the optimum muscle length and
is the angle of the muscle bres relativeto the direction of the muscle
Kinematics of the lumbar spine
Kinematics of the lumbar spine
Section established that muscle length impacts on the maximum force able to
b e develop ed within a muscle Since b oth ends of a muscle are typically attached
to b ones the only mechanism which can result in length changes in a muscle is
movement of these b ones Therefore the range of motion of the lumbar spine
and the way in whichthespine moves between these extremes can in uence the
force generating capacity of the muscles
Range of motion
Numerous studies have rep orted the maximum voluntary range of motion of the
lumbar spine in exion extension lateral bending and twisting White and
Panjabi summarise some of these studies by rep orting an estimate of a
representative range of motion per segment in each direction These values are
given in Table
Table Average values for the voluntary range of motion of each jointof
the lumbar spine for exion plus extension lateral b end and axial twist as
rep orted by White and Panjabi Values rep orted for lateral b end and
axial twist are from uprightto the full range of motion
Motion Range of motion degrees
L L L L L L L L L S Total
Flexion plus extension
Lateral b end
Axial twist
Anatomy and biomechanics of the lumbar spine
Movement within the range of motion
The wayinwhich the spine moves b etween the extremes of motion in uences the
moment generating capacity of the muscles since it changes the global position
of the muscle attachment points relative to the centre of rotation Surprisingly
few studies have investigated the sequential movements within the spine during
motion even though this information is required as input into any biomechanical
mo del which allows the p osture of the lumbar spine to vary
To address this lack of information a study was designed to investigate spinal
movement during exion extension lateral b end and axial twist The metho dol
ogy and results for exion are rep orted in Gatton and Pearcy App endix
B The results from this study indicate that the way in which the spine moves
between two p oints is highly variable Di erentmovement patterns were detected
between individuals and also within the same individual rep eating a given task
with no one movement sequence dominating Given these results it seems accept
able to assume that the motion of the lumbar spine is prop ortionally allo cated to
individual joints One way to determine the appropriate prop ortions is to divide
the maximum voluntary range of motion p er joint Table by the total max
imum range of motion Using this approach pro duces the prop ortions detailed
in Table
Table Prop ortion of total motion allo cated to each intervertebral joint
in the lumbar spine
Motion Prop ortion of total lumbar motion
L L L L L L L L L S
Flexion and extension
Lateral b end
Axial twist
Instantaneous centres of rotation
Instantaneous centres of rotation
In order to estimate the moments generated bythemusculature the p ointabout
which motion o ccurs must be known Various fulcrums have been used in past
mo dels with the most p opular b eing the disc centroid However the disc centroid
pro duces pure rotation of the upp er vertebra ignoring the asso ciated translation
which is seen during exion and extension in the sagittal plane Alternatively
the instantaneous axis of rotation IAR is a measure which accounts for both
rotation and translation
Pearcy and Bogduk rep orted the mean p ositions along with standard
deviations of the IARs for L L to L S standardised for vertebral b o dy size
These p ositions were obtained from lateral radiographs resulting in the values
only b eing rep orted in two dimensions To apply this data to a D mo del it is
necessary to make some assumption ab out the lo cation of the IAR in the missing
dimension If it is assumed that the IARs corresp ond to the instantaneous centres
of rotation ICRs then the ICRs can b e assumed to b e lo cated in the mid sagittal
plane To allow movement of the thorax relative to L it has been assumed in
later chapters that the lo cation of the ICR for the T L joint is in the same
relative p osition as the ICR for L L
To apply the values rep orted by Pearcy and Bogduk to the spinal geom
etry of the Visible Man the metho dology describ ed in App endix D was used
Table lists the p ositions of the ICRs within the vertebra obtained using this
metho dology and also rep orts the p ositions of each ICR relative to the caudal
ICR
The information presented in this chapter provides a review of the anatomyand
biomechanics of the lumbar spine relevant to the development of an anatomical
mo del Some issues whichwere not discussed in this chapter e g muscle lines of
action are discussed in detail in Chapter in conjunction with the metho dology
Anatomy and biomechanics of the lumbar spine
Table Positions of the ICRs within the spine of the Visible Man and the
vectors relating the p ositions of adjacentICRs The p ositions of the ICRs are
given relativetothe most anterior p oint on the sup erior endplate of the
caudal vertebra of the joint for which the ICR applies Position vectors
represent the relative p osition of the ICR to the adjacent caudal ICR All
values areinmmwhere ve i is rostral ve j is anterior and ve k is left
Position of ICR Position vector of
adjacent ICRs
i j k i j k
T L
L L
L L
L L
L L
L S
develop ed to predict the forces and moments generated by the muscles of the
lumbar spine
Chapter
D mo del of the lumbar spine
A quasi static D mo del of the lumbar spine was created to investigate the max
imum forces and moments that may be generated by the muscles crossing the
lumbar region of the spine The aim was to develop an anatomical mo del which
includes as many muscles and as much anatomical detail as p ossible Emphasis
has b een placed on improving the calculation of the muscle lines of action and
developing a metho d of determining the contribution of the TLF to moments
develop ed around each intervertebral joint in the lumbar spine The metho dol
ogy which has b een develop ed is detailed in this chapter although the MatLab
co de used to implement the mo del has not b een included in the thesis due to
its p otential commerical value This co de may be available from the university
up on request a con dentiality agreement mayapply
Since the mo del is only an anatomical mo del it do es not contain a force distri
bution algorithm Toovercome this problem and allow force and moment predic
tions to be made published muscle activation data were utilised Although the
moment and force equilibrium conditions have not been explicitly considered it
is assumed that the muscle activation patterns rep orted from exp erimen tal tri
als approximate the muscle activation patterns required to maintain equilibrium
simultaneously across all intervertebral joints
D mo del of the lumbar spine
Mo del Assumptions
As with all biomechanical mo dels a number of assumptions have b een made to
decrease the level of complexity within the system The assumptions made in
the mo del are outlined b elow
The nine muscles included in the mo del that is the multi dus erector
spinae quadratus lumb orum psoas ma jor latissimus dorsi rectus ab do
minis internal oblique external oblique and transverse ab dominis are re
sp onsible for all of the moments pro duced across the lumbar spine Smaller
muscles suchastheintertransversii laterales and mediales and the lumbar
interspinales are not included in the mo del However their contribution to
moment pro duction would be exp ected to be negligible due to their small
size and close proximityto the ICR
Tendons are inelastic and show no signi cant length change The role of the
tendon is assumed to be one of force transmission and muscle attachment
only Due to the relative sti ness of tendons compared to muscles any
length change within a muscle tendon complex is assumed to b e the result
of changes in the length of the muscle b elly
The maximum force pro duced byamuscle can b e estimated using a length
tension relationship which combines active and passive forces and requires
information on the maximum muscle intensity PCSA muscle bre orien
tation and muscle strain only as describ ed in Section
The orientation of muscle bres within a fascicle are parallel to the direction
of the fascicle such that the index of architecture i is
a
Muscles achieve their maximum active force in the upright p osture This
corresp onds to muscles exp eriencing zero strain in upright stance Figure
Mo del Assumptions
of the maximum active force is able to be voluntarily neurally acti
vated by an individual with all muscles able to be activated at the same
time to giveasimultaneous contraction
Muscle activation patterns do not change with p osture This assumption
is made due to a lack of detailed muscle activation data for p ostures other
than upright standing
The intervertebral disc is incompressible
The thorax is rigid during movement of the lumbar spine This assumption
is made to limit the amount of kinematic information required in the mo del
The p osition of the ICR is xed during movement Some authors Bogduk
and Twomey Gertzb ein Seligman and Holtby Ogston King
and Gertzb ein suggest that the p osition of the ICR moves during
spinal rotation thus creating a lo cus or centro de of motion Although
displayed diagrammatically no data on the exact p osition of the ICR at
various spinal p ositions has been do cumented The work by Pearcy and
Bogduk rep orts the p osition of the IAR for upright to exion and
upright to extension The means and standard deviations for the IAR po
sitions for each movement indicate that the p ositions are not signi cantly
di erentbetween upright to exion and upright to extension P In
developing a lo cus of motion small increments of spinal movement are re
quired Ogston et al The exp erimental errors asso ciated with these
small movements is likely to be larger than that rep orted by Pearcy and
Bogduk This combined with the variability between individuals
allows the assumption that the p osition of the IAR do es not change sig
ni cantly during the normal range of spinal motion For this reason the
D mo del of the lumbar spine
p osition of the IAR has b een xed for all motion at the p osition describ ed
by Pearcy and Bogduk for extension to exion As a consequence
the p osition of the ICR is also xed for all motion
Co ordinate system
A lo cal co ordinate system was develop ed for each vertebra from L to S Each
is an orthogonal basis set de ned relativetothe lo cal vertebra such that the jk
plane is parallel to the sup erior endplate of the vertebra i is p erp endicular to
the jk plane ve is rostral ve is caudal j lies in the midsagittal plane of the
vertebra ve is anterior ve p osterior and k is p erp endicular to i and j ve
is left ve right Figure The unit vectors i j k act in the direction of
the i j and k axes resp ectively App endix D describ es how the lo cal orthogonal
basis sets were determined for eachvertebral level using the data from the Visible
Man A global co ordinate system was also established using the same basis set as
describ ed but with the jk plane parallel to the global transverse plane parallel
to the o or
Mo del input
A variety of data is required as input into the mo del Much of this data has
h are been describ ed in Chapter however the few remaining comp onents whic
required to implement the mo del are discussed b elow Table details the data
required as input into the mo del and gives the appropriate lo cation within the
thesis where the details of this data are discussed further
Mo del input
Figure Co ordinate system used in the mo del
Table Data required as input into the mo del
Data Source
D co ordinates of fascicle attachment points Table
Vertebrae to which fascicles attach Table
PCSA for each fascicle Table
Fascicle muscle b elly length Table
Position of the ICRs relativetothe caudal Table
vertebra of the joint
Lo cation of each ICR relativetothe adjacent caudal ICR Table
Co ordinates de ning the p osition of the lower ribs and App endix C
p osterior asp ect of the lumbar vertebral bodies
Intersegmental angles de ning upright stance Table
Allo cation of rotation to individual intersegmental joints Table
Muscle activation patterns Table
Upright stance
Data on spinal geometry in the upright stance is required since this is the most
common p osture used in exp erimental studies and is the starting point for all
rotations in the mo del Ideally the spinal p osture used in the mo del should
match that of sub jects in the isometric strength trials which the mo del was to
D mo del of the lumbar spine
be validated against However no information describing the spinal p osture of
the sub jects in these studies was lo cated Hence alternative studies detailing
the intervertebral angles in an upright stance were sort
Five studies rep orting these angles in the midsagittal plane were found with a
combined sample size of p eople Jackson and McManus Gelb Lenke
Bridwell Blanke and McEnery Chen and Lee Vedantam Lenke
Keeney and Bridwell Korovessis Stamatakis and Baikousis The
studies included b oth male and female sub jects from a variet y of age and ethnic
groups Table details the results from each of the studies Aweighted mean
which is included in Table was calculated for eachintersegmental angle using
X
n
j ji
j
i
X
n
j
j
where is the mean intersegmental angle for level i degrees
i
n is the sample size of study j and
j
is the mean intersegmental angle rep orted by study j for level i degrees
ji
From these studies the S vertebra was de ned as b eing inclined to the
global transverse plane ve value represents exion resulting in the sup erior
endplate of L b eing approximately parallel to the global transverse plane
Muscle Activation
to the Information relating to muscle activation levels is required as input in
mo del to overcome the problem of not having a force distribution algorithm
Two studies rep ort muscle activation levels during maximal isometric exertions
Mo del input
Table Details of studies providing information on spinal alignmentin
upright stance and the weighted mean of these studies ve values indicate
extension in the mid sagittal plane
Author s Sample Intersegmental angles degrees
size L L L L L L L L L S
Jackson and McManus
Gelb et al
Chen and Lee
Vedantam et al
Korovessis et al
Weighted mean
Unfortunately these studies did not overlap in the information they provided
since the rst a study by Zetterb erg et al rep orts muscle activations for
exion extension and lateral bend tasks while the second a study by McGill
rep orts activation levels for axial twist only Both studies rep ort mus
cle activation as a p ercentage of the maximum voluntary contraction MVC
recorded for each muscle However it should be noted that the study under
taken by Zetterb erg et al to ok the MVC to b e the maximum EMG signal
recorded during the tasks p erformed and did not p erform other tasks for the
purp ose of eliciting a maximum contraction This di ers from the metho dology
rep orted by McGill who conducted a variety of tests in an e ort to nd
the activity which pro duced a maximal contraction for each muscle Table
provides the results from these studies including the muscles measured and the
MVC recorded for each task McGill rep orts two sets of data which
di er in the values used to representtheMVC The data set describ ed as Norm
A represents the muscle activation relative to the maximum activation achieved
C for each muscle Data describ ed as Norm during several tests to achieve MV
B are the MVC values achieved when the EMG data were normalised to the
maximum signal recorded during twisting exertions only It is imp ortant to note
D mo del of the lumbar spine
Table Results from studies rep orting muscle activation levels during
maximum isometric exertions in upright stance Only muscles measured
during the study are included The average of values for the rightand left
muscles are presented for the symmetric tasks of exion and extension while
values for lateral b end and axial rotation are the average for rightand left
exertions
MVC for maximum isometric exertion
Flexion Extension Lateral b end Axial rotation
Contra Ipsi Contra Ipsi
lateral lateral lateral lateral
Zetterb erg et al
Longissimus
Multi dus
Rectus ab dominis
Internal oblique
External oblique
McGill Norm A
Upp er erector spinae
Lower erector spinae
Rectus ab dominis
Internal oblique
External oblique
Latissimus dorsi
McGill Norm B
Upp er erector spinae
Lower erector spinae
Rectus ab dominis
Internal oblique
External oblique
Latissimus dorsi
that the activites from which these data were obtained involved resisted motion
meaning that the tasks may not mimic those normally asso ciated with the ex
ertion For example resisted exion exertions do not pro duce the same muscle
activation patterns as unloaded exion which o ccurs as part of many everyday
activities
Mo del structure
Mo del structure
The mo del consists of a number of discrete steps which are applied to the input
data in order to derive the maximum forces and moments that maybedevelop ed
by the musculature in the required p osture These general steps are outlined in
Figure and discussed in detail in the remainder of this chapter
Change of basis calculations
The co ordinate data obtained from the reconstruction of the Visible Man Table
uses a global co ordinate system which varies from that used in the mo del
Likewise the data rep orted by Stokes and Gardner Morse b also uses a
di erent co ordinate system Thus the rst step in the mo del is to convert the
co ordinates obtained from various sources into co ordinates relative to the lo cal
basis of the vertebra to which the muscle attaches This is done using Equation
The lo cal basis B foreach vertebra are detailed in App endix D
c
B u c B
u c
where c is the co ordinate vector in the lo cal basis B
c
u is the co ordinate vector of the external data source and
B is the basis set of the external data source
u
For computational simplicity during rotation the mo del expresses muscle attach
ment co ordinates relativeto the basis set of the attachment vertebra However
to calculate the lines of action and moments the rostral attachment pointmust
in the same basis set as the caudal attachment point Again for be expressed
computational simplicity this common basis was chosen to be the basis of the
D mo del of the lumbar spine
Input data
Convert muscle attachment coordinates from coordinate system of data source to model's local coordinate system
Align the spine in the required posture (either upright or upright plus rotation)
For each muscle (or fascicle) convert the upper attachment point into coordinates relative to the basis of the lower attachment point
Calculate the line of action of each fascicle
Repeat for each Calculate the maximum force produced by required posture each fascicle
Calculate the maximum moments generated by each fascicle about each ICR the fascicle crosses
Calculate the total moment about each joint by summing the moments produced by each
fascicle
Figure General steps involved in calculating the maximum moments
that maybe develop ed by muscles of the lumbar spine
Mo del structure
caudal attachment To change the co ordinates from basis a to basis b where b
is the basis immediately caudal to a Equation is used
B c r c B
a a b b
where c is the vector of co ordinates expressed relativetolocalbasis B
b b
c is the vector of co ordinates expressed relative to lo cal basis B and
a a
r is the vector describing the lo cation of the origin of basis B relative
a
to the origin of basis B
b
If basis b is not immediately caudal to basis a Equation is applied iteratively
for each pair of basis sets bet ween a and b inclusive
Aligning the spine in the required p osition
The mo del allows the simulated spine to be aligned in any p osture within the
b ounds of the normal range of motion of each joint The spine of the Visible
Man as used in the development of the lo cal basis sets do es not represent a
normal spine in upright stance due to the measurements b eing taken p ost
mortem in the supine p osition Thus the mo delled spine needs to be adjusted
normal spine in upright stance The angles calculated in to better represent a
Table were used to represent the upright stance From this initial p osition
further rotations to sp eci ed p ostures can b e made
All rotations of the spine are achieved by using the rotation metho dology de
velop ed by Cheng and rep orted in Cheng Nicol and Paul This
metho d assumes that rotation is a two step pro cess one is the rotation of the
limb in a plane ab out the proximal joint and the other is a rotation ab out
the long axis of the limb Here the limb is taken to be the vertebral body
D mo del of the lumbar spine
with the i axis representing the long axis The rotation matrix corresp onding to
this technique is given by Equation where is the angle between j and the
pro jection of the long axis of the vertebra in the rotated state on the jk plane
this angle de nes the orientation of is the elevation angle measured from
the initial p osition of i to the long axis of the vertebra in the rotated p osition
and is the twist angle ab out the long axis of the vertebra Figure
R
cos sin cos cos sin sin sin cos sin sin cos
cos cos cos cos sin cos
sin cos
sin cos cos sin sin sin sin cos cos sin
cos sin cos cos cos cos
sin sin
cos sin sin cos cos cos cos sin sin cos
This technique was used since the nal p osition of the vertebra is indep endentof
the order of rotation unlike most other forms of D rotation Additionally the
angles used in the rotation matrix closely resemble the descriptions of p osture
commonly used by clinicians For instance if the rotated position
represents exion of while a left lateral bend of is represented when
and Pure axial twist o ccurs when and
To align the basis set for each of the lumbar vertebrae in the initial p osition of
upright standing Equation was used
Mo del structure
Figure Angles de ning the rotation of the vertebra where the darker
vector represents the long axis of the vertebra in the rotated p osition
Y
B R
i i i
j
i j
where B is the basis set at vertebral level j in upright standing where
j
j represents L and j represents S and
are the intersegmental angles de ning the rotation
i i i
of vertebra i relativeto vertebra i for i or the
in tersegmental angles b etween S and the global co ordinate
system i in upright standing
It is assumed that the intersegmental angles determined in Section represent
exion or extension in the midsagittal plane thus forall i and
i i i
are the angles rep orted in Table for the resp ective levels From this initial
D mo del of the lumbar spine
p osition the spine can then be aligned in any new p osture using Equation
Y
R
R R B
i i i i i i
j
i j
R
where B is the basis set at vertebral level j in the rotated p osture
j
are the intersegmental angles de ning the rotation
i i i
of vertebra i relativeto vertebra i for i or the
intersegmental angles b etween S and the global co ordinate
system i inuprigh t standing
are the intersegmental angles de ning the rotation
i i i
from upright to the new posture of vertebra i relative
to vertebra i for i or the intersegmental angles
between S and the global co ordinate system i
Muscle lines of action
For all fascicles except those discussed separately in Section the line of
action is assumed to b e linear b etween the caudal and rostral attachment p oints
Once b oth points are expressed relative to the same basis that is the basis of
the caudal attachment the direction vector of the line of action is calculated
using
l u
i i
loa
i
j l u j
i i
where loa is the unit vector representing the line of action of fascicle i
i
l is the p osition vector of the caudal attachment pointof fascicle i and
i
u is the p osition vector of the rostral attachment point of fascicle i
i
Mo del structure
Output moment calculations
Moments are calculated ab out each ICR lo cated between fascicle attachment
p oints This requires the p osition of the ICR to b e expressed relative to the basis
set of the caudal fascicle attachment The vector from the ICR to the caudal
attachment p oint pos is then calculated by subtracting the p osition vector
ij
of the ICR from the p osition vector of the caudal attachment The maximum
force able to b e develop ed by the fascicle is then determined Equation and
the maximum moments that may b e generated by fascicle i calculated Equation
F exp ln PCSA K
i i i
where F is the maximum force able to b e develop ed by fascicle i N
i
is the strain in fascicle i
i
PCSA is the PCSA of fascicle i cm and
i
K is the maximum muscle intensity Ncm
moment F pos loa
ij i ij i
where moment is the maximum moment generated by fascicle i
ij
ab out ICR j Nm
pos is the vector from ICR j to the caudal attachment of fascicle
ij
i m and
loa is the unit v ector representing the line of action of fascicle i Eq
i
D mo del of the lumbar spine
The moments calculated using Equation are expressed relative to the basis
set of the caudal fascicle attachment This is of little use when calculating the
overall moment ab out a particular ICR Hence the basis set of the moments is
changed such that the moments ab out ICR j are expressed relative to basis set
j This then allows the total moment ab out each ICR to be calculated as the
sum of the moments for each fascicle ab out the ICR of interest Equation
n
X
moment moment
j ij
i
where moment is the total moment generated ab out ICR j
j
n is the number of fascicles crossing ICR j
Metho ds for calculating lines of action for
muscles with curvature between origin and
insertion
Longissimus thoracis pars thoracis
The fascicles b elonging to the longissimus thoracis pars thoracis which attach
rostrally to the thoracic spine follow the contour of the spine If a straightlineis
used to represent the line of action of these fascicles particularly those attaching
to the upp er thoracic spine the line of action in upright standing will act anterior
to the ribs and lower thoracic spine This is an anatomical imp ossibility Instead
a curved line of action should be used
Since this mo del is only concerned with the lumbar spine from T downwards
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
the line of action from the lumbar or sacral attachmenttoT is of primary im
p ortance A curved line of action can be approximated by several linear pieces
or splines The larger the number of linear segments the b etter the represen
tation of the curve For the purp oses of the mo del a two spline representation
need only to b e used since it is assumed that the thoracic spine is rigid implying
the length of the muscle is constant from T to the thoracic attachment
Consider a two piece representation of a fascicle of the longissimus thoracis pars
thoracis with one segment going from the thoracic attachment to T and the
second segment going from T to the lumbar sacral attachment For the pur
p oses of the mo del the thoracic attachment and T are assumed to be xed
p oints relative to each other Assuming that each fascicle of the longissimus
thoracis pars thoracis must pass directly p osterior to T an arti cial origin can
be established at the T level In order to do this the original alignment of
the fascicle in the ik orientation needs to b e maintained but the j value changed
to force the fascicle to pass directly p osterior to T In addition to this the
length of the fascicle needs to b e estimated as the length from the lumbar sacral
insertion to T plus the constant length from T to the thoracic insertion
In upright standing the two piece spline forces the fascicles of the longissimus
thoracis pars thoracis to pass close to the p osterior of the spine at T However
when the spine is exed it is p ossible that the vector representing the line of
action between the lumbar sacral insertion and the arti cial T origin could
pass in front of the intervening lumbar vertebrae This problem can b e resolved
by considering the p osition of the fascicle in the j direction relative to the bony
structure of eachvertebra between the lumbar sacral insertion and the arti cial
T origin and making adjustments to the line of action whenever it is found to
act anterior to the bony structure The steps in Figure illustrate how this
pro cedure is implemented
D mo del of the lumbar spine
counter =1
Is No End counter <=5? procedure
Yes
Is j coord of fascicle at lumbar level (6-counter ) increment Yes <= j coord of the base of counter by 1 transverse process at lumbar level (6-counter )?
No
Change line of action to be (lumbar insertion - coords of fascicle at lumbar level (6-counter ) with j coord being replaced by j coord of base of transverse process)
Fascicle length = length from lumbar/sacral insertion to lumbar level (6-counter ) + length from lumbar level (6-counter ) to level of T12 + length
from level of T12 to thoracic insertion
Figure Flow diagram illustrating the steps required to ensure fascicles
of the longissimus thoracis pars thoracis remain p osterior to the vertebrae
Fascicles attaching to the ribs
Fascicles b elonging to the ilio costalis lumb orum pars thoracis and some fascicles
of the longissimus thoracis pars thoracis attach to the surface of the ribs In a
similar way to the thoracic bres of the longissimus thoracis these fascicles may
not have a straight line of action due to the physical constraint imp osed by the
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
rib cage Therefore the mo del needs to identify those fascicles which if a straight
line of action is used will pass in frontofthe ribs
In order to do this the D system needs to be viewed as two D images one
in the ik plane equivalent to the p osterior view and the other in the jk plane
equivalent to a transverse slice In each of the planes a regression mo del de
scribing the shap e of each rib needs to b e develop ed Two di erentmodelswere
trialed using data p oints to represent eachrib The rst was a regression mo del
using a third order p olynomial The point of intersection between the fascicle
and rib x z in the ik plane can be estimated by solving Equation for
p p
x then substituting this x value into Equation to determine z
p p p
z x z
x c z s s x s x
p
p p
x x
x x
p
z z z
p
x
where s s s and c are the regression co e cients for x to x resp ectively
x z are the co ordinates of the fascicle at its upp er attachment and
x z are the co ordinates of the fascicle at its lower attachment
This regression technique was found to over t the data generating predictions
between data p oints which were unacceptably di erent to that exp ected
The second technique used was linear interp olation between data p oints The
steps involved in this pro cess are outlined in Figure Equations and
are used to estimate the p ointof intersection b etween the muscle fascicle and rib
in the ik plane
D mo del of the lumbar spine
Starting at the 12th rib
Is the x coordinate of the upper fascicle attachment No larger than the x End coordinate of at least one data point on the rib?
Yes
Calculate point of intersection in the jk plane between fascicle and rib using the extreme right and left data points of the rib as ribA and ribB in Equation 4.13
Determine the rib data points which are adjacent to the calculated z value at the point of intersection
Calculate the point of intersection in the jk plane between fascicle and rib using the adjacent data points of the rib as ribA and ribB in Equation 4.13
Does the calculated x value (Equation 4.14) No lie within the x values of the ribA and ribB data points?
Yes Calculate the y value of the line approximating the rib between ribA and ribB at the z value corresponding to the point of interesection
Calculate the y value of the fascicle at the z value corresponding to the point of interesection
Consider the adjacent Yes Is the y from rib rostral rib calculation > y from muscle calculation?
