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w w w . r b o . o r g . b r

Original

Article

Analysis

on

the

mechanical

resistance

of

fixation

of

femoral

neck

fractures

in

synthetic

bone,

using

the

dynamic

hip

system

and

an

anti-rotation

screw

,

夽夽

Anderson

Freitas

a,∗

,

Gustavo

Melo

Torres

b

,

André

Cezar

de

Andrade

de

Mello

e

Souza

b

,

Rafael

Almeida

Maciel

b

,

Diogo

Ranier

de

Macedo

Souto

a

,

George

Neri

de

Barros

Ferreira

a

aOrthopedicHospitalforSpecializedMedicine,Brasília,FederalDistrict,Brazil

bGamaRegionalHospital,Brasília,FederalDistrict,Brazil

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received18November2013 Accepted6January2014 Availableonline27October2014

Keywords:

Femoralneckfractures Internalfixators Biomechanics

a

b

s

t

r

a

c

t

Objective:Tostatisticallyanalyzetheresultsobtainedfrombiomechanicaltestsonfixation offemoralneckfracturesofPauwelsIIItype,insyntheticbone,usingthedynamichipsystem withananti-rotationscrew,versusacontrolgroup.

Methods:TensyntheticbonesfromaBrazilianmanufacturer(modelC1010)wereusedand dividedintotwogroups:testandcontrol.Inthetestgroup,fixationofanosteotomywas performedwith70◦ ofinclinationatthelevel ofthefemoralneck,using DHSwithan

anti-rotationscrew.Theresistanceofthisfixationwasevaluated,alongwithitsrotational deviationat5mmofdisplacement(phase1)andat10mmofdisplacement(phase2),which wasconsideredtobefailureofsynthesis.Inthecontrolgroup,themodelsweretestedin theirentiretyuntilfemoralneckfracturingoccurred.

Results:Thetestvaluesinthetestgroup(samples1–5)inphase1 were:1512N,1439N, 1205N,1251Nand1273N,respectively(mean=1336N;standarddeviation[SD]=132N).The rotationaldeviationswere:4.90◦,3.27, 2.62,0.66and0.66,respectively(mean=2.42;

SD=1.81◦).Inphase2,weobtained:2064N,1895N,1682N,1713Nand1354N,respectively

(mean=1742N;SD=265N).Thefailureloadingvaluesinthecontrolgroupwere:1544N, 1110N,1359N,1194Nand1437N,respectively(mean=1329N;SD=177N).Thestatistical analysisusingtheMann–Whitneytestshowedthatthetestgrouppresentedmaximum loadingatadisplacementof10mm,i.e.significantlygreaterthanthefailureloadingofthe controlgroup(p=0.047).

Conclusion:Themechanicalresistanceofthetestgroupwassignificantlygreaterthanthat ofthecontrolgroup.

©2014SociedadeBrasileiradeOrtopediaeTraumatologia.PublishedbyElsevierEditora Ltda.Allrightsreserved.

Pleasecitethisarticleas:FreitasA,TorresGM,SouzaACAM,MacielRA,SoutoDRM,FerreiraGNB.Análisedaresistênciamecânicade fixac¸ãodefraturadocolofemoralemossosintéticocomDHSeparafusoantirrotatório.RevBrasOrtop.2014;49:586–592.

夽夽

WorkdevelopedattheOrthopedicHospitalforSpecializedMedicine,Brasília,FederalDistrict,Brazil,andattheMechanicalTest Laboratory,DepartmentofMaterialsEngineering,SchoolofMechanicalEngineering,StateUniversityofCampinas(UNICAMP),Campinas, SP,Brazil.

Correspondingauthor.

E-mail:andfreitas28@gmail.com(A.Freitas).

http://dx.doi.org/10.1016/j.rboe.2014.01.016

(2)

Análise

da

resistência

mecânica

de

fixac¸ão

de

fratura

do

colo

femoral

em

osso

sintético

com

DHS

e

parafuso

antirrotatório

Palavras-chave:

Fraturasdocolofemoral Fixadoresinternos Biomecânica

r

e

s

u

m

o

Objetivo: Analisarestatisticamenteresultadosobtidosemensaiosbiomecânicosdefixac¸ão defraturadocolofemoraltipoPauwelsIII,emossosintético,comousodosistemadinâmico doquadril(DHS)comparafusoantirrotatóriovsumgrupocontrole.

