Acta of Bioengineering and BiomechanicsVol. 10, No. 3, 2008Biomechanical changes of hip jointfollowing different types of corrective osteotomy photoelastic studiesNICOLAE ILIESCU1, *, STEFAN DAN PASTRAMA1, LUCIAN GH. GRUIONU2, GABRIEL JIGA11 Politehnica University of Bucharest, Romania.2 University of Craiova, Romania.The paper presents the results of some comparative experimental studies that show the biomechanical changes which appear following dif-ferent types of corrective osteotomy. The photoelastic technique was applied to plane models. The modifications in the stress distribution on thecontour after the osteotomy in comparison with the situation before surgery were studied. Three types of osteotomy are considered: valgus oste-otomy,varusosteotomyandChiaripelvisosteotomy.Usingthesameexperimentaltechnique,thedistributionofthecontactpressureattheinterfacebetweenthepolyethylenecupandthefemoralheadisinvestigated,foratotalhipprosthesis,astheextremesolutioninthecaseofadvanced hip arthroses. Both a normal situation and the malposition of prosthetic components were analyzed.Key words: corrective osteotomy, hip prosthesis, hip arthroses1. IntroductionThehipjoint,whichisthemostimportantjointofthehumanosteoarticularsystem,isaball-and-socketjoint having three degrees of freedom. Due toitscom-plex biomechanical functions, it plays an important rolein the locomotion process, both for statics and dynamicsofthetorso.Havingaspecificarchitectonicconfigura-tion,thefemoraljointprovidesmaximumstabilitybytransmitting the weight of the torso to pelvic members.At the same time, it represents the center around whichthe pelvis modifies its position during walking.Important modifications in the biomechanics of thenormalhip,witharthriticdegenerationwhichevolvesquite rapidly over time, appear due to different diseasesofthisjoint.Inordertodiminishthesemodifications,surgeryisperformed,preferablyinanearlystage,which allows us to avoid limited late solutions.Someofthemostfrequentdisordersofthehip,possiblyleadingtohiparthroplastyasthelasttreat-mentsolution,arethecoxarthrosisandthehipdys-plasia.Inthispaper,someresultsofcomparativeexperi-mentalresearchusingthephotoelastictechniquearepresented.Differentmodelswereusedinordertoiden-tifythebiomechanicalchangesofthestressstateinthecase of hip diseases or architectonic defects, in compari-sonwiththenormalanatomicsituations.Somecorrec-tiveandrepairosteotomiesappliedinthesurgeryprac-ticetotreathipjointdiseasesoranomaliesarestudiedusingthesametechnique.Finally,thebiomechanicalbehaviour of some hip prostheses, both for normal situa-tions and malposition, is studied.2. Physiopathology of hip jointCongenitalluxationofthehipcanbedefinedasa complete loss of the normal links between the femo-ral head and the cotyle. This illness can appear at birth______________________________* Corresponding author: Politehnica Universityof Bucharest, Bucharest, Romania, e-mail: nviliescu@yahoo.comReceived: April 28, 2008Accepted for publication: November 6, 2008N. ILIESCU et al. 66orlater,progressively,asanincreaseofthefemoralheadinabnormalposition.Therearethreestagesofthe hip luxation: i) simple dysplasia of the cotyle withthefemoralhead,ii)sub-luxation,wherethefemoralheadisinabnormalposition,andiii)highluxation,wherefemoralheadhasacontactwithcotyleona very small surface [1].Iftheorientationdefectsoftheheadandcotylefollowingthisillnessarediscoveredatanadvancedstage,inter-trochanteriancorrectiveosteotomiesforderotation,varusorvarusderotationshouldbeper-formed.Surgicalcorrectionsofthedefectsofthecotyle are made either to reorient the whole cavity fora better coverage of the head (Salter pelvis osteotomy)or to increase the covering surface (Chiari pelvis oste-otomy).Forhipdysplasiaorluxationwithimportantarthriticmodifications,thearthroplastywithtotalhipprosthesis is performed.The arthrosis of hip joint is characterized by aflat-teningoftheanteroexternalfemoralheadandtheacetabularsupportsurfacethatmovestotheantero-upperside.Theseshapechangesareresponsiblefornewbiomechanicalconditionsinthehipjoint.Thesphericalhead,thathadonerotationcenterinanun-deformedstate,hasmorecentersafterthedeforma-tion.Thecontactsurfacebetweenthefemoralheadand