No Change the fascicle line of action to be (lower insertion point - [x,y(rib),z]) where x and z are the coordinates for the point of intersection in the jk plane
End
Figure Flow diagram illustrating the steps required to ensure fascicles
which attach to the ribs remain p osterior to the ribs during spinal rotation
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
r ibA ribB musA musB
x x x x
ribB ribB musB musB
x z x z
ribA ribB musA musB
z z z z
z
p
ribA r ibB musA musB
x x x x
musA musB ribA r ibB
z z z z
ribA ribB
x x
z ribB ribB x
p z x p
ribA ribB
z z
where x z are the co ordinates representing the pointof intersection between
p p
the muscle fascicle and rib in the ik plane
r ibA ribA r ibA are the co ordinates of pointA on the rib
x y z
r ibB ribB ribB are the co ordinates of p oint B on the rib
x y z
musA musA musA are the co ordinates of the rostral attachment
x y z
pointofthe muscle fascicle and
musB musB musB are the co ordinates of the caudal attachment
x y z
pointofthe muscle fascicle
The corresp onding y values can then be determined for the rib and the muscle
using Equations and
r ibA ribB
y y
z ribB r ibB y
p z y rib
ribA ribB
z z
musA musB
y y
z musB musB y
p z y mus
musA musB
z z
where y is the j co ordinate corresp onding to z on the surface of the rib and
rib p
y is the j co ordinate corresp onding to z on the fascicle
mus p
D mo del of the lumbar spine
Once the y values corresp onding to the p ointofintersection in the ik plane have
b een calculated it is p ossible to determine if the muscle runs anterior or p osterior
to the rib of interest if y y then the muscle runs p osterior to the rib and
mus rib
the line of action of the muscle is left unchanged if y y then the line of
mus rib
action of the muscle acts anterior to the rib and must be changed to constrain
the muscle b ehind the rib cage This is achieved by making the line of action of
the fascicle act b etween the caudal insertion p ointand the point x y z
p rib p
The ab ove pro cess is rep eated for eac h rib included in the mo del starting at
th
the rib until the line of action of the muscle is changed in which case the
pro cess is terminated For the purp oses of this mo del ribs to are included
since rib was deemed to protrude the most p osteriorly It should b e noted that
the data used to obtain information on the rib co ordinates originated from the
Visible Man where images were taken p ost mortem in the supine p osture This
posture may not be a true representation of the rib p osition in other p ostures
since the pressure placed on the ribs in the supine p osture may act to push the
rib cage anteriorly
Psoas ma jor muscle insertion on the femur
The psoas ma jor muscle attaches rostrally to the lumbar vertebrae and discs
with fascicles progressively joining the long central tendon which inserts into the
lesser tro chanter of the femur To achieve this distal insertion the muscle or
its tendon passes over the anterior surface of the ilium and hip capsule b efore
inserting on the medial surface of the femur at the lesser tro chanter In the
standing p osture the front of the hip capsule is p ositioned anterior to the head
of the femur causing the muscle to angle anteriorly from the spinal attachments
to the anterior of the hip capsule and then angle p osteriorly from the hip capsule
to the lesser tro chanter Hence the anterior of the hip capsule acts as a pivot
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
p oint by changing the line of action of the muscle Thus the force generated
by the psoas ma jor muscle acts along the vector from the spinal attachment
to the anterior of the hip capsule Using the anterior of the hip capsule as a
determinant of the line of action instead of the lesser tro chanter causes the psoas
ma jor muscle to b ecome a greater exor of the spine
To mo del this feature it is assumed that the line of action of the psoas ma jor
muscle is from the spinal attachment to anterior of the hip capsule The length
of the muscle can be determined by straightening out the muscle along this
line of action This is made easier to implement by assuming that the distance
from the anterior of the hip capsule to the lesser tro chanter is constant If the
distance from the anterior rim of the p elvis to the lesser tro chanter is h and a
is the vector from the spinal attachmenttotheanterior of the hip capsule then
the straightened vector a is given by Equation For the Visible Man h
is mm
a j a j h a
Ab dominal obliques
The internal and external oblique muscles attach to the pelvis and the rib cage
and wrap around the torso between these attachment points Most researchers
acknowledge that a straight line b etween origin and insertion is not appropriate
to mo del the line of action for this set of muscles Various authors have used
numerous techniques such as presp eci ed orientations Schultz and Andersson
Granata and Marras Marras and Granata and arcs McGill
Cholewicki et al However there is little published work which
details the development of a mo del sp eci cally for determining the line of action
of the oblique muscles This section addresses this de ciency by introducing a
D mo del of the lumbar spine
new metho d for determining the line of action of the oblique muscles accounting
for the shap e of the torso
Torso mo del
To mo del the line of action of the oblique muscles the shap e de ning the surface
on which each of the oblique muscles lie must be determined This shap e is
hereafter referred to as the torso Assume that in the transverse plane the
torso can be represented as a right elliptical cylinder de ned by the parameters
a and b such that the ma jor axis a is parallel to k and the minor axis b parallel
to j To make the cylinder created by stacking these ellipses more anatomically
realistic the parameters a and b are allowed to vary linearly with height from
the base of the torso The p osition of the centre of the ellipse is also allowed to
move linearly in the direction represented by j The parameter values de ning
the shap e and p osition of the ellipses are b ound by the values at the caudal and
rostral ends of the torso and are de ned by
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
a a
ribs pel v is
x x a x a
pel v is pel v is
x x
ribs pel v is
b b
ribs pel v is
x x b x b
pel v is pel v is
x x
ribs pel v is
c c
ribs pel v is
x x c x c
pel v is pel v is
x x
ribs pel v is
where x is the height from an arbitrary origin
a x is half the width of the torso at height x
b x is half the depth of the torso at height x
c x is the distance from the origin along j of the pro jection of the
centre of the ellipse at height x onto the jk plane
x is the heightofthe p elvis from the origin i e base of torso
pel v is
x is the height of the rib cage from the origin i e top of torso
r ibs
a is half the width of the torso at the pelvis
pel v is
a is half the width of the torso at the rib cage
ribs
b is half the depth of the torso at the pelvis
pel v is
b is half the depth of the torso at the rib cage
r ibs
c is the distance from the origin along j of the pro jection of the
pel v is
centre of the ellipse at height x onto the jk plane and
pel v is
c is the distance from the origin along j of the pro jection of the
r ibs
centre of the ellipse at height x onto the jk plane
ribs
The shap e of the torso in the jk plane at any height x where z is the distance
from the origin along k and y is the distance from the origin along j is represented
by Equation Figure isaschematic diagram of the mo del parameters
D mo del of the lumbar spine
a(x) b(x) r(x)
x
i
k j
c(x)
Figure Schematic representation of the parameters used in the torso
mo del
y c x z
a x b x
The parametric equation describing the position vector of a point on the torso
r x is given by
r x xi fc x m sin g j m cos k
where is the angle in radians b etween the pointon the torso and k
measured in a clo ckwise direction from the p ositive k axis
and
low up
m is the distance from the centre of the ellipse to the point r x such
a x b x
p
that m
b x cos a x sin
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
Since it is assumed that the oblique muscles attach to the torso Equation
can be used to describ e the lo cation of the muscle attachment p oints If
x y z are the co ordinates of the lower attachment of the muscle and
low low low
x y z are the co ordinates of the upp er attachment of the muscle can
up up up
be calculated using
up low
x x
low low
x x
up low
z
low
p
if y c x cos
low low
y c x z
low low
low
where
low
z
low
p
if y c x cos
low low
y c x z
low low
low
z
up
A
q
if y c x cos
up up
y c x z
up up
up
up
z
up
A
q
if y c x cos
up up
y c x z
up up
up
The length of the vector representing the muscle between the upp er and lower
attachment points can be calculated by numerical intergration or approximated
x
up
X
length jr i r i j
i x
low
The line of action of the bre describ ed by the p osition vector r x will have its
direction determined by the derivativeofr x This derivative can b e calculated
explicitly or approximated at its lower attachment pointby
r x r x
low low
r x
low
where is a small numb er taken to b e in this study
D mo del of the lumbar spine
Bending the torso
The shap e of the torso changes in resp onse to changes in p osture resulting in
the lines of action of the oblique muscles also changing If it is assumed that the
torso maintains its elliptical shap e in the transverse plane then the following
metho dology can b e used to calculate the lines of action in any de ned p osture
Assume that the rostral end of the torso is rotated to a prede ned p osition from
its initial p osition in the upright stance Let this position be de ned by the
angles and as de ned in Section Assuming the base of the torso
is xed and that rotation is distributed evenly along the torso the angles of
rotation at any height x on the torso are
x
x x
ribs pel v is
x
x x
ribs pel v is
Alternatively if the lower section of the torso is required to rotate to a new
p osition while the upp er section remains straight as is the case of the lumbar
spine rotating without any corresp onding rotation of the thoracic spine the
angles of rotation can be determined using
x if x x
mid
x x
mid pel v is
if x x
mid
x if x x
mid
x x
mid pel v is
if x x
mid
where x is the height where the two comp onents meet
mid
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
The p osition vector for any p oint on the torso in the rotated p osition r x can
R
be calculated using
r x R r x
R
where R isthe D rotation matrix de ned by Equation
The new line of action of the bre can then be calculated by substituting r x
R
for r x in Equation
This metho dology is based on the assumption that the torso maintains its el
liptical shap e in the transverse plane This assumption is violated if adjacent
ellipses intersect at any p oint during rotation During exion the rst p oints on
adjacent ellipses to intersect are the most anterior points on the ellipse lo cated
at x b x c x Likewise during lateral b ending the most lateral point
x a x is the rst to intersect with the adjacent ellipse Simple trigonom
etry can be used to calculate the maximum rotation allowable before adjacent
elipses intersect Table The allowable rotation is inversely prop ortional to
the distance of the most extreme point from the origin along the appropriate
axis j axis for exion and k axis for lateral b ending such that as the distance
increases the allowable rotation per unit decreases see Table The total
allowable rotation is dep endent on the value of x Data from the Visible Man
mid
indicates that L and hence x is lo cated approximately mm ab ove the
mid
centre of the S vertebral b o dy Using the maximum allowable rotation p er unit
for exion and lateral b end the total rotation p ossible b efore violation of the
assumption is approximately and in exion for the external and internal
obliques resp ectively and and for the external and internal obliques re
sp ectively in lateral b ending These values are larger than the average range of
voluntary motion Table meaning that the assumption requiring the torso
to maintain an elliptical shap e in the transverse plane is acceptable for spinal
D mo del of the lumbar spine
Table Maximum rotation ab out the centre of the S vertebral b o dy
allowable b efore adjacent transverse slices of the mo delled torso intersect
Transverse slice are lo cated at mm intervals
Motion Muscle p osition Max rotation Distance of
on torso per mm furtherest point
y
interval degrees from origin mm
Flexion Internal oblique ribs
External oblique p elvis
External oblique ribs
Internal oblique pelvis
Lateral b end External oblique ribs
External oblique p elvis
Internal oblique ribs
Internal oblique pelvis
y
Distance is along j for exion and k for lateral b ending
motion within the range of normal values
Application of metho dology
Stokes and Gardner Morse b have rep orted upp er and lower attachment
points for the internal and external oblique muscles These attachment points
de ne six vectors representing eachmuscle with a sub jective empirical metho d
Stokes and Gardner Morse b based on transverse section photographic
images of the muscles b eing used to derive the attachment p oints These points
were used in this study
In order to calculate the line of action of these vectors the torso which best
ts the data points was determined using the minimum sum of squares as the
criterion The sum of squares was de ned as the di erence b etween the rep orted
and predicted z values given the rep orted x and y values The predicted z values
were obtained by rearranging and solving Equation for z The torso mo del
was tted separately to the data rep orted for the external oblique and the data
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
for the internal oblique resulting in a torso for each muscle
The use of Stokes and Gardner Morse s b data and the torso mo del ad
dresses two of the issues arising when considering the oblique muscles how to
represent the broad at muscle and how to ensure that the line of action follows
the constraints imp osed by the anatomy One additional p oint also needs to be
considered Most muscles contained in the mo del a x to bony attachments at
either end making the point of application of the force generated within the
muscle easy to determine However the anterior attachment of the oblique mus
cles is not so clear since these muscles terminate in an ap oneurosis covering the
anterior of the ab domen At the midline this ap oneurosis interlaces with the
ap oneurosis of the opp osite muscle to form the linea alba which extends from the
thorax to the symphysis pubis Gray Thus one must consider carefully
the point of application of forces develop ed by the oblique muscles
The mo del assumes that the force generated byamuscle is applied to the caudal
attachment Maintaining this convention the internal oblique muscle exerts its
force at the lower attachment on the lateral and p osterior margins of the torso
while the external oblique exerts its force through the ap oneurosis except Ext
and Ext whichattach to the iliac crest If it is assumed that the linea alba acts
like a xed structure since it is rmly attached at the caudal and rostral ends
then the p oint of application of forces generated by the external oblique muscle is
the linea alba since it is continuous with the muscle bres However some of the
lower bres do not reach the linea alba instead attaching to Poupart s ligament
Therefore when considering the point of application of the force generated by
each comp onent of the external oblique consideration must be given to the
p osition where the ap oneurosis joins either the linea alba or Poupart s ligament
This is achieved by assuming the ap oneurotic bres act in the same ik orientation
as the bres of the external oblique and xing the heightatwhich the linea alba
D mo del of the lumbar spine
ends caudally
The height on the torso where the bres attach to the linea alba x is determined
e
using Equation which is the rearrangement of Equation with at
the midline
low
n o
x x
low e
up
low
x x
up
low
This height is compared to the height representing the caudal end of the linea
alba x If x x then the bre joins the linea alba at x y x If x x
l e l e e e l
then the bre is assumed to attach to Poupart s ligament at x y x z x
l l l
These p oints b ecome the new point of application for the forces generated by
Ext to Ext
TLF
a structure which provides a means of attachment to the spine for The TLF is
the transverse ab dominis muscle and parts of the latissimus dorsi and internal
oblique muscles To date the detailed structure of the TLF has not b een mo delled
in three dimensions Hence a D mo del of the entire TLF has b een develop ed to
enable the contribution from the muscles attaching to the TLF to b e included in
the calculation of moments
Anatomy of the TLF
The TLF consists of three layers two of which the middle and p osterior layers
have b een rep orted as having a biomechanical e ect on the lumbar spine Fibres
of the middle layer attach to the tips of the transverse pro cesses of the lumbar
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
Figure Schematic illustrating the general structure of the TLF as seen
in a transverse slice on the left side of the trunk
vertebrae Tesh Shaw Dunn and Evans suggest that there is little con
nective tissue in the intertransverse space with most bres attaching to the tips
of the transverse pro cesses This causes the bres of the middle layer to take
on an archlike app earance From the transverse pro cesses bres from the middle
layer enter the lateral raphe where they either merge with the ap oneuroses of
the transverse ab dominis muscle and the p osterior part of the internal oblique
muscle or b ecome continuous with the deep lamina of the p osterior layer see
Figure
The p osterior layer of the fascia is attached at the midline to the thoracic and
lumbar spinous pro cesses and interspinous and supraspinous ligaments with
most bres attaching to the spinous pro cesses This layer runs p osterior to the
erector spinae muscle b efore joining the lateral raphe Figure The p osterior
layer consists of laminae the sup er cial lamina and the deep lamina The
ma jor comp onent of the sup er cial lamina is the ap oneurosis of the latissimus
D mo del of the lumbar spine
dorsi muscle while the bres of the deep lamina are continuous with the middle
layer of the fascia The bres of the sup er cial lamina are oriented caudomedially
and the bres of the deep lamina caudolaterally This arrangement gives rise to
the mesh like structure commonly observed in this layer in vivo The two laminae
of the p osterior layer are not free to act indep endently due to their fusion at the
lateral raphe Bogduk and Macintosh
The lateral raphe is formed by the con uence of the middle and p osterior layers
of the TLF The precise interaction of bres as they pass through the raphe is ill
understo o d For the purp oses of this mo del it is assumed that the bres entering
the lateral raphe from muscles at a sp eci ed spinal level fuse with other bres
at that level to form a tight network which acts to distribute the force between
the p osterior and middle layers of the fascia In this way force transmitted to
the lateral raphe from a particular muscle will in uence b oth the middle and
p osterior layers of the fascia not just the one to which the muscle is attached
Mo delling the TLF
The mo del of the TLF presented comprises three distinct stages These are
the calculation of the lines of action the changes in the lines of action caused
as a result of changing the spinal alignment or p osture and the calculation
of moments ab out the ICR for each intervertebral joint Each of these stages is
is used to represent all bres attaching to discussed in detail b elow One vector
an individual vertebra in a sp eci ed layer or lamina of the fascia For simplicity
all calculations given b elow assume vectors are expressed relative to a global
co ordinate system so that no change of basis calculations are included
The mo del assumes that the area of the erector spinae is constant throughout the
lumbar spine and indep endent of p osture and that the muscle forces pro duced
are constant
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
Lines of action for the p osterior layer
The p osterior layer of the fascia passes b ehind the erector spinae muscle mean
ing the angle at which it leaves the spinous pro cesses in the jk plane can alter
with changes in the shap e or cross sectional area of this muscle Therefore to
determine the line of action of the bres of the p osterior layer the muscle size
and shap e must rst be considered
The erector spinae muscle is mo delled as a combination of two geometric shap es
in the transverse jk plane Figure The segmen t of the muscle closest to
the spine is mo delled using a p olygon with corners at the fascia s attachmentto
the transverse pro cess and the spinous pro cess the p oint of intersection of the
transverse and spinous pro cesses and the lateral raphe The remaining segment
of the erector spinae muscle is mo delled using an arc of a circle with variable cen
tre and radius The ends of the arc are lo cated at the lateral raphe and spinous
pro cess with the area contained within this shap e being that enclosed when
the two ends of the arc are joined with a straight line Figure The radius
and centre of the circle are determined such that the area b ounded by the p oly
gon and arc equals the true area of the muscle as determined from transverse
scans using standard image pro cessing techniques in MatLab MathWorks
Inc Massachusetts USA Mathematically the radius and centre of the circle
can b e determined using Equations and Figure illustrates diagram
matically the variables used in the mo del
D mo del of the lumbar spine
a Geometric shap es used to represent the erec
tor spinae muscle
b Variables used in mo del of the TLF
Figure Schematic illustrating the comp onents of the left TLF
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
j LR SP j
r
sin
where r is the radius of the circle
LR is the p osition of the lateral raphe in the jk plane
LR LR j LR k
SP is the p osition of the spinous pro cess attachment in the jk plane
SP SP j SP k and
is the angle in radians subtended by lines from the lateral raphe
and spinous pro cess to the centre of the circle calculated by solving
Equation a measured from k in an anti clo ckwise direction
K
c
a
j LR SP j
sin tan
where K area within arc total area of muscle area of p olygon
c
p
r
A
R LR SP SP
j LR SP j
m
where p and m are the co ordinates of the centre of the circle in the
j and k directions resp ectively and
D rotation matrix for sin cos
A
R
sin a rotation of cos
D mo del of the lumbar spine
The vector representing the line of action in the jk plane of a bre attaching to
the spinous pro cess loa pos is calculated by determining the tangent of the
curve at its attachment to the spinous pro cess
pos loa
B C
A
A
SP p
loa pos
SP m
In Equation the erector spinae to the left of the spinous pro cess is b eing
considered when SP m while the right erector spinae is represented
when SP m
To calculate the i comp onent of the lines of action the angle of the bre to the
transverse plane that is the angle in the ij plane must b e known If this angle
is then the D lines of action for the p osterior layer are given by
p
loa pos loa pos tan
C B
C B
C B
loa pos
loa pos
C B
A
loa pos
It is assumed that for the deep lamina and for the sup er cial
lamina However this assumption can b e easily mo di ed to allow di erent angles
for each of the laminae The value of has b een used for Bogduk and
Macintosh The length of the bres in the jk plane f ibr e length is r
Lines of action for the middle layer
Fibres of the middle layer are assumed to connect the tip of the transverse pro cess
to the lateral raphe and act parallel to the transverse jk plane A straight line
is used to represent this layer since it app ears that it is constrained to take a near
straight path from transverse pro cess to lateral raphe due to its p osition b etween
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
the erector spinae and quadratus lumborum muscles The vector representing
mid is calculated using the line of action for this layer of the fascia loa
B C
B C
B C
mid loa
LR TP
B C
A
LR TP
where TP is the p ointatwhich the fascia attaches to the transverse
pro cess in the jk plane Note that TP TP j TP k
Altering the p osture of the spine
There is an inherent assumption in the ab ove calculations that bres of the same
layer or lamina have parallel lines of action This assumption is based on the fact
that anatomical studies only rep ort one angle of orientation in the ik plane
Further the angles of the bres rep orted in the literature have been obtained
from observation in cadavers Generally a cadaver spine has little curvature and
can be assumed to be straight In order to investigate the biomechanics of the
fascia in other p ostures some assumption ab out the movement of the bres needs
to be made Bogduk and Macintosh state that the lateral raphe is xed
to the ilium and is inextensible in the caudo cranial direction In addition to this
constraint it is assumed that the p osition of the lateral raphe is xed relative
to the erector spinae muscle This is equivalent to assuming the lateral raphe is
lo cated at a xed p oint in the transverse plane relative to the architecture of the
lo cal vertebra Thus when the erector spinae muscle b ends to follow the contour
of the spine so to o do es the lateral raphe In order to take this assumption into
account the shap e and p osition of the lateral raphe needs to b e considered
For mathematical convenience the lateral raphe can b e thought of as conprising
D mo del of the lumbar spine
B1,1 origin of basis set 1 "Fixed" Raphe1 a1 B1,3 r "Joiner" 2 Raphe2
"Fixed" Raphe3 a2
r3 "Joiner" Raphe4
"Fixed" Raphe5 a3
r4 "Joiner" Raphe6 B4,1
a4 B4,3 origin of
basis set 4
Figure Schematic illustrating the vectors used in the calculation of the
lateral raphe see Equation for the left side from L to L
two comp onents The rst is a xed region where the jk co ordinates of the
lateral raphe are xed relative to the lo cal basis system This ensures the xed
regions run parallel to the vertebral body The second comp onent is a joiner
region which links the xed regions to ensure continuity of the raphe across the
spinal levels By alternating these comp onents the lateral raphe from L to S
or the ilium can b e thought of as indep endentvectors representing xed
regions and representing joiner regions The total length of these vectors is
to satisfy the assumption that the lateral raphe is inextensible constant
Within the xed regions the lateral raphe is assumed to run parallel to the
basis vector i that is parallel to the vertebral body The length of this vector
is variable and is expressed as a prop ortion of the vertebral body height If the
lateral raphe consists of xed and joiner regions alternatively with the rst
region at the L level b eing xed then Equation can b e used to calculate
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
the length and direction of the vectors representing the lateral raphe Figure
illustrates the various vectors used in Equation
height of vertebral body h B if j integ er
h
Raphe
i
a r a Raphe if j integ er
i g g i
where i where i is rostral and i is caudal
h i
g i
is a parameter b etween and
B is the basis vector i for level h
h
a a isthe vector from the origin of basis set i g to the
g
i
lateral raphe in the transverse plane assuming a and
i
r is the vector from the origin of basis set g to the origin of basis
g
set g
Once the vectors representing the lateral raphe have b een calculated the p osition
at which the bres from the sp eci ed vertebra attach to the lateral raphe can
be calculated provided that the distance between the attachment points along
the lateral raphe is known from the initial p osition of the spine This calcula
tion needs to be conducted for each of the three layers laminae mo delled The
pro cedure detailed b elow can be used to calculate the vectors from the ICRs to
the bre attachment on the lateral raphe for each level From this information
the angle of the bres to the transverse plane and the lines of action can be
calculated for the new p osition
Let lat b e the vector along the lateral raphe from the attachment p oint of bres
i
from lumbar vertebra L to the attachment point of bres from L where i
i i
D mo del of the lumbar spine
Let lat be the vector from the attachment of the lateral raphe on the
ilium to the attachmentof bres from L on the lateral raphe
Calculation of lat
jlat j Raphe if jlat j jRaphe j
lat
X X
Raphe jlat j jRaphe j Raphe if jlat j j Raphe j
j j
k
j k j k
where k indicates the number of raphe levels lat extends over and is obtained
X X
by solving jlat j jRaphe j AN D jlat j jRaphe j
i i
i k i k
Calculation of lat i
i
Find the segment where lat b egins by solving the following for m
i
X X X X
jlat j jRaphe j AN D jlat j jRaphe j
n j n j
n i j m n i j m
Next nd the segment where lat nishes by solving the following for k
i
X X X X
jRaphe j jlat j jRaphe j AN D jlat j
j n j n
n i n i
j k j k
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
Then
jlat j Raphe if k m
i
k
X X
Raphe jlat j Raphe
j j
m
j m j i
X X
jlat j jRaphe j Raphe if k m
j j
k
lat
i
j i
j k
m
X X X
Raphe Raphe jlat j Raphe
j j j
m
j m j i
j k
X X
Raphe if k m jlat j jRaphe j
j j
k
j i
j k
Once lat has b een calculated for all i LR and l thevectors from ICR and
i i i i
ICR to the attachment of the bre from vertebra i on the lateral raphe can b e
i
calculated as follows
p elvis lat if i
LR
i
l lat if i
i i
l r LR
i i i
where p elvis is the vector from ICR to the attachmentof the lateral
L S
raphe to the ilium
If attach is the vector from ICR to the attachment of the bre on the verte
i i
bra then the vector from this bony attachment to the lateral raphe is given by
