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Christophe SAURET, Hélène PILLET, Wafa SKALLI, Morgan SANGEUX - On the use of knee
functional calibration to determine the medio-lateral axis of the femur in gait analysis: Comparison
with EOS biplanar radiographs as reference - Gait & Posture - Vol. 50, p.180-184 - 2016
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On
the
use
of
knee
functional
calibration
to
determine
the
medio-lateral
axis
of
the
femur
in
gait
analysis:
Comparison
with
EOS
biplanar
radiographs
as
reference
Christophe
Sauret,
PhD
a,*
,
Hélène
Pillet,
PhD
a,
Wafa
Skalli,
PhD
a,
Morgan
Sangeux,
PhD
b,ca
InstitutdeBiomécaniqueHumaineGeorgesCharpak,ArtsetMétiersParisTech,151boulevarddel'Hôpital,F-75013Paris,France
b
HughWilliamsonGaitAnalysisLaboratory,TheRoyalChildren’sHospital,50FlemingtonRoad,ParkvilleVictoria,3052Melbourne,Australia
c
TheMurdochChildren’sResearchInstitute,Melbourne,Australia
Keywords: Biplanarradiographs Femur Functionalcalibration Gaitanalysis Knee Medio-lateralaxis ABSTRACT
Accuratecalibrationofthemedio-lateralaxisofthefemuriscrucialforclinicaldecisionmakingbasedon gaitanalysis.Thisstudyproposesaprotocolutilizing biplanarradiographstoprovideareferencemedio-lateralaxisbasedontheanatomyofthefemur.Thebiplanarradiographsallowed3Dmodellingofthe bonesof thelowerlimbsandthemarkersusedformotioncapture,inthestandingposture.A comprehensiveanalysiswasperformedandresultsfrombiplanar radiographswerereliablefor3D markerlocalization(0.35mm)andfor3Dlocalizationoftheanatomicallandmarks(1mm),leadingto aprecisionof1 forthe orientationofthecondylaraxisofthefemuranda95%confidenceintervalof3 afterregistrationwithmotioncapturedata.Theanatomicalcondylaraxiswas
comparedtoa conventional,marker-based,axisandthreefunctionalcalibrationtechniques(axistransformation, geometricaxisfitandDynaKAD).Resultsfor theconventionalmethodshowanaveragedifferencewith thecondylaraxisof15 (SD:6).ResultsindicateDynaKADfunctionalaxiswastheclosesttothe anatomicalcondylaraxis,mean:1 (SD:5)whenappliedtopassivekneeflexionmovement.However, therangeoftheresultsexceeded15 forallmethods.
Hence,theuseofbiplanarradiographs,oran alternativeimagingtechnique,mayberequiredtolocatethemedio-lateralaxisofthefemurreliablyprior toclinical decisionmakingforfemurderotationalosteotomies.
1. Introduction
Gaitanalysisquantifieskinematicsandkineticsofthelower limbsduringwalkingtoinformsurgicaldecisionmaking[1].For example,itiscrucialtointerprethiprotationkinematicsinrelation totheanatomyofthefemur(e.g.femoralneckanteversion)priorto deciding upon femur derotation osteotomy [2]. However, hip rotationkinematicsisamongtheleastrepeatableoutputofgait analysis[3].Hiprotationiscalculatedastheanglebetweenthe medio-lateralaxesofthefemurandthepelvisinthetransverse planeof the femur [4]. The medio-lateral axisof the femur is consideredtheculprit for the lackof reliability of hiprotation kinematics[5].
