-
Annals of Biomedical Engineering,Vol. 29, pp. 263–274, 2001
0090-6964/2001/29~3!/263/12/$15.00Printed in the USA. All rights
reserved. Copyright © 2001 Biomedical Engineering Society
Evaluation of a Deformable Musculoskeletal Model for
EstimatingMuscle–Tendon Lengths During Crouch Gait
ALLISON S. ARNOLD, SILVIA S. BLEMKER, and SCOTT L. DELP
Mechanical Engineering Department, Biomechanical Engineering
Division, Stanford University, Stanford, CA
(Received 14 September 2000; accepted 22 January 2001)
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Abstract—The hamstrings and psoas muscles are often lenened
surgically in an attempt to correct crouch gait in perswith
cerebral palsy. The purpose of this study was to determif, and
under what conditions, medial hamstrings and pslengths estimated
with a ‘‘deformable’’ musculoskeletal modaccurately characterize
the lengths of the muscles during wing in individuals with crouch
gait. Computer models of fosubjects with crouch gait were developed
from magnetic renance~MR! images. These models were used in
conjunctwith the subjects’ measured gait kinematics to
calculatemuscle–tendon lengths at the body positions
correspondinwalking. The lengths calculated with the MR-based
modwere normalized and were compared to the lengths estimusing a
deformable generic model. The deformable modeleither left
undeformed and unscaled, or was deformed or scto more closely
approximate the femoral geometry or bodimensions of each subject.
In most cases, differences betwthe normalized lengths of the medial
hamstrings computed wthe deformable and MR-based models were less
than 5Differences in the psoas lengths computed with the deformaand
MR-based models were also small~,3 mm! when thedeformable model was
adjusted to represent the femoral geetry of each subject. This work
demonstrates that a deformmusculoskeletal model, in combination
with a few subjespecific parameters and simple normalization
techniques,provide rapid and accurate estimates of medial
hamstringspsoas lengths in persons with neuromuscular disord© 2001
Biomedical Engineering Society.@DOI: 10.1114/1.1355277#
Keywords—Musculoskeletal model, Muscle, Hip, Knee, GaMagnetic
resonance imaging, Cerebral palsy.
INTRODUCTION
‘‘Tight’’ muscles that are thought to restrict movement are
often lengthened surgically in an effort to iprove walking in
persons with cerebral palsy.5,20 Forexample, short or spastic
hamstrings are presumedlimit knee extension in many children who
walk withtroublesome crouch gait; these patients frequentlydergo
hamstrings lengthening surgery.20 Excessive flex-
Address correspondence to Allison S. Arnold, Mechanical
Enneering Department, Biomechanical Engineering Division,
StanfUniversity, Stanford, CA 94305-3030. Electronic
[email protected]
263
n
.
-
.
ion of the hip during walking is commonly treated bsurgical
lengthening of the psoas tendon.35
Unfortunately, the outcomes of muscle–tendon sgeries to correct
crouch gait and other movement abnmalities in persons with
neuromuscular disorders areconsistent and sometimes
unsatisfactory.20 Lengtheningof the hamstrings often decreases
excessive knee flexHowever, the hamstrings produce an extension
momabout the hip as well as a flexion moment aboutknee, and
interventions that weaken the hamstringslead to other problems
during walking, such as exaggated hip flexion during the stance
phase, or insufficiknee flexion and foot clearance during
swing.18,36 Surgi-cal lengthening of the psoas, in some patients,
diminisexcessive hip flexion.35 However, a scientific basis
fopredicting which patients are likely to benefit from hamstrings
and/or psoas lengthening procedures curredoes not exist. We believe
that analyses of the musctendon lengths during crouch gait may help
distingupatients who have short muscles from those who dohave short
muscles, and thus may provide a more eftive means to identify
candidates who would benefrom surgery.
Several investigators have used computer modelsthe lower
extremity, in conjunction with joint anglemeasured during gait
analysis, to estimate the lengththe hamstrings and psoas muscles
during normalcrouch gait.16,21,32,37 In these studies,
muscle–tendolengths corresponding to crouch gait were normalizand
were compared to the lengths averaged for unpaired subjects to
determine if patients’ muscles woperating at normal lengths, or
lengths shorter than nmal. These analyses have suggested that many
indivals with crouch gait do not walk with ‘‘short’’ ham-strings;
in such cases, factors other than the hamstrmay be contributing to
knee flexion.16,21,32
Estimates of the muscle–tendon lengths in previostudies were
based on a generic model of the lowextremity,17 representing the
musculoskeletal geomeof an average-sized adult male. It is not
known hovariations in musculoskeletal geometry due to size, a
-
264 ARNOLD, BLEMKER, and DELP
FIGURE 1. Evaluation of a ‘‘deformable’’ musculoskeletal model.
The normalized lengths of the medial hamstrings and psoasmuscles
estimated with a deformable generic model „A… were compared to the
lengths calculated from models of four individu-als with crouch
gait developed from MR images †e.g., subject 4 „B…‡.
onon
s aif-lsy
ntf ati-h aoreion
ndzedele-
ried
de-deric
leith
ifictic
deldingalteicalee ofthsndatem
ect-ral
or pathology affect the accuracy of muscle–tendlength
calculations. In prior studies, the muscle–tendlengths were
normalized by the lengths of the musclethe anatomical position in
an effort to account for dferences in size. However, children with
cerebral pafrequently exhibit excessive anteversion of the femur.5
Ifthis torsional deformity substantially alters the momearms ~i.e.,
the lever arm, or mechanical advantage omuscle at a joint! of
muscles about the hip, then esmates of the muscle–tendon lengths
calculated witgeneric model may be inaccurate or misleading.
Befgeneric models can be used to guide treatment decisfor specific
patients, the models must be tested.
Schutte et al.32 modified an existing lower limbmodel17 to
investigate the sensitivity of hamstrings apsoas lengths to femoral
anteversion angle. Normalihamstring lengths computed with the
‘‘deformed’’ modwere similar to the lengths calculated with the
undformed model; however, normalized psoas lengths vawith
deformation of the femur. Schutteet al. did notvalidate their model
on the basis of patient-specificscriptions of musculoskeletal
anatomy, such as datarived from medical images. Hence, whether a
gene
t
s
-
model—deformed or undeformed—can provide reliabestimates of the
muscle–tendon lengths in persons wfemoral deformities remains
unclear.
Methods to construct highly accurate, subject-specmodels of the
musculoskeletal system from magneresonance~MR! images have been
developed.1,11,33 Atthe present time, however, building an MR-based
mofor every child with crouch gait would be costly anlabor
intensive. Other investigators have proposed usgeneric models in
combination with multidimensionscaling techniques, or ‘‘hybrid’’
models that incorporajust a few subject-specific parameters, to
analyze clinproblems.7,9 However, validation studies that confirm
thefficacy of these approaches are lacking. The purposthis study
was to determine if the muscle–tendon lengestimated with a generic
musculoskeletal model asimple normalization techniques are
sufficiently accurto distinguish patients who have short muscles
frothose who do not have short muscles, or whether subjspecific
variations in bone dimensions and/or femogeometry need to be
considered.
-
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265Evaluation of a Deformable Musculoskeletal Model
METHODS
A graphics-based model of the lower extremity with‘‘deformable’’
femur was developed, and the accurawith which this model
characterizes the lengths of tmedial hamstrings and psoas muscles
in individuals wcerebral palsy, at the body positions
correspondingcrouch gait, was evaluated~Fig. 1!. To test the
deform-able model, detailed models of four subjects with crougait
were created from an extensive set of MR imagThese models were
used, in conjunction with each sject’s measured gait kinematics, to
determine the lengof the medial hamstrings and psoas muscles at the
jangles corresponding to walking. The lengths calculawith the
MR-based models were normalized and wcompared to the lengths
estimated using four variatiof our deformable generic model. In the
first variatiothe deformable model was left undeformed and unscaIn
subsequent variations, the deformable model eitwas deformed or was
scaled to more closely approximthe femoral geometry or bone
dimensions of each sject.
Development of the Deformable Generic Model
The deformable musculoskeletal model developedthis study
characterizes the geometry of the pelvis,mur, and proximal tibia,
the kinematics of the hip atibiofemoral joints, and the paths of
the medial hastrings and psoas muscles for an average-sized amale.
This model is similar to the deformable lower limmodels we have
used in previous studies,31 with thefollowing improvements. First,
we refined the locatioof the muscle attachments reported by Delpet
al.17 to beconsistent with three-dimensional surface representatof
the muscles and bones of three lower extremitydaveric specimens
generated from MR images. Secwe implemented a description of
tibiofemoral kinematthat accounts for the three-dimensional
rotations atranslations of the tibia relative to the femur;40 in
previ-ous models, we neglected the rotations of the tibia infrontal
and transverse planes. Third, we defined ‘‘wraping surfaces,’’39 in
addition to ‘‘via points,’’17 to simu-late interactions between the
muscles and surroundanatomical structures, thereby providing an
improvemover previous models that used straight-line approximtions
of the muscle–tendon paths. Finally, we developnew algorithms to
alter the geometry of the proximfemur. These algorithms were based
on careful insption of the deformed femurs of four subjects with
cerbral palsy constructed from MR images. Our resultimodel was
capable of estimating the lengths of the mdial hamstrings and psoas
muscles for a range of femdeformities commonly observed in persons
with cereb
t
.
lt
s
,
-
l
palsy and a variety of body positions, including hip aknee
angles that corresponded to normal and crouch
We defined the bone geometry, joint kinematics, amuscle–tendon
paths of our deformable model usinmusculoskeletal modeling
package,SIMM.13 The surfacegeometry of each bone was described by a
polygomesh. Coordinate systems for the pelvis, femur, and twere
established from anatomical landmarks,1 and kine-matic descriptions
of the hip and tibiofemoral joints wespecified based on the bone
surface geometry. Thewas represented as a ball-and-socket joint.
Thebiofemoral joint prescribed the translations and rotatioof the
tibia relative to the femur as functions of kneflexion angle, and
was based on published experimemeasurements of tibiofemoral
kinematics.29,40 Our proce-dures for establishing the segment
coordinate systand joint kinematics have been reported in
detpreviously.1
The paths of the semimembranosus and semitendsus muscles, which
comprise the medial hamstrings,the psoas muscle were defined for a
range of hipknee motions. The line of action of each muscle
wcharacterized by a series of line segments. The attament sites of
the muscles were identified, and wrappsurfaces and via points were
introduced to simulatederlying structures and other anatomical
constraints.refined the muscle attachment sites by graphically
supimposing three-dimensional surface meshes ofmuscles and bones,
generated from MR images of thlower extremity cadaveric specimens,
onto our deforable model. Although the psoas originates from
ttransverse processes of the lumbar vertebrae, we fixeorigin to the
model’s pelvis reference frame, rather thto a separate sacral or
lumbar reference frame. Hechanges in the length of the psoas in our
model reflchanges in hip angles only.
We prescribed the paths of the muscles throughrange of hip and
knee motions by specifying wrappisurfaces and via points as
follows. First, for each of thlower extremity cadaveric specimens,
we createdgraphics-based kinematic model of the hip joint,
thebiofemoral joint, and the surrounding musculature froMR images.1
Second, for each muscle, we developedalgorithm to specify the
position, orientation, and dimesions of an ellipsoidal wrapping
surface and the locatioof via points relative to skeletal
landmarks. We cholandmarks that could be identified on each of the
Mbased models and on the deformable model. Wesigned the path of
each muscle to be consistent withmuscle surfaces constructed from
MR images, whminimizing penetration into bones or other muscles.
Fthe medial hamstrings, wrapping surfaces were potioned at the
distal femur to prevent the muscle–tendpaths from penetrating the
posterior femoral condyand adjacent soft tissues with knee
extension. A via po
-
266 ARNOLD, BLEMKER, and DELP
FIGURE 2. Description of femoral geometry: H is the center of
the femoral head, G is the most superior point on the
greatertrochanter, D is the most distal point on the lesser
trochanter, Lt is the tip of the lesser trochanter, P is the
attachment of theposterior cruciate ligament, O is the center of
the base of the femoral neck, which was determined by iteratively
locating thecentroid of the femoral diaphysis on a cross section
passing through the midpoint of the vector joining points G and
D,perpendicular to the vector joining points O and P. Lc and Mc are
the posterior aspects of the lateral and medial condyles.
Thefemoral neck axis is defined by points O and H, the femoral
shaft axis by points O and P; these two axes define the plane ofthe
femoral neck. Anteversion is the angle formed by the plane of the
femoral neck and the plane of the condylar axis, whichpasses
through points O and P parallel to the vector joining points Lc and
Mc . Neck–shaft angle is the angle formed by thefemoral neck axis
and the femoral shaft axis. Lesser trochanter torsion angle is the
angle formed by the plane of the condylaraxis and the plane, which
passes through points O, P, and Lt . If point Lt is anterior to the
condylar axis, this angle is definedas positive. If point Lt is
posterior to the condylar axis, the angle is defined as negative.
The figure is adapted from Murphyet al. „Ref. 27… and
Calais-Germain „Ref. 8….
no-ingwa
pinipniatotheeo-theter
cle
theel.urandithedcectsy-ctsricand
a
hisomto
was added proximal to the insertion of the semitendisus to mimic
the constraints produced by surroundconnective tissues. For the
psoas, a wrapping surfaceplaced near the acetabulum to characterize
the wrapand sliding of the muscle over the pelvic brim and
hcapsule. A via point representing the ‘‘effective’’ origiof the
psoas was fixed at the pelvic brim. Another vpoint was located
proximal to the muscle’s insertionprevent the muscle–tendon path
from penetratingfemoral neck with hip internal rotation. We
verified thefficacy of each algorithm by comparing the muscle mment
arms calculated with the MR-based models ofthree cadaveric
specimens to the moment arms demined experimentally on the same
specimens.1 Once analgorithm was developed that could predict the
musmoment arms with sufficient accuracy~i.e., moment armswithin 10%
of the experimental data! for all three speci-
sg
-
mens, the same algorithm was used to specifymuscle–tendon paths
of our deformable generic mod
We developed techniques to deform the femur of ogeneric model to
represent excessive anteversionother deformities commonly observed
in persons wcrouch gait. To do this, we compared the undeformfemur
of our generic model to three-dimensional surfarepresentations of
the deformed femurs of four subjewith cerebral palsy generated from
MR images. We hpothesized that the deformed femurs of the
subjecould be well characterized by three
geometparameters—anteversion angle, neck-shaft angle,lesser
trochanter torsion angle—and we developedmathematical description
of each parameter~Fig. 2!. Thesubjects with cerebral palsy who were
imaged in tstudy had femoral anteversion angles that ranged fr34°
to 47°, neck-shaft angles that ranged from 129°
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267Evaluation of a Deformable Musculoskeletal Model
TABLE 1. Characteristics of the cerebral palsy subjects and the
undeformed generic model.
Subject 1 Subject 2 Subject 3 Subject 4 Generic model
Gender F M M M MAge (yrs) 7 14 14 27 adultHeight (cm) 126 132
169 165 NAe
Weight (kg) 24.7 25.6 51.9 45.4 NAe
Femur lengtha 31.1 36.0 40.3 37.5 39.6Anteversion angleb 47 34
44 46 20Neck-shaft angleb 129 131 138 142 125Lesser trochanter
torsion angleb 216 214 27 113 233Hip flexion during stance
phasec
of gait (max/min)51/3 14/7 39/17 61/28 NAe
Knee flexion during stance phased
of gait (max/min)33/3 39/29 39/26 83/73 NAe
aSuperior–inferior dimension from center of femoral head to
midpoint between femoral epicondyles, in units of cm.bDefined in
Fig. 2, in units of degrees.cAngle formed in the sagittal plane
(i.e., the plane perpendicular to the medial–lateral axis of the
pelvis, as defined by the left and rightanterior superior iliac
spines) between the long axis of the thigh and a vector
perpendicular to the plane formed by the left and rightanterior
superior iliac spines and posterior superior iliac spines, in units
of degrees; hip flexion is represented as a positive angle and
isapproximately 12° at the anatomical position.
dAngle formed in the sagittal plane (i.e., the plane
perpendicular to the medial–lateral axis of the femur, as defined
by a knee alignmentdevice) between the long axis of the thigh and
the shank, in units of degrees; knee flexion is represented as a
positive angle and is 0°at the anatomical position.
eNot applicable.
ried
20°he
arethe
hased
hisan
cts.aft
rm-rti-. Toanxis,thexisralxis
theustnteralcesasthese
ce,thecleheterthe
bleoasR-bralerg a
beder
ctedto
g-chre-esro-
on-es,
142°, and lesser trochanter torsion angles that vafrom 216° to
113° ~Table 1!. The femur of our unde-formed generic model has an
anteversion angle ofand a neck-shaft angle of 125°, which are
within tnormal range for unimpaired adults.10,38 Our definitionsof
femoral anteversion angle and neck-shaft angleconsistent with
descriptions that have been used inpast by clinicians and other
investigators.27 A definitionof lesser trochanter torsion angle, to
our knowledge,not appeared previously in the literature. We
examinthe orientation of the lesser trochanter carefully in tstudy
because it influences the path of the psoas,because it varied
substantially among our four subje
We altered the femoral anteversion angle, neck-shangle, and
lesser trochanter torsion angle of our defoable model by rotating
and/or translating the bone veces that make up the femoral head,
neck, and shaftincrease the anteversion angle, the femoral headneck
were rotated anteriorly about the femoral shaft athereby increasing
the angle between the plane offemoral neck axis and the plane of
the condylar a~Fig. 2!. To increase the neck-shaft angle, the
femohead and neck were rotated superiorly about an athrough the
diaphysis of the femur, perpendicular toplane formed by the femoral
neck and shaft. To adjthe lesser trochanter torsion angle, the
lesser trochawas rotated anteriorly or posteriorly about the
femoshaft axis. After each transformation, the bone vertiproximal
to the femoral condyles were translatedneeded to restore the
position of the femoral head inacetabulum. The insertion of the
psoas on the les
d
d
r
r
trochanter was displaced with the bone vertices. Henthe length
of the psoas at the anatomical position,moment arms, and the length
changes of the musduring movement were altered by these
deformities. Tposition of the knee center with respect to the hip
cenin our deformable model was not changed; thus,paths of the
medial hamstrings were not affected.
Construction of the MR-Based Models
We assessed the accuracy with which our deformamodel could
estimate medial hamstrings and pslengths during crouch gait by
creating detailed, Mbased models of four subjects selected from the
cerepalsy clinics at the Children’s Memorial Medical Centin
Chicago. Each subject underwent gait analysis usinfive-camera
motion measurement system~VICON, Ox-ford Metrics, Oxford, U.K.!.
The subject’s three-dimensional gait kinematics were computed as
describy Kadabaet al.,22 based on estimates of the joint
centlocations as suggested by Daviset al.12 The limb thatshowed the
greatest degree of knee flexion was selefor further analysis. The
subjects ranged in age from 727 yr and walked with different gait
abnormalities, raning from a relatively mild crouch gait to a
severe crougait ~Table 1!. None of the subjects had undergone
pvious surgery, and all were able to walk without orthosor other
assistance. All subjects and/or their parents pvided informed
written consent.
The process of creating each MR-based model csisted of six
steps. Step 1 was to acquire the MR imag
-
achicalurera-erarucasesct’ki-eds tibecolc-
the
le
R-f thel.ths
soare-ics.thas
ive
oasandedwer
e
gaitongthsgedcle
heg,
ls.ub-m-of
to
ion
ionion
268 ARNOLD, BLEMKER, and DELP
which was done using a 1.5 T Signa MR Scanner~GEMedical Systems,
Milwaukee, WI!. Approximately 200T1-weighted spin echo images were
collected for esubject. Step 2 was to identify and outline the
anatomstructures of interest on each image. These structincluded
the pelvis, sacrum, femur, tibia, semimembnosus, semitendinosus,
and psoas. Step 3 was to genthree-dimensional surface
reconstructions of each stture from the two-dimensional outlines,
and step 4 wto register the surfaces from adjacent series of
imagThis yielded an accurate representation of each subjeanatomy at
one limb position. Step 5 was to definenematic models of the hip
and tibiofemoral joints bason each subject’s bone surface geometry.
Step 6 wacharacterize the muscle–tendon paths, as descrabove, for a
range of hip and knee motions. Our protofor MR imaging, our
techniques for surface reconstrution and registration, and our
methods for specifyingjoint kinematics are described in detail
elsewhere.1
Comparison of Lengths Calculated with the Deformaband MR-Based
Models
Muscle–tendon lengths determined from the Mbased models were
used to examine the accuracy olengths estimated with the deformable
generic modFor each of our four cerebral palsy subjects, the lengof
the semimembranosus, semitendinosus, and pmuscles were calculated
at the limb positions corsponding to the subject’s measured gait
kinematSemimembranosus length was calculated betweenmuscle’s origin
and insertion. Semitendinosus length wcalculated between the
muscle’s origin and its effect
FIGURE 3. Deformation and scaling of the generic model.The
undeformed femur of the generic model †„A…, solid bone ‡was altered
to more closely approximate the bone dimen-sions and femoral
geometry of each subject „e.g., subject 4,wireframe bone … by
scaling the model along anatomical axes„B…, increasing its femoral
anteversion angle „C…, or adjust-ing its femoral anteversion angle,
neck-shaft angle, andlesser trochanter torsion angle „D….
s
te-
.s
od
e
s
e
insertion near the posterior femoral condyles. Pslength was
computed between the muscle’s insertionits effective origin at the
pelvic brim; hence, we assumthat changes in psoas length due to
rotations at the lolumbar spine and lumbosacral joint were
negligible.
The lengths of the muscles during crouch gaitLi werenormalized
based on the maximum averaged lengthLmaxand the minimum averaged
lengthLmin of the muscleduring normal gait as follows:
L̂ i5~Li2Lmin!/~Lmax2Lmin!,
where L̂ i is the normalized length of the muscle at thi th
point of the gait cycle. Values ofLmax andLmin wereobtained for
each model based on the measuredkinematics of 18 unimpaired
subjects. This normalizatitechnique is relevant because the
muscle–tendon lenof cerebral palsy subjects are often compared to
averadata from unimpaired subjects to determine if a musis shorter
or longer than normal during walking.16,32,37
Using this technique, the normalized lengths of tmuscles for
unimpaired subjects, during normal walkinwere similar when
calculated with the different mode
The muscle–tendon lengths calculated with each sject’s MR-based
model were normalized and were copared to the lengths estimated
using four variationsthe deformable generic model:~i! the
undeformed ge-neric model,~ii ! the undeformed generic model
scaledthe subject along anatomical axes,~iii ! the generic
modeldeformed to match the subject’s femoral anteversangle, called
Deformed Model A, and~iv! the genericmodel deformed to match the
subject’s anteversangle, neck-shaft angle, and lesser trochanter
tors
TABLE 2. Factors a for scaling the generic model to theMR-based
models.
Subject 1 Subject 2 Subject 3 Subject 4
PelvisAP dimensionb 0.65 0.61 0.95 0.90SI dimensionc 0.82 0.72
0.98 0.88ML dimensiond 0.69 0.64 1.01 0.92
Femur and TibiaAP dimensione 0.74 0.79 0.86 0.85SI dimensionf
0.78 0.89 1.01 0.93ML dimensiong 0.86 0.89 1.03 0.94
aScale factors represent the ratio of the MR-based model
dimen-sion to the generic model dimension.
bAnterior–posterior dimension from anterior superior iliac
spine(ASIS) to hip center.
cSuperior–interior dimension from ASIS to ischial
tuberosity.dMedial–lateral dimension from right ASIS to left
ASIS.eLength of the tibial plateau in the sagittal plane.fDistance
from hip center to the midpoint between spheres fit tothe medial
and lateral posterior femoral condyles.
gMedial–lateral dimension between femoral epicondyles.
-
dur
oonericthethed to
asial–o-
-theliedres
en-wo
onablyd b-
ntthejecsesst-
ts insedcala-
ndclele–
Wecheakesayal-ith
d in
at-is-els
onehelenhe
1.8
ithSDed-
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za-us
del-
un-an
so,ingsed
theed
nd-al-al-ng
269Evaluation of a Deformable Musculoskeletal Model
angle, called Deformed Model B~Fig. 3!. In variation II,we
altered the bone dimensions~change in size! prior tonormalization;
in variations III and IV, we introducelocalized changes in the
geometry of the proximal fem~change in shape! prior to
normalization. Our goal was tdetermine whether the normalized
muscle–tendlengths estimated with our undeformed, unscaled genmodel
are generally of sufficient accuracy to guideplanning of
muscle–tendon surgery, or whetherfemoral geometry or bone
dimensions of patients neebe considered.
In variation II, the undeformed generic model wscaled to each
subject along anterior–posterior, medlateral, and superior–inferior
axes using a linear homgeneous transformation.24 All bones, joints,
muscle attachments, via points, and wrapping surfaces inmodel were
scaled. Different scale factors were appto structures associated
with the pelvis, and to structuassociated with the femur and tibia.
We chose dimsions for computing the scale factors according to
tcriteria. First, we required each dimension to be basedskeletal
landmarks that could be palpated or reasonestimated. This ensured
that the scaling scheme woulapplicable to other individuals with
crouch gait, if desired, without having to build a model of every
patiefrom image data. Second, we attempted to scalebones of the
generic model to the bones of each subas accurately as possible. We
used an iterative clopoint method4 and a Gauss–Newton nonlinear
leasquares algorithm~MATLAB Optimization Toolbox, TheMathWorks,
Natick, MA! to calculate scale factors thaminimized the total
distance between the bone verticethe generic model and bone
vertices in each MR-bamodel. We then selected anatomical dimensions
for sing that produced scale factors similar to the optimiztion
solution ~Table 2!.
The normalized lengths of the medial hamstrings apsoas muscles
were plotted at every 2% of the gait cyFor each subject and each
model, the peak musctendon lengths during crouch gait were
computed.were particularly interested in the accuracy with whiour
deformable generic model could estimate the plengths of the muscles
during crouch gait, because thare the times in the gait cycle when
tight muscles mrestrict movement. Differences in the peak lengths
cculated with the MR-based models and estimated weach version of
the deformable model were expresse‘‘standard deviations’’~SD! of
the peak lengths duringnormal gait, determined from the averaged
gait kinemics of 18 unimpaired subjects. This unit enabled constent
comparisons of the errors to be made across modFor the
semimembranosus, the equivalent length ofSD ranged from 2.8 to 4.4
mm, as calculated with tdifferent models. For the semitendinosus,
the equivalength of one SD ranged from 3.4 to 5.4 mm. For t
e
tt
-
.
e
.
t
psoas, the equivalent length of one SD ranged fromto 3.0 mm.
RESULTS
The peak medial hamstrings lengths computed wthe undeformed
generic model differed by at most 1from the peak lengths calculated
with each MR-basmodel ~Table 3!, with the exception of the
semitendinosus of subject 4~Fig. 4!. The discrepancy for
subjectreflects the abnormally posterior path of the
subjecsemitendinosus in the popliteal region, which was edent in
the MR images. Scaling the generic modeleach subject along
anatomical axes prior to normalition did not improve the accuracy
of semimembranosor semitendinosus lengths estimated with the
mo~Table 3!. The normalized lengths of the medial hamstrings
estimated with the generic model, scaled orscaled, were not
systematically greater or smaller ththe lengths calculated with the
MR-based models. Alerrors in the normalized muscle–tendon lengths
durcrouch gait were not consistently increased or decreaat any
particular part of the gait cycle.
Errors in the peak psoas lengths computed withundeformed generic
model during crouch gait rangfrom 0.5 to 1.8 SD~Table 3!. The
smallest error wasobtained for subject 2, who was the least
impaired aleast deformed subject~Fig. 5!. For the other three
subjects, the undeformed model underestimated the normized length
of the psoas throughout the gait cycle. Scing the undeformed model
to each subject alo
TABLE 3. Errors a,b in peak muscle–tendon lengths estimatedwith
the deformable model.
Subject 1 Subject 2 Subject 3 Subject 4
Semimembranosusc
Generic model 20.9 20.2 11.0 10.6Scaled model 21.0 21.0 11.2
10.7
Semitendinosusd
Generic model 20.9 10.3 10.3 13.2Scaled model 21.0 20.5 10.6
13.3
Psoase
Generic model 20.8 10.5 21.8 21.6Scaled model 20.7 10.6 21.8
21.8Deformed Model A 10.3 0.0 20.9 20.9Deformed Model B 10.2 0.0
20.2 20.6
aError defined as the difference in peak muscle–tendon
lengthduring crouch gait calculated with the deformable and
MR-basedmodels, expressed in standard deviations of the peak
lengthduring normal walking.
bPositive value indicates that the peak length estimated with
thedeformable model is greater than the peak length computed
withthe MR-based model.
c1 SD52.8–4.4 mm, as calculated with the different models.d1
SD53.4–5.4 mm, as calculated with the different models.e1
SD51.8–3.0 mm, as calculated with the different models.
-
270 ARNOLD, BLEMKER, and DELP
FIGURE 4. Plots of normalized semitendinosus length vs gait
cycle, estimated with the undeformed generic model „dotted line
…and calculated with the MR-based model „solid line … for subject 2
„best result … and subject 4 „worst result …. The normalizedlength
of the semitendinosus during normal gait, averaged for 18
unimpaired subjects „meanÁ1 SD, shaded region … is shownfor
comparison.
thedel
the
ct-redfor.9
anatomical axes did not improve the accuracy ofnormalized psoas
lengths estimated with the mo~Table 3!.
The generic model more accurately estimated
length of the psoas during crouch gait when subjespecific
variations in femoral geometry were conside~Fig. 5!. Errors in the
peak psoas lengths computedDeformed Model A ranged in magnitude
from 0 to 0
FIGURE 5. Plots of normalized psoas length vs gait cycle,
estimated with the undeformed generic model „dotted line …,
thegeneric model deformed to match the subject’s femoral
anteversion angle, neck–shaft angle, and lesser trochanter
torsionangle „Deformed Model B, dashed line …, and calculated with
the MR-based model „solid line … for subject 2 „best result …
andsubject 4 „worst result …. The normalized length of the psoas
during normal gait, averaged for 18 unimpaired subjects „meanÁ1SD
shaded region …, is shown for comparison.
-
m
ndcyan-ro-
inby
re-lterle–fterusdo
inee–acihathastryWetalandcannts.cu-r
seedurediarmcesandble
eregedheble
gthelych
thede-at
ry.ne
gle
nearinrgleialvethsel.ble-
ides inical
fo-
deltorss inith
hatthslderic
gestl inthser-ca-ways,owerethehethesti-ay
edericb-
-la-/ortheandithser-
gthscalthesese-
271Evaluation of a Deformable Musculoskeletal Model
SD; errors computed for Deformed Model B ranged fro0 to 0.6
SD~Table 3!.
DISCUSSION
Biomechanical models that compute the lengths amoment arms of
soft tissues with sufficient accurahave tremendous potential to
impact the design, plning, and evaluation of a variety of
musculoskeletal pcedures. Surgeons frequently introduce
changesmuscle force- and moment-generating capacitiesmodifying the
lengths or moment arms of muscles. Pdicting the biomechanical
consequences of surgical aations, therefore, requires detailed
knowledge of musctendon lengths and moment arms before and
asurgery. Generic models, representing normal adult mculoskeletal
geometry, have been used to simulate tenlengthenings,15 tendon
transfers,7,14,25 osteotomies,3,6,19,31
and other procedures. These analyses have determhow variations
in surgical parameters affect muscltendon lengths, moment arms,
force-generating capties, and joint contact forces
postoperatively—data tare relevant to surgical planning. However,
no studyreported how variations in musculoskeletal geomeacross
patients might influence the simulation results.believe that the
accuracy with which musculoskelemodels represent individuals of
different sizes, ages,pathologies must be investigated before
simulationsbe widely used to guide treatment decisions for
patie
Descriptions of muscle–tendon lengths are partilarly applicable
to the planning of interventions focrouch gait and other movement
abnormalities becautight muscle that restricts movement is often
lengthensurgically. In this study, we developed models of
foindividuals with crouch gait from MR images, and wused these
models to examine the accuracy of mehamstrings and psoas lengths
estimated with a defoable generic model. In seven of eight cases,
differenin the normalized lengths of the
semimembranosussemitendinosus muscles estimated with the
deformamodel and calculated with the MR-based models wless than 5
mm, or about 1 SD of the lengths averafor unimpaired subjects
during normal gait. Errors in tnormalized psoas lengths estimated
with the deformamodel were also less than 1 SD of the averaged
lenfor unimpaired subjects—if the model was appropriatdeformed to
approximate the femoral geometry of easubject.
To put these errors into perspective, we calculatedlength
changes of the medial hamstrings for a 30°crease in popliteal
angle, a typical improvement thmight result from hamstrings
lengthening surgePopliteal angle measures the degree to which the
kcan be passively extended with the hip flexed 90°.5,23
Several studies have reported average popliteal an
-
-n
d
-
a
l-
s
e
s
near 60° before surgery and average popliteal angles30°
following surgical lengthening of the hamstringspersons with
cerebral palsy.2,18 We determined, using oudeformable model, that a
decrease in popliteal anfrom 60° to 30° increases the lengths of
the medhamstrings by about 2.5 cm. This is approximately fitimes
larger than errors in the muscle–tendon lengduring crouch gait
estimated with our deformable modBased on these data, we believe
that a deformamodel, in conjunction with a few subject-specific
parameters and simple normalization techniques, can provreasonable
estimates of the muscle–tendon lengthmost cases. Whether such
estimates can aid surgdecision-making for persons with cerebral
palsy is acus of our ongoing work.
We found that scaling our undeformed generic moto each subject
along orthogonal axes, using scale facbased on the bone dimensions,
did not reduce errorthe normalized muscle–tendon lengths estimated
wthe undeformed, unscaled model. This result implies tour scheme
for normalizing the muscle–tendon lengwas effective in minimizing
errors that otherwise wouhave been caused by size variations
between the genmodel and each MR-based model. The data also sugthat
our homogeneous scaling method was not helpfureducing discrepancies
in the muscle–tendon lengfrom other potential sources, such as
nonsystematicrors caused by variations in the muscle attachment
lotions relative to the joint centers. In a study of elbomuscles in
ten upper extremity specimens, Murret al.28 reported that the
dimensions of the humeruulna, and radius bones were not good
predictors of elbflexion moment arms unless the bone dimensions
walso correlated with the shortest distances betweenmuscle
attachments and the axis of elbow flexion. Tfact that our simple
scaling method did not enhanceaccuracy of the normalized
muscle–tendon lengths emated with the generic model is consistent
with Murret al.’s observations.
A large difference was observed in the normalizlength of the
semitendinosus estimated with the genmodel and calculated with the
MR-based model of suject 4 ~Fig. 4 and Table 3!, due to the
abnormally posterior path of the subject’s semitendinosus tendon
retive to the knee. Whether any generic model andnormalization
scheme would accurately characterizesemitendinosus length of
subject 4 is questionable,the incidence of such abnormalities among
persons wcrouch gait is not known. However, scaling algorithmbased
on the muscle’s effective attachments could phaps reduce such
errors in the muscle–tendon lenestimated with a generic model.
Developing a practimethod to locate the muscle attachments relative
tohip and knee joints in persons with cerebral palsy poa challenge,
but minimal MR protocols, or thre
-
.iththeof
estroto
elstro-Alllesoneof
de-edith
orwhoThitte
erheal-ectntsispad
n.noowbe
de-
sod-dono-llyav-are
oftome
csoncedthehi
int,hipactud-
nd
s
oflsandeegedk-ng-m-atein-a-
cts
dyodidonsmeedheectbeea-ch
oaser-en-ontoon
ingy-xi-scleot,
oashipal-er-ndter-ur-ts
ti-dur-bleve
272 ARNOLD, BLEMKER, and DELP
dimensional ultrasound techniques, might be feasibleThe
normalized lengths of the psoas estimated w
the undeformed generic model were shorter thanlengths calculated
with the MR-based models for threethe four subjects in this study.
It is likely that differencin femoral anteversion angle, neck-shaft
angle, lesserchanter torsion angle, and neck length all
contributedvariations in the muscle–tendon lengths across
modDifferences in size and development of the lesserchanter, for
the younger subjects, were also factors.of the subjects in this
study walked with psoas muscthat were substantially shorter than
normal; hence, nwould have been ‘‘misclassified’’ as having a
psoasnormal length based on the predictions of the unformed model.
However, the tendency of the undeformmodel to underestimate psoas
length in persons wfemoral deformities, and in particular, the
potential fthe model to underestimate psoas length in patientsmay
not have a short psoas, is cause for concern.observation agrees
with the conclusions of Schuet al.32
Reasonably accurate estimates of psoas length wobtained for all
four subjects in this study when tfemoral anteversion angle of the
generic model wastered to match the anteversion angle of each
subjThus, for future analyses of psoas lengths in patiewith femoral
deformities, use of a deformable modelrecommended. The femoral
anteversion angle of atient could be rapidly estimated from
ultrasounimages,26,38 palpation of the greater trochanter,30 or
mea-surement of the patient’s hip rotation range of motio5
Such methods for determining anteversion angle maybe as accurate
as the methods used in this study; hever, the resulting
muscle–tendon lengths are likely tomore accurate than would be
obtained from an unformed generic model.
It is important to keep in mind some of the limitationof this
study. First, we assumed that the MR-based mels provided accurate
estimates of the muscle–tenlengths in the subjects with cerebral
palsy. Our algrithms to define the muscle–tendon paths were
initiaused to construct models of three lower extremity caderic
specimens; hence, they were validated through cful anatomical
dissections and detailed comparisonsthe muscle moment arms
calculated with the modelsthe moment arms determined experimentally
on the saspecimens.1 Nevertheless, errors in the joint kinematior
invalid assumptions about how the muscle–tendpaths change with bone
deformities could have produerrors in the muscle–tendon lengths
determined fromMR-based models. For example, we assumed that
thecould be well represented by a ball-and-socket joeven though
some persons with cerebral palsy havethat are subluxed or
dislocated. Subjects 3 and 4, in fshowed some evidence of hip
subluxation. In future st
-
.
s
e
.
-
t-
-
p
s,
ies, detailed analyses of how skeletal orientations
amuscle–tendon paths change with joint configurationinvivo may
improve the reliability of kinematic modelderived from static MR
images.
Second, we developed models from MR imagesonly four subjects
with crouch gait. The four individuawho were imaged spanned a wide
range of sizesages; their femur dimensions from hip center to
kncenter ranged from 31 to 40 cm, and their ages ranfrom 7 to 27
yr. They also exhibited various musculoseletal impairments, with
femoral anteversion angles raing from 34° to 47° and gait
abnormalities ranging froa ‘‘jump knee’’ pattern34 to a severe
crouch. Nevertheless, whether our deformable model is suitably
accurfor estimating medial hamstrings or psoas lengths individuals
with more severe bone deformities, or in ptients with gait patterns
much different from the subjewho were analyzed, remains
untested.
We calculated the length of the psoas in this stufrom the
muscle’s effective origin at the pelvic brim tits insertion on the
lesser trochanter. Thus, our modelnot account for changes in psoas
length due to rotatiat the lower lumbar spine and lumbosacral
joint. Sochildren with crouch gait, however, exhibit increaslumbar
lordosis in addition to excessive hip flexion. Tdegree to which
these variations in spine position affthe length of the psoas is
unknown. If this issue is toaddressed in future studies, a system
to accurately msure the kinematics of the lumbar spine during
crougait is needed.
Finally, accurate estimates of hamstrings and pslengths during
crouch gait may be insufficient to detmine the most appropriate
treatment. Ideally, recommdations for muscle–tendon surgery might
be basedquantitative descriptions of how a procedure is likelyalter
the muscle force-generating properties, andknowledge of how the
altered muscle force-generatproperties are likely to influence a
patient’s gait. Analsis of the muscle–tendon lengths only weakly
appromates this ideal. Such analyses can determine if a muis
‘‘short’’ during crouch gait, but such analyses canncurrently
explainwhy a muscle is short. Furthermoreseveral factors other than
tight hamstrings or psmuscles may contribute to crouch gait such
as: weakextensors, deficient plantar flexors, or problems with
bance. Certainly, much more work is needed to undstand how surgical
lengthening of the hamstrings apsoas muscles affect the muscle
actions, and to demine how these muscles, altered by pathology or
sgery, contribute to the motions of the limb segmenduring crouch
gait.
Despite these limitations, we remain cautiously opmistic that
analyses of hamstrings and psoas lengthsing crouch gait, based on a
well-tested deformamodel, could aid in the development of more
effecti
-
onstiveblesis,m.ota-eacfo
nd
elpnaith
ski,b
er,-dofe-
e-l-eate
lp.sed
m-
P.s of
of
lsy.
ofofmt.
e-cs.
A:
u-
ip
.n.
ry:reirst
ndA..
ait
ys-ruc-
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e.ait:
p,thees.
n-.
ipce-
ac
-
n.el
es
g
ando-
-bral
273Evaluation of a Deformable Musculoskeletal Model
treatment plans. Surgical recommendations for perswith crouch
gait, at present, are based on qualitaobservations of the patient’s
gait, assessment of variameasured during clinical examination and
gait analyand the intuition and experience of the clinical
teaMuscle–tendon lengths provide information that is nreadily
available from gait analysis or clinical examintion, but which is
relevant to surgical planning. Thdeformable model presented here
enables rapid andcurate estimation of hamstrings and psoas
lengthsindividuals with a range of movement abnormalities afemoral
deformities.
ACKNOWLEDGMENTS
Special thanks to Peter Loan and Ken Smith for hwith development
of the modeling software; to DeanSchmidt Asakawa and JoAnn Mason
for assistance wdata collection and analysis; and to Stephen
VankoCarolyn Moore, Claudia Kelp-Lenane, Julie Witka, RoNovak, and
Tony Weyers of the Motion Analysis CentChildren’s Memorial Medical
Center in Chicago, for providing the gait data. Much of this work
was performewhile the authors were affiliated with the
DepartmentsBiomedical Engineering and Physical Medicine and
Rhabilitation at Northwestern University and with the Rhabilitation
Institute of Chicago. We gratefully acknowedge funding from NIH
Grant No. R01 HD33929, thUnited Cerebral Palsy Foundation, and a
NSF GraduResearch Fellowship to S.B.
REFERENCES
1Arnold, A. S., S. Salinas, D. J. Asakawa, and S. L. DeAccuracy
of muscle moment arms estimated from MRI-bamusculoskeletal models
of the lower extremity.Comput. Aid.Surg. 5:108–119, 2000.
2Baumann, H. U., H. Reutsch, and K. Schurmann. Distal hastring
lengthening in cerebral palsy.Int. Orthop. 3:305–309,1980.
3Benvenuti, J. F., L. Rakotomanana, P. F. Leyvraz, D.Pioletti,
J. H. Heegaard, and M. G. Genton. Displacementthe tibial
tuberosity.Clin. Orthop. Relat. Res.343:224–234,1997.
4Besl, P. J., and N. D. McKay. A method for registration3D
shapes.IEEE Trans. Pattern Anal. Mach. Intell.14:239–256, 1992.
5Bleck, E. E. Orthopaedic Management in Cerebral PaLondon: Mac
Keith Press, 1987, pp. 282–391.
6Brand, R. A., and D. R. Pedersen. Computer modelingsurgery and
a consideration of the mechanical effectsproximal femoral
osteotomies. In: The Hip: Proceedings frothe 12th Open Scientific
Meeting of the Hip Society. SLouis: C. V. Mosby, 1984.
7Buford, W. L., and D. E. Thompson. A system for thredimensional
interactive simulation of hand biomechaniIEEE Trans. Biomed.
Eng.34:444–453, 1987.
s
-r
8Calais-Germain, B. Anatomy of Movement. Seattle, WEastland
Press, Inc., 1993, p. 183.
9Chao, E. Y. S., J. D. Lynch, and M. J. Vanderploeg. Simlation
and animation of musculoskeletal joint system.J. Bio-mech.
Eng.115:562–568, 1993.
10Clark, J. M., M. Freeman, and D. Witham. The relationshof neck
orientation to the shape of the proximal femur.J.Arthrop. 2:99–109,
1987.
11Cohen, Z. A., D. M. McCarthy, H. Roglic, J. H. Henry, WG.
Rodkey, J. R. Steadman, V. C. Mow, and G. A. AteshiaComputer-aided
planning of patellofemoral joint OA surgeDeveloping physical models
from patient MRI. In: LectuNotes in Computer Science 1496.
Proceedings from the FAnnual Conference on Medical Image Computing
aComputer-Assisted Interventions, edited by W. M. Wells,Colchester,
and S. Delp. Berlin: Springer, 1998, pp. 9–20
12Davis, R. B., S. Ounpuu, D. Tyburski, and J. R. Gage. A
ganalysis data collection and reduction technique.Hum. Mov.Sci.
10:575–587, 1991.
13Delp, S. L., and J. P. Loan. A graphics-based software stem to
develop and analyze models of musculoskeletal sttures.Comput. Biol.
Med.25:21–34, 1995.
14Delp, S. L., D. A. Ringwelski, and N. C. Carroll. Transfer
othe rectus femoris: effects of transfer site on moment arabout the
knee and hip.J. Biomech.27:1201–1211, 1994.
15Delp, S. L., K. Statler, and N. C. Carroll. Preserving
planflexion strength after surgical treatment for contracture
oftriceps surae: a computer simulation study.J. Orthop.
Res.13:96–104, 1995.
16Delp, S. L., A. S. Arnold, R. A. Speers, and C. A.
MoorHamstrings and psoas lengths during normal and crouch
gimplications for muscle–tendon surgery.J. Orthop. Res.14:144–151,
1996.
17Delp, S. L., J. P. Loan, M. G. Hoy, F. E. Zajac, E. L. Topand
J. M. Rosen. An interactive graphics-based model oflower extremity
to study orthopaedic surgical procedurIEEE Trans. Biomed.
Eng.37:757–767, 1990.
18Dhawlikar, S. H., L. Root, and R. L. Mann. Distal lengtheing
of the hamstrings in patients who have cerebral palsyJ.Bone Jt.
Surg.74–A:1385–1391, 1992.
19Free, S. A., and S. L. Delp. Trochanteric transfer in total
hreplacement: effects on the moment arms and forgenerating
capacities of the hip abductors.J. Orthop. Res.14:245–250,
1996.
20Gage, J. R. Gait Analysis in Cerebral Palsy. London: MKeith
Press, 1991, pp. 101–172.
21Hoffinger, S. A., G. T. Rab, and H. Abou-Ghaida. Hamstrings in
cerebral palsy crouch gait.J. Ped. Orthop.13:722–726, 1993.
22Kadaba, M. P., H. K. Ramakrishnan, and M. E. WootteMeasurement
of lower extremity kinematics during levwalking. J. Orthop.
Res.8:383–392, 1990.
23Katz, K., A. Rosenthal, and Z. Yosipovitch. Normal rangof
popliteal angle in children.J. Ped. Orthop.12:229–231,1992.
24Lew, W. D., and J. L. Lewis. An anthropometric scalinmethod
with application to the knee joint.J. Biomech.10:171–181, 1977.
25Lieber, R. L., and J. Friden. Intraoperative
measurementbiomechanical modeling of the flexor carpi
ulnaris-textensor carpi radialis longus tendon transfer.J.
Biomech.Eng. 119:386–391, 1997.
26Miller, F., F. Y. Liang, M. Merlo, and H. T. Harcke. Measuring
anteversion and femoral neck-shaft angle in cerepalsy. Dev. Med.
Child Neurol.39:113–118, 1997.
27Murphy, S. B., S. R. Simon, P. K. Kijewski, R. H. Wilkin-
-
akper
n-
a.
p.lting
ofs o
.ns
or-
.rim
ch-
gait.
ry,in-a-
.o-
H.m-.
ctsan-
274 ARNOLD, BLEMKER, and DELP
son, and N. T. Griscom. Femoral anteversion.J. Bone Jt.Surg.
69–A:1169–1176, 1987.
28Murray, W., T. S. Buchanan, and S. L. Delp, Scaling of
pemoment arms of elbow muscles with dimensions of the upextremity.
J. Biomech.~accepted for publication!.
29Nisell, R., G. Nemeth, and H. Ohlsen. Joint forces in extesion
of the knee.Acta Orthop. Scand.57:41–46, 1986.
30Ruwe, P. A., J. R. Gage, M. B. Ozonoff, and P. A.
DeLucClinical determination of femoral anteversion,J. Bone Jt.Surg.
74–A:820–830, 1992.
31Schmidt, D. J., A. S. Arnold, N. C. Carroll, and S. L.
DelLength changes of the hamstrings and adductors resufrom
derotational osteotomies of the femur.J. Orthop. Res.17:279–285,
1999.
32Schutte, L. M., S. W. Hayden, and J. R. Gage.
Lengthshamstrings and psoas muscles during crouch gait:
effectfemoral anteversion.J. Orthop. Res.15:615–621, 1997.
33Smith, D. K., T. H. Berquist, K.-N. An, R. A. Robb, and EY. S.
Chao. Validation of three-dimensional reconstructioof knee anatomy:
CT vs MR imaging.J. Comput. Assist.Tom. 13:294–301, 1989.
34Sutherland, D. H., and J. R. Davids. Common gait abnmalities
of the knee in cerebral palsy.Clin. Orthop. Relat.Res.288:139–147,
1993.
f
35Sutherland, D. H., J. L. Zilberfarb, K. R. Kaufman, M. PWyatt,
and H. G. Chambers. Psoas release at the pelvic bin ambulatory
patients with cerebral palsy: operative tenique and functional
outcome.J. Pediatr. Orthop.17:563–570, 1997.
36Thometz, J., S. Simon, and R. Rosenthal. The effect onof
lengthening of the medial hamstrings in cerebral palsyJ.Bone Jt.
Surg.71–A:345–353, 1989.
37Thompson, N. S., R. J. Baker, A. P. Cosgrove, I. S. Corand H.
K. Graham. Musculoskeletal modelling in determing the effect of
botulinum toxin on the hamstrings of ptients with crouch gait.Dev.
Med. Child Neurol.40:622–625,1998.
38Upadhyay, S. S., T. O’Neil, R. G. Burwell, and A. MoultonA new
method using medical ultrasound for measuring femral anteversion:
technique and reliability.J. Anat. 155:119–132, 1987.
39van der Helm, F. C. T., H. E. J. Veeger, G. M. Pronk, L.V. van
der Woude, and R. H. Rozendal. Geometry paraeters for
musculoskeletal modelling of the shoulder
systemJ.Biomech.25:129–144, 1992.
40Walker, P. S., J. S. Rovick, and D. D. Robertson. The effeof
knee brace hinge design and placement on joint mechics. J.
Biomech.21:965–974, 1988.