D mo del of the lumbar spine
Equation
bre l attach
i i i
For the p osterior layer the angle of the bre to the transverse plane in the new
p osition can be calculated using Equation with the corresp onding line of
action b eing describ ed by Equation For the middle layer the line of action
is loa bre
i i
fibre
i
new tan
i
fibre length
p
tan new loa pos loa pos
i
B C
B C
B C
loa
loa pos
i
B C
A
loa pos
Calculation of moments
Once the lines of action have b een determined moments ab out each of the ICRs
from L L to L S can b e calculated The moments acting on the lumbar spine
as a result of the TLF are generated by both layers of the fascia a combination
of three bre directions According to Bogduk and Macintosh the fascia is
fused to the ilium via the lateral raphe This connection means that any tension
force exerted on the lateral raphe will generate moments ab out all ICRs caudal
to the level to which the force is applied to the spine
Having noted this it has b een observed that not all bres from the di erent
layers of the fascia are present at each level Bogduk and Macintosh state
and L end in that in the deep lamina of the p osterior layer only bres from L
the lateral raphe with bres from L and L attaching directly to the iliac crest
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
In the sup er cial lamina the bres from L L and L end in the lateral raphe
Fibres emanating from the middle layer of the fascia at L L and L end in
th
the lateral raphe while bres from L and L attachtothe rib forming the
lumb o costal ligament
Taking these anatomical considerations into account the moments generated by
the TLF ab out ICR p can be calculated using
p p
l
X X X
c c c
Moment d F loa d F loa b F loa
p p i i p i i p i i
i i i
p if p
where l
if p
d is the vector from ICR p to the attachment of the bre to
p i
the spinous pro cess of vertebra i
b is the vector from ICR p to the attachment of the bre to
p i
the transverse pro cess of vertebra i
F is the force in layer lamina m of the fascia m for deep lamina of
m
the p osterior layer m for sup er cial lamina of the p osterior layer
and m for the middle layer and
loa is the vector representing the bre line of action for layer m at
m i
vertebra i
Application of the mo del
The mo del was applied to the spinal geometry of the Visible Man to investigate
the magnitude of moments capable of b eing generated by the TLF in living
sub jects Although the spinal geometry of the Visible Man was used the lines of
D mo del of the lumbar spine
action for the fascia were estimated from published images taken from three living
individuals at the L or L level Figure Visual assessment of images taken
from living sub jects and images taken p ostmortem reveal signi cant di erences
in the shap e of the p osterior surface of the torso in the region neighb ouring
the spine Figure Thus it is imp ortant that images taken from living
sub jects b e used to represent correctly the anatomy of the TLF Scans of several
individuals were used in order to investigate the amountofvariability in the lines
of action and moments generated by the fascia caused by individual variation in
the size and shap e of the erector spinae muscles Lines of action were estimated
for one side only with the other side calculated assuming trunk symmetry The
dimensions of the vertebrae from the scans were scaled to match those of the
Visible Man
The moments generated by the fascia dep end on the line of action of the bres and
the forces pro duced bythemuscles attached to the fascia Three muscles attach
to the fascia the transverse ab dominis latissimus dorsi and internal obliques
Macintosh Bogduk and Gracovetsky state that the mean cross sectional
area of the transverse ab dominis is approximately cm The raphe bres of the
latissimus dorsi as de ned by Bogduk et al attach to the fascia and have
a rep orted PCSA of cm Bogduk and Macintosh rep ort that only the
most p osterior bres of the internal oblique muscle attach to the lateral raphe
Stokes and Gardner Morse b represent the internal oblique muscle by six
vectors Int to Int For our purp oses the most p osterior of these vectors In t
is used as an approximation to the p ortion of the internal oblique attaching to
the lateral raphe with a PCSA of cm
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
a Scan L level
b Scan L level
c Scan L level
Figure Scans used to estimate the line of action for the p osterior and
middle layers of the thoracolumbar fascia
D mo del of the lumbar spine
a Images of L from a living sub ject
b Images of L taken p ostmortem
Figure Di erences in the shap e of the erector spinae muscle between
living sub jects and cadaveric sp ecimens In images taken p ostmortem the
erector spinae app ears to be much atter when compared with images taken
of living sub jects
Currently there is no information ab out to how the lateral raphe redistributes
the forces applied to it It is assumed here that the total force transmitted is
distributed evenly across the layers of the fascia and also across spinal levels On
each side of the mid line the layers laminae of the fascia are represented in the
mo del by eight bres two in the deep lamina three in the sup er cial lamina of
the p osterior la yer and three in the middle layer Assuming K is the maximum
Metho ds for calculating lines of action for muscles with curvature
between origin and insertion
P
PCSA K muscle intensity the force transmitted p er bre is K
i
K N
The results of applying the TLF mo del and the torso mo del developled in Section
to the anatomy of the Visible Man are discussed in Chapter along with
the predictions made by the entire mo del Chapter also discusses the validation
of the mo del and the issues arising from this validation
Chapter
Results and Validation
This chapter describ es the results obtained from the application of the mo del
using the input data describ ed previously Results relating to three of the mo del
comp onents the lines of action for fascicles attaching to the ribs ab dominal
obliques and the TLF are presented rst followed by results from the entire
mo del Validation and discussion of these results is presented in Section
Comp onents of the mo del
As discussed in Section the mo del of the lumbar spine which has b een devel
op ed consists of a number of sub mo dels which enhance the anatomical reality
of the fascicle lines of action The results of each of these comp onents are dis
cussed below with particular emphasis on internal validation of the techniques
develop ed
Results and Validation
Fascicles attaching to the ribs
The pro cedure develop ed for ensuring that muscle fascicles which attach to the
rib cage pass p osterior to the caudal rib s Section was implemented for
avariety of p ostures Fascicles of the longissimus thoracis pars thoracis and the
ilio costalis lumborum pars thoracis were found to pass p osterior to the lowest
four ribs during upright stance extension lateral b end and axial twist In these
p ostures no mo di cation to the lines of action was required
During exion changes to the lines of action were required for exion angles of
or greater Table with the number of fascicles requiring mo di cation
increasing with exion angle It is imp ortant to note that the fascicles which
needed to b e mo di ed at exion also needed to b e adjusted at larger exion
angles and that in all cases the level at which the fascicle passed anterior to
the rib is the same or caudal at the greater angle compared to the lesser angle
This is exp ected intuitively and provides a means of internal validation of the
technique
Table Muscle fascicles which required changes to their line of action due
to it passing anterior to the rep orted rib in various exed p ostures
Posture Muscle fascicle Rib
Upright
exion
exion LT
LT
exion IT
LT
LT
exion IT
IT
LT
LT
LT
Comp onents of the mo del
Table Data on the attachment points for the left side of the b o dy for
each of the bres of the oblique muscles rep orted by Stokes and
y
Gardner Morse and the predicted z values all values are expressed
relative to the centre of the S vertebral body
Upp er attachment Lower attachment
x y z Predicted x y z Predicted
mm mm mm z mm mm mm mm z mm
External oblique
Ext
Ext
Ext
Ext
Ext
Ext
Internal oblique
Int
Int
Int
Int
Int
Int
y
The original data rep orted has b een scaled and rotated by and resp ectively
in the ij plane to adjust to match the spinal height of the Visible Man
Ab dominal obliques
The torso as describ ed in Section was tted using the x and y co ordinates
of the attachment points of the six vectors comprising the external oblique and
the six vectors of the internal oblique Table The parameter set which
pro duces the torso that b est ts the data was determined by nding the minimum
sum of squares between the predicted and rep orted z values for each muscle
Table The height of the torso in both mo dels has been taken as mm
from the origin at the centre of the S vertebral body
Paired t tests indicate that there is no statistical di erence b etween the rep orted
z values and the z values predicted by the torso mo del for either the external
or internal oblique muscles P For the external obliques the mean dif
Results and Validation
Table Parameter values for the torsos which b est t the data rep orted
in Table all values are relativeto the centre of the S vertebral body
External oblique Internal oblique
x mm
pel v is
x mm
ribs
a mm
pel v is
a mm
r ibs
b mm
pel v is
b mm
ribs
c mm
pel v is
c mm
r ibs
Sum of squares
Numb er of data points
ference between the predicted and rep orted z values is mm SE mm
Similar analysis for the internal obliques reveals a mean di erence of mm
SE mm Figure illustrates the shap e and p osition of the bres rep
resenting the internal and external oblique muscles as determined by the torso
mo del The b ene ts of using the metho dology develop ed is best illustrated in
Figure c which clearly shows the mo del s ability to represent the curved
bres
The torso mo del although simple in concept app ears to t the muscle attac h
ment data well In addition to the statistical analysis which concluded there
was no signi cant di erence between the observed and predicted z values the
p osition of the lines representing the bres of the oblique muscles app ear anatom
ically correct with the internal oblique b eing lo cated inside the external oblique
Figure
As discussed in Section the p oints of application for the forces develop ed by
Ext to Ext need to b e determined Assuming the linea alba ends mm b elow
the centre of the S vertebral body that it x it was determined from
l
Equation that Ext and Ext right side join the linea alba at
Comp onents of the mo del
300
300 250 250
200 L 200 1 L 1 150 150 i
100 i
100 50 S 0 1 50
−50 100 0 0 S 50 1 0 50 −50 100 −100 −50 j 0 50 100
k j
a D representation b Sagittal view
160
140
120
100
80
j 60
40
20
0 S 1 −20
−40
−100 −50 0 50 100
k
c Transverse view
Figure The shap e and p osition of the lines representing the internal
light line and external obliques dark line as obtained from the torso
mo del represents the centre of the L and S vertebral bodies
Results and Validation
and resp ectively while Ext and Ext join Poupart s ligament at
and resp ectively These co ordinates are expressed
in mm relative to the most anterior point on the S sup erior endplate in the
global co ordinate system of the Visible Man and replace the lower attachment
points rep orted in Table To obtain these values it has b een assumed that
the centre of the S vertebral b o dy is lo cated mm b elow mm p osterior and
mm lateral to the most anterior p ointon the S sup erior endplate
The lower level of the torso onto which the Ext and Ext fascicles attach was
arbitrarily taken to be mm b elow the centre of the S vertebral body A
sensitivity analysis investigating the e ect of changing this level was undertaken
to determine the imp ortance of this height When the height of the caudal
end of the linea alba was assumed to be mm instead of mm the point
of application of the forces from Ext changes from the linea alba to Poupart s
ligament while the p oints of application for Ext and Ext also change However
the changes in the moments asso ciate with this shift in the p oints of application
were less than Nm during maximal exion extension exertions and
Nm during maximal lateral b end exertions Similarly onlysmallchanges in
the moments resulted when the height of the caudal end of the linea alba was
lowered to mm in the mo del Thus it app ears that the moments pro duced
by the external obliques are not critically sensitive to the level of attachmentat
the b ottom of the torso As a consequence the value of mm is used in the
application of the full mo del
the oblique The new metho dology develop ed to calculate the line of action for
muscles requires more computational e ort than assuming a straight line of ac
tion between attachment points As such it might be reasonable to ask if such
e ort is warranted App endix E provides the results of an investigation in which
the line of action using a straight line approach and the torso mo del are com
Comp onents of the mo del
pared along with the moments predicted using the two metho dologies Results
from this investigation indicate that the axial twist moments are most e ected
with the moments predicted using the torso mo del during axial twist exertions
in upright stance being almost larger than those predicted using a linear
approach This di erence is ampli ed when the spine is exed or extended Thus
it app ears that the new approach can signi cantly mo dify the predicted moments
contributed by the oblique muscles
TLF
The mo del describ ed in Section was applied to the spinal anatomy of the
Visible Man using information on muscle shap e obtained from living sub jects It
is imp ortant to use the images from living sub jects as opp osed to similar images
obtained from cadavers since the shap e of the erector spinae app ears to b e atter
on the dorsum in cadaver images when compared to images of living sub jects
The accuracy of the geometric mo del in estimating the line of action of the
p osterior layer of the fascia was investigated by comparing the predicted line
of action to the true muscle b order around which it wraps The true muscle
b order was determined using standard image pro cessing to ols in MatLab
MathWorks Inc Massachusetts USA The mo delled b order the true muscle
b order and calculated line of action are illustrated in Figure for each of the
three scans used
The use of three scans from di erent p eople illustrates the versatility of the mo del
in representing the size and shap e of the erector spinae muscle For these scans
the predicted line of action app ears to approximate the muscle b order well with
the di erence in the mo delled line of action and the true line of action b eing
less than across the three scans Figure Therefore it would app ear that
the use of two simple shap es a p olygon and segment of a circle is adequate to
Results and Validation
LR LR
SP
SP
a Scan b Scan
LR
SP
c Scan
Figure Comparison of the erector spinae b order as determined by image
pro cessing to ols and the mo delled muscle b order The line of action
of the fascia predicted by the mo del is indicated by the solid line LR and
SP represent the p ositions of the lateral raphe and spinous pro cess
resp ectively The anterior of the trunk is toward the top of each image
de ne the natural shap e of the erector spinae muscle particularly in the region
neighbouring the tip of the spinous pro cess Scan was chosen to represent
the characteristics of the erector spinae and TLF in the full mo del since it gave
for the line of action see Figure intermediate values
The repro ducibility of the line of action of the fascia in the TLF mo del is af
fected by the manual selection of the input data The repro ducibility of the
calculated line of action for the p osterior and middle layers of the fascia was
Results from the entire mo del
investigated by taking eight samples of each scan The standard errors of the
mean for the comp onent of the line of action in the k direction obtained from
the eight samples for the p osterior layer are and for scans
and resp ectively Likewise the standard errors for the middle layer are
and The variability in the lines of action is much less
for the middle layer compared to the p osterior layer since only two p oints are
needed to de ne the middle layer the transverse pro cess attachment and the
lateral raphe while four p oints are needed to calculate the line of action for the
p osterior layer the transverse pro cess and spinous pro cess attachments the lat
eral raphe and a corner b etween the transverse and spinous pro cesses For the
scans sampled the transverse pro cess attachment and the lateral raphe were the
two most readily identi able points However the variabilityintro duced by the
manual selection of these data p oints app ears small compared to the di erences
seen among individuals A full discussion of the moments predicted by the TLF
mo del is contained in App endix F
Results from the entire mo del
Upright stance
Table gives the moments predicted by the mo del during isometric maximum
exion extension left lateral b end and left axial twist exertions in upright stance
A more detailed summary of the results is contained in App endix G All moments
are expressed relative to the global co ordinate system The values displayed in
Table were obtained using the spinal alignmentand muscle activation levels
given in Tables and resp ectively and a maximum muscle intensity of
Ncm for all muscles Since muscle activation data was not available for all
muscles in the mo del it is assumed that for exion extension and lateral b end
Results and Validation
Table Mo del output for the predicted maximum moments achievable in
the upright stance for a variety of exertions Positive values represent exion
right lateral b end or left axial twist dep endent on the momentbeing
considered
Predicted maximum moments Nm
Exertion Moment L L L L L L L L L S
Flexion Flexion extension
Lateral Bend
Axial Twist
Extension Flexion extension
Lateral Bend
Axial Twist
L lateral b end Flexion extension
Lateral Bend
Axial Twist
L twist norm A Flexion extension
Lateral Bend
Axial Twist
L twist norm B Flexion extension
Lateral Bend
Axial Twist
exertions the psoas ma jor ilio costalis lumb orum and quadratus lumb orum have
the same activation as the longissimus thoracis that the latissimus dorsi has
the same activation as the internal oblique and that the transverse ab dominis
has the same activation as the rectus ab dominis For axial twist exertions it
is assumed that the psoas ma jor multi dus and quadratus lumb orum have the
same activation as the lower erector spinae and that the transverse ab dominis
has the same activation as the rectus ab dominis
During exion and extension exertions only moments ab out the exion extension
axis are pro duced by the mo del due to the symmetry of the anatomy ab out the
mid sagittal plane The magnitude of these moments follow a pattern across
the spinal joints which is consistent with the changes in moment arms caused
by the lordosis of the spine e g exion moments are smallest at L L and
Results from the entire mo del
L L where the spine is closest to the exor muscles In contrast lateral b end
and axial twist moments develop ed during the resp ective exertions are relatively
constant across the spinal levels
The predicted extension moments are considerably lower at L L compared to
the other joints This may b e the result of omitting the thoracic multi dus from
the mo del This muscle attaches rostrally to the thoracic spine and caudally to
the lumbar vertebra with most fascicles attaching rostral to L
The contribution from individual muscles to the overall moments is displayed
graphically in Figures and for each of the exertions only moments in the
primary axis of motion are displayed In these gures the longissimus thoracis
pars thoracis and the ilio costalis lumb orum pars thoracis have been collectively
referred to as the thoracic ES while the longissimus thoracis pars lumb orum
and ilio costalis lumb orum pars lumb orum are referred to as the lumbar ES
During extension exertions the longissimus thoracis pars thoracis pro duces the
greatest moments of the agonistic muscles followed by the ilio costalis lumb orum
pars thoracis for L L to L L and pars lumb orum for L L and L S
The rectus ab dominis and oblique muscles which form the antagonist muscles
are quite active during extension exertions pro ducing total moments of
and Nm ab out L L to L S Most of these moments are generated
by the internal and external oblique muscles with the anterior bres
of each muscle contributing the greatest moments The moments pro duced by
the internal obliques are largest at L L Nm decreasing to Nm at L S
while the moments pro duced by the external obliques gradually increase from
L to L S Nm at L L to Nm at L S When expressed as a L
p ercentage of the total extension moment the internal obliques contribute the
most of the antagonist muscles in the upp er lumbar spine Nm Nm
at L L while the external obliques contribute the most in the lower lumbar
spine Nm Nm at L S see Figure
Results and Validation
150.00 130.00 110.00 Psoas major 90.00 Multifidus 70.00 Lumbar ES 50.00 Thoracic ES Quadratus lum. 30.00 Rectus abdom. 10.00 Ext. oblique
% of extension moment -10.00 Int. oblique Other -30.00 -50.00
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 a Extension exertions
70.00 60.00 50.00 40.00 Lumbar ES Thoracic ES 30.00 Rectus abdom. 20.00 Ext. oblique Int. oblique 10.00 Other
% of flexion moment 0.00 -10.00 -20.00
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 b Flexion exertions
50.00 45.00 40.00 35.00 Psoas major Lumbar ES 30.00 Thoracic ES 25.00 Quadratus lum. 20.00 Ext. oblique Int. oblique 15.00 Other 10.00 % of lateral bend moment 5.00 0.00
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Left lateral b end exertions
Figure Contribution of muscles to the primary moment generated
during exion extension and lateral b end exertions
Results from the entire mo del
80.00 70.00 60.00 50.00 40.00 Thoracic ES Ext. oblique 30.00 Int. oblique 20.00 Other 10.00 % of twist moment 0.00 -10.00 -20.00
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Axial twist moments using EMG Norm A
80.00 70.00 60.00 50.00 Psoas major 40.00 Thoracic ES 30.00 Ext. oblique 20.00 Int. oblique Other 10.00 % of twist moment 0.00 -10.00 -20.00
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Axial twist moments using EMG Norm B
Figure Contribution of muscles to axial twist moments generated
during maximal axial twist exertions
During exion exertions the rectus ab dominis pro duces b etween and of
the net moment The remaining moments are generated by the oblique muscles
with the internal oblique dominating at the rostral end of the lumbar spine and
the external oblique dominating at the caudal end internal oblique Nm at
L L decreasing to Nm at L S external oblique Nm at L L increasing
to Nm at L S There is a small amount of predicted activity from the
antagonist muscles but the moments pro duced do not exceed Nm
Results and Validation
During lateral b end exertions the muscles pro duce a net lateral b end momentin
the same direction as the exertion with the internal and external oblique muscles
b eing the largest contributors Nm for internal obliques and Nm for
external obliques The contribution of the psoas ma jor muscle increases from
L L Nm to L S Nm suchthatatL S it is the next ma jor contributor
after the obliques The remaining muscles pro duce smaller moments which are
relatively constant across the spinal levels During lateral bend exertions the
contralateral muscles act as antagonists pro ducing a Nm moment while the
ipsilateral muscles generate amoment of Nm
The internal and external oblique muscles contribute almost of the mo
ment develop ed during axial twist exertions Figure When EMG Norm
B data is used the external oblique muscles pro duce anet moment of approxi
mately Nm Nm generated by the contralateral external oblique and Nm
generated by the ipsilateral external oblique Likewise the contralateral inter
nal oblique pro duces Nm the ipsilateral internal oblique Nm resulting in
a net moment of Nm The prop ortioning of moment between the left and
right obliques is equivalent to the prop ortioning of the EMG data from these
muscles When the contralateral external oblique and ipsilateral internal oblique
m uscles are deactivated the axial twist moments predicted are much larger at
approximately Nm
Alternative p ostures
The simulated spine was orientated in a variety of p ostures within the normal
range of motion to examine the e ect of p osture on the moment generating
potential of the muscles Figures and provide a graphical repre
sentation of how the predicted moments ab out L L during exion extension
lateral b end and axial twist exertions change with p osture Moments ab out all
Results from the entire mo del
three axis of rotation have been included for each exertion The L L joint has
been chosen for illustrative purp oses only Similar representations of the changes
ab out other joints are contained in App endix H
The graphs contained in Figures and represent the primary and
secondary moments for the sp eci ed exertion in upright standing and exed
extended and laterally bent p ostures graphs on the left side of the gures as
well as twisted p ostures graphes on the right side of the gures Considering
the graphs on the left side of the gures the moments for exed extended or
laterally b end spines are displayed for each increment in exion extension
or lateral bend upto for exion and for extension and right and left
lateral b end Spines were rotated only in exion extension or lateral b end not
combinations of the directions The twisted p ostures demonstrated in the gures
graphs on the right side of the gures represent rightorlefttwist ve angles
represent right twist No combination of twist with exion extension or twist
with lateral b end are displayed
During exion and extension exertions the exion extension moments remain
symmetric ab out the midsagittal plane for all exed and extended p ostures but
b ecome asymmetric in laterally b entandtwisted p ostures The magnitude of this
asymmetry as measured by the coupled lateral bend and axial twist moments
increases as the magnitude of the lateral bend or axial twist increases Figures
and The magnitude of the exion moments develop ed during exion
exertions decreases as the amount of spinal exion increases Conversely the
magnitude of the extension moments develop ed during extension e orts increases
with spinal exion These changes are as would be exp ected and are primarily
related to the force generated by the muscle increasing with muscle strain
Results and Validation
80 60 40 20 -20 80 0 0 70 -20 30 20 20 60 10 0 -40 -10 -20 50 40 -60 30
Flexion moment (Nm) -80 Right 20 Lateral -100 10
Bend Flexion moment (Nm) -120 0 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Flexion moments primary moment
30
20
10 8 -20 6 0 0 4 30 20 20 2 -10 10 0 -10 -20 0 Right -2 -5 0 5 -20 Lateral Lateral bend moment (Nm) Bend -4 -30 -6 Left Lateral bend moment (Nm) -8 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
3
2
1 6 -20 4 0 0 2 30 20 20 -1 10 0 -10 -20 0 -2 Right -2 -5 0 5 Axial twist moment (Nm) Lateral -3 Bend -4
Left Axial twist moment (Nm) -6 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure Moments generated ab out L L by a maximum exion exertion
in various p ostures ve exion moments represent exion ve lateral b end
and axial twist moments represent moments to the left Black columns
represent upright standing
Results from the entire mo del
300
250
200 250
150 200
100 150 50 -20 100
Extension moment (Nm) Right 0 0 Lateral 50 30 20 Bend 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
20 15 10 1.5 5 -20 1 0 0 0.5 30 20 20 -5 10 0 -10 -20 0 -10 Right -5 0 5 -15 Lateral -0.5 Lateral bend moment (Nm) Bend -20 -1 Left Lateral bend moment (Nm) -1.5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
40 30 20 20 10 -20 15 0 0 10 30 20 20 5 -10 10 0 -10 -20 0 -20 Right -5 -5 0 5 Axial twist moment (Nm) -30 Lateral -10 Bend -40 -15
Left Axial twist moment (Nm) -20 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure Moments generated ab out L L by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
Results and Validation
180 160 140 120 40 100 35 80 30 60 25 40 20 -20 15 20 Right Extension moment (Nm) 0 0 Lateral 10 Bend 5 -20 30 20 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
180 160 140 120 200 100 80 150 60 40 100 -20 20 Right Lateral bend moment (Nm) 0 0 Lateral 50 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 30 20 20 10 0 -10 -10 -20
-20 -5 0 5 0 -30 -10
-40 -20 Right -50 -30
Axial twist moment (Nm) Lateral Bend -60 -40 Left
Axial twist moment (Nm) -50 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure Moments generated ab out L L by a maximum left lateral
bend exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
Results from the entire mo del
200
150 100
100 80
60 50
Extension moment (Nm) -20 40 Right 0 0 Lateral 20 Bend 30 20 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
45 40 35 30 50 25 20 40 15 30 10 -20 20 5 Right Lateral bend moment (Nm) 0 0 Lateral 10 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
50
40
30 50 40 20 30 10 -20 20
Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure Moments generated ab out L L by a maximum left axial twist
exertion using EMG Norm B data in various p ostures ve extension
moments represent extension ve lateral b end and axial twist moments
represent moments to the left Black columns represent upright standing
Results and Validation
150 100 50 0 -50 20 Exten. -100 10 Exten. -150 Upright -200 10 Flex. 20 Flex. -250 30 Flex. % contribution (relative to rectus) -300 Lumbar Thoracic Rectus Ext. Int.
ES ES abdom. oblique oblique
Figure Contribution from each of the ma jor agonist and antagonist
muscles to the exion moment predicted ab out L L during exion exertions
in a variety of p ostures Contributions are expressed as a p ercentage relative
to the moment generated by the rectus ab dominis muscle
The mo del predictions indicate that at and exion the muscles pro duce a
net extension moment during maximal exion exertions Figure Intuitively
this seems incorrect Investigation of the contributions made by eachofthemus
cles indicates that the longissimus thoracis pars thoracis contributes a very large
antagonist moment so large in fact that it exceeds the moments pro duced by
the agonist muscles Figure The reason b ehind this large moment app ears
to be an extraordinarily large strain develop ed in the fascicles attaching to the
ribs particularly those attaching to ribs and Table
The mo del predicts that during lateral bend exertions the magnitude of the
lateral b end moments increases as the spine is bent away from the direction
of the exertion Considering rotations in the mid sagittal plane the largest
moments are achieved when the spine is near upright with values decreasing as
Results from the entire mo del
Table Maximum muscle strains predicted by the mo del in avarietyof
p ostures
Posture Fascicle Side Strain
Extension
Int Right and Left
Int Right and Left
Flexion
LT rib Right and Left
LT rib Right and Left
LT rib Right and Left
LT rib Right and Left
LT rib Right and Left
LT rib Right and Left
Left Lateral Bend
IT Right
IT Right
Right Lateral Bend
IT Left
IT Left
Left Axial Twist
Ext Left
Right Axial Twist
Ext Right
the spine is exed or extended Lateral bend moments also decrease relative to
those in upright stance when the spine is twisted with the contralateral twists
causing a larger reduction in moments than an ipsilateral twist The axial twist
moments develop ed during lateral bend exertions tend to decrease with spinal
exion lateral b ending in the same direction and twist in the opp osite direction
as the exertion
The maximum axial twist moments able to be generated during twist exertions
do not app ear to be signi cantly a ected when the spine is exed In contrast
extension of the spine results in a decrease in twist moments However axial twist
moments develop ed during twist exertions seem to b e more sensitive to laterally
b ending or twisting the spine suchthattwist moments generated during left twist
Results and Validation
exertions increase during left lateral bend and right twist and decrease during
right lateral b end and left twist
Validation of the mo del
Validation of the mo del output has b een achieved by comparing the mo del pre
dictions to rep orted exp erimentally derived moments from isometric contractions
in volunteers Validation is always a di cult task with biomechanical mo dels
but it was felt that comparison of the mo del output to exp erimental maximum
moments would highlightany de ciencies in the anatomical mo del No compar
isons were made to outputs from other mathematical mo dels since the current
mo del is purely an anatomical mo del and do es not use any force distribution
technique to ensure equilibrium ab out the intervertebral joints
Twelve exp erimental studies which rep ort mean maximum isometric moments for
exion extension lateral b ending and or axial twist exertions were collated to
b e used for validation However only nine of these studies rep orted any measure
of variation in the estimated moments Consequently only these nine studies are
considered further Only the results for male volunteers were utilised since the
mo del was based on the anatomyofamale Table summarises the details of
the nine studies used in the validation Unfortunately only the mo del predictions
ab out L L L L and L S can b e included in the validation study since the
Also all exp erimental results do not rep ort moments for the joints ab oveL L
exp erimental data except that rep orted by Gomez et al for exion and
extension was obtained in upright stance limiting the validation primarily to
upright stance
Validation of the mo del
Table Details of studies providing information on mean maximum
moments generated under isometric conditions by male volunteers
Study Sub ject Moments rep orted
characteristics
Cholewicki et al males Extension Flexion
mean age yrs Lateral b end
Zetterb erg et al males Extension Flexion
mean age yrs Lateral b end
Potvin and O Brien males Lateral b end
aged yrs
O Brien and Potvin males Axial twist
mean age yrs
McGill males Axial twist
mean age yrs
Guzik et al males Extension Flexion
mean age yrs Lateral b end
Parnianp our et al males Extension Flexion
mean age yrs Lateral b end Axial twist
Masset et al males Extension Flexion
mean age yrs Lateral b end Axial twist
Gomez et al males Extension Flexion
mean age yrs Lateral b end Axial twist
The con dence intervals for the mean maximum moment for each of the
exp erimental studies are given in Table Table provides the upp er and
lower b ounds de ning of the sample distribution of maximum moments from
each of the exp erimental studies These b ounds de ne the limits b etween which
of the sample moments lay assuming the moments are normally distributed
These values are designed to b e more representative of the range of values likely
to be obtained in a sample than the con dence interval for the mean
Results and Validation
Table con dence intervals for the mean maximum moments
obtained exp erimentally from the studies outlined in Table study number
in brackets The con dence intervals for study have been estimated using
the rep orted SD for force
Maximum moments Nm
Direction L L L L L S Level not sp eci ed
Flexion
y
Extension
y
L Lateral Bend
R Lateral Bend
L Axial Twist
R Axial Twist
y
Sub jects wereat exion
Figure graphically displays the sample b ounds for studies rep orting moments
for exion extension and left lateral bend for each level Figure contains
the results for left axial twist exertions for each study ab out the L S level or
the trunk as sp eci ed in each study The moments predicted by the mo del in
upright stance are included in b oth gures
Validation of the mo del
350
300 Model 250 Study 1 Study 2 200 Study 7 150 Study 8
100
Flexion moment (Nm) 50
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Maximum exion exertion
350
300 Model 250 Study 1 Study 2 200 Study 7 150 Study 8
100
Extension moment (Nm) 50
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Maximum extension exertion
250
Model 200 Study 1 Study 2 150 Study 3 Study 7 Study 8 100 Study 9
50 Lateral bend moment (Nm) 0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Maximum left lateral b end exertion
Figure Comparison of predicted moments to the sample b ounds
for exp erimentally derived moments
Results and Validation
Table bounds on the sample for the maximum moments obtained
exp erimentally from the studies outlined in Table study number in
brackets Bounds are calculated assuming a normal distribution of moments
centred ab out the rep orted mean
Maximum moments Nm
Direction L L L L L S Level not sp eci ed
Flexion
y
Extension
y
L Lateral Bend
R Lateral Bend
L Axial Twist
R Axial Twist
y
Sub jects were are exion
180 160 140 120 100 80 60 40
Axial twist moment (Nm) 20 0 Study 4 Study 5 Study 7 Study 8 Study 9 Model B
Model A
Figure Comparison of predicted moments to exp erimentally derived
sample b ounds for left axial twist exertions Moments are either ab out
L S or the trunk as sp eci ed in the individual studies Mo del A and Mo del
Buse EMG Norm A and EMG Norm B data resp ectively
Validation of the mo del
Comparison of the predicted moments to exp erimental data indicates that for
attempted exion and extension the predicted moments ab out L L L L
and L S fall within the sample bounds of all exp erimental data for the same
levels Figure The predicted moments also fall within the sample b ounds
rep orted by Guzik et al study at L S and L L to L S for
exion and extension resp ectively Table The predicted extension moments
tend to fall into the central region of the exp erimentaldataatL L and L L
as indicated by their inclusion within the con dence interval for the mean
maximum moment rep orted by Zetterb erg et al and Cholewicki et al
Table and Figure Although the predicted exion moments fall
into the sample b ounds for the ma jority of exp erimental data the predictions
app ear to consistently fall at the lower end of the distribution particularly at
L L and L L
The predicted moments for lateral b end exertions t within the sample b ounds
for all exp erimental studies rep orting this moment except those rep orted by
Cholewicki et al study which are lower than the prediction At all
levels the predicted moments are larger than the exp erimentally derived mean
moments
The moments predicted by the mo del for axial twist exertions using EMG Norm
A data are smaller than those obtained from any of the exp erimental studies
Using EMG Norm B data the predicted moments fall within the sample
b ounds for studies and Parnianp our et al Gomez et al but are
smaller than achieved in the other studies Similar results havebeenreportedby
McGill whose EMG driven mo del predicted a net moment at the L L
joint of Nm using EMG Norm A and Nm using EMG Norm B when
sub ject sp eci c EMG data and anatomical prop erties were used
The study by Gomez et al is the only study reviewed which rep orted
Results and Validation
exion and extension moments means and standard deviations in a exed p os
ture At exion the mo del predicts the muscles can develop a Nm exion
moment during maximal exion e orts and a Nm extension moment during
maximal extension e orts Both these values fall within the exp erimental b ounds
calculated from the data rep orted by Gomez et al but are both in the
extreme lower p ortion of the distribution Table
Validation of the predicted changes in moments for di erent p ostures was achieved
by comparing the patterns observed with the trends rep orted from various exp er
imental studies Although the values di er the changes observed in the mo del
output for extension lateral b end and axial twist moments during the resp ective
exertions agree with the trends rep orted by Gra vel et al in exed and
twisted p ostures The patterns in the mo del output for twist moments during
axial twist exertions in twisted p ostures agree with the results rep orted byPop e
Svensson Andersson Broman and Zetterb erg and McGill
Generally the mo del predictions compare well with the exp erimental results ob
tained from a variety of sources in exion extension and lateral b end but app ear
to be to o low in axial twist However there are several points which should be
considered when comparing the mo del predictions to the exp erimental results
These points can be considered in two distinct groups comparison of mo delled
and exp erimental conditions and the validity appropriateness of the data used
in the mo del
Considering the exp erimental data rst it is imp ortant to consider how the
exp erimental moments were calculated Most of the exp erimental rigs used in
the studies listed in Table restrain the sub jects at the p elvis and upp er torso
Generally the upp er attachment is via a strap which runs under the arms thus
acting quite high on the torso This means that the values recorded by the force
transducers or other force measuring devices will b e those generated bymuscles
Validation of the mo del
in the lumbar spine and lower thoracic spine In comparison the mo del only
accounts for forces pro duced by muscles which cross some part of the lumbar
spine The impact of this di erence is not likely to be ma jor during exion
extension or lateral b end exertions since most muscles whichcontribute to these
movements cross b oth the lower thoracic and lumbar regions and are included in
the mo del In contrast pure lumbar rotation o ccurs only secondary to thoracic
rotation Gomez et al resulting in there b eing some muscles which help
develop axial twist that are lo cated solely in the thoracic region These muscles
which include the serratus anterior levator costae and rhomb oid ma jor are not
included in the mo del To illustrate this point consider the latissimus dorsi
muscle Bogduk et al divide the latissimus dorsi into ve bre typ es
the thoracic transitional raphe iliac and costal bres Only the raphe and iliac
bres have been included in the mo del since these are the only bres which are
asso ciated with the lumbar spine Omission of the other bres results in of
the latissimus dorsi muscle area not b eing included in the mo del This equates to
an additional N of force which is applied to the thoracic spine to p otentially
help generate axial twist Hence it is exp ected that the moments predicted by
the mo del would be smaller than those obtained exp erimentally by measuring
the force generated by the torso
Another di erence b etween the exp erimental and mo delled scenario is the spinal
alignment The mo del was applied assuming volunteers were standing in an av
erage uprigh t p osture Although the volunteers in the studies were all standing
upright there is no data on the actual p osture adopted by the volunteers nor is
there any indication of the movement of the spine during the maximal exertions
Although the overall movement of the spine is limited by the chest and p elvis
harnesses there is no way to monitor the movement between these xed p oints
As displayed in Figures to spinal p osture can have a large e ect on the
moments predicted
Results and Validation
The mo del predictions are dep endent on the input data used and assumptions
made The muscle activation levels used in the mo del originated from two dif
ferent sources Since each exertion has data on activation levels from one study
only there is no means of assessing the reliability of the EMG data nor extract
ing any information on the variability between EMG studies The two studies
rep orted activation as MVC although the metho d of determining the MVCs
di ered The impact of this di erence is demonstrated well by the di erences
in activation rep orted b y McGill using normalisation metho ds A and B
Table The consistency b etween the EMG studies is also questionable given
that the activation patterns rep orted by Zetterb erg et al in left lateral
bend generate coupled axial twist moments exceeding those generated during
attempted maximum twist using McGill s activation levels Table In fact
the nature of the coupling between lateral bend and axial twist changes under
the di erent activation regimes with left lateral b end being coupled with right
twist using Zetterb erg s EMG data for left lateral b end while left axial t wist is
coupled with left lateral b end using McGill s EMG data for axial twist
A recent study by Jorgensen and Marras rep orted EMG data for ve bi
lateral muscles at and of the maximum extension moment Figure
displays the normalised EMG for each muscle at the di erent extension ef
forts Although extrap olation outside the range of the three data points may
lead to erroneous conclusions tting an exp onential curve and extrap olating to
of the extension moment indicates near maximal activation of the erector
spinae activation This is asso ciated with a high activation level for the
internal oblique m uscle activation and lower levels of activation for the
external oblique and rectus ab dominis and resp ectively It is inter
esting to note that this data set rep orts the internal obliques to be more active
than the external obliques during extension e orts the opp osite of that rep orted
by Zetterb erg et al Using these muscle activations leads to decreased
Validation of the mo del
0.7
0.6
0.5 Lat dorsi 0.4 ES Rectus 0.3 Ext Obl Int Obl 0.2 Normalised EMG
0.1
0 0 20406080
% Maximum extension moment
Figure Normalised muscle activation levels foravariety of muscles as
rep orted by Jorgensen and Marras for sub maximal extension e orts
predictions of extension moments ab out L L to L L from Nm to Nm
for L L from to Nm for L L and from to Nm for L L and
increased moments ab out L L and L S from Nm to Nm for L L
and from Nm to Nm for L S Obviously there is a need to investigate
the quality of the EMG data further
uscle activation levels originates from studies using The data used to representm
two surface or ne wire electro des to represent each muscle bilaterally Mirka
Kelaher Baker Harrison and Davis rep ort that during axial twist exer
tions volunteers are capable of di erentially activating di erent regions of the
external oblique muscle The authors suggest that muscle activation decreases
from the anterior to the p osterior of the muscle and that the p osition recording
the largest activation correlates with the p osition most commonly used in pre
vious EMG studies This would result in an overestimate of the activation of
the p osterior comp onents of the external oblique muscle Ext to Ext Fur
Results and Validation
ther work Davis and Mirka con rms the results of the previous study and
rep orts similar ndings during extension exertions as well as during axial twist
Simulations which mimic these ndings for extension exertions by reducing the
activation of Ext to Ext result in a decrease in extension moments for joints
rostral to L L and an increase at the caudal levels If this nding is applied to
other exertions it would b e exp ected that increased exion moments at L L to
L L and decreased exion moments at the caudal levels during exion exertions
would result while lateral b end moments would decrease across all joints during
lateral b end exertions The lateral b end moments would be most a ected since
Ext Ext and Ext pro duce the largest b end moments of all bres of the exter
nal oblique muscle To date no sp eci c study has been rep orted which provides
EMG data for di erent regions of the muscles with broad attachments during
isometric maximal exertions When this data b ecomes available the impact of
di erential activation of muscles can be investigated further
The simulation of the spine in various p ostures was conducted using EMG data
recorded for maximal exertions in upright stance There is little data to indicate
how the muscle activation levels change with p osture McGill rep orts
muscle activation levels during axial twist exertions in upright and pre rotated
p ostures using EMG Norm A These values are displayed in Figure Sta
tistical analysis of this data indicated that there was no signi cant di erence in
rom the mean MVC recorded in the three p ostures for eachmuscle P F
the published data it is not p ossible to determine if there were any consistent
trends for individual sub jects nor how much lumbar twist was develop ed since
the pre rotation angle of was the angle between p elvis and shoulders To
enable the mo del to b etter represent varied p ostures more information on the
changes in muscle activation patterns are required foravariety of p ostures
It was noted in Section that large strains were develop ed in some of the
Validation of the mo del
60
50 Rectus 40 Ext. oblique 30 Int. oblique
% MVC Lat. dorsi 20 Upper ES 10 Lower ES
0 -30 0 30
Right twist Left twist
a Contralateral muscle activity
80 70 60 Rectus 50 Ext. oblique 40 Int. oblique Lat. dorsi % MVC 30 Upper ES 20 Lower ES 10 0 -30 0 30
Right twist Left twist
b Ipsilateral muscle activity
Figure Mean muscle activitylevels rep orted by McGill during
isometric maximal axial twist exertions in three p ostures
fascicles of the longissimus thoracis pars thoracis during exion There are several
p ossible reasons for the development of this large strain Firstly the attachment
p oints of the fascicles on the ribs may be incorrect However it is unlikely that
these errors would be large enough to e ect the strain predictions signi cantly
The most probable explanation for the high strain value relates to the assumed
optimum length of the muscle The mo del assumes that the optimum muscle
h a muscle can generate its maximum active force is length the length at whic
the length of the muscle in upright standing There is no basis for this assumption
Results and Validation
other than simplicity McGill and Norman use the fetal p osition as the
p osition representing the optimal muscle length Using this p osition do es not
allow the p osterior muscles to b e stretched b eyond their optimal length since the
fetal p osition represents the extreme p osture of full exion This scenario would
app ear to be non optimal biomechanically since the p osterior muscles are never
elongated which do es not allow them to generate any passive tension while the
ab dominal muscles are always elongated A more probable interpretation given
the results of using the upright stance as the optimum length is that the rest
length of the longissimus thoracis par thoracis is somewhere between upright
and full exion e g at exion This would cause the moments generated
by the longissimus thoracis par thoracis in upright stance to decrease since the
muscle would b e working at a contracted length while the moments generated in
more exed p ostures would also decrease due to the lower strain If the assumed
optimal length is changed from that in upright standing to that at exion for
all muscles then the maximum muscle strain obtained at exion decreases
from to The predicted moments under this altered assumption are
displayed in Tables and for a variety of p ostures Changing the p osition
of the optimal length results in an increase in exion and extension moments
during exion and extension exertions resp ectively and decreases in the primary
moment for lateral b end and axial twist exertions As a consequence of changing
the optimal muscle length the maximum strain obtained during extension of the
spine increases from to
PCSA has been used in the mo del as a measure of muscle area A variety of
sources have b een used to obtain this data Data on the PCSA of the multi dus
longissimus thoracis ilio costalis lumb orum psoas ma jor and latissimus dorsi was
obtained from dissection studies using cadavers aged over years The PCSA
values used for the rectus ab dominis and the oblique muscles was approximated
from transverse photographic images of two cadavers one male and one female
Validation of the mo del
Table Predicted maximum moments develop ed by the muscles during
exion and extension exertions assuming the optimal muscle length is
obtaining during upright standing A or that the optimal length is achieved
when the spine is exed B Only the exion extension moments are
displayed ve values represent exion and ve values extension
Exertion Position of Maximum moment Nm
Posture optimal length L L L L L L L L L S
Flexion
Upright A
B
exion A
B
exion A
B
extension A
B
extension A
B
Extension
Upright A
B
exion A
B
exion A
B
extension A
B
extension A
B
aged and years resp ectively while the quadratus lumb orum PCSA was es
timated from living sub jects Thus the PCSA of the ma jorityofdorsalmuscles
was derived from measurementofmuscle length and volume in older male cadav
ers while the PCSA of the ab dominal muscles was estimated using transverse
section photographic images of a male and female cadaver These di erences
raise some interesting questions regarding the consistency of the PCSA data Is
muscle PCSA sex dep endent Do es muscle volume obtained from reconstruction
Results and Validation
Table Predicted maximum moments develop ed by the muscles during
lateral b end and axial twist exertions assuming the optimal muscle length is
obtaining during upright standing A or that the optimal length is achieved
when the spine is exed B Only the primary moments are displayed
ve bend moments are to the right while ve twist moments are to the
left
Exertion Position of Maximum moment Nm
Posture optimal length L L L L L L L L L S
Left lateral bend
Upright A
B
Left axial twist
Upright A
B
of transverse images equate to the measured volume
Muscle PCSA is calculated as muscle volume divided by length For male and
female PCSA values to equate the ratio of volume to length must be similar
Stokes and Gardner Morse b rep ort the estimated muscle volumes for the
male and female cadaver as and mm for the rectus ab dominis
and mm for the external oblique and and mm for
the internal oblique resp ectively If it is assumed that the length of eachmuscle is
prop ortional to sub ject height then a comparison of the male and female cadaver
muscle areas can be made using
Volumeofmuscle for female Volumeofmuscle for male
x
Height of female Height of male
If x is close to one then the pseudo muscle area is comparable b etween the male
and female cadavers If x is less than one the female muscle area is smaller
than the male s and vice versa for x greater than one Applying this formula
to the muscle volume data rep orted by Stokes and Gardner Morse b and
Validation of the mo del
using heights of m for the male and m for the female cadaver x values
of and were obtained for the rectus ab dominis external oblique
and internal oblique muscles resp ectively These values indicate no di erence in
the area of the rectus ab dominis between the male and female sp ecimens but
smaller areas for the oblique muscles in the female
The PCSA values used in the mo del for the ab dominal muscles are an average
of the male and female PCSAs The simple calculations ab ove indicate that this
averaging has the e ect of de ating the combined area of the oblique muscles
relative to the male value Toinvestigate the e ect this has on mo del predictions
the male PCSA value for the obliques was estimated using
PCSA PCSA
mal e combined
x
For the external obliques the male PCSA is estimated to be times the
combined PCSA while for the internal obliques the male PCSA is approximately
times the combined value
The relationship between the volume obtained from reconstructing transverse
images and the measured volume also needs to be investigated Stokes and
Gardner Morse b rep ort that the volume for each of the muscle comp o
nents was calculated as the area calculated from transverse section photographic
images multiplied by the separation distance between cross sections For the
oblique muscles the area observed in transverse sections is likely to overestimate
the true cross sectional area of the muscle due to the angle of the muscles to
the transverse plane This results in an overestimate of muscle volume The
magnitude of this overestimation can b e approximated using
Results and Validation
T C
CSA cos sin CSA
j j
j j
T
where CSA is the CSA of the muscle p erp endicular to the direction
j
of the muscle bre j
is the angle of muscle bre j to the sagittal plane in p osterior view
j
is the angle of muscle bre j to the transverse plane in sagittal view
j
C
CSA is the CSA measured from transverse images
j
The approximate values for and are given in Table along with the ap
j j
proximate correction factors required to adjust the rep orted PCSA of the oblique
muscles to account for sex di erences and scan angle The combined correction
factors rep orted in Table indicate that the PCSA values used in the mo del
are likelytobeoverestimated for the external obliques particularly the most an
terior bres Ext and Ext and underestimated for the internal obliques As
the values in Table indicate incorp orating these adjusted PCSA values into
the mo del has little impact on the overall predicted moments since the changes
only a ect a small number of the fascicles included in the mo del Thus it is not
likely that di erences in the determination of muscle PCSA impact signi cantly
on the results presented
It has b een suggested that cadavers provide p o or estimates of geometrical mea
sures of muscle bulk due typically to their older age and inactivity prior to death
McGill et al Although the cause of death of the cadavers is unknown it
is true that the age of the sp ecimens used to approximate the muscle area of the
dorsal muscles was signi cantly older than the age of the volunteers recruited for
the exp erimental studies This age e ect is di cult to account for except to say
young healthy sub jects that the PCSA of the dorsal muscles may be larger in
Validation of the mo del
Table Angles of the oblique muscle bres to the transverse plane along
with the correction factors required to convert the rep orted PCSA values to
male only PCSA values adjusted for scan angle
Correction factors
degrees degrees Sex Scan angle Total
Ext
Ext
Ext
Ext
Ext
Ext
Int
Int
Int
Int
Int
Int
Table Mo del predictions in upright stance using adjusted PCSA
values for the external and internal obliques
Predicted maximum moments Nm
L L L L L L L L L S
Flexion
Original PCSA values
Adjusted PCSA values
Extension
Original PCSA values
Adjusted PCSA values
Left lateral b end
Original PCSA values
Adjusted PCSA values
than the values used in the mo del
The mo del requires the maximum muscle intensity as an input The value of
Ncm has b een used although this is a somewhat arbitrary choice lying within
Results and Validation
the range of values used by other authors Ncm Guzik et al de
termined the maximum muscle intensity exp erimentally based on the measured
momentandmuscle area of individual sub jects They rep ort muscle intensities of
Ncm Ncm and Ncm during exion extension and left lateral
bend resp ectively However the calculation of muscle intensity assumed no an
tagonist muscle activity such that the measured exion moments were generated
solely by the rectus ab dominis and internal and external obliques that during
extension the psoas ma jor quadratus lumborum erector spinae and latissimus
dorsi were the only activemuscles and that no muscles on the ipsilateral side as
the lateral b end exertion w ere active during lateral bend Thus the calculated
muscle intensities do not account for the net recorded moments b eing lower than
the moments pro duced by the agonist muscles As Figure illustrates there is
considerable antagonist muscle activity during some exertions confounding the
calculation of muscle intensity Although the values of muscle intensity rep orted
by Guzik et al are questionable they do indicate the p otential for di er
ent muscle groups to have di erent force pro ducing capacities If the muscles of
the lumbar region are considered to consist of three groups the dorsal muscles
the rectus ab dominis and the obliques the e ect of di ering the muscle intensity
between groups can b e considered Figure displays the predicted moments in
exion extension and lateral bend exertions in upright standing using muscle
intensities of Ncm for the dorsal muscles Ncm for the rectus ab domi
nis and Ncm for the oblique muscles These values were chosen to re ect
the pattern observed in the values rep orted by Guzik et al The mo
ments predicted using a constant muscle intensity of Ncm are also included
in Figure for reference to previously rep orted results The use of di erent
maximum muscle intensities results in a decrease in the extension and lateral
b end moments and an increase in the exion moments changes which bring the
mo delled data closer to the mean moments rep orted in the exp erimental studies
Validation of the mo del
350
300 Study 1 250 Study 2 Study 7 200 Study 8 Model 1 150 Model 2 100
Flexion moment (Nm) 50
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Maximum exion exertion
350
300 Study 1 250 Study 2 Study 7 200 Study 8 Model 1 150 Model 2 100
Extension moment (Nm) 50
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Maximum extension exertion
250 Study 1 200 Study 2 Study 3 Study 7 150 Study 8 Study 9 100 Model 1 Model 2 50 Lateral bend moment (Nm) 0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Maximum left lateral b end exertion
Figure Comparison of predicted moments using a maximum muscle
intensity of Ncm for all muscles Mo del and muscle intensities of
and Ncm for the dorsal muscles rectus ab dominis and oblique muscles
resp ectively Mo del to exp erimentally derived sample b ounds
Results and Validation
There are many de ciencies in the input data required in the mo del The discus
sion ab ove highlights these de ciencies and tries to explore the impact they may
have on the mo del results presented The validity of the assumptions made in
the mo del were also investigated with reference to the mo del predictions Overall
the mo del app ears to adequately predict the maximum muscle moments It is
unrealistic to exp ect the mo del to match the exp erimental data exactly given
the anatomy used is for one p erson whichmayormay not match that of the vol
unteer p opulation and the unknown reliability of some of the input data The
novel techniques develop ed to approximate the lines of action of oblique muscles
fascicles crossing the ribs and the TLF app ear to enhance the anatomical reality
of the mo del although direct validation is not p ossible using currently published
data
The primary aim of developing a detailed anatomical mo del was to provide a
to ol with which to investigate the biomechanical changes resulting from various
muscle injuries particularly those induced by surgery The mo del develop ed
contains the detail required to do this as highlighted by the examples given in
Chapter Although many mo di cations to the mo del have b een discussed the
mo del in its original form with original input data has b een used for the clinical
examples explored in Chapter
Chapter
Application of the mo del
The mo del was applied to simulate three typ es of muscle injury which commonly
arise as a result of surgical pro cedures The rst lo oks at the e ect on the spine
of the p ermanent muscle injury resulting from p osterior lumbar surgery The
second example investigates the e ect of reduced ab dominal muscle function re
sulting from retraction of the ab dominal muscles during anterior or anterio lateral
surgery The nal example investigates the impact on the spine of the detach
ment of the psoas ma jor muscle from the femur during Total Hip Replacement
THR surgery
The results presented here are designed to illustrate the application of the mo del
The same limitations apply as discussed in Chapter since the same input data
and assumptions are used These include the unknown reliability of the EMG
data representing muscle activation levels the assumption that the muscle acti
vation levels are the same in all p ostures the assumption that muscles are at their
optimal length in upright stance and have a maximum intensityof Ncm and
that anymovement of the spine is constantly partitioned b etween the joints The
p ostures explored in this chapter have b een restricted to in exion extension
and lateral b end and in axial twist to avoid the problems identi ed in Section
Application of the mo del
during extreme exion The terms intact and normal have b een used to
refer to the complete uninjured spinal system
Posterior lumbar surgery
A p osterior approach to the lumbar spine requires muscles to be dissected from
theregionofinterest so that surgeons can gain access to the required structures
The metho d recommended by Harms for p osterior fusion requires muscles
to b e removed from the spinous pro cesses and laminae on b oth sides of the spine
laterally to the level of the transverse pro cess To simulate the injury induced
by this approach at various levels of the spine the muscles listed in Table
were deactivated bilaterally During the simulations it was assumed that only
the muscle fascicles listed in Table were disabled or injured by the surgery
and that the activation levels for other muscles are unchanged from that of a
normal spine in upright stance Thus the simulations represent the b est p ossible
outcome from the surgery with resp ect to muscle damage
Table Muscles whose function is disabled during p osterior lumbar
surgery at various spinal levels
Muscle Level of surgery
L L L L L S
Multi dus m s m s m t
m s m t m s
m t m s m t
m s m s m s
m t m t m s
m s m t
m t
Longissimus thoracis pars thoracis LT LT LT
LT LT LT
LT LT
Posterior lumbar surgery
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 0
-5
-10 L3/L4 L4/L5 -15 L5/S1 L3/L4 & L4/L5 -20 L4/L5 & L5/S1
-25 % Change in extension moment
-30
Figure Predicted changes in extension moments pro duced during a
maximal extension exertion in upright stance after p osterior surgery at
various spinal levels Changes are expressed as a p ercentage relativeto the
maximum extension momentabletobe generated by the muscles in an intact
spine The legend indicates the level s of surgery
Figure displays the predicted changes in extension moments in upright
stance at all levels of the lumbar spine resulting from the deactivation of the
sp eci ed muscle fascicles for single level and multi level surgery It is exp ected
that the ma jor impact of the simulated changes on the moments able to b e gen
erated by the muscles is in extension since all of the a ected muscle fascicles
can be classed as extensors of the spine
The mo del predicts that deactivation of the sp eci ed fascicles results in a consid
erable decrease in the maximum moments able to be generated by the muscles
ab out all joints particularly L L and L S For single level surgery it app ears
that surgery at the L L level has a larger impact on the moments able to be
generated ab out L S compared to surgery at L L reduction compared
to an reduction while surgery at the L S level has a larger impact com
pared to other levels of surgery on the moments able to b e generated ab out L L
and L L Similar patterns are seen in two level surgery but the magnitudes
Application of the mo del
of the predicted changes are larger Interestingly the smallest change in the
extension moments able to be develop ed by the muscles after p osterior surgery
o ccurs at the joint immediately rostral to the level of surgery These results
indicate there is a considerable decrease in the moments able to b e generated by
the muscles ab out joints remote from the level of surgery
The compressive and shear forces exp erienced bytheintervertebral discs IVDs
following p osterior surgery during exertions in upright stance are displayed in
Table In all exertions the compressive forces decrease from that exp erienced
by a normal spine This change is also exp erienced by the IVDs remote to
the level of surgery see Figure An interesting relationship exists between
the changes in anterior p osterior AP shear at the joints involved in two level
surgery It app ears that during two level surgery the rostral op erative level
exp eriences a decrease in AP shear while the caudal level exp eriences an increase
This relationship occurs during all exertions and is indep endent of the change
exp erienced by the joints during single level pro cedures Results also indicate
that the lateral shear exp erienced by the IVDs during lateral b end exertions can
change directions following p osterior surgery
The in uence of p osture on the changes in extension moments compression and
shear during maximal extension exertions following p osterior surgery is displayed
in Figure for L L The results for other joints are displayed in App endix
I The changes in the extension moment in exed laterally bent or twisted
p ostures is comparable to those seen in upright stance The largest reduction
in extension moments following p osterior surgery o ccurs in extended p ostures at
the L L joint The large di erence observed between the changes in extension
moment in extended p ostures versus other p ostures at L L diminishes at caudal
AP shear is the AP force exp erienced at the ICR Since the ICRs generally lie within
the lower vertebra of the joint a p ositive shear is equivalent to the lower vertebra of a joint
exp eriencing an anterior force This situation is commonly referred to as p osterior shear by
clinicians
Posterior lumbar surgery
Table Maximum forces N exp erienced by the intervertebral joints at
the level of surgery in the upright stance ve AP shear values represent
shear in the anterior direction while ve lateral shear is towards the left
The p ercentage change in the magnitude of the force from that exp erienced
by an intact spine is expressed in brackets
Exertion Level of surgery
Moment Single level Two level Two level
L L L L L S L L L L L L L S
Extension
Compress
AP shear
Lat shear
Flexion
Compress
AP shear
Lat shear
Left lateral bend
Compress
AP shear
y y y y
Lat shear
Left axial twist
Compress
AP shear
Lat shear
y
The direction of the force changed as a result of the muscle injury caused by p osterior surgery
joints such that there is minimal di erence between the p ostures at the L L
and L L joints App endix I In contrast the reductions exp ected in joint
compression show little p ostural variation At all levels p osterior surgery results
in a reduction of AP shear in extended laterally b ent and twisted p ostures In
exed p ostures the AP shear decreases in magnitude at L L L L and L S
and has mixed changes at L L and L L dep ending on the level of surgery
The magnitude of the lateral shear exp erienced b y the IVDs decreases in laterally
bent and twisted p ostures at all joints for all levels of surgery investigated
To date no study has been conducted to investigate if or how the body adjusts
to the muscle dysfunction induced by p osterior surgery If the body do es not
Application of the mo del
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -5 -1 -10 -2 -15 -3 -20 -4 -25 -5
moment -30 L3/L4 -35 L4/L5 -6 -40 L5/S1 -7 % change in extension -45 L3/L4&L4/L5 -8 % change in compression
-50 Posture L4/L5&L5/S1 -9 Posture
a Extension moments b Compressive forces
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 -12
% change in AP shear -12 -14 % change in lateral shear
-14 Posture -16 Posture
c AP shear forces d Lateral shear forces
Figure Predicted changes in the maximum moments and forces able to
be generated by the muscles ab out L L during a maximal extension
exertion inavarietyof p ostures following p osterior spinal surgery at various
levels The legend in a applies to all graphs The p ostures used were
exion extension and lateral b end and axial twist
adjust to the change then the patient will have decreased strength ab out joints
remote from the level of surgery This in turn may lead to p otential injury if the
patient tries to undertake activities requiring near maximal extension e orts
y be as low as In fact the exertion required to lead to muscular injuries ma
of the maximal extension e ort dep ending on the number and levels of
surgery and the p osture Figure Alternatively the body may comp ensate
for the loss in strength by increasing the activation of other muscles crossing
the region If this o ccurs then the muscles exp eriencing higher activation may
be sub ject to the earlier onset of fatigue and fatigue related injuries Although
Posterior lumbar surgery
the problems asso ciated with decreased strength may be initially overcome by
avoiding strenuous activities such as heavy lifting maximal exertions can also
be achieved involuntarily by other means such as sneezing muscle spasms and
cramps
The mo del results indicate that there is a reduction in joint compression of
between and at all levels in all p ostures following p osterior surgery
Gardner Morse Stokes and Laible and Cholewicki and McGill sug
gest that the stability of the spine is related to joint compression with increased
stability b eing asso ciated with increases in compression Based on this result
it might be hyp othesised that the muscle impairment resulting from p osterior
surgery reduces the stability of the spine by reducing the compressive forces
However the exact nature of the relationship between stability and compres
sion is unknown and as such the true implications of the reduced compression
resulting from p osterior surgery are indeterminable
Posterior surgery is the most common approach used to access the spine for
surgical pro cedures such as laminectomies fusion and other forms of xation
Although joint immobilisation has not been incorp orated in to this example it
is easily done if information ab out the altered spinal kinematics is available
Should this be included the mo del will provide valuable information ab out
the forces and moments which are likely to be exp erienced by the immobilised
joint implanted instrumentation combination in vivo Most pieces of surgical
instrumentation have b een sub jected to mechanical testing to determine the fail
ure strength and or sti ness e g Lo e er Stanford Stanford and Walsh
This information is used by many surgical houses to promote their pro ducts as
stronger than their comp etitors Indeed some orthopaedic surgeons cho ose a
system purely b ecause it is stronger This practice has develop ed as a strat
egy to minimise the p otential for instrument related complications after surgery
Application of the mo del
However the ultimate failure strength of instrumentation is irrelevant provided
that the failure strength is signi cantly larger than the physiological loads likely
to be exp erienced in vivo What is more imp ortant when considering the likely
success of the surgery is the p erformance of the complete implant system relative
to the physiological loads likely to b e exp erienced Hence in addition to testing
failure mechanical testing should try to represent realistic activities by coupling
extension bend and twist forces in the magnitudes likely to be exp erienced in
vivo and testing for fatigue related failure The mo del may be applied to the
study of implants by providing estimates of all the forces to which they are likely
to b e exp osed
Impairment of ab dominal muscles
Some surgical techniques such as anterior lumbar interb o dy fusion require the
surgeon to makeananterior or anterio lateral approach to the spine Fraser and
Gogan rep ort an extrap eritoneal approach for such surgery where the left
external oblique and rectus ab dominis muscles are split along the line of their
bres by blunt dissection These muscles are then retracted to allow access to the
underlying structures This technique is rep orted to minimise muscle damage to
the ab dominal muscles since the rectus ab dominis and external oblique muscles
are split not transected while the internal oblique and transverse ab dominis
su er no incision at all
However it has b een observed by the author that retraction of muscles during
surgery interrupts the blo o d ow through the bres causing muscle discoloura
tion and slower weaker twitch resp onses These changes might be exp ected to
be temp orary but the time until normal function returns is unknown Gejo
Matsui Kawaguchi Ishihara and Tsuji rep ort that impairment of the
Impairment of ab dominal muscles
multi dus muscle following retraction during p osterior lumbar surgery is related
to retraction time with changes lasting in excess of months in cases requiring
retraction for longer than minutes It can only b e assumed that the e ect of re
traction on the ab dominal muscles pro duces similar results Additionally Fraser
and Gogan rep ort that retraction of the rectus medially as suggested
denervates that part of the rectus ab dominis which lies between the transverse
ab dominis and the internal oblique Although this injury is describ ed as not
clinically imp ortant there must be some asso ciated biomechanical changes
Toinvestigate the impact of these changes simulations were conducted using the
mo del with partially reduced left rectus and left external oblique function There
is no indication of how much the muscle function is reduced in reality so the
simulation has been conducted under three di erent scenarios Table Per
manent muscle impairmentis asso ciated with the denervation of the left rectus
ab dominis while temp orary muscle impairment is related to the injuries resulting
from retraction It is assumed that the external oblique muscle is split between
fascicles Ext and Ext and that the asso ciated retraction injury is con ned to
these two comp onents Scenario represents a mo derate level of p ermanentand
temp orary muscle injury while scenario represents a more severe temp orary
injury The third scenario mo dels minimal muscle injury The values used to
simulate the p ermanent injury to the rectus ab dominis are relatively low since
only part of the muscle is denervated by the surgical pro cedure A wider range
of values have been used to represent the temp orary muscle injuries since it has
been rep orted that retraction injuries are related to retraction time Gejo et
al
The maximum moments able to be generated by the muscles in each of the
mo delled scenarios are displayed in Figures to for exion extension
wist exertions The moments predicted by the mo del lateral bend and axial t
representing the p ermanent injury alone show very little if any change from
Application of the mo del
Table Simulated scenarios representing temp orary impairment of the
left rectus ab dominis and external oblique and p ermanent impairmentofthe
left rectus ab dominis following anterior lumbar interb o dy fusion Impairment
is expressed as a p ercentage of the function in a normal spine
Scenario Rectus ab dominis External oblique
Permanent Temp orary Ext and Ext
that of the intact spine This is a result of the relatively low level of impairment
or and the fact that the rectus ab dominis do es not pro duce signi cant
moments other than exion As a consequence only the changes resulting from
the combined temp orary and p ermanent injuries have been included in these
gures
During exion and extension exertions the asymmetry in the muscle function
generates coupled right lateral bend and left twist moments Scenario rep
resents the largest muscle impairment and consequently generates the largest
coupling of rotations Under this condition the lateral b end moment asso ciated
with extension exertions decreases from Nm at L L to Nm at L S while
the coupled axial twist moments are in the order of Nm Lateral bend mo
ments are slightly larger during exion exertions decreasing from Nm at L L
to Nm at L S whereas the coupled axial twist moments are of the same
magnitude as obtained during extension exertions
Impairment of ab dominal muscles
120
100
80 Normal Scenerio 1 60 Scenerio 2 Scenerio 3 40 Flexion moment (Nm) 20
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Flexion moments
25
20
15 Normal Scenerio 1 Scenerio 2 10 Scenerio 3
5 Lateral bend moment (Nm)
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Lateral b end moments
12
10
8 Normal Scenerio 1 6 Scenerio 2 Scenerio 3 4
Axial twist moment (Nm) 2
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Axial twist moments
Figure Maximum moments that may be generated by the muscles
during a maximal exion exertion in a spine with reduced ab dominal muscle
function and an intact spine ve bend moments are to the right while ve
twist moments are to the left The three scenarios are describ ed in Table
Application of the mo del
In addition to the development of asymmetric moments the reduced muscle func
tion alters the magnitude of the exion and extension moments obtained during
the resp ective exertions As Figure illustrates there are noticeable decreases
in the exion moments develop ed during exion exertions for the combined tem
p orary and p ermanent injuries This decrease is largest at L L during scenario
where the momentisapproximately lower than in an intact spine
The decrease in ab dominal muscle function results in an increase in the magni
tude of the extension moments able to be generated This change is largest at
L L and L S Figure
The biomechanical changes induced by the prop osed muscle injury di er for right
and left lateral b end exertions The changes are more severe during attempted
left lateral b end since it is the left ab dominal muscles which have b een a ected
Consequently the maximum lateral b end moments develop ed during left lateral
bend exertions decreases by up to scenario The lateral b end moments
generated during right lateral bend exertions increase marginally although the
changes are less than at all levels The axial twist moments coupled with
lateral b end exertions also change with the p ercentage change exp erienced b eing
larger than the changes pro duced in the lateral b end moments
The largest changes which o ccur as a result of the injury to the rectus ab do
minis and external oblique muscles are seen during axial twist exertions The
an increase of up to in the axial twist moments simulated injury causes
develop ed during left twist exertions Twist exertions to the right result in de
creased axial twist moments Again these decreases are largest under scenario
at approximately The moments coupled with axial twist exertions are also
sub ject to large changes as displayed in Figure
The development of lateral b end and axial twist moments during exion and
extension exertions is a situation which would not usually be exp erienced by
Impairment of ab dominal muscles
250
200
150 Normal Scenerio 1 Scenerio 2 100 Scenerio 3
Extension moment (Nm) 50
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Extension moments
25
20
15 Normal Scenerio 1 Scenerio 2 10 Scenerio 3
5 Lateral bend moment (Nm)
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Lateral b end moments
12
10
8 Normal Scenerio 1 6 Scenerio 2 Scenerio 3 4
Axial twist moment (Nm) 2
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Axial twist moments
Figure Maximum moments that may be generated by the muscles
during a maximal extension exertion inaspine with reduced ab dominal
muscle function and an intact spine ve b end moments are to the right ve
twist moments to the left The three scenarios are describ ed in Table
Application of the mo del
30 30 20 20 10 10 0 0 -10 -10 -20 -20 -30 -30 Normal -40 Scenerio 1 -40 Flexion moment (Nm) Flexion moment (Nm) -50 Scenerio 2 -50 Scenerio 3 -60 -60
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Flexion moments during left lateral b end b Flexion moments during right lateral
exertion b end exertion
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 200 0 180 -20 160 -40 140 -60 120 -80 100 -100 80 -120 60 -140 40 -160 20 Lateral bend moment (Nm) -180 0 Lateral bend moment (Nm)
-200 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Lateral b end moments during left lateral d Lateral b end moments during right lat
b end exertion eral b end exertion
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 45 0 40 -5 35 -10 30 -15 25 -20 20 -25 15 -30 10 -35 5 Axial twist moment (Nm) Axial twist moment (Nm) -40 0
-45 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
e Axial twist moments during left lateral f Axial twist moments during right lateral
b end exertion b end exertion
Figure Maximum moments that may be generated by the muscles
during maximal left and right lateral b end exertions in a spine with reduced
ab dominal muscle function and an intact spine ve bend moments are to
the right while ve twist moments are to the left The legend in a applies
to all graphs The three scenarios are describ ed in Table
Impairment of ab dominal muscles
40 40 20 20 0 0 -20 -20 -40 -40 -60 -60 -80 Normal -80 Scenerio 1 -100 -100 Scenerio 2 Flexion moment (Nm) Flexion moment (Nm) -120 Scenerio 3 -120 -140 -140
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Flexion moments during left axial twist b Flexion moments during right axial twist
exertion exertion
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 70 0 60 -10 50 -20 40 -30 30 -40 20 -50 10 -60 Lateral bend moment (Nm) Lateral bend moment (Nm) 0
-70 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Lateral bend moments during left axial d Lateral b end moments during right axial
twist exertion twist exertion
50 L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 45 0 40 -5 35 -10 30 -15 25 -20 20 -25 15 -30 10 -35
Axial twist moment (Nm) 5 -40 Axial twist moment (Nm) 0 -45
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 -50
e Axial twist moments during left axial f Axial twist moments during right axial
twist exertion twist exertion
Figure Maximum moments that may be generated by the muscles
during maximal left and right axial twist exertions in a spine with reduced
ab dominal muscle function and an intact spine ve bend moments are to
the right while ve twist moments are to the left The legend in a applies
to all graphs The three scenarios are describ ed in Table
Application of the mo del
the body The implications of this change are unknown since little is known
ab out how the neuro muscular system adapts to muscular injury For instance
do the muscle activation patterns and or activation levels change to prevent the
coupled lateral b end and axial twist moments developing at all or are the coupled
moments detected by proprio ceptive sensors in the muscles and joint capsules
and consequently corrected If the muscle activation patterns do change it is
unlikely that this change occurs automatically following surgery Instead it is
more probable that the new muscle activations are a learnt b ehaviour In either
case the intervertebral joints are sub ject to unnatural b end and twist moments
either temp orarily if the body learns new activation patterns or p ermanently
if the moments are controlled by proprio ception These additional moments
are equivalent to the spine working in a bent or twisted p osture all the time
The e ect this has on the low back is unknown but it maybehyp othesised that
the generation of unbalanced moments and forces predisp oses the intervertebral
joints or other comp onents of the spine to injury particularly during sudden
movements or rep etitive activities
It is exp ected that the injury to the ab dominal muscles would result in a decrease
in the exion and twist moments able to b e generated since the injured muscles
are primarily resp onsible for generating these moments This loss of strength
might be comp ensated for by recommending that a patient not p erform tasks
which overload the muscles during exion or twist exertions The increase in
extension moments asso ciated with ab dominal impairment is a result of a de
crease in the antagonistic moment generated by the ab dominal muscles The
implications of this change need further consideration
During extension exertions the ab dominal muscles pro duce a signi cantmoment
which works against the moments pro duced by the muscles lo cated p osterior to
of these antagonist muscles is the spine It has b een suggested that the role
Impairment of ab dominal muscles
Scenario 3
Injuried Stability Strength Scenario 1
Normal
0% 25% 50% 75% 100%
Agonist moment
Figure Prop ortion of agonist momentwhich can b e attributed to
providing stability during maximal extension exertions under the simulated
scenarios
to provide stability Gardner Morse et al Cholewicki and McGill
Cholewicki Juluru and McGill If it is assumed that this is the sole role of
the antagonist muscles then a corresp onding comp onent of the moment pro duced
by the agonist muscles go es toward counteracting the action of the antagonists
In this way the moment pro duced by the agonist muscles can be thought of
as consisting of two comp onents stability and strength Figure displays the
prop ortion of the agonist moment whichmay b e classi ed as stability or strength
under the di erent scenarios mo delled
As the amount of antagonist activity decreases due to injury of the ab dominal
muscles the prop ortion of the agonist moment attributed to strength increases
at the exp ense of stability During maximal extension exertions under scenario
the stability of the lumbar spine decreases by relative to the intact
spine This is a large change which can not be overlo oked Cholewicki and
McGill suggest that a reduction in spinal stability could b e imp ortantin
the aetiology of chronic low backpain The simulations discussed ab ove indicate
that the largest changes in stability are asso ciated with temp orary muscle injury
Application of the mo del
o ccurring in resp onse to retraction of muscles during surgery This temp orary
loss of stabilitymayhave implications for the rehabilitation of patients since this
period of reduced stability provides a window of opp ortunity in which to injure
the spine
Although retraction injuries to the ab dominal muscles have b een simulated sim
ilar injuries to the dorsal muscles such as the multi dus o ccur during p osterior
surgery Gejo et al The progress of recovery from the retraction injury
needs to b e investigated further in order to develop optimal rehabilitation strate
gies If the rate of muscle recovery is rapid so on after surgery then a few days
of relativ ely little movement immediately following surgery may help to reduce
the p otential for further injury While it might b e app ealing to suggest that pa
tients undertake simple activities likewalking or sitting Cholewicki and McGill
and Gardner Morse et al b oth rep ort that the stability of the
lumbar spine diminishes during p erio ds of low muscular activity meaning that
even the simplest tasks requiring little muscle involvement still have the p oten
tial to injury the spine This go es against the current rehabilitation principle
that it is imp ortantto get the patient moving as so on as p ossible after surgery
This is only one p ossible scenario but it do es highlight the need to investigate
further how the body recovers from muscle injuries This knowledge will then
ensure that patients receive the typ e of rehabilitation which b est suits the total
complement of injuries sustained
Total Hip Replacement surgery
During THR surgery some surgeons detach the psoas ma jor muscle from its
femoral attachment This allows the surgeon greater freedom to rotate the femur
giving better exp osure of the proximal end However the femoral attac hment
Total Hip Replacement surgery
of the psoas ma jor muscle is not generally reattached at the end of surgery
creating a p ermanent biomechanical change This has an impact on the moments
develop ed ab out the lumbar spine since the rostral attachment of the psoas ma jor
muscle is within this region of the spine
To simulate the e ect of THR the right psoas ma jor muscle was deactivated in
the mo del The muscle was deactivated uni laterally since it is most common for
patients to have only one hip replaced at a time
In the mo del the psoas ma jor muscle is assumed to b e most active during exten
sion exertions Thus the largest changes in muscle forces and moments resulting
from deactivation of the psoas ma jor muscle are also exp ected during these ex
tension exertions Figure displays the predicted muscle momen ts asso ciated
with a maximal extension exertion in the upright stance The extension mo
ments develop ed by the muscles during this exertion are not much di erent to
those develop ed in an intact spine However extension exertions in the mo d
i ed system generate coupled lateral bend and axial twist moments during an
action which was previously symmetric Figure The coupled lateral b end
moments increase from L L to L S suchthatatL S the momentof Nm
is approximately of the lateral bend moment develop ed during a maximal
lateral b end exertion at that joint The direction of the lateral bend moment
generated is contralateral to the deactivated psoas ma jor muscle The coupled
axial twist moment is ipsilateral to the deactivated psoas ma jor muscle and is
largest at L L Nm This represents approximately of the twist moment
able to b e develop ed during a maximal axial twist exertion using EMG Norm
B data
The development of lateral bend and axial twist moments during an extension
exertion is a constant feature in the mo di ed system irresp ective of spinal p os
ture Interestingly the di erence in magnitude of these moments from those
Application of the mo del
250 Intact Psoas deactiv. 200
150
100
50 Extension moment (N)
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Extension moments
35 30 25 Intact 20 Psoas deactiv. 15 10 5 Lateral bend moment (Nm) 0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
b Lateral b end moments
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 0 -1 -2
-3 Intact -4 Psoas deactiv. -5 -6
Axial twist moment (Nm) -7
-8
c Axial twist moments
Figure Moments generated by the muscles during a maximal extension
exertion in upright stance in an intact spine and one which has had the right
psoas ma jor muscle deactivated ve bend and twist moments are to the left
Total Hip Replacement surgery
develop ed in the intact spine is also relatively constant irresp ective of the p os
ture adopted For lateral b end moments these di erences are always contralateral
to the deactivated psoas ma jor muscle with values of Nm at L L Nm
at L L Nm at L L Nm at L L and Nm at L S The
axial twist moments follow a similar trend although the moments in the mo di ed
system are always more ipsilateral such that the axial twist moments are larger
in the mo di ed system when the twist moments in the normal spine are towards
the right e g during postures such as right lateral bend and left axial twist
and smaller when the moments in the normal spine are to the left e g during
left lateral b ending or right axial twist The magnitude of the di erences is
approximately Nm at L L and L L and Nm at the lower joints
The impact of unilateral deactivation of the psoas ma jor muscle on the forces
exp erienced by the IVDs during a maximal extension exertion in upright stance
is illustrated in Figure Irresp ective of the spinal p osture adopted the com
pressive forces exp erienced by the IVDs are reduced in the mo di ed system The
magnitude of the AP shear also decreases when the shear acts anteriorly but
increases relative to the shear in the intact spine when the shear in the normal
system acts p osteriorly Although changes in compression and AP shear result
from the deactivation of the psoas ma jor muscle the most noticeable change
o ccurs in lateral shear In the mo di ed system the IVDs are sub ject to lateral
shear during extension in sagittally symmetric p ostures when there was previ
ously none in the intact spine This lateral shear is largest at L S N and
acts contralateral to the deactivated psoas ma jor muscle The lateral shear de
velop ed during symmetric p ostures acts as a constantbywhich the lateral shear
values are o set relativetothevalues in the normal spine for all other p ostures
The developmen t of asymmetric moments during symmetric tasks following THR
surgery raises the same issues as discussed previously in relation to the asym
metry intro duced by impaired ab dominal muscle function Section These
Application of the mo del
7000
6000
5000 Intact 4000 Psoas deactiv. 3000
Compression (N) 2000
1000
0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
a Compressive forces
900 800 700
600 Intact 500 Psoas deactiv. 400 300 AP shear (N) 200 100 0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1 b AP shear forces
140 120 100 Intact 80 Psoas deactiv. 60 40 Lateral shear (N) 20 0
L1/L2 L2/L3 L3/L4 L4/L5 L5/S1
c Lateral shear forces
Figure Forces generated by the muscles during a maximal extension
exertion in upright stance in an intact spine and one which has had the right
psoas ma jor muscle deactivated ve AP and lateral shear are to the anterior
and left resp ectively
Total Hip Replacement surgery
include the lack of understanding of how the body adjusts to the changes in
tro duced by surgery and the p otential for the unnatural coupled moments to
increase the risk of injury to the IVDs
The change in compression exp erienced by L L and L S equates to an
reduction from that exp erienced by the normal spine Gardner Morse et al
and Cholewicki and McGill suggest that the stabilityof the spine
increases with joint compression Based on this result it mightbehyp othesised
that uni lateral deactivation of the psoas ma jor muscle reduces the stabilit y of
the spine via reduced compressive forces Gardner Morse et al also rep ort
that during extension exertions the primary mo de of buckling is lateral b ending
Thus it might also be hyp othesised that this buckling characteristic may be
enhanced by the additional lateral shear force exp erienced by the IVDs after
uni lateral psoas ma jor deactivation Both of these hyp otheses suggest that
the uni lateral deactivation of the psoas ma jor muscle may increase the risk of
injury to the spine The magnitude of this increase in risk is unknown since
there have b een no studies investigating the biomechanical changes in lumbar
m uscle function following THR surgery The risk of injury may not increase
signi cantly if the muscles act to restore the compressive forces exp erienced in
a normal spine However if the muscle activation levels change so that the
moments are balanced but at the lower level of compression then the risk of
injury maychange considerably In order to assess the true impact of uni lateral
deactivation of the psoas ma jor muscle further research is needed particularly
with resp ect to investigating how the neuro muscular system resp onds to the
changes induced by surgery
Application of the mo del
Conclusion
The use of the mo del to simulate the e ect of a variety of muscle injuries oc
curring as a result of surgical intervention has b een demonstrated by the three
examples discussed in this chapter Such applications are not p ossible using
most other anatomical mo dels since there is insu cient anatomical detail to ad
equately mimic the injuries sustained In contrast the mo del which has b een
develop ed is well suited to such studies since it represents the muscles using mul
tiple fascicles allowing sp eci c injuries to be repro duced it is three dimensional
and also has the option to customise the muscle and kinematic data for sp eci c
individuals
The three examples discussed di er in the typ e and lo cation of the muscle injury
sustained However all three examples share a common result reduced stability
resulting from either reduced joint compression or reduced antagonist activity It
is interesting to note that the largest changes are exp ected following THR surgery
even though this surgery is remote from the spine Also worthy of comment is
the fact that the examples represent the minimum injury which o ccurs in each
approach It is probable that the actual injuries sustained exceed those mo delled
For instance the p osterior surgery example in Section simulated the changes
resulting from the removal of muscle fascicles from the vertebrae to gain access to
the joint requiring surgery The injuries sustained by other muscles a ected by
surgery via retraction are not included This is an imp ortant p oint to consider
when assessing the impact of the surgery since the loss due to retraction injuries
can be signi cant as illustrated by the example in Section
Although the illustrative examples used in this Chapter are based on injuries re
sulting from spinal surgery or total hip replacement the application of the mo del
extends far beyond this For instance the inclusion of the detailed ab dominal
musculature in the mo del allows the e ect on the spine of any ab dominal surgery
Conclusion
to b e assessed Although the mo del has the p otential to b e applied to many sit
uations its use is currently limited by a lack of understanding of how the body
resp onds to the various injuries and biomechanical changes exp erienced The
examples given have made a number of assumptions regarding movement of the
spine and muscle activations following surgery namely that they don t change
from normal values It is unlikely this is the case Only when this information
b ecomes available can the mo del b e used to its full p otential This includes simu
lating di erent surgical techniques in order to investigate the likely biomechanical
changes intro duced investigating the moments develop ed ab out the spine dur
ing rehabilitation exercises for b oth surgically induced and naturally o ccurring
injuries and exploring the forces and moments exp erienced within spines su er
ing spinal deformities such as scoliosis and abnormal kyphosis and the exp ected
changes intro duced by the correction of such deformities Additionally the mo del
could b e used to investigate the development of conditions resulting from muscle
imbalances e g paralytic scoliosis and suggest strategies for the correction of
these condititions through electrical stimulation of the muscles Investigating
the internal forces and moments in these di erent situations is fundamental if
researchers and clinicians are to truly understand the consequences of muscular
injury and the e ect this has on the aetiology of chronic lowback pain
Chapter
Conclusions and directions for
further research
Over the past three decades there has been an increasing interest in the biome
chanics of the lumbar spine This interest has b een primarily driven by the lack
of understanding of the aetiology of low back pain and the factors which may
predisp ose p eople to it Although many mechanical studies of spinal comp onents
have b een conducted biomechanical mo delling remains the only non invasiveway
to explore the interactions of the lumbar spine its muscles and other soft tissues
There is no shortage of biomechanical mo dels which predict the distribution of
forces within the various force pro ducing comp onents of the lumbar region and
the forces and momen ts exp erienced by the intervertebral joints Chapter re
views some of the more p opular mo dels which have been develop ed There has
been a trend in more recent mo dels to include more detailed anatomical infor
mation of the lumbar region This is an acknowledgement by researchers of the
imp ortance of the realism of the anatomical mo del on which force and moment
predictions are based
The level of anatomical detail contained within a biomechanical mo del not only
Conclusions and directions for further research
a ects the predictions from the mo del but also the potential application of
the mo del to simulate di erent scenarios Past mo dels have concentrated on
ergonomic issues primarily related to investigating the forces and moments exp e
rienced by the intervertebral joints in a variety of p ostures and also determining
safe lifting loads and lifting techniques Although these are imp ortant issues
there are many others which could also b e addressed using biomechanical mo dels
The initial aim of this researchwas to investigate the p otential use of biomechan
ical mo dels to predict biomechanical changes resulting from muscle injury Few
existing mo dels contain enough anatomical information to accurately mimic mus
cle injuries which may o ccur from muscle strain and overuse or muscle injuries
whic h result from surgical pro cedures As well as not containing enough detailed
information some comp onents of the lumbar musculature such as the ab dominal
oblique muscles and the transverse ab dominis are p o orly represented Thus a
new anatomical mo del has b een develop ed to overcome some of these di culties
The three dimensional anatomical mo del develop ed in Chapter uses multiple
fascicles to represent muscles Co ordinates for the attachment points for each
fascicle were determined using a D reconstruction of a human spine or using
similar information as rep orted by other authors Once the attachment co or
dinates were known lines of action were determined for each fascicle Because
of the ne detail intro duced by using muscle fascicles most muscles were as
sumed to have a straight line of action b etween the attachment p oints Di erent
techniques were used to determine the lines of action for the psoas ma jor and
external and internal oblique muscles due to constraints imp osed by the anatomy
Additionally a mo del was develop ed to represent the action of the TLF which
forms the attachment point to the spine for the transverse ab dominis muscle
The mo del also and parts of the internal oblique and latissimus dorsi muscles
provides a check that the lines of action for the fascicles of the longissimus tho
racis pars thoracis and the ilio costalis pars thoracis do not violate the constraints
imp osed on them by the thoracic and lumbar vertebrae and ribs
The muscle attachment p oints lines of action maximum forces and spinal geom
etry are the comp onents required to predict the forces and moments generated
by the musculature and exp erienced by the intervertebral joints One of the
advantages of developing a Dmo del of this typ e is that information on muscle
moment arms traditionally required in transverse cutting plane mo dels b ecomes
redundant This allows the spine to be rotated to any p osture without having
to approximate the muscle moment arms in the new p osture
The mo del develop ed is a representation of the anatomy and mak es no attempt
to address other biomechanical issues such as maintaining equilibrium ab out
the joints To avoid the numerous issues asso ciated with allo cating forces to
individual muscles in such a way as to maintain equilibrium with the external
loads the mo del was applied using muscle activation information in the form of
EMG data Although the reliability of this data has been questioned Section
EMG data was used since it was assumed that the sub jects from which
EMG data was obtained would activate their muscles in suchasway as to main
tain equilibrium within the spine thus providing muscle activation data which
approximates that under equilibrium conditions The validation of the mo del
predictions for a normal intact spine Chapter reveals that the mo del p er
forms well during exion extension and lateral bend exertions The predicted
moments for axial twist exertions are lower than those recorded exp erimentally
but p otential reasons for this have b een discussed Section
Having ascertained that the mo del pro duces realistic estimates of the moments
exp erienced by the intervertebral joints the application of the mo del to spines
exp eriencing muscle injury was demonstrated Chapter The examples used
all relate to muscle injuries resulting directly from surgical intervention although
simulation of other injuries could have just as easily b een p erformed The results
Conclusions and directions for further research
from these simulations suggest that any interference with the muscles of the
lumbar region reduces the compressive forces exp erienced by the spine This in
turn may result in a reduction in spinal stability
The mo del which has b een develop ed forms the basis from which more mo delling
work could evolve The mo del currently only considers the musculature of the
lumbar spine This su ces for the current application of the mo del but a more
complete representation of the spinal anatomy could be achieved by including
other structures such as the ligaments and discs Additionally some of the prob
lems highlighted during axial twist exertions could be addressed by extending
the mo del to allow movement of the thoracic spine and incorp orating some of
the ma jor muscles attaching to this region
The mo del develop ed to address the problem of determining the line of action
of the ab dominal oblique muscles Section app ears to p erform well but
several improvements could be made Firstly the development of the torso
assumes that the elliptical shap e changes depth width and lo cation linearly
between the xed endp oints This metho dology do es not account for the lordosis
of the spine nor a waistline This is not a fundamental limitation since the
torsos b eing develop ed are indicative of the shap es de ning each of the oblique
muscles and it is not exp ected that either of the oblique muscles has a waistline
However the lordosis of the spine could be included in the mo del by changing
the constraints placed on the p osition of the center of the ellipse For instance
a two piece spline or an arc or a cubic p olynomial could be used to de ne
the p osition of the centre of the ellipse Each of these alternatives adds to the
complexity of the mo del and one should b e cautious ab out over tting the mo del
given the limited amountofavailable data on muscle attachment points
The second area in which the ab dominal obliques mo del could b e improv ed is in
the rotation of the torso to represent alternative p ostures The current metho d
ology used to rotate the torso inherently assumes that rotation o ccurs ab out the
centre of the S vertebral b o dy This results in the volume of the torso not b eing
conserved particularly at the rostral end of the torso An alternative approach
would be to rotate smaller groupings of the ellipses by the intervertebral angle
for that group This would require linking the torso with the spine in order to de
termine whichlevels should b e rotated bywhichintervertebral angles e g torso
heights to mm might be rotated ab out the L S IAR using the interseg
mental angles for this level heights mm to mm might b e rotated ab out the
L L IAR by the corresp onding intersegmental angles etc This technique will
still not conserve torso volume but it will be an improvement over the current
technique
The mo del of the TLF simulates the characteristics of the middle and p osterior
layers of the TLF by determining realistic lines of action However it was not
p ossible to match the muscle characteristics used in this mo del to those of the
Visible Man due to images of the Visible Man being taken p ost mortem If
the anatomical mo del is applied to other living sub jects this problem will be
resolved The TLF mo del assumes that the area of the erector spinae m uscle is
constant throughout the lumbar spine The assumption was made to simplify the
mo del during development Further work on the TLF mo del could remove this
assumption by incorp orating the changes in muscle size seen across the lumbar
spine thus intro ducing asso ciated changes in the line of action of the p osterior
layer of the TLF
As mentioned previously the anatomical mo del develop ed was designed to im
prove on the anatomical representation currently b eing used in biomechanical
mo dels One avenue for further w ork is to incorp orate this anatomical mo del
into a biomechanical mo del either existing or new to allow comparisons of the
predicted forces and moments to be made with other anatomical mo dels This
Conclusions and directions for further research
will provide the opp ortunity to investigate the relative imp ortance of the novel
techniques develop ed as part of this research The improved anatomical repre
sentation of the oblique muscles will also provide a to ol which can be used to
investigate the role of intra ab dominal pressure in the maintanance of equilibrium
within the spine
The anatomical mo del which has been develop ed is based on the spinal geom
etry of one male cadaver No investigation has b een conducted to determine
how representative this spine is of the general p opulation For use as part of a
biomechanical mo del techniques to scale the current information to match that
of the spinal characteristics under consideration need to be incorp orated This
could b e as simple as rotating and scaling the values to matchtheoverall spinal
length and orientation or more detailed so as to match the dimensions of the
individual vertebrae
Another alteration whichmay bemadetothe anatomical mo del is to convert it
from b eing quasi static to dynamic This could be achieved by incorp orating a
velo city comp onent into the calculation of maximum muscle force
The application of the mo del to surgical scenarios highlights the need for further
clinical research of spinal biomechanics pre and p ost surgery injury As discussed
in Chapter there is little information ab out how the b o dy recovers or adjusts
to injury Nor is there information ab out how the kinematics of individual joints
change after pro cedures such as spinal fusion This typ e of data provides valuable
information ab out the injury pro cess as well as providing input into the mo del
With the incidence of spinal surgery on the increase and new surgical techniques
and instrumentation b eing develop ed it is fundamental that clinicians have an
understanding of the various issues asso ciated with the pro cedure of interest
Currently patients are advised of the p ossible complications with any surgical
technique Ideally the patient should also b e advised of the p otential side e ects
of surgery which include changes to the biomechanics of the spine However it
is not p ossible to do this if these changes are not known The anatomical mo del
which has b een develop ed provides a to ol to investigate these changes however
further clinical research is also required in order for the mo del to be used to its
full p otential
In conclusion a comprehensive anatomical mo del of the lumbar spine has been
develop ed incorp orating novel techniques to simulate the actions of all the ma
jor trunk muscles Simulations of muscle injuries have been p erformed with the
mo del which have provided new insight into the biomechanics of the spine with
muscle injury Further application of the mo del is exp ected to provide advice on
the most appropriate treatments and rehabilitation regimes for patients under
going spinal surgery or who have injured their trunk muscles
App endix A
A study to compare PCSA and
CSA values for the psoas ma jor
muscle
App endix B
Investigation of spinal kinematics
during exion
App endix C
Co ordinates representing the ribs
and vertebrae of the Visible Man
C Posterior margin of the lumbar vertebrae
Section describ es the metho d used to ensure that the lines of action of the
fascicles of the longissimus thoracis pars thoracis remain p osterior to the lumbar
vertebrae To apply this metho dology the p ositions of the p osterior margin of
the vertebrae need to be sp eci ed The values used are listed in Table C and
represent the bony region b etween the spinous and transverse pro cesses
Table C Data p oints representing the base of the right spinous pro cess
near the vertebral body Co ordinates are relativetothe most anterior p oint
on the sup erior endplate of the resp ective vertebra All values are in mm
where ve i is rostral ve j is anterior and ve k is left
Vertebra Data p oints
i j k
L
L
L
L
L
Co ordinates representing the ribs and vertebrae of the Visible Man
C Ribs to
The lo cation of the lower ribs is required in order to apply the metho dology
decrib ed in Section for determining the lines of action of the fascicles of
the ilio costalis lumb orum pars thoracis and the longissimus thoracis pars tho
racis which attach to the ribs Four points on each rib were identi ed on the
reconstructed spine of the Visible Man Table C These p oints were selected
to capture the shap e of the rib particularly the anterior p osterior p osition
Table C Data p oints representing the p ositions of ribs to right side
Co ordinates are relativetothe most anterior p oint on the sup erior endplate
of L All values are in mm where ve i is rostral ve j is anterior and ve k
is left
Data p oints
i j k
Rib
Rib
Rib
Rib
App endix D
Determining lo cal co ordinate
systems and lo cations of the
IARs from the spinal anatomy of
the Visible Man
D Setting up an orthogonal basis on the ver
tebral body
In order to p erform three dimensional rotations and rep ort forces and moments
an orthogonal set of basis vectors needs to be de ned for each vertebra with
origin at the ICR This set of vectors will be denoted as B fe e e g for
i
th
the i vertebra where e is the axis ab out which torsion o ccurs p ositiveinthe
cranial direction e is the axis ab out which lateral b end o ccurs p ositive in the
anterior direction and e is the axis ab out which exion or extension o ccurs
p ositivetothe left
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
For the purp oses of developing an orthogonal set of basis vectors it is assumed
that when a vertebra rotates in torsion the axis ab out which rotation occurs
that is e is p erp endicular to the sup erior endplate of the caudal vertebra
Similarly lateral bend is assumed to o ccur ab out an axis in the mid sagittal
plane of the caudal vertebra while exion extension is assumed to o ccur ab out
an axis p erp endicular to the mid sagittal plane and sup erior endplate In order
to calculate these basis vectors the following steps need to b e p erformed
Identify three p oints on the sup erior endplate of the vertebra In the global
co ordinate system these p oints are represented as p p and p Construct
two vectors d and d such that
d p p
d p p
Calculate e such that it is normal to the plane representing the sup erior
endplate as de ned by d and d
d d
e
j d d j
Determine the vector which represents the mid saggital plane of the verte
bra e The mid saggital plane is de ned as the plane p erp endicular to
the sup erior endplate which passes through the most anterior p oint on the
sup erior endplate and the p oint representing the inferior tip of the spinous
pro cess
Let p be the vector from the inferior tip of the spinous pro cess to the
most anterior p oint of the sup erior endplate The vector p consists of two
comp onents p and p such that p p p Let e be the unit vector
x y x y
App endix D
corresp onding to p The following pro cess is used to calculate e
y
If p pro jection of p onto e p e e
x
then p p p
y x
p
y
and e
j p j
y
Calculate e where e e e
The vectors calculated using the ab ove steps can be checked for orthogonality
by determining the dot pro ducts for each pair of vectors If the vectors are
orthogonal the dot pro duct is zero
D Basis vectors for the spine of the Visible Man
Using the steps outlined ab ove and data obtained from the reconstructed spine
of the Visible Man see Section for reconstruction metho dology the basis
vectors for each level of the lumbar spine can be calculated These basis sets
represent the initial orientation of the vertebra of the Visible Man prior to any
rotation
The values used in the following calculations were obtained from the ANA
software using a global co ordinate system where i j and k vectors YZE
L
are in the rostral anterior and left directions resp ectively and the origin is in
the top left p osterior corner of the image
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
Basis set for L
Points on the L vertebra are used to obtain the set of basis vectors ab out which
rotation of the thorax o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
D e
j d d j
T
The most anterior point on the sup erior endplate is while
T
the inferior tip of the spinous pro cess is lo cated at Further
calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
so that
p
y
T
D e
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D Any
rotation of the thorax relativetoL o ccurs relativetothisbasis set
App endix D
Basis set for L
Points on the L vertebra are used to obtain the set of basis vectors ab out which
rotation of L o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
e D
j d d j
T
The most anterior p oint on the sup erior endplate is while
T
the inferior tip of the spinous pro cess is lo cated at Further
calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
so that
p
y
T
D e
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D The
rotation of L relativetoL occurs relativeto this basis set
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
Basis set for L
The points on the L vertebra are used to obtain the set of basis vectors ab out
which rotation of L o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
D e
j d d j
T
The most anterior point on the sup erior endplate is while
T
the inferior tip of the spinous pro cess is lo cated at Further
calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
so that
p
y
T
D e
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D The
rotation of L relativetoL occurs relativetothis basis set
App endix D
Basis set for L
The p oints on the L vertebra are used to obtain the set of basis vectors ab out
which rotation of L o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
e D
j d d j
T
The most anterior p oint on the sup erior endplate is while
T
the inferior tip of the spinous pro cess is lo cated at Further
calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
so that
p
y
T
D e
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D The
rotation of L relativetoL occurs relativeto this basis set
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
Basis set for L
The points on the L vertebra are used to obtain the set of basis vectors ab out
which rotation of L o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
D e
j d d j
T
The most anterior point on the sup erior endplate is while
T
the inferior tip of the spinous pro cess is lo cated at Further
calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
so that
p
y
T
D e
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D The
rotation of L relativetoL occurs relativetothis basis set
App endix D
Basis set for S
The p oints on the S vertebra are used to obtain the set of basis vectors ab out
which rotation of L o ccurs This results in
T
p
T
p
T
and p
so that
T
d p p
T
and d p p
so that
d d
T
e D
j d d j
T
The most anterior p oint on the sup erior endplate is while
T
the p osterior point on the sup erior endplate is lo cated at
Further calculations show that
T T T
p
T
p p e e
x
T
and p p p
y x
p
y
T
e D
j p j
y
T
and e e e D
The set of basis vectors are given by equations D D and D The
rotation of L relativetoL occurs relativeto this basis set
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
D Determining the lo cation of ICRs
Pearcy and Bogduk rep ort the position of the IARs as a prop ortion of
verteral body height and depth for the lower vertebra of a joint relative to the
p osterior sup erior corner of the vertebra In order to lo cate the p osition of the
ICR for the vertebrae from the Visible Man it is assumed that the IAR lies in the
mid sagittal plane of the vertebrae The basis vectors calculated in the previous
section are used to determine the p ositions of the ICRs
Let a s e be the most anterior p ointonthe sup erior endplate ofavertebra
IAR be the distance from a s e to the pro jection of the IAR onto e and
x
IAR be the distance from a s e to the pro jection of the IAR onto e
y
Values for a s e the x and y values of the most p osterior pointon the sup erior
endplate p s e and the x value of the most p osterior point on the inferior
endplate p i e are known Hence the height and depth of the vertebral body
along e and e can b e approximated by
Di erence in x values from p s e to p i e
heig ht
x comp onent of e
Di erence in y values from p s e to a s e
depth
y comp onentofe
with
IAR p osition of IAR as prop ortion of vertebra height heig ht
x
and IAR p osition of IAR as prop ortion of vertebra depth depth
y
The ICR expressed as a point in the co ordinate system of the Visible Man is
given by
ICR a s e IAR e IAR e D
x y
App endix D
Using equation D the p ositions of the ICR for each of the lumbar vertebra
can be determined as follows
ICR for L L rotation
T
a s e
T
e
T
and e
x value of p s e
y value of p s e
and x value of p i e
so that heig ht
depth
IAR
x
and IAR
y
so that
B C C B C B B C
B C C B C B B C
B C C B C B B C
ICR
B C C B C B B C
A A A A
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
ICR for L L rotation
T
a s e
T
e
T
and e
x value of p s e
y value of p s e
and x value of p i e
so that heig ht
depth
IAR
x
and IAR
y
so that
C B C B C B C B
C B C B C B C B
B C B C B C B C
ICR
B C B C B C B C
A A A A
App endix D
ICR for L L rotation
T
a s e
T
e
T
and e
x value of p s e
y value of p s e
and x value of p i e
so that heig ht
depth
IAR
x
and IAR
y
so that
C C C C B B B B
C C C C B B B B
C C C C B B B B
ICR
C C C C B B B B
A A A A
Determining lo cal co ordinate systems and lo cations of the IARs from
the spinal anatomy of the Visible Man
ICR for L L rotation
T
a s e
T
e
T
and e
x value of p s e
y value of p s e
and x value of p i e
so that heig ht
depth
IAR
x
and IAR
y
so that
C B C B C B C B
C B C B C B C B
C B C B C B C B
ICR
C B C B C B C B
A A A A
App endix D
ICR for L S rotation
T
a s e
T
e
T
and e
x value of p s e
y value of p s e
and x value of p i e
so that heig ht
depth
IAR
x
and IAR
y
so that
C C C C B B B B
C C C C B B B B
C C C B B B B C
ICR
C C C B B B B C
A A A A
App endix E
A comparison of techniques for
mo delling the oblique muscle
lines of action
A new metho d of predicting the lines of action for the internal and external
oblique muscles was develop ed in Section This metho d uses an eliptical
mo del of the torso to b etter describ e the shap e of the oblique muscles However
this metho d is computationally more complex than other metho ds typically used
to determine muscle lines of action This app endix rep orts the results of a study
whichwas conducted to determine the di erences in lines of action and moments
created by using the new metho d compared to a straight approach
It is not common to use a straight line of action to mo del the internal and
external oblique muscles However Stokes and Gardner Morse b rep ort
that when the origin and insertion of the oblique fascicles rep orted by them
are connected by straight lines these lines are completely contained within the
b ounds of the relevant fascicle This result may justify the use of straight lines of
action created by linking the attachments points For this reason the new torso
A comparison of techniques for mo delling the oblique muscle lines of
action
Table E Data on the attachment points for the left side of the body for
each of the vectors rep orted by Stokes and Gardner Morse the
predicted z values and rep orted PCSAs
Upp er attachment Lower attachment
PCSA x y z Predicted x y z Predicted
mm mm mm mm z mm mm mm mm z mm
External oblique
Ext
Ext
Ext
Ext
Ext
Ext
Internal oblique
Int
Int
Int
Int
Int
Int
mo del approach is compared to an approach using straight lines of action
This study uses the data rep orted by Stokes and Gardner Morse b for the
attachmentpoints and PCSA of the internal and external oblique muscles Table
E These data di er from that presented in Table since the original data
rep orted by Stokes and Gardner Morse b is used in Table E while Table
uses an adjusted data set in which the original data has b een scaled and
rotated by and resp ectively in the ij plane to match the spinal
height of the Visible Man The parameter values which pro duce the torsos best
tting these data are listed in Table E with the predicted z values contained
in Table E The height of the torso in b oth mo dels has b een taken as mm
from the origin at the centre of the S vertebral body
App endix E
Table E Parameter values for the torsos which best t the data rep orted
by Stokes et al values are relative to the centre of the S vertebral
b o dy
External oblique Internal oblique
x mm
pel v is
x mm
r ibs
a mm
pel v is
a mm
ribs
b mm
pel v is
b mm
r ibs
y mm
pel v is
y mm
ribs
Sum of squares
Number of data p oints used
The lengths of the fascicles are given in Table E for the straight line approach
using the rep orted z values the straight line approach using the predicted z val
ues and the torso mo del The lines of action obtained from the two metho dologies
are rep orted in Table E
The maximum moments able to be generated by each muscle comp onent are
displayed in Table E These values were obtained assuming neural acti
vation with a muscle intensity of Ncm The p oint of application of the force
generated bythemuscle is assumed to b e the lower attachment p oint to maintain
compatability with previous mo dels A comparison of the predicted maximum
moments able to b e generated by the left internal oblique muscle under the same
assumptions in a variety of p ostures is giv en in Table E
A comparison of techniques for mo delling the oblique muscle lines of
action
Table E Comparison of the lengths of the comp onentvectors using
straight lines and the torso mo del to mo del the line of action
Length mm
y y
Linear l o a Linear l o a Torso mo del
using rep orted z using predicted z
External oblique
Ext
Ext
Ext
Ext
Ext
Ext
Internal oblique
Int
Int
Int
Int
Int
Int
y
l o a line of action
Table E Predicted lines of action for the left side of the torso using a
striaght line approach and the torso mo del with x x
low
Linear mo del Torso mo del
i j k i j k
External oblique
Ext
Ext
Ext
Ext
Ext
Ext
Internal oblique
Int
Int
Int
Int
Int
Int
App endix E
Table E Predicted maximum moments able to b e pro duced by the left
oblique muscles in upright stance ab out the centre of the S vertebral body
using lines of action displayed in Table E
Moments Nm
Linear mo del Torso mo del
Axial twist Lateral Flexion Axial twist Lateral Flexion
y z y z
i b end j k i b end j k
External oblique
Ext
Ext
Ext
Ext
Ext
Ext
Total
Internal oblique
Int
Int
Int
Int
Int
Int
Total
Combined
y
vevalues represent left twist vevalues righttwist
z
vevalues representright b end vevalues left b end
vevalues represent exion vevalues extension
E Discussion
The use of the torso mo del to represent the muscle bres instead of straight
lines can a ect the size of the predicted moments in two ways Firstly using
curves to represent the muscle bres will change the line of action of the bre
Table E The size of this change dep ends on the p osition of the bre on the
As can b e seen with the Int bre it is also p ossible for the lines of action torso
to change direction This o ccurs when the bre wraps around the torso in the
A comparison of techniques for mo delling the oblique muscle lines of
action
Table E Predicted maximum moments able to b e generated by the left
internal oblique muscle ab out the centre of the S vertebral body in a
variety of p ostures assuming a straight line of action and using the torso
mo del
Posture Moments Nm
Linear mo del Torso mo del
Axial twist Lateral Flexion Axial twist Lateral Flexion
y y
z z
i b end j k i b end j k
Flexion
Extension
R lat bend
L lat b end
R twist
L twist
y
vevalues represent left twist vevalues righttwist
z
vevalues represent right b end vevalues left b end
vevalues represent exion vevalues extension
p ositive k direction in order to reach its upp er attachment which is p ositioned in
the negative k direction relativetothe lower attachment point see Figure
The e ect the changes in the lines of action have on the predicted moments are
displayed in Table E for the upright stance For the external oblique muscle
the largest change in moments occurred in lateral bend with a decrease
in the predicted moment The use of the torso mo del also resulted in a
increase in the uni lateral axial twist moment and a decrease in the exion
moment For the internal oblique the axial twist moment was most a ected
decrease while the lateral b end moment also decreased by and the
exion moment increased by When the combined action of the internal
and external oblique muscles was considered the use of the torso mo del resulted
in a increase in the magnitude of the axial twist moment Nm and
a and decrease in the lateral bend and exion moments resp ectively
Nm and Nm
App endix E
The second way in which the torso mo del can a ect the predicted moments is
via the length of the muscle bres Both the active and passive muscle force is
related to muscle strain A prescrib ed length change in a muscle of length k will
result in a larger strain than the same length change in a longer muscle The
use of curved muscle bres as opp osed to straight bres would be exp ected to
increase the muscle lengths However as the values in Table E indicate this
increase is minimal mm Therefore the torso mo del would b e exp ected to
have little impact on the strain and therefore force of the muscle in any p osture
Generally the di erences created by the use of the torso mo del are small in
upright standing However the di erences caused by using the torso mo del
b ecome more obvious when the p osture of the spine is altered When the torso is
extended by the maximum axial twist moment predicted by the torso mo del
is almost twice that predicted by a linear mo del Nm versus Nm At
exion the torso mo del predicts a exion moment approximately larger and
an axial twist moment approximately smaller than a linear mo del Likewise
when the torso is orientated with right axial twist the torso mo del predicts
maximum twist moments for the left internal oblique which are appro ximately
lower than a linear mo del while these values are approximately higher
during a left twist of the same magnitude The choice of mo del app ears to make
minimal di erence in lateral bend p ostures with all changes b eing or less
Thus the impact of using the torso mo del app ears to b e larger in p ostures other
than upright standing and particularly in exion and extension
These results indicate that the predicted moments generated by the oblique mus
cles can be signi cantly a ected by the metho d used to determine the lines of
action of the muscle bres Given that the torso mo del is an improvementinthe
anatomical realityover the linear mo del it app ears that the increased computa
tional e ort required by the torso mo del is a go o d investment
App endix F
Moments predicted by the TLF
mo del
The TLF mo del presented in Section provides a means of predicting the
moments generated by the muscles attaching to the spine via the TLF This
App endix presents the predicted moments for each TLF estimated from medi
cal images Figure and discusses the relative imp ortance of including this
structure in biomechanical mo dels
There is some variability in the moments pro duced in the upright p osture ob
tained by using the three di erent scans with the extension moments ab out
L L and L S b eing largest using scan followed by scan then scan Fig
ure F This trend is related to the predicted line of action with more p osterior
lines of action pro ducing larger extension moments These di erences in lines of
action are related to the size and shap e of the erector spinae muscle An increase
in the moments was also seen when the angle of the bres in the p osterior
layer to the transverse plane decreased from to This increase is a result
of the p osterior comp onent of the unit vector increasing as decreases
It is known that spinal posture a ects the moments capable of b eing generated
Moments predicted by the TLF mo del
4 2 0 (Nm) k -2 L2/L3 L3/L4 -4 L4/L5 -6 L5/S1 -8
Moment about -10 -12
Scan 1 Scan 2 Scan 3
a Moments generated using
4 2 0 (Nm) k -2 L2/L3 L3/L4 -4 L4/L5 -6 L5/S1 -8
Moment about -10 -12
Scan 1 Scan 2 Scan 3
b Moments generated using
Figure F Maximum exion extension moments ab out the ICRs pro duced
by the TLF in upright stance using erector spinae characteristics from three
individuals and and Positive moments represent exion
negative moments represent extension Moments were calculated assuming
activation of the attached muscles
by the fascia Figure F illustrates the predicted moments at the full range of
motion in each direction assuming activation of the attached muscles The
uni lateral moments pro duced during bend and twist p ostures are larger than
F At the lower spinal levels the axial the net moments rep orted in Figure
twisting moments generated during full right twist are approximately Nm on
the right side and Nm on the left side of the fascia During full right lateral
App endix F
0.8
0.6
0.4
0.2 Upright 0 Flexion Extension -0.2 Right Twist Right Bend -0.4 Moment (Nm)
-0.6
-0.8
-1
L2/L3 L3/L4 L4/L5 L5/S1
a Axial rotation moments ve values are left
twist vevalues righttwist
0.8
0.6
0.4
0.2 Upright 0 Flexion Extension -0.2 Right Twist Right Bend -0.4 Moment (Nm)
-0.6
-0.8
-1
L2/L3 L3/L4 L4/L5 L5/S1
b Lateral b ending moments vevalues are right
b end vevalues left b end
4
2
0
Upright -2 Flexion Extension -4 Right Twist Right Bend Moment (Nm) -6
-8
-10
L2/L3 L3/L4 L4/L5 L5/S1
c Flexion extension moments ve values are
exion vevalues extension
Figure F Net moments ab out the ICRs pro duced by the TLFinavariety
of p ostures All p ostures are at the full range of motion as describ ed by
Pearcy with activation of the attached muscles
Moments predicted by the TLF mo del
bend the b ending moments pro duced by the right and left sides of the fascia
are Nm and Nm resp ectively The net values are small since there is no
di erential activation b etween muscles on the rightand left sides of the body
The moments estimated by the mo del in the upright stance indicate that the
fascia applies small exion moments to the upp er p ortion of the lumbar spine
L L and L L and larger extension moments to the lower regions L L and
L S This would suggest that the fascia could act as a stabiliser of the spine by
applying a force to balance that imp osed bygravity However the direction and
size of the moments are dep endent on the particular spinal alignment adopted
to represent upright stance
The maximum extension moment generated by the fascia ab out L S in the
upright p osture is b etween Nm and Nm This range represents a contribution
of to towards the total maximum voluntary extension momentinthe
upright p osture as measured by McNeill et al using the rep orted moment
for males aged over years Although this app ears to b e a small contribution
to the overall moment it is not much di erent to the predicted contribution of
Nm from the psoas muscle at L L McGill et al Most mathematical
mo dels of the lumbar spine incorp orate the psoas muscle which suggests that
the TLF should also b e included in such mo dels since it is capable of pro ducing
comparable extension moments ab out some joints
At full exion the extension moments generated by the fascia ab out L L and
L S are smaller than those in the upright stance This result contradicts the
work of Macintosh et al who state that the extension moment will in
crease from Nm in the erect p osition to Nm when the vertebral column
is fully exed Macintosh et al s calculations are correct in the two
dimensional system describ ed by them however not all the conclusions from the
two dimensional analysis are applicable to a three dimensional system During
App endix F
exion in the D mo del the angle between the p osterior layer and transverse
plane increases for the bres of the deep lamina and decreases for the bres of
the sup erior lamina due to the assumption that the lateral raphe is inextensible
As a consequence the line of action for the deep lamina b ecomes more vertical
thereby reducing the anterior p osterior comp onent leading to a reduction in the
extension moments generated The increase in the caudo cranial comp onent of
the unit vector representing the line of action generates larger lateral b ending mo
ments The opp osite is true for the sup erior lamina where the anterior p osterior
comp onent of the line of action increases generating more extension p otential by
reducing the exion moment In contrast the two dimensional system describ ed
by Macintosh et al has no anterior p osterior comp onent to the line of ac
tion resulting in the extension moment being prop ortional to the caudo cranial
comp onent only This comp onent increases as the angle of the bres increase
resulting in larger extension moments at full exion compared to upright
The net twisting and b ending moments generated at full twist and full lateral
b end resp ectively are less than Nm across all joints although the uni lateral
values are slightly larger The small twisting moments asso ciated with full trunk
twist are exp ected since the mo del assumes that the erector spinae muscle follows
the contour of the spine resulting in little change in the line of action of the fascial
bres during axial twist The small b ending moments achieved during full lateral
b end do not supp ort the suggestion byTesh et al that the middle layer of
the TLF mightcontribute almost of the total gravitational b ending moment
in extreme lateral b ending Our results suggest that the maximum moment the
fascia can contribute is less than assuming that the total b ending moment
on the lower spine is Nm under body w eight Tesh et al However this
value will increase when di erential activation of the right and left muscles is
considered
Moments predicted by the TLF mo del
Past studies on the biomechanical e ect of the thoracolumbar fascia have con
centrated on the p osterior layer Output from the mo del indicates that in the
upright p osture the middle layer contributes approximately and of the
total extension moment able to be pro duced by the fascia at L L and L S
resp ectively The middle layer also provides restorative moments opp osing the
direction of a lateral b end
The mo del presented assumes that any force applied to the lateral raphe from
the attached muscles is distributed evenly between layers and also across spinal
levels Currently there is no exp erimental evidence to supp ort or dispute this
assumption There are numerous ways in which force can be allo cated to the
individual bres This allo cation will a ect the moments able to be generated
by the fascia
The mo del also assumes that the bres of the fascia are purely passive force
transmitters with the forces in the bres b eing those generated by the muscles
only Whilst forces transmitted from the muscles will induce strain in the fascicle
system additional strain may also be intro duced by p ostural change Thus the
force exp erienced by the fascia could be in excess of that develop ed by muscle
contraction alone This issue b ecomes more apparent in a three dimensional
representation of the TLF compared to a two dimensional system Hence the
moments generated by the fascia may be larger than estimated here for full
exion lateral b end and axial twist
The moments predicted by the mo del are sensitive to the PCSAs and activation
of the muscles The muscle areas used are conservative estimates For instance
the moments generated by the TLF in the upright stance will increase by
if the area of the transverse ab dominis rep orted by McGill and Norman
is used instead of Macintosh et al s estimate Although little data has
been rep orted for the activation levels of the muscles attaching to the fascia
App endix F
it might be exp ected that activation in all three attaching muscles is not
achievable and that di erential activation o ccurs between some muscles on the
right and left sides of the body during lateral bend and axial twist These
di erences in activation will impact on the size of the net moments particularly
in non symmetric p ostures
App endix G
Mo del output for individual
muscle fascicles in upright stance
Tables G to G contain the moments predicted by the mo del for each fascicle
during isometric maximal exion extension left lateral b end and left axial twist
exertions All calculations are conducted with the simulated spine in upright
stance with values being expressed relative to the global co ordinate system A
maximum muscle intensity of Ncm has been used in the calculations and
muscle activation levels are the same as those describ ed in Table Where no
activation data exists for a sp eci ed muscle the assumptions discussed in Section
have been applied For the axial twist exertion muscle activation levels
describ ed by EMG data resulting from the use of normalisation metho d B has
been applied T A axial being during t T A S LB t momen L fascicles the momen uscle F E on m t b end T A dep enden individual lateral L LB for wist L t LB t fascicle R the left fascicle L and the t axial stance F E t left momen y the righ T or A uprigh in Nm b end t L LB able L lateral ts generated b hiev Momen t ac exion extension F E ts righ T A the momen F E momen t exion t T um L LB L maxim represen fascicles F E fascicle represen left alues v h e T predicted and A t the ositiv righ P for L LB the L for output exertion ts F E alues rep orted for eac t L R R T R T T L L R R T T L L Mo del momen exion The v the G momen of maximal ascicle able wist Muscle F Multi dus m s m t m t m s m t T a cosidered t sum T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E R R T L T R L T L R R L T T R T L L ascicle Muscle F m t m s m t m t m t m t T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E R R L T T R L T L R R T L T R T L L ascicle Muscle F m t m s m t m s m t m t T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A thoracis L LB pars L F E thoracis R L T L R R T L T L R R L T T R T L us ascicle T T T Muscle F m t L Longissim L L m t m t T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L L L R R R T T T L L L R R R T T T VB VB rib rib ascicle T T T T T Muscle F L TL L L L L T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L R T L L L R R R T T T L L R R T T VB rib VB rib VB rib ascicle T T T T T T L L Muscle F L L L L T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T b orum A lum L LB pars L F E thoracis L R T L L R R L T T R L T R T L R T us VB rib VB rib ascicle T T T T L L Muscle F L Longissim L L L T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A thoracis L LB pars L b orum F E lum R L T R L R T L T R L T R L T R T L ascicle Muscle F L Ilio costalis IT IT L IT L T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E borum T A lum L LB pars L b orum F E lum L R R T R T T L L R L R T R T T L L ascicle Muscle F IT IT IT i Ilio costalis IT IT T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L R R L T T R T L L R L R T R T T L ma jor IVD TP VB L ascicle Muscle F i Psoas pL pL i pL i T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L L L R R R T T T L L L R R R T T T IVD IVD IVD TP TP TP L L L ascicle Muscle F pL pL pL pL pL pL T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L b orum F E lum dorsi L L R R T T L L R R T T L R T us ab dominis TP VB T ascicle Latissim Quadratus QL Muscle F pL Rectus pL T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E R R L T T R T L L R R L T T R T L L oblique ascicle Muscle F QLL Ext QLL QLL External Ext QLL T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L R R R T T T L L R L R T R T T L L oblique ternal t t ascicle Muscle F Ext In Ext Ext In In Ext T A S LB L F E T A L LB L F E T A Nm t L ued LB L tin Momen con F E T A able G T L LB L F E T A L LB L F E L R L T R T L R L T R T t t t otal ascicle Muscle F In TLF In T In a T A axial b eing t during T LB S A L t momen fascicles the F E momen on uscle t m bend T A dep enden lateral individual LB L wist t L for LB t fascicle R the left fascicle L and the t axial F E stance t left momen y the righ or T A uprigh b end in t Nm LB L able L lateral ts generated b t hiev Momen exion extension ac righ F E ts the momen F E T t exion momen A t T um LB L represen L maxim fascicles alues left v F E h fascicle represen e and predicted t T ositiv A the P righ for the L LB for L exertion output ts alues rep orted for eac F E t Mo del momen The v extension L R R R T T L L T R R T L L T the G momen of able wist ascicle T maximal cosidered sum t Muscle F Multi dus m s m t m t m t m s T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A L LB L F E L R R T L R R T L R T L T L R T L T ascicle Muscle F m t m t m s m t m t m t T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E T A L LB L F E L R L T R R T R L T L R T L T R L T ascicle Muscle F m t m s m t m t m s m t T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A thoracis pars L LB L thoracis F E us L L R R L T R L T R L T R L T R T T ascicle T T T Muscle F m t L m t L Longissim L m t T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E T A L LB L F E L L R L R T L R R T T L R T L T R T ascicle T T T T T T Muscle F L L VB L rib VB L rib L L T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A L LB L F E L R T L R T L R L R T T L R L R T T ascicle T T T T T T L VB L rib Muscle F L VB L VB L rib L rib T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E borum T A lum pars L LB L thoracis F E us L R L T R L R L R T L R L R T T T T ascicle T T T T L Longissim L Muscle F L VB L VB L rib L rib T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T thoracis A pars L LB L borum F E lum L L R T L R R L T T L R R R T L T T ascicle Muscle F L L Ilio costalis IT IT L IT T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E borum T lum A pars L LB L borum F E lum L R R L L T R T R R L T L T R T L T ascicle Muscle F IT IT Ilio costalis i IT IT IT T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A L LB L F E L R L T L R R R T L T R L T L R T T ma jor TP VB L ascicle Muscle F i i Psoas pL i pL IVD pL T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E T A L LB L F E L R T R L T L L R R L R L R T T T T TP L TP TP L L ascicle pL IVD pL Muscle F pL pL pL IVD pL IVD T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A L LB L b orum F E lum dorsi L L L R R R L T T T L R R T T us ab dominis TP VB T ascicle Muscle F pL Latissim Quadratus QL pL Rectus T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E T A L LB L F E oblique L R L T R R R L T T L L T R R T L T ascicle Muscle F QLL QLL QLL Ext QLL External Ext T A LB S L F E T A LB L L F E T A Nm t ued LB L tin L con Momen F E T able G A T LB L L F E T A L LB L F E oblique L R R L L T R L T R T R R L T L T T ternal t t ascicle Muscle F Ext Ext Ext In Ext In In T A LB S L F E T A LB L L F E T A t Nm ued LB L tin L con Momen F E G T able A T LB L L F E T A L LB L F E L L R L T R R L T T R T t t t otal ascicle Muscle F In In TLF In T t a T A L T t A momen during S fascicle LB the L left momen on t fascicles the F E uscle R m T dep enden A lateral b end wist fascicle t t L individual LB t LB righ L axial for the left y momen b or F E stance t b end T A uprigh generated in ts lateral t t Nm L LB exion extension able L righ momen hiev Momen ac the F E F E t ts exion t T T A momen represen represen um L left fascicles fascicle LB alues L v h maxim e eac tand for ositiv F E righ P predicted T the A for the rep orted ts for exertion alues L v LB b end L momen output t The the lateral F E Mo del momen left sum of L R R L T R T L R T R T L T L G wist cosidered the able axial t T maximal being and ascicle Muscle F Multi dus m s m t m t m t m s T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A L LB L F E L R R T R T L T L R L R T R T T L L ascicle Muscle F m t m t m s m t m t m t T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L R R R T L T L L T R R R T L L T T ascicle Muscle F m t m s m t m s m t m t T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A thoracis pars L LB L thoracis F E us L L R R R T T T L L L R R R T T T L ascicle T T T Muscle F m t L Longissim L L m t m t T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L R L R R T L R L R T T L T T R T ascicle T T T T T T Muscle F L L VB VB L rib L rib L L T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A L LB L F E L R T L R L L T R R T T L L R R T T ascicle T T T T T T L VB L rib L Muscle F L VB VB L L rib rib T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E b orum T A lum pars L LB L thoracis F E us L R T L R T L L R R T L R T L T R T ascicle T T T T L VB L rib L Longissim Muscle F L VB L rib L T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A thoracis pars L LB L b orum F E lum L L R R R T T T L L L R R R T T T L ascicle Muscle F L Ilio costalis IT L IT IT L T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E borum T A lum pars L LB L b orum F E lum L R R R T T T L L L R R R T T T L L ascicle Muscle F IT IT IT Ilio costalis i IT IT T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A L LB L F E L L R R R T T T L L L R R R T T T L ma jor TP L VB ascicle Muscle F i pL Psoas pL i IVD pL i T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L L R R R T L T R T L R L R T T T TP TP TP L L L ascicle Muscle F pL pL pL pL IVD pL IVD pL IVD T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A L LB L borum F E lum dorsi us L R T L R L L T R R T T L R T ab dominis TP VB T ascicle Latissim Rectus Muscle F pL Quadratus QL pL T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E oblique L R R R T L L T T L R R R T L T T L ascicle Muscle F QLL QLL Ext QLL QLL Ext External T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E G T able A T L LB L F E T A L LB L F E oblique L R R R T T T L L L R R R T T T L L ternal t t ascicle Muscle F Ext In Ext Ext In Ext In T A S LB L F E T A L LB L F E T A ued t Nm L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L R L R T R T L T R T t t t otal ascicle Muscle F In In TLF In T t a L T T A A t momen during fascicle the S LB left momen on L fascicles t the F E uscle R m dep enden lateral b end T A wist fascicle t t individual t LB L righ LB axial for L the left y momen b or F E stance t b end T A uprigh generated in ts lateral Nm t t L LB able L exion extension righ momen hiev Momen ac the F E F E t ts exion T t T A momen represen represen um L LB left fascicles fascicle L alues h maxim v and e eac t F E for righ ositiv P predicted T the A the for rep orted ts for exertion L LB alues L v wist momen t output t The F E axial of the Mo del momen L R R T T R T L L R R T T L L left sum G wist cosidered the ascicle Muscle F Multi dus m s m t m t m t m s able axial t and being maximal T T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E R L T R R L T T R L L T R R T T L L ascicle Muscle F m t m t m t m s m t m t T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E R L R R T T T L R L L T R R T T L L ascicle Muscle F m t m s m s m t m t m t T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A thoracis pars L LB L thoracis F E us L L R R R T T T L L L R R R T T T L ascicle T T T Muscle F m t L m t Longissim L L m t T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L R L R T R T T L L R L R T R T T ascicle T T T T T T Muscle F L L VB VB L L rib L rib L T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L R R T T L L L R R R T T T L R T ascicle T T T T T T L L VB VB L L Muscle F L rib rib VB L rib T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E borum T A lum pars L LB L thoracis F E us L L R R T T L L L R R R T T T L R T ascicle T T T T L Longissim L VB L L Muscle F L rib VB L rib T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T thoracis A pars L LB L b orum F E lum L L R R R T T T L L L R R R T T T L ascicle Muscle F L Ilio costalis IT L IT IT L T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E b orum T lum A pars L LB L b orum F E lum R L T R T L R T L R T L R T L R T L ascicle Muscle F IT IT IT Ilio costalis i IT IT T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L R L R R T T T L L R R L T T R L T ma jor TP L VB ascicle Muscle F i pL i Psoas pL IVD i pL T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L L L R R R T T T L L L R R R T T T TP TP TP L L L ascicle Muscle F pL pL pL pL pL pL IVD IVD IVD T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L b orum F E lum dorsi L R T L L R L R T R T T L R T us ab dominis TP VB T ascicle Latissim Rectus Muscle F pL Quadratus QL pL T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E oblique R L R R T T T L L R L R T R T T L L ascicle Muscle F QLL Ext QLL QLL QLL External Ext T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E oblique R L R T R T L T L L R R R T T T L L ternal t t ascicle Muscle F Ext Ext Ext In In In Ext T A S LB L F E T A L LB L F E T A Nm ued t L LB tin L con Momen F E T able G A T L LB L F E T A L LB L F E L R L T R T L R L T R T t t t otal ascicle Muscle F In In TLF In T
App endix H
Moments ab out a normal spine
in a variety of p ostures
Moments ab out a normal spine in a variety of p ostures
160 140 120 100 120 80 60 100 40 80 -20 20 60 0 0 40
Flexion moment (Nm) Right -20 30 20 20 -40 10 0 Lateral 20 -10 -20 Bend Flexion moment (Nm) -60 0 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Flexion moments primary moment
60
40
20 10 -20 8 0 0 6 30 20 4 20 10 -20 0 -10 2 -20 0 Right -40 -2 -5 0 5 Lateral -4 Lateral bend moment (Nm) Bend -60 -6 Left -8 Lateral bend moment (Nm) -10 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
4 3 2 5 1 -20 4 0 0 3 2 30 20 20 -1 10 0 1 -10 -20 -2 0 Right -1 -5 0 5 Axial twist moment (Nm) -3 Lateral -2 Bend -3 -4 -4
Left Axial twist moment (Nm) -5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum exion
exertion in various p ostures ve exion moments represent exion ve
lateral b end and axial twist moments represent moments to the left Black
columns represent upright standing
App endix H
120 100 80 60 100 40 80 20 -20 0 0 60 -20 30 20 20 10 40 0 -10 Flexion moment (Nm) -40 -20 Right -60 Lateral 20
Bend Flexion moment (Nm) -80 0 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Flexion moments primary moment
40 30 20 8 10 -20 6 0 0 4 30 20 20 -10 10 0 2 -10 -20 -20 0 Right -2 -5 0 5 -30 Lateral Lateral bend moment (Nm) Bend -4 -40 -6 Left Lateral bend moment (Nm) -8 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
4 3 2 5 1 -20 4 0 0 3 2 30 20 20 -1 10 0 1 -10 -20 -2 0 Right -1 -5 0 5 Axial twist moment (Nm) -3 Lateral -2 Bend -3 -4 -4
Left Axial twist moment (Nm) -5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum exion
exertion in various p ostures ve exion moments represent exion ve
lateral b end and axial twist moments represent moments to the left Black
columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
120
100
80
60 80 40 70 -20 20 -10 60 0 0 50 Flexion moment (Nm) 10 30 20 -20 10 20 40 0 -10 -20 30 -40 Right Lateral Bend 20 -60 10
-80 Flexion moment (Nm) Left 0 Lateral Flexion Bend -5 0 5
Extension Right twist Left twist
a Flexion moments primary moment
30
20
10 8 -20 6 0 0 4 30 20 20 10 2 -10 0 -10 -20 0 Right -2 -5 0 5 -20 Lateral Lateral bend moment (Nm) Bend -4 -30 -6 Left Lateral bend moment (Nm) -8 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
3
2
1 6 -20 4 0 0 30 20 20 2 -1 10 0 -10 -20 0 Right -2 -2 -5 0 5 Axial twist moment (Nm) Lateral -3 Bend -4
Left Axial twist moment (Nm) -6 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum exion
exertion in various p ostures ve exion moments represent exion ve
lateral b end and axial twist moments represent moments to the left Black
columns represent upright standing
App endix H
80 60 40 20 -20 80 0 0 70 -20 30 20 20 60 10 0 -40 -10 -20 50 -60 40 30
Flexion moment (Nm) -80 Right 20 Lateral -100 10
Bend Flexion moment (Nm) -120 0 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Flexion moments primary moment
30
20
10 8 -20 6 0 0 4 30 20 20 10 2 -10 0 -10 -20 0 Right -2 -5 0 5 -20 Lateral Lateral bend moment (Nm) Bend -4 -30 -6 Left Lateral bend moment (Nm) -8 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
3
2
1 6 -20 4 0 0 30 20 20 2 -1 10 0 -10 -20 0 Right -2 -2 -5 0 5 Axial twist moment (Nm) Lateral -3 Bend -4
Left Axial twist moment (Nm) -6 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum exion
exertion in various p ostures ve exion moments represent exion ve
lateral b end and axial twist moments represent moments to the left Black
columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
150
100 104 50 102 -20 100 0 0 98 30 20 96 20 10 0 -10 94
Flexion moment (Nm) -50 -20 Right 92 Lateral 90
Bend Flexion moment (Nm) -100 88 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Flexion moments primary moment
40 30 20 8 10 -20 6 0 0 4 30 20 20 -10 10 0 2 -10 -20 -20 0 Right -2 -5 0 5 -30 Lateral Lateral bend moment (Nm) Bend -4 -40 -6 Left Lateral bend moment (Nm) -8 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
6
4
2 6 -20 4 0 0 30 20 20 2 -2 10 0 -10 -20 0 Right -4 -2 -5 0 5 Axial twist moment (Nm) Lateral -6 Bend -4
Left Axial twist moment (Nm) -6 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L S by a maximum exion
exertion in various p ostures ve exion moments represent exion ve
lateral b end and axial twist moments represent moments to the left Black
columns represent upright standing
App endix H
200
150 90 100 80 70 60 50 -20 50 40 0 0 Right 30
Extension moment (Nm) Lateral 20 30 20 20 10 0 Bend 10 -50 -10 Extension moment (Nm) 0 -20 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
50 40 30 20 4 -20 10 3 0 0 2 30 20 -10 20 10 1 0 -10 -20 -20 0 Right -30 -1 -5 0 5 Lateral Lateral bend moment (Nm) -40 Bend -2 -50 -3 Left Lateral bend moment (Nm) -4 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
30
20
10 10 -20 8 0 0 6 4 30 20 20 -10 10 0 2 -10 -20 0 -2 -20 Right -5 0 5 Axial twist moment (Nm) Lateral -4 Bend -6 -30 -8
Left Axial twist moment (Nm) -10 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
250
200
150 160 140 100 120 100 50 80 -20 60 Extension moment (Nm) Right 0 0 Lateral 40 20 30 20 Bend 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
30
20
10 5 -20 4 0 0 3 2 30 20 20 10 1 -10 0 -10 -20 0 Right -1 -20 -5 0 5 Lateral -2 Lateral bend moment (Nm) Bend -3 -30 Left -4 Lateral bend moment (Nm) -5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
40 30 20 15 10 -20 10 0 0 30 20 20 5 -10 10 0 -10 -20 -20 0 Right -5 -5 0 5 Axial twist moment (Nm) -30 Lateral -40 Bend -10
Left Axial twist moment (Nm) -15 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
App endix H
300
250
200 250
150 200
100 150
50 -20 100
Extension moment (Nm) Right 0 0 Lateral 50 30 20 Bend 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
10
5 4 -20 3 0 0 2 30 20 20 10 1 0 -10 -20 0 -5 Right -1 -5 0 5 Lateral Lateral bend moment (Nm) Bend -2 -10 -3 Left Lateral bend moment (Nm) -4 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
40 30 20 15 10 -20 10 0 0 30 20 20 5 -10 10 0 -10 -20 -20 0 Right -5 -5 0 5 Axial twist moment (Nm) -30 Lateral -40 Bend -10
Left Axial twist moment (Nm) -15 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
300
250
200 250
150 200
100 150
50 -20 100
Extension moment (Nm) Right 0 0 Lateral 50 30 20 Bend 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
20 15 10 4 5 -20 3 0 0 2 30 20 -5 20 10 1 0 -10 -20 0 -10 Right -1 -5 0 5 -15 Lateral Lateral bend moment (Nm) Bend -2 -20 -3 Left Lateral bend moment (Nm) -4 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
40 30 20 15 10 -20 10 0 0 30 20 20 5 -10 10 0 -10 -20 -20 0 Right -5 -5 0 5 Axial twist moment (Nm) -30 Lateral -40 Bend -10
Left Axial twist moment (Nm) -15 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
App endix H
250
200
150 140 120 100 100 80 50 -20 60 Extension moment (Nm) Right 40 0 0 Lateral 20 30 20 Bend 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments primary moment
40 30 20 6 10 -20 4 0 0 30 20 2 -10 20 10 0 -10 -20 0 -20 Right -5 0 5 -30 Lateral -2 Lateral bend moment (Nm) Bend -40 -4 Left Lateral bend moment (Nm) -6 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
30
20
10 15 -20 10 0 0 30 20 20 5 -10 10 0 -10 -20 0 Right -20 -5 -5 0 5 Axial twist moment (Nm) Lateral -30 Bend -10
Left Axial twist moment (Nm) -15 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L S by a maximum extension
exertion in various p ostures ve extension moments represent extension
ve lateral b end and axial twist moments represent moments to the left
Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
120 100 80 60 -5 0 5 40 20 -20 0 0 0 -5 -20 30 20 20 10 -10 -40 0 -10 -20 -15 -60 Right Extension moment (Nm) Lateral -20 -80 Bend -100 -25 Left
Extension moment (Nm) -30 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
200
150 200 100 150
50 100 -20 Right Lateral bend moment (Nm) 0 0 Lateral 50 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 20 30 20 10 0 -10 -20 -10 -5 0 5 -20 0 -5 -30 -10 -15 -20 -40 Right -25
Axial twist moment (Nm) Lateral -30 Bend -35 -50 Left -40
Axial twist moment (Nm) -45 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum left lateral
bend exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix H
120 100 80 60 14 40 12 20 -20 10 8 0 0 6 -20 30 20 20 Right 10 0 4 Extension moment (Nm) -40 -10 -20 Lateral Bend 2
-60 Extension moment (Nm) 0 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
180 160 140 120 180 100 160 80 140 60 120 100 40 -20 80 20 Right 60 Lateral bend moment (Nm) 0 0 Lateral 40 30 Bend 20 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 20 30 20 10 0 -10 -20 -10 -5 0 5 -20 0 -5 -30 -10 -15 -20 -40 Right -25
Axial twist moment (Nm) Lateral -30 Bend -35 -50 Left -40
Axial twist moment (Nm) -45 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum left lateral
b end exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
120
100
80 40 60 35 30 40 25 20 20 -20 Right 15
Extension moment (Nm) 0 0 Lateral 10 Bend 5 30 20 20 -20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
180 160 140 120 200 100 80 150 60 40 100 -20 20 Right Lateral bend moment (Nm) 0 0 Lateral 50 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 30 20 20 10 0 -10 -10 -20
-20 -5 0 5 0 -30 -10
-40 -20 Right -50 -30
Axial twist moment (Nm) Lateral Bend -60 -40 Left
Axial twist moment (Nm) -50 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum left lateral
bend exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix H
180 160 140 120 40 100 35 80 30 60 25 40 20 -20 20 Right 15 Extension moment (Nm) 0 0 Lateral 10 Bend 5 -20 30 20 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
180 160 140 120 200 100 80 150 60 40 100 -20 20 Right Lateral bend moment (Nm) 0 0 Lateral 50 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 30 20 20 10 0 -10 -10 -20
-20 -5 0 5 0 -30 -10
-40 -20 Right -50 -30
Axial twist moment (Nm) Lateral Bend -60 -40 Left
Axial twist moment (Nm) -50 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L L by a maximum left lateral
b end exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
120 100 80 60 -5 0 5 40 0 -2 20 -20 -4 0 0 -6 -8 -20 30 20 20 Right 10 0 -10 Extension moment (Nm) -40 -10 -20 Lateral -12 Bend -14 -60 Left -16
Extension moment (Nm) -18 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
200
150 200 100 150
50 100 -20 Right Lateral bend moment (Nm) 0 0 Lateral 50 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments primary moment
-20 0 0 20 30 20 10 0 -10 -20 -10 -5 0 5 -20 0
-10 -30 -20 Right -40 -30
Axial twist moment (Nm) Lateral Bend -50 -40 Left
Axial twist moment (Nm) -50 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments secondary moment
Figure H Moments generated ab out L S by a maximum left lateral
bend exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix H
150
100
50 -5 0 5 -20 0 0 0 -5 30 20 20 10 -10 -50 0 -10 -20 -15 Right Extension moment (Nm) -20 -100 Lateral Bend -25 -150 -30 Left
Extension moment (Nm) -35 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
80
60
40 30 25 20 -20 20 0 0 15 30 20 20 Right 10 -20 10 0 -10 -20 Lateral Lateral bend moment (Nm) 5 Bend -40 0 Left Lateral bend moment (Nm) -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
50
40
30 50 40 20 30 10 -20 20
Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure H Moments generated ab out L L by a maximum left axial
twist exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
160 140 120 100 39 80 38 60 37 36 40 -20 35 20 34 0 Right 33 Extension moment (Nm) 0 Lateral 32 -20 30 20 20 10 0 Bend 31 -40 -10 Extension moment (Nm) 30 -20 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
50
40
30 35 20 30 25 10 -20 20 0 0 15 Right 30 20 10 -10 20 10 Lateral
Lateral bend moment (Nm) 0 -10 -20 Bend 5 -20 0 Left Lateral bend moment (Nm) -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
50
40
30 50 40 20 30 10 -20 20
Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure H Moments generated ab out L L by a maximum left axial
twist exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix H
200
150 100
100 80
60 50
Extension moment (Nm) -20 40 Right 0 0 Lateral 20 Bend 30 20 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
40 35 30 25 40 20 35 30 15 25 10 20 -20 5 Right 15 Lateral bend moment (Nm) 0 0 Lateral 10 5 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
50
40
30 50 40 20 30 10 -20 20
Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure H Moments generated ab out L L by a maximum left axial
twist exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
Moments ab out a normal spine in a variety of p ostures
200
150 25
100 20
15 50
Extension moment (Nm) -20 10 Right 0 0 Lateral 5 Bend 30 20 20 10 Extension moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
45 40 35 30 60 25 50 20 15 40 10 30 -20 5 Right 20 Lateral bend moment (Nm) 0 Lateral 0 10 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
50
40
30 50 40 20 30 10 -20 20
Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure H Moments generated ab out L L by a maximum left axial
twist exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix H
160 140 120 100 25 80 20 60 40 15 -20 20 10 0 Right Extension moment (Nm) 0 Lateral 5 -20 30 20 20 10 0 Bend -40 -10 Extension moment (Nm) 0 -20 Left -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
a Extension moments secondary moment
70 60 50 60 40 50 30 40 20 30 10 -20 Right 20 Lateral bend moment (Nm) 0 Lateral 0 10 30 Bend 20 10 20 0 0 -10 Left Lateral bend moment (Nm) -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
b Lateral b end moments secondary moment
45 40 35 30 50 25 20 40 15 30 10 -20 5 20 Axial twist moment (Nm) Right 0 0 Lateral 10 Bend 30 20 20 10 Axial twist moment (Nm) 0 0 -10 Left -20 -5 0 5 Flexion Lateral
Extension Bend Right twist Left twist
c Axial twist moments primary moment
Figure H Moments generated ab out L S by a maximum left axial
twist exertion in various p ostures ve extension moments represent
extension ve lateral b end and axial twist moments represent moments to
the left Black columns represent upright standing
App endix I
Changes in forces and moments
ab out a spine after p osterior
surgery
Changes in forces and moments ab out a spine after p osterior surgery
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -1 -5 -2 -3 -10 -4 -5
moment -15 -6 -20 -7
% change in extension -8 % change in compression
-25 Posture -9 Posture
a Extension moments b Compressive forces
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -2 -2 -4 -4 -6 -8 -6 L3/L4 -10 -8 L4/L5 -12 -10 L5/S1 -14 -12 L3/L4&L4/L5 -16 L4/L5&L5/S1 % change in AP shear -18 -14 % change in lateral shear
-20 Posture -16 Posture
c AP shear forces d Lateral shear forces
Figure I Predicted changes in the maximum moments and forces able to
be generated by the muscles ab out L L during a maximal extension
exertion in a variety of p ostures following p osterior surgery atavarious
levels The legend in d applies to all graphs The p ostures used were
exion extension and lateral b end and axial twist
App endix I
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -2 -1 -4 -2 -6 -3 -8 -4 -10 -5 moment -12 -6 -14 -7
% change in extension -16 -8 % change in compression
-18 Posture -9 Posture
a Extension moments b Compressive forces
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 15 0 10 -2 5 -4 0 -6 -5 L3/L4 -8 -10 L4/L5 -10 L5/S1 -15 -12 L3/L4&L4/L5 -20 L4/L5&L5/S1 % change in AP shear -25 -14 % change in lateral shear
-30 Posture -16 Posture
c AP shear forces d Lateral shear forces
Figure I Predicted changes in the maximum moments and forces able to
be generated by the muscles ab out L L during a maximal extension
exertion inavariety of p ostures following p osterior surgery at a various
levels The legend in d applies to all graphs The p ostures used were
exion extension and lateral b end and axial twist
Changes in forces and moments ab out a spine after p osterior surgery
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -2 -1 -4 -2 -6 -3 -8 -4 -10 -5 moment -12 -6 -14 -7
% change in extension -16 -8 % change in compression
-18 Posture -9 Posture
a Extension moments b Compressive forces
200 Upright Flex. Ext. Bend Twist 0 150 -2 100 -4 50 -6 L3/L4 0 -8 L4/L5 Upright Flex. Ext. Bend Twist -10 L5/S1 -50 -12 L3/L4&L4/L5
% change in AP shear L4/L5&L5/S1 -100 -14 % change in lateral shear
-150 Posture -16 Posture
c AP shear forces d Lateral shear forces
Figure I Predicted changes in the maximum moments and forces able to
be generated by the muscles ab out L L during a maximal extension
exertion in a variety of p ostures following p osterior surgery atavarious
levels The legend in d applies to all graphs The p ostures used were
exion extension and lateral b end and axial twist
App endix I
Upright Flex. Ext. Bend Twist Upright Flex. Ext. Bend Twist 0 0 -1 -5 -2 -10 -3 -15 -4
moment -5 -20 -6 -25 % change in extension -7 % change in compression
-30 Posture -8 Posture
a Extension moments b Compressive forces
100 Upright Flex. Ext. Bend Twist 0 50 -2 -4 0 Upright Flex. Ext. Bend Twist -6 L3/L4 L4/L5 -50 -8 L5/S1 -10 L3/L4&L4/L5 -100 % change in AP shear L4/L5&L5/S1 -12 % change in lateral shear
-150 Posture -14 Posture
c AP shear forces d Lateral shear forces
Figure I Predicted changes in the maximum moments and forces able to
be generated by the muscles ab out L S during a maximal extension
exertion inavariety of p ostures following p osterior surgery at a various
levels The legend in d applies to all graphs The p ostures used were
exion extension and lateral b end and axial twist
Bibliography
Anderson C K Cha n D B Herrin G D and Matthews L S
A biomechanical mo del of the lumb osacral joint during lifting activities J
Biomech
Bean J C Cha n D B and Schultz A B Biomechanical mo del cal
culation of muscle contraction forces a double linear programming metho d
J Biomech
Bogduk N A reapprasial of the anatomy of the human lumbar erector
spinae J Anat
Bogduk N and Macintosh J E The applied anatomy of the thora
columbar fascia Spine
Bogduk N and Twomey L T Clinical anatomy of the lumbar spine
nd
edn Churchill Livingstone Edinburgh
Bogduk N Johnson G and Spalding D The morphology and biome
chanics of latissimus dorsi Clin Biomech
Bogduk N Macintosh J E and Pearcy M J a A Universal mo del of
the lumbar back muscles in the upright p osition Spine
Bogduk N Pearcy M and Had eld G b Anatomy and biomechanics
of psoas ma jor Clin Biomech
Chen Y L and Lee Y H A non invasive proto col for the determination
of lumb osacral vertebral angle Clin Biomech
Cheng P L Biomechanical study of upper limb activities of daily living
PhD thesis Bio engineering Unit University of Strathclyde Glasgow UK
Cheng P L Nicol A C and Paul J P Determination of axial rotation
angles of limb sigments a new metho d J Biomech
Bibliography Bibliography
Cholewicki J and McGill S M EMG assisted optimization a hybrid
approach for estimating muscle forces in an indeterminate biomechanical
mo del J Biomech
Cholewicki J and McGill S M Mechanical stability in the in vivo lum
bar spine implications for injury and chronic low back pain Clin Biomech
Cholewicki J Juluru K and McGill S M Intra ab dominal pressure
mechanism for stabilizing the lumbar spine J Biomech
Cholewicki J McGill S M and Norman R W Comparison of muscle
forces and joint load from an optimization and EMG assisted lumbar spine
mo del towards development of a hybrid approach J Biomech
Crowninshield R D and Brand R A Aphysiologically based criterion
of muscle force prediction in lo comotion J Biomech
Davis J R and Mirka G A Transverse contour mo deling of trunk
muscle distributed forces and spinal loads during lifting and twisting Spine
Dumas G A Poulin M J Roy B Gagnon M and Jovanovic M
A three dimensional digitization metho d to measure trunk muscle lines of
action Spine
Fraser R D and Gogan W J A mo di ed muscle splitting approachto
the lumb osacral spine Spine
Gardner Morse M Stokes I A F and Laible J P Role of mus
cles in lumbar spine stability in maximum extension e orts J Orthop Res
Gareis H Solomonow M Baratta R Best R and D Ambrosia R
The isometric length force mo dels of nine di erent skeletal muscles J
Biomech
Gatton M L and Pearcy M J Kinematics and movement sequencing
during exion of the lumbar spine Clin biomech
Gatton M L Pearcy M J and Pettet G J Di culties in estimating
muscle forces from muscle cross sectional area an example using the psoas
ma jor m uscle Spine
Bibliography
Gejo R Matsui H Kawaguchi Y Ishihara H and Tsuji H Serial
changes in trunk muscle p erformance after p osterior lumbar surgery Spine
Gelb D E Lenke L G Bridwell K H Blanke K and McEnery K W
An analysis of sagittal spinal alignment in asymptomatic middle
and older aged volunteers Spine
Gertzb ein S D Seligman J and Holtby R Centro de patterns and
segmental instability in degenerative disc disease Spine
Gielen C and vanZuylen E J Co ordination of arm muscles during
exion and supination application of the tensor analysis approach Neuro
science
Gomez T Beach G Co oke C Hrudey W and Goyert P Normative
database for trunk range of motion strength velo city and endurance with
the isostation B lumbar dynamometer Spine
Gracovetsky S and Farfan H The optimum spine Spine
Gracovetsky S Farfan H and Helleur C The ab dominal mechanism
Spine
Gracovetsky S Farfan H F and Lamy C A mathematical mo del of the
lumbar spine using an optimized system to control muscles and ligaments
Orthopedic Clinics of North America
Gracovetsky S F arfan H F and Lamy C The mechanism of the
lumbar spine Spine
Granata K P and Marras W S An EMG assisted mo del of loads on the
lumbar spine during asymmetric trunk extensions J Biomech
Granata K P and Marras W S An EMG assisted mo del of trunk
loading during free dynamic lifting J Biomech
Gravel D Gagnon M Plamondon A and Desjardins P Develop
ment and application of predictive equations of maximal static moments
generated by the trunk musculature Clin Biomech
Gray H Anatomy descriptive and surgical The Bo ok Company Sydney
Australia
Bibliography Bibliography
Guzik D C Keller T S Szpalski M Park J H and Sp engler D M
A biomechanical mo del of the lumbar spine during upright isometric exion
extension and lateral b ending Spine
Han J S Go el V K and Kumar S A nonlinear optimization mo del
of the human lumbar spine Int J Indust Erg
Harms J Moss Transforaminal PLIF DePuy Motech Inc
Miami
Hawkins D and Bey M Muscle and tendon force length prop erties and
their interactions in vivo J Biomech
Hollinshead W H Anatomy for surgeons Volume The back and
rd
limbs edn Harp er Row Publishers Pennsylvania
Hughes R E Empirical evaluation of optimization basedlumbar muscle
forceprediction models PhD thesis The UniversityofMichigan Ann Arb or
MI
Hughes R E Choice of optimization mo dels for predicting spinal forces
in a three dimensional analysis of heavy work Ergonomics
Hughes R E Bean J C and Cha n D B Ev aluating the e ect of
co contraction in optimization mo dels J Biomech
Hughes R E Cha n D B Lavender S A and Andersson G B J
Evaluation of muscle force prediction mo dels of the lumbar trunk using
surface electromyography J Orthop Res
Jackson R P and McManus A C Radiographic analysis of sagittal
plane alignment and balance in standing volunteers and patients with low
back pain matched for age sex and size a prosp ective controlled clinical
study Spine
Jorgensen M J and Marras W S The e ect of lumbar back supp ort
tension on trunk muscle activity Clin Biomech
Kaufman K R An K and Chao E Y S Incorp oration of muscle archi
tecture into the muscle length tension relationship J Biomech
Korovessis P Stamatakis M and Baikousis A Segmental ro entgeno
graphic analysis of vertebral inclination on sagittal plane in asymptomatic
versus chronic low back pain patients J Spinal Disord
Bibliography
Ladin Z and Ne K M Testing of a biomechanical mo del of the lumbar
muscle force distribution using quasi static loading exercises JBiomech Eng
Ladin Z Murthy K R and De Luca C J Mechanical recruitment
of low back muscles theorectical predictions and exp erimental validation
Spine
Ladin Z Murthy K R and De Luca C J The e ects of exter
nal b ending moments on lumbar muscle force distribution J Biomech Eng
Lavender S A Tsuang Y H Andersson G B J Hafezi A and Shin C C
a Trunk muscle co contraction the e ects of moment direction and
moment magnitude J Orthop Res
Lavender S A Tsuang Y Hafezi A Andersson G B J Cha n D B and
Hughes R E b Coactivation of the trunk muscles during asymmetric
loading of the torso Human Factors
Lo e er A Stanford R Stanford P and Walsh W R A mechanical
analysis of p olyaxial p edical screws Spine Society of Australia Annual
Scienti c Meeting
Macintosh J E and Bogduk N The morphology of the lumbar erector
spinae Spine
Macintosh J E Bogduk N and Gracovetsky S The biomechanics of
the thoracolumbar fascia Clin Biomech
Macintosh J E Valencia F Bogduk N and Munro R R The
morphology of the human lumbar multi dus Clin Biomech
Marras W S Predictions of forces acting up on the lumbar spine under
isometric and isokinetic conditions a mo del exp eriment comparison Int J
Indust Erg
Marras W S and Granata K P A biomechanical assessment and mo del
of axial twisting in the thoracolumbar spine Spine
Marras W S and Granata K P Spine loading during trunk lateral
b ending motions J Biomech
Masset D F Piette A G and Malchaire J B Relation between
functional characteristics of the trunk and the o ccurrence of low back pain
Spine
Bibliography Bibliography
McGill S M Electromyographic activity of the ab dominal and lowback
musculature during the generation of isometric and dynamic axial trunk
torque implications for lumbar mechanics J Orthop Res
McGill S M Amyo electrically based dynamic three dimensional mo del
to predict loads on lumbar spine tissues during lateral b ending J Biomech
McGill S M and Norman R W Partitioning of the L L dynamic
moment into disc ligamentous and muscular comp onents during lifting
Spine
McGill S M and Norman R W E ects of an anatomically detailed
erector spinae mo del on L L disc compression and shear J Biomech
McGill S M and Norman R W Potential of lumb o dorsal fascia
forces to generate back extension moments during squat lifts J Biomed
Eng
McGill S M Patt N and Norman R W Measurement of the trunk
musculature of active males using CT scan radiography implications for
force and moment generating capacity ab out the L L joint J Biomech
McGill S M Santaguida L and Stevens J Measurement of the trunk
musculature from T to L using MRI scans of young males corrected for
muscle bre orientation Clin Biome ch
McNeill T Warwick D Andersson G and Schultz A Trunk strenghts
in attempted exion extension and lateral b ending in healthy sub jects and
patients with low back disorders Spine
Mirka G Kelaher D Baker A Harrison A and Davis J Selective
activation of the external oblique musculature during axial torque pro duc
tion Clin Biomech
Mo at D B and Mottram R F Anatomy and Physiology for Physio
therapists Blackwell Scienti c Publications Oxford
Nussbaum M A and Cha n D B a Development and evaluation of a
scalable and deformable geometric mo del of the human torso Clin Biomech
Bibliography
Nussbaum M A and Cha n D B b Evaluation of arti cial neural net
work mo delling to predict torso muscle activity Ergonomics
Nussbaum M A Cha n D B and Martin B J a Aback propagation
neural network mo del of lumbar muscle recruitment during mo derate static
exertions J Biomech
Nussbaum M A Cha n D B and Rechtien C J b Muscle lines of
action a ect predicted forces in optimization based spine muscle mo deling
J Biomech
Nussbaum M A Martin B J and Cha n D B A neural network
mo del for simulation of torso muscle co ordination J Biomech
O Brien P R andPotvin J R Fatigue related EMG resp onses of trunk
muscles to a prolonged isometric twist exertion Clin Biomech
Ogston N G King G J and Gertzb ein S D Centro de patterns in
the lumbar spine Baseline studies in normal sub jects Spine
Parnianp our M Nordin M Kahanovitz N and Frankel V The
triaxial coupling of torque generation of trunk muscles during isometric
exertions and the e ect of fatiguing isoinertial movements on the motor
output and movement patterns Spine
Pearcy M J and Bogduk N Instantaneous axes of rotation of the
lumbar intervertebral joints Spine
Pedersen D R Brand R A Cheng C and Arora J S Direct com
parison of muscle force predictions using linear and nonlinear programming
J Biomech Eng
Pop e M H Svensson M Andersson G B J Broman H and Zetterb erg C
The role of prerotation of the trunk in axial twisting e orts Spine
Potvin J R and O Brien P R Trunk muscle co contraction increases
during fatiguing isometric lateral b end exertions Spine
Raschke U and Cha n D B Supp ort for a linear length tension re
lation of the torso extensor muscles an investigation of the length and
velo city EMG force relationships J Biomech
Bibliography Bibliography
Reid J G Costigan P A and Comrie W Prediction of trunk
muscle areas and moment arms by use of anthrop ometric measures Spine
Robb R A and Hanson D P D Imaging in Medicine NATO ASI
Series Vol F chapter A software system for interactiveand quantitative
analysis of biomedical images pp
Robb R A Hanson D P Karwoski R A Larson A G Workman E L
and Stacy M C ANALYZE A comprehensive op erator interactive
software package for multidimensional medical image display and analysis
Computerized Medical Imaging and Graphics
Schultz A Loads on the lumbar spine in M Jayson ed The lumbar
spine and back pain rd edn Churchill Livingston UK chapter
Schultz A Andersson G Ortengren R Hadersp eck K and Nachemson A
Loads on the lumbar spine J Bone Joint Surg A
Schultz A B Mo dels for analyses of lumbar spine loads Appl Mech Rev
S S
Schultz A B and Andersson G B J Analysis of loads on the lumbar
spine Spine
Schultz A Hadersp eck K Warwick D and Portillo D Use of lumbar
trunk muscles in isometric p erformance of mechanically complex standing
tasks J Orthop Res
Seroussi R E and Pop e M H The relationship b etween trunk muscle
electromyography and lifting moments in the sagittal and frontal planes J
Biomech
Stokes I A F and Gardner Morse M Lumbar spine maximum ef
forts and muscle recruitment patterns predicted by a mo del with multijoint
muscles and joints with sti ness J Biomech
Stokes I A F and Gardner Morse M a Lumbar spinal muscle ac
tivation predicted by multi criteria cost function International Society of
th
Congress Book of Abstracts Biomechanics XVII
Stokes I A F and Gardner Morse M b Quantitative anatomy of the
lumbar musculature J Biomech
Bibliography
Tesh K M Shaw Dunn J and Evans J H The ab dominal muscles
and vertebral stability Spine
Tracy M F Gibson M J Szypryt E P Rutherford A and Corlett E N
The geometry of the muscles of the lumbar spine determined by
magnetic resonance imaging Spine
Tsuang Y H Novak G J Schipplein O D Hafezi A Tra mow J H and
Andersson G B J Trunk muscle geometry and centroid lo cation
when twisting J Biomech
van Die en J H Are recruitment patterns of the trunk musculature
compatible with a synergy based on the maximization of endurance J
Biomech
Vedantam R Lenke L G Keeney J A and Bridwell K H Compar
ison of standing sagittal spinal alignment in asymptomatic adolescents and
adults Spine
nd
White A and Panjabi M Clinical biomechanics of the spine edn
J B Lippincott Company Philadelphia
th
Williams P L and Warwick R eds Gray s Anatomy edn
Churchill Livingstone Edinburgh
Woittiez R D Huijing P A Bo om H B K and Rozendal R H
A three dimensional muscle mo del a quanti ed relation b etween form and
function of skeletal muscles J Morphol
Zetterb erg C Andersson G B J and Schultz A B The activity of
individual trunk muscles during heavy physical loading Spine