acetabulum decreases due to the deformation, thusleading to an important increase of the pressure on thejointsurface.Thepressurepeak,whichdevelopsonthe reduced contact surface, with time leads to a localdestructionofthecartilaginoustissueandappearanceof pains [2].Fig. 1. Deformed femoral headUnlikeanormalhip,wheretheresultantRoftheforces G (weight of the torso) and Fm (force developedby the abductor muscles) is oriented at 16 with respectto the vertical direction, in this casetheresultantforcedecreases and modifies its position: it is oriented slant-wisedownwardsaswell,butatanangleof8withrespect to the vertical position (figure 1). The resultanttends to the vertical position in proportion with the incli-nationofacetabularsurface;consequently,thecontactbetweenthefemoralheadandtheacetabulummoves.ThereactionforceR1=RthatappearsinthecontactpointiseccentricwithrespecttoR[2],givingrisetoa couple that rotates the femoral head (figure 2).Fig. 2. Normal hip (a), abnormal hip with an inclinedacetabulum surface (b)Thecup,thesynovialmembraneandtheroundligament are stressed by this couple, thus favouring theformationoftheosteophytes,acharacteristicfeaturea)b)Biomechanical changes of hip joint following different types of corrective osteotomy photoelastic studies 67ofthehiparthrosis.Atthesametime,theslidingofthe femoral head outwards leads to a plastic deforma-tion of the acetabular surface.PAUWELS[3]presentssometypesofosteotomyforsurgicaltreatmentofthehiparthrosis.Themaingoalofsuchatreatmentistoreducethevalueofthemaximumpressureonthejointsurface,bothbyade-creaseoftheresultantforceRandbyanincreaseofthebearingareaonwhichtheforceisdistributed.Whenthecontactsurfacesarereduced,theymaybeincreased by a proper rotation of the femoral head intothecotyle,eitherinwardsoroutwards,dependingonthejointconfiguration.Inincipienthiparthroses,a varus osteotomy is performed when an inwardrota-tionisnecessaryforthereconstructionofthejointcongruence(figure3).Thus,thebearingsurfaceisincreased,thecontactpressureisdiminishedandthelever arm of Fm is also increased [4].Fig. 3. Incipient hip arthrosis (a), varus osteotomy (b)Fig. 4. Advanced hip arthrosis (a), valgus osteotomy (b)In advanced hip arthrosis, when the rotation is madeoutwards (figure 4a), the valgus osteotomy (figure 4b) isindicated for the reconstruction of the joint congruence.ThebearingisincreasedinthiscasewhilethecontactpressuredecreasesandtheresultantforceRbecomesvertical.TheleverarmofthemuscularforceFmde-creases;inordertokeepitscoupleconstant,thevalueofFmincreases.Asaresult,asmallincreaseoftheresultant force R can be noticed. Since the bearing sur-facebecomesbiggeraftertheosteotomy,thecontactpressure remains almost constant.Anothermethodforenlargingthebearingsurfaceof the hip and thus to diminish the contact pressure istheChiarihiposteotomy(figure5).Aninternaldis-placementofthewholejointisobtainedduetooste-otomyofthistype,whichleadstoareductionoftheleverarmoftheweightGandtoachangeofthedi-rectionoftheforceFmdevelopedbytheabductormuscles; this force becomes vertical. These modifica-tions determine a diminution of the resultant R and anincreaseofthebearingsurfaceofthejoint;thusthecontact pressure is substantially decreased [5], [6].Fig. 5. Chiari osteotomy3. Experimental research:description and resultsTheexperimentalinvestigationswereundertakenonplanephotoelasticmodelsofthebonestructuresexamined. The models were machined from an epoxyresin,accordingtoX-raypictures.Inordertobettermodeltherealstructures,thecartilaginoustissuesweremadefromathinsoftrubberlayer.Theelasticconstantsofthematerialsusedinthisexperimentaregiveninthetable.Specialloadingdeviceswithcali-b) a)b) a)N. ILIESCU et al. 68bratedweightswereusedinordertoapplytheloadconsidered, scaled down to the proper values. All themodels were analyzed in a polariscope with white ormonochromaticlight,whosepolarizationwaseitherplaneorcircular.Photographsoftheisochromaticfringesweretakenforfurtherdeterminationoftheprincipalstress fieldson thecontoursofthemodels.Beforetheexperimentalinvestigationofthemodelsconsidered,acalibrationofthephotoelasticmaterialwasmade,yieldingavalueofthephotoelasticcon-stant of the material f = 1.85 MPa/fringe.Elastic constants of the materialsused in the photoelastic analysisMaterialYoungs modulus[MPa]Poissons ratioPhotoelastic epoxy resin 3,200 0.38Soft rubber 12 0.49a) b) Fig. 6. Isochromatic fringes for normal hip (a),isochromatic fringes for hip with dysplasia (b)The first study was undertaken in order to show thebiomechanicalchangesthatappearinthestressfieldduetoarchitecturaldefectsofthehipjoint.Thestressstatewasobtainedbothforanormalhipintwo-legsupport and a hip with luxation and lateral dysplasia inone-legsupport.Theisochromaticfieldsrecordedonplanemodelsofthehiparepresentedinfigure6forbothcases:anormalhip(figure6a)andahipwithluxationanddysplasia(figure6b).Apolariscopewithcircularly polarized white light was used for this analy-sis.Themodelofthejointintwo-legsupportwasloadedwithaforceof1kN,representingtheresultantforceR(betweenGandFm)transmittedtothepelvisand applied in the sacrum area, at a scale of 1: 2.4.Usingtheisochromaticfringefieldfromfigure6the variation of the principal stress difference 12onthecontourofthecotyloidcavitywasplottedforboth cases (figure 7).2.254.56.758.01 - 2 [MPa]13.511.259.04.52.251 - 2 [MPa]a) b)Fig. 7. Variation of the principal stress difference for a normal hip (a),variation of the principal stress difference for a hip with dysplasia (b)Thenextstudyemphasizedtheimprovementsinthe biomechanics of the hip following the Chiari oste-otomy.Aplanephotoelasticmodelofthehip,manu-facturedaccordingtoanX-raypicturetakenafterosteotomy,wasstudiedinapolariscopewithcircu-larlypolarizedlight(figure8a).Aloadof800N(three times smaller than the real force) was applied inthe sacrum area, for two-leg support.Thevariationoftheprincipalstressdifference12onthesurfaceofthecotyleinthiscaseofosteotomy is presented in figure 8b. The isochromaticfringefieldwasalsoobtainedfromamodelmanu-factured according to an X-ray picture taken two yearsafteraChiariosteotomy(figure9a).Thevariationoftheprincipalstressdifference12inthiscaseisplottedinfigure9b.Onecanobservethatthestressdistribution in the latter case tends to be similar to theonecharacteristicofanormalhip(figure7a).Thisbetterdistributionisduetothenew,biggercontactzonebetweenthecotyleandfemoralhead,obtainedBiomechanical changes of hip joint following different types of corrective osteotomy photoelastic studies 69throughtherecoveryandremodellingofthebonetissue after the surgery.Sometimes the hip arthroplasty used in advanced hiparthrosispresentspost-surgerycomplicationsduetotardydecementationoftheprosthesesfollowingtheimplantation defects [7], [8]. The last experimental studydeals with the determination of abnormal stress state dueto the malposition of the prosthetic components. A planemodel of the prosthetic hip joint was manufactured fromtwodifferentphotoelasticmaterials:epoxyresinforthebone tissue of the iliac crest and femoral diaphysis (withtheelasticconstantsfromthetable)andpolymethyl-methacrylate(PMMA,plexiglas),withloweropticalsensitivity,forthecupandfemoralpiece(havingtheYoungsmodulusE=2800MPaandPoissonsratio = 0.37). The acetabular cup was fixed in the cotyle inthreedifferentpositions:normal,verticallydisplacedandhorizontallydisplaced.Aspecialadhesive(X-60),simulatingthecementlayerwasused.Usingthesameadhesive, the femoral piece was implanted also in threepositions:normal,varusandvalgus.Usingasystemwithleversandweights,themodelswereloadedwithaforceof800N(scaleof1:2.4oftherealforce)ap-plied to the top of the cotyle. The photoelastic analysiswas done usingapolariscopewithcircularlypolarizedlight (both white and monochromatic).The field of isochromatic fringes recorded in whitelight for the first analyzed case (cup and femoral piecein a normal position) is shown in figure 10a, while theone for the third case (normal position of the cup andthe femoral piece in varus) is presented in figure 11a.Using the information extracted from these fields, thea) b) 2.254.59.011.51 - 2 [MPa]a) b) 4.57.06.54.51 - 2 [MPa]Fig. 8. Isochromatic fringes after the Chiari osteotomy (a),variation of the principal stress differenceafter the Chiari osteotomy (b)Fig. 9. Isochromatic fringes two years afterthe Chiari osteotomy (a), variation of the principalstress difference two years after the Chiari osteotomy (b)N. ILIESCU et al. 70variationoftheprincipalstress1forthefirstcaseandforthethirdcase(attheinterfacesofcupiliacbone and prosthesisfemoral bone and on the contourofthefemurintheepiphyseal-diaphysealzone)arepresented in figures 10b and 11b, respectively.a) b) Fig. 10. Isochromatic fringes in the bone tissue fora normal position (a), variation of the principal stress 1at the interfaces of cupbone tissue and femoral piecebone tissuefor a normal position of the prosthetic components (b)a) b)Fig. 11. Isochromatic fringes in the femoral diaphysis fora varus implantation of the femoral piece (a), variation ofthe principal stress 1 for a varus implantationof the femoral piece (b)Biomechanical changes of hip joint following different types of corrective osteotomy photoelastic studies 714. ConclusionsSomeimportantconclusions regardingthecontactpressuredistributioninsomecasesofhipjointdisor-dersmaybedrawnfromthephotoelasticinvestiga-tions undertaken. Improvements that may be obtainedfollowingthecorrectiveosteotomiesinthecaseofthese diseases are also emphasized.Ascanbeseeninfigure7b,aninsufficientcover-age of the femoral head due to a deficient developmentindepthofthecotyloidcavitycanbefoundforahipwithluxationandlateraldysplasiainone-legsupport.In this case, cotyle has a contact with femoral head onareducedsurface;asaresult,thestressdistributionshowninfigure7bhasapeakwhosevalueisby70%greater than the one for a normal hip.Theresultsofthephotoelasticinvestigationsonthe Chiari corrective osteotomy (figure 8a) show that,immediatelyaftertheoperation,themaximumvalueof the principal stress difference on the surface ofthecotyleis11.5MPa(by43.7%greaterthanforanor-mal hip and by 17.4% smaller than before osteotomy).With time, after the surgery, a new and larger contactzoneisestablishedbetweenthecotyleandfemoralhead due to the recovery and remodelling of the bonetissue. Consequently, the contact pressure distributionis modified, tending to the normal one, as is shown infigure 9b.Theinvestigationsonthehipprosthesesshowthat the distribution of theprincipalstressdifference12onthesurfaceofthecotyleisclosetothenormal one (figure10b).Greaterstresses appearduetothedifferencebetweentheelasticmoduliofthematerials(boneandacetabularcup).Theshearingstressesattheinterfaceofbonefemoralpiecehavesmallconcentrationsintheareaofthefemoralspurandinternalcortex,alongthelengthoftheprosthe-sis.Theresultsoftheresearchonmodelswithmal-positionofprostheticcomponents(figure11b)re-vealedthattheprincipalstressdifferenceonthecotylesurfaceisby52%greatercomparedtothenormalsituation.Agreaterstressconcentrationonthe diaphysis, at the femoral spur, is noticed (by 32%greater than in the case of correct implantation). Thesamephenomenon is observed in thecontactareaofthe prosthesis with the great trochanter, while adimi-nutionof thestressesmaybefound at theinner cor-texalongthewholelengthoftheprosthesis.Theselowvaluesshowthattheloadoftheprosthesisce-mentassemblyinthecaseofincorrectimplantationis greater compared to the normal situation. Thus, theload of the cement layer is higher.Theprincipalstressdifference12isalwaystwiceaslargeasthemaximumshearstressmax.Un-dertheshearstress,cementfailsleadingtoapartialdecementation of the prosthesis. With time, due to thecontinuousloading,thetotaldecementationmayoccur,bothatthefemoralpieceandtheacetabularpiece.Localmicromovementsloadboththebonesandthefemoralpiecebytilting,leadingtoapossiblefailureof the prosthesis due to fatigue.References[1] GARWINK.L.,BOWENM.K.,SALVATIE.A.,RANAWATC.S.,Long-term results of total hip arthroplastyin congenital disloca-tion and dysplasia of the hip, J. 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