Conventional gait models determine the medio-lateral axis frommarkersplacedoverthelateralandmedialepicondyles,or fromthepositionofakneealignmentdevice[6].Thesemodelsare affectedbymarkerplacementerrorsandauthorshaveproposed alternativefunctional methods [7].Functional methods usethe movement of the knee joint to determinean optimal flexion-extension axis (FLEXaxis) embedded in the femur coordinate system[7,8].Ingaitanalysis,thecross-productofthisaxiswiththe longitudinal axis (defined from knee to hip joint centres) determines theanterior-posterior axis.Then, the cross product oftheanterior-posterioraxisandthelongitudinalaxisdetermines themedio-lateralaxis.Therefore,bothFLEXaxisandmedio-lateral axesareinthefrontalplaneofthefemurbutonlythemedio-lateral axisisconstrained tobeperpendicular tothelongitudinalaxis. These functional methods were validated in silico [7] and sometimesbymeansofmechanicaldevices[9,10].Thevalidation invivohasfocusedonintraandinterexaminerreliability[5,11,12]. New 3Dmodelling fromlow dosebiplanarradiographs [13]
allows the simultaneous acquisition of the position of
bone-* Correspondingauthor.
E-mailaddresses:christophe.sauret@ensam.eu(C.Sauret), helene.pillet@ensam.eu(H.Pillet),wafa.skalli@ensam.eu(W.Skalli), morgan.sangeux@rch.org.au(M.Sangeux).
embedded joint centresand axes as well as markers used for motionanalysisinvivo,withthesubjectsin aneutral standing posture[14,15].Theaimsofthis studywere(1)toproposeand evaluateabenchmarktolocatethemedio-lateralaxisofthefemur basedonbiplanarradiographs(BPR)and(2)tocomparearangeof conventional and functional methods based on skin-mounted markersagainsttheBPRmedio-lateralaxis.
2. Materialsandmethod
Followingapprovalbytherelevantethicscommittee, 13healthy volunteers(8malesand5females)participatedtothisstudy.On average,thesubjectswere33years(SD:14,range:22–60),height was1.74m(SD:0.09m,range:1.55–1.92m),bodymasswas73kg (SD: 12kg, range: 54–91kg) and Body Mass Index (BMI) was 23.9kg/m2(SD:3.8kg/m2,range:16.8–29.4kg/m2).Theprotocol
forthestudyhasbeendescribedpreviously[14].Thesubjectswere equippedwith14mmskinmarkers(Fig.1a)trackedat100Hzwith 8T10Viconcameras(Vicon,OxfordMetrics,UK).Standingstatic calibrationacquisitionwasperformed,followedbykneefunctional calibration and walking trials. Low-dose biplanar radiographs (EOS1system,EOSimaging,France)wereacquiredimmediately after,withoutremovingthemarkers.
2.1.Proposalandevaluationofabenchmarktolocatethe medio-lateralaxisofthefemur
Three-dimensionalshapemodelsofthefemursweredeformed andfittedtothefrontalandsagittalradiographs[16](Fig.1b).We definedthecentreofthefemoralhead(FH)andthecentresofthe medial(MPC) andlateral(LPC)posterioraspectofthecondyles (Fig.1c)byleastsquarefittingspherestothenodeofthemeshin thecorrespondinganatomicalregions.Thekneejointcentre(KJC) wasdefinedasthemid-pointbetweenMPCandLPC.The medio-lateralaxiswasdefinedbythetranscondylaraxis(TCA),theaxis passing through MPC and LPC (Fig.1c) [17]. The skinmarkers positionsinEOSwereobtainedfrom14mmspherespositionedby matchingtheircontourswiththat of themarkersin the radio-graphs(Fig.1b).
ThejointcentresandTCAaxiswasassessedontherightfemurs of six subjects three times by two skilled examiners. The
reproducibly variance (SRi2, [18]) which include intra- and
between-assessors repeatability variances was calculated as follows:
SRi2¼Sri2þSLi2 ð1Þ
whereSri2isthemeanoftheassessorvariances,and SLi2isthe
variance of the mean results obtained by each assessor, for a particularithsubject.Theglobalreproducibilityestimate(S
R)was calculatedas: SR¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn i¼1SRi2 n s ð2Þ wherenisthenumberofsubjects.
ReliabilityofthemarkerpositionsfromBPRwasassessedbased ontheentiremarkersetsforfoursubjects,assessedthreetimesby fourexaminers.Wecalculatedtherigidtransformationbetween thethighmarkersetsdeterminedfromBPRandmotioncapture systemsthroughleastsquarefit[19].Reliabilitywascalculatedas therootmeansquaredistance(RMSD)betweenthetwomarker setsafterregistration.
Thecombineduncertaintywasquantifiedfrom100000 Monte-Carlosimulations persubject.Randomisotropic Gaussiannoise wasaddedtotheBPRandmotioncapturedata.Noisemagnitude wasdefinedfromtheestimatesobtainedaboveforBPRdataandby astandarddeviationof1mmforthemotioncapturedata[20].This procedurewasperformedforallsubjectsandtheoverallreliability wascalculatedusingEq.(2)withSRicorrespondingtothestandard
deviationofthesimulationsfortheithsubject,andn=13.
2.2.Evaluationofconventionalandfunctionalmethodstodefinethe medio-lateralaxis
Theconventionalgaitmethodusedtwomarkerslocatedover themedialandlateralepicondylesoftheknee.Theepicondyles were palpated and the markers positioned by an orthopedic surgeon.Weimplementedthreefunctionalmethodstodetermine thekneeaxis:theaxistransformation technique(ATT, [7]), the geometricaltechnique[21]andDynaKAD,whichfindstheaxisthat minimisesthevarianceinthefrontalplanekinematicsattheknee
[8].Thefunctionalmethodswereappliedtotwomovements:five
Fig.1.A)Frontviewofthesubjectequippedwithreflectivemarkers.Whitemarkersarethoseusedinthisstudytoperformtheregistrationwhereasgreymarkerswerenot presentduringthebiplanarradiographsacquisitionornotusedhere.B)Lateralandcoronalradiographsfortherightlimbwithsuperimposedbonyreconstructionsand registeredmarkers.C)Subject-specificreconstructionoftherightfemurwithspheresfittedonposterioraspectsofthecondylesandtranscondylaraxis.
kneeflexion-extensions(openkinematicchain)andthreewalking strides.Trialswerecapturedwithsubjectswalkingcontinuouslyat 5km/honatreadmillforapproximatelyoneminute.Footcontact andfootoffeventswereselectedvisuallyforonestrideand auto-correlated in Nexus (Vicon, Oxford Metrics Group, UK). Three stridesinthemiddleofthetrialwereprocessedforthefunctional calibration. The five knee flexion-extensions were performed assistedorunassisted tosimulatetheeffectof lackofselective motorcontrolinpathologicalpopulations[15].Foreachframe,the transformationmatrixbetweenthestaticanddynamicposesof thethighandshankmarkersetswereobtainedfromleastsquare fit[19].
The location of the anatomical transepicondylar axis (BPR-basedTEA)wasalsodetermined,asthe3Dshape modelofthe femurcontainedregionsthatcorrespondtothemedialandlateral epicondylesofthefemur.
Thereferenceanatomicalcoordinatesystemofthefemurwas constructedfrom the BPR-based data registered in the motion captureenvironment(FH,KJCandTCA,Fig.1).Theprimaryaxis(Z, inferior-superior, perpendicular to the transverse plane of the femur)was specifiedby thevectorfrom KJC toFH.The X-axis (posterior-anterior, perpendicular to the frontal plane of the femur)wascalculatedfromthecrossproductbetweentheprimary axisandTCAasthesecondaryaxis.TheY-axis(perpendicularto thesagittalplaneofthefemur)wasdefinedasthecrossproduct betweenZ-andX-axes.Similarfemurcoordinatesystemswere constructedusingthesameprimaryaxisbutdifferentsecondary axes,fromfunctionalcalibrationsormarker-basedinsteadofTCA. The angular difference between the Y-axes of the different femurcoordinatesystemswascalculatedtocomparethedifferent medio-lateral axes. Repeated measure ANOVA and post-hoc Tukey’spairwisecomparisonswereperformedtorankandgroup themethodsaccordingtotheangulardifferencewithBPR-based TCA.
Hip and kneekinematicswerecalculated duringwalking to investigatetheimpactonkinematics.Thepelviscoordinatesystem wasdefinedusing4markerstapedovertheleft,andright,anterior, andposterior, superior iliacspines (L/RA/P SI).The originwas defined from the mid-point between LASI and RASI, and the medio-lateralaxis(primary,Y-)fromRASItoLASI.The superior-inferioraxis(Z-,pointingup)wasperpendiculartothetransverse planecontainingLASI,RASIandthemid-pointbetweenLPSIand RPSI.Theanterior-posterioraxis(X-,pointingforward)resulting fromthecross-productofY-andZ-.Thetibiacoordinatesystem wasdefinedusingtwoadditionalmarkerstapedoverthemedial andlateralmalleoli(MEDandANKrespectively).Thelongitudinal axis(primary,Z-)was definedfromthemid-pointbetweenthe ANKandMEDmarkerstotheKJC.Theanterior-posterioraxis(X-, pointingforward)wasperpendiculartotheplanecontainingKJC, andtheANKandMEDmarkers.Themedio-lateralaxis(Y-)resulted fromthecross-productof Z-andX-.Hip andkneeangleswere calculated following ISB recommendations [22] adapted tothe coordinatesystemsdefinedabove.Allprocessingwasperformedin Matlab1(TheMathworks,USA)andstatisticalanalysisinMinitab (MinitabInc.,USA).
3. Results
3.1.ReliabilityofBPR-baseddataandregistrationwithmotioncapture system
Thereproducibilityestimate(SR)fortheBPR-basedparameters
rangedbetween1.0and1.4mmforthelocationofFH,MPCandLPC (Table 1) and was 0.8mm for KJC and 1.0 for TCA. The reproducibilityestimate for markerlocation was similarfor all markersandabout0.35mm.Meandifferencesinmarkerpositions
afterleastsquarefittingbetweenBPR-basedandmotioncapture basedmarkersshowedRMSDof2.2mm(range:0.7–4.4mm).No correlationwasfoundbetweenRMSDandsubjectheight(r=0.23; p=0.24), body weight (r=0.27; p=0.16) nor body mass index (r=0.39, p=0.04). The overall uncertainty of the protocol, estimated from the Monte-Carlo simulations, was 1.5mm for the jointcentre location and 1.5 for axisorientation. The95% confidenceintervalsweretherefore3mmforKJC and3 for
TCA.
3.2.Evaluationofconventionalandvariousfunctionalmethodsto definethemedio-lateralaxisofthefemur
Fig.2presentstheresultsforthecomparison ofmethodsto definethemedio-lateralaxisofthefemurinthemotioncapture environment. Themeandifferencebetweenthe BPR-basedTCA andTEAwasmean(SD):5.7(1.4).Allthemethodsusedingait analysisprovidedmedio-lateralaxesmoreexternalthanTCA.The DynaKADmethod providedaxes that wereclosest toTCAwith meanangular differencesof9 (5.4),1 (5.1),8 (4.8)forthe active FE, passive FE and walking calibration movements, respectively. Results for the geometrical method were further externalcomparedtoTCAandwithlargerstandarddeviationthan DynaKAD:14(6.8),4(7.5),15(11.8)fortheactiveFE,passive FE andwalkingcalibrationmovements, respectively.Resultsfor the ATTtransformation technique produced standard deviation valuesofasimilarmagnitudetoDynaKADbutmoreexternalmean angulardifferencesof14(6.5),10(5.5),12(6.0)fortheactive FE,passiveFE andwalking calibrationmovements,respectively. Forallmethods,theactiveFEandwalkingmovementsresultedin largerdeviationthanforthepassiveFEmovement.Resultsforthe markerbased methodwere external withrespect toTCAwith averagedifferenceof15(5.9).
Theorientation ofthefemurmedio-lateralaxishad adirect effectonthehiprotationkinematics,andsomeeffectonthefrontal planekneekinematics,duringgait.Fig.3illustratestheseeffects when the functional calibration methods were applied to the passive FE movement. On average during the gait cycle, hip rotationwasabout10 internalfortheBPR-basedmodel(black) whereasallothermodelsweremoreexternal,exceptforDynaKAD. Theorientationofthefemurmedio-lateralaxishadnoeffectonthe kneekinematicsinthesagittalplanesincebothFHandKJCwere definedfromthesameBPR-baseddata.
4. Discussion
Ingaitanalysis,themedio-lateralaxisofthefemurcontributes tothedefinitionofhiprotationkinematics,akeyvariabletoinform decisionmakingaboutfemurderotationalosteotomy.Weaimedto proposeareferencemethodtolocatethemedio-lateralaxisofthe femur based on bi-planarradiographs (BPR) and to evaluate a rangeofconventionalandfunctionalmethods.
WeestimatedthereliabilityofBPR-basedkneeparameters(FH, KJC andTCA), markerlocalization andtheregistrationbetween BPR and motion capture systems. Reliability of 3D marker
Table1
Reliabilityofspecificpointsandkneejointcentrefollowingeachdirectionofthe femur reference frame and the norm. Reliability is expressed through the reproducibilityestimate(SR).
Unit X-axis Y-axis Z-axis Norm
Femoralhead mm 1.2 0.6 0.5 1.4
Lateralposteriorcondyle mm 0.7 0.9 0.4 1.2
localization from bi-planar radiographs (SR=0.35mm) appears
satisfactory compared to other sources of error in human movement analysis [20,23,24] and confirms previous results
[14].ThereliabilityofBPR-basedkneeparameterswassatisfactory withreproducibility around 1mm for KJC and 1 for TCA.The registrationofthethighmarkerclustersbetweenthetwostatic standingposes led to RMSDof 2mm onaverage. Monte-Carlo simulationsrevealedthe95%confidenceintervalwas3mmfor KJC location and 3 for TCA. These results demonstrate the
suitability of a biplanar radiographic system such as the EOS systemwiththeassociated3Dreconstructionmethodstoserveas areferencemethodtolocatethemedio-lateralaxisofthefemur. TheBPR-basedtranscondylaraxis(TCA)wascomparedwitha range of conventional and functional calibration methods. The conventionalmethodused markersover themedialand lateral epicondylesof thefemurand showed a differencewithTCAof about15external.Suchadifferencemaynotbeattributedtothe angulardifferencebetweentheTEAandTCAaxessincedifferences foundintheliteraturerangedbetween2.7and6.9[25–27].We
founda differencebetweentheBPR-basedTEA andTCAof5.7 external,inagreementwiththeliterature.Theangulardifference
betweenmarker-basedTEAandTCAislikelytobeduetomarker misplacement.Alimitationofourstudyisthatthepersonwho palpatedtheepicondyles didnot performmarkerplacement as part of routine clinical practice. However, the intra-observer reliability (6) in our study was in agreement with previous findings[28].
Functionalcalibrationmethodsusethekneeaxisasaproxyfor themedio-lateralaxisofthefemur.Wetestedthreealgorithms, thegeometricalmethod,theAxisTransformationTechnique(ATT) and DynaKAD. The methods were tested on three different movements, 5repetitions ofa passive(assisted)oractive (self-performed) openkinematic chainkneeflexion-extension and 3 walkingstrides.TheDynaKADmethodprovidedtheclosestaxisto theBPR-basedTCA.Thegeometricalfunctionalmethodwasclose to theBPR-based TCAwhen used in combination withpassive flexion-extensionbutwithmorevariableresults(SD:7.5)thanfor
DynaKAD(SD:5.1).TheATTfunctionalmethodwasmoreexternal (average mean: 12, average SD: 5.5)than thereference BPR-basedTCA.Overall,ourresultswereinagreementwitharecent studyusing3Dfreehandultrasound(ratherthanBPR)tolocatethe TCAaxis[29].
Fig.2. Boxplotoftheangulardifferenceofthedifferentmedio-lateralaxesofthefemurwithrespecttotheEOS-basedtranscondylaraxis(TCA).Theboxesarerepresented withadifferentcolourforeachmethod:redformarkerbased,blueforATT/SARAfunctional,orangeforgeometricalfunctional,andgreenforDynaKADfunctional.Forthe functionalmethods,threeboxesareplottedcorrespondingtothethreepossiblecalibrationmovements:activeflexion-extension(ActiveFE),passiveflexion-extension (PassiveFE)andWalking.Themeanforeachboxisrepresentedwithacrossinacircle,asterisksrepresentoutliers.Thelettersatthebottomofeachboxrepresentthe groupingresultsfromthepost-hocTukey’srankingfromA,theclosesttotheBPR-basedTCA,toF,thefurthest.Groupswhoshareletterswerenotsignificantly(a<0.05) differentfromeachother.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
Fig.3.Effectofthefemurmedio-lateralaxisdefinitiononhipandkneekinematicsforeachfunctionalmethodassociatedwiththepassivekneeflexion/extensionmovement. Thevariabilityinkinematicsisrepresentedbyshadedbandsrepresentingtheonestandarddeviationateachtimeinstant.ThemarkerandEOS-basedTCAinducedkinematics werealsorepresentedforvisualcomparisons.ThereferencekneekinematicscorrespondingtotheEOS-basedTCAisshowninblack,kinematicsfromthemarkerbased methodisshowninred,kinematicsfromthegeometricalfunctionalmethodisshowninorange,kinematicsfromtheATT/SARAfunctionalmethodisshowninblueandthe kinematicsfromtheDynaKADfunctionalmethodisshowningreen.Thefootcontactandfootoffeventsweredeterminedvisually(ratherthanfromforceplatedata)which ledtoagaitcycleslightlyshifted.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
TheATTandgeometricalfunctionalmethodsmodeltheknee jointasasinglefixedaxishingejoint.However,thekneeaxishas beenshowntomove,bothinlocationandinorientation,during knee flexion [30,31]. The motion of the knee may be better modelledasatwohingesjoint:oneforflexion-extensionandone forinternal/external rotation.Sucha modelofthekneedefines flexion-extensionasthemovementaroundthemedio-lateralaxis of the femur and internal/external rotation as the movement aroundthelongitudinalaxisofthetibia.Itcorrespondswellwith theCardananglesusedforthekneejoint:first,flexion-extension aroundtheY-axisof thefemurcoordinate system,then, varus/ valgus around the anterior-posterior axis of the intermediate coordinatesystemandlast,internal/externalrotationaroundthe longitudinalaxisofthetibia[32].TheDynaKADmethodfindsthe orientation of the Y-axis of the femur which minimises the varianceinkneevarus/valgus.Thisapproachisequivalenttousing thetwohingesmodeldescribedaboveandmayexplainwhythe axisprovidedbyDynaKADwasfoundtobetheclosesttothe BPR-basedTCAaxis.
A limitation of our study is that it only included subjects withoutkneeormotorcontrolpathologies,andthemeanangular differences reported therein may not generalise directly to populations with pathologies of the knee joint. Functional methodsmayrequire relatively largerange ofmovementtobe accurate.Itmaybedifficultforpatientswithwalkingdisabilitiesto performsuchmovementandthefindingsofthisstudy,onan able-bodiedpopulation,maynottranslatedirectlytopopulationswith restrictionintheirrangeofmovement.Itishoweverpossibleto assistpatientswithperformingthefunctionalcalibration move-ment [33] and our results show that functional methods performedwellwithpassiveflexion-extensionmovements.
Itisimportanttonotethattherangeoftheresultsexceeded15 forallconventionalandfunctionalmethods(Fig.2),whichindicate thatthesemethodsmayprovideinconsistentresults.Hence,EOS biplanar radiographs or an alternative medical image based technology (e.g. 3D freehand ultrasound, [29]) may still be required when major surgical decision, such as derotational osteotomies, depend on the reliable orientation of the frontal planeofthefemurandaccuratehiprotationkinematics.
Conflictofintereststatement
The authors declare they have no financial or personal relationships with other people or organization that could inappropriatelyinfluencetheirwork.
Acknowledgment
The authors are grateful to Vicon Motion Systems (Oxford MetricsGroup, UK)for the loan of themotion capture system necessaryforthefulfillmentofthisstudy.
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