Métodos: Foramusadosdezossossintéticos,deumfabricantenacional,domodeloC1010, divididos emdoisgrupos:testee controle.Nogrupoteste foifeitafixac¸ãode osteoto-mia,com70◦ deinclinac¸ãoemníveldecolofemoral,comousodeDHScomparafuso

antirrotatório.Avaliou-searesistênciadessafixac¸ãoeseudesviorotacionalem5mmde deslocamento(fase1)eem10mmdedeslocamento,consideradocomofalênciada sín-tese(fase2).Nogrupocontrole,osmodelosforamensaiadosemsuaintegridadeatéque ocorresseafraturadocolofemoral.

Resultados: Os valores do ensaio no grupo teste na fase 1, nas amostras de 1 a 5, foram:1.512N,1.439N,1.205N,1.251Ne1.273N,respectivamente(média=1.336N;desvio padrão [DP]=132N).Os desviosrotacionais foram:4,90◦;3,27;2,62;0,66e 0,66,

res-pectivamente (média=2,42◦; DP=1,81).Na fase 2, obtivemos: 2.064N, 1.895N,1.682N,

1.713Ne1.354N,respectivamente(média=1.742N;DP=265N).Osvaloresdacargade falên-cianogrupocon-troleforam:1.544N,1.110N,1.359N,1.194Ne1.437N,respectivamente (média=1.329N;DP=177N).AanáliseestatísticapelotestedeMann-Whitneydemonstrou queogrupotesteapresentoucargamáxima,em10mmdedeslocamento,significativamente maiordoqueacargadefalênciadogrupocontrole(p=0,047).

Conclusão: Aresistênciamecânicadogrupotestefoisignificativamentesuperioràdogrupo controle.

©2014SociedadeBrasileiradeOrtopediaeTraumatologia.PublicadoporElsevier EditoraLtda.Todososdireitosreservados.

Introduction

Hipfractures account for around 20% ofthe surgical frac-turesseenatorthopedictraumaunitsandgeneratesignificant

annual cost in any healthcare system. Femoral neck

frac-turesaccountforapproximately50%ofallfracturesofthehip region.Theymainlyaffectelderlypeopleandareuncommon amongindividualsundertheageof60years.1

TheWorldHealthOrganizationhaspredictedthatthe inci-denceof osteoporoticfractures of the proximalfemur will tripleby2050.2Inthepopulationundertheageof65years,

theincidenceoffemoralneckfracturesis2–4casesper10,000 inhabitants.However,theincidenceismuchhigherinthe

pop-ulationover theageof70years:28/10,000amongmenand

64/10,000amongwomen.3,4

Amongyoungadults,fracturesinthehipregionare gen-erallyuncommon.However,becauseofhigh-energyaccidents involvingsportspracticesandtrafficaccidents,thisincidence

has been increasing. The pattern of this type of fracture

frequentlyhasa verticallinewith unstable characteristics, classified as Pauwels III. This classification correlates the prognosiswiththeangleofthefractureplane:astheangle increases, theinstability ofthefracture also increasesand thecomplications relatingto itsfixation and consolidation worsen.1

Thetreatmentforfemoralneckfractures varies

accord-ingtothepatient’s ageandthefracture pattern.5Inyoung

patients,osteosynthesisshouldalwaysbeprioritized,whilein

olderpatients,arthroplastyshouldbecogitated.For middle-agedpatients(40–65years),theindicationshouldbedefined individually.6

For femoral neck fractures without displacement,

rigid fixation with early mobility for the patients is the

standard treatment. Multiple cannulated screws (MCS) or

the Dynamic Hip System (DHS) is commonly used in the

treatment.5

Failureoffixationandpseudarthrosisarethemainformsof complicationfollowingfixationoffemoralneckfractures,with

or withoutdisplacement.Pseudarthrosisoccurs more

com-monlyandaffectsbetween3.1%and8.8%ofthecases,witha meanofaround6%.1

Inthelightofthesituationdescribedabove,weproposed to conduct a statistical analysis in order to evaluate the mechanicalresistanceofthefixationoffemoralneckfractures classifiedasPauwelsIII,inwhichtheDHSandantirotational

screwswereusedinsyntheticbones,incomparisonwitha

controlgroup.

Material

and

methods

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Allthesamplesofthetestgroupwerepreviouslydrilled fortheinitialplacement ofthe implant underfluoroscopic guidancebeforetheosteotomy,inordertofacilitate

anatom-ical reduction and ideal positioning for the implant. The

osteotomiesofthe testgroupwere performedusinga

pre-fabricatedtemplatesothattherewouldnotbeany angular differencebetweenthemandinordertosimulateafemoral neckfractureofPauwelsIIItypethatwouldbethesameinall thebones.

Thefixationsofthefivebonesofthetestgroupwere

per-formedonebyone usingthe DHS,withthree holes and a

guideof135◦.Thereferencepointestablishedforplacingthe

90mmslidingscrewwas2cmdistallytothelessertrochanter, atthecenterofthelateraldiaphysis.Theplatewasfixedtothe femoraldiaphysisusingthree4.5mmcorticalscrews.Lastly, thesystemwaslockedusingacotterpin,whichprovided com-pressiontothefocusoftheosteotomy.Anantirotationalscrew wasthenplacedbyhand,positionedparalleltoandabovethe slidingscrew.Tocheckforcorrectpositioning,fluoroscopyin anteroposteriorandlateralviewswasusedduringeachstage ofthe procedure.After theprocedure, all the bonesinthe testgroup(Fig.1)weresubjectedtoradiographytoevaluate thereductionandwhetherthesynthesiswaswellpositioned (Fig.2).

Theotherfiveboneswereusedwithoutinterferencewith theirintegrityandwereidentifiedasthecontrolgroup.Inthis

manner,theysimulatedthemaximumresistanceloadofthe

femoralneckofintactsyntheticbone.Thus,theydefinedthe goldstandardforresistancepriortotheoccurrenceofthe frac-tureandthecomparisonparameterfortheneedforresistance inthesynthesismethodusedinthetestgroup(Fig.3AandB).

Testgroup

Thefixedsyntheticfemurswere200mminlengthandwere

positioned vertically with an inclination of 25◦ of valgus

(Fig.4A).Theloadapplicationsystemtransmittedtheforce

ontheapex ofthe femoralheadanddetermined theforce

Fig.2–RadiographonsyntheticbonefixedwithDHS beforethetest.

appliedandloadatthetimeoffailure.Theanalysisonthe mechanicaltestonthisgroupwasdividedintotwophases:

Phase1:resistanceofthefixationwith5mmof displace-ment(Fig.4B).

Phase2:resistanceofthefixationwith10mmof

displace-ment,which was taken tobefailure ofthe osteosynthesis

(Fig.4C).

Duringphase1,therotationaldisplacementsofthefemoral neckwerealsoevaluated(Fig.5).

The format ofthis test sought toconcentrate the force

appliedon the focus oftheosteotomy, inorder tomakea

(4)

Fig.3–(A)Controlinthemachinebeforethetest.(B)Controlafterthetest,showingfailure.

Fig.4–(A)DHSinthemachinebeforethetest.(B)DHSinphase1ofthetest.(C)DHSinphase2ofthetest.

moreappropriateanalysisontheresistanceofthesynthesis assembly.

Controlgroup

Thenon-fixedsyntheticfemurswere125mminlengthand

werepositionedvertically,withneutralinclination.Theload applicationsystemtransmittedtheforceattheapexofthe

femoralheadandthiswasapplieduntilthefemoralneck frac-tured(Fig.3),inordertosimulatethemaximumpre-fracture resistance.

A load application velocity of 20mm/min was used, in

the Materials Testing System (MTS)machine (model 810 –

FlexTest 40) with a capacity of100kN. In the test, a

cali-bratedand measured loadcell ofcapacity10kNwas used.

An axial force was applied tothe femoