evaluation of a deformable musculoskeletal model for estimating … · 2005. 11. 8. · deformities...

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]

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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…‡.

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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

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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

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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


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….

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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-

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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°


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.

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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

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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

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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….

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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.

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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

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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.


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.

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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.

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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

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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

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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

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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

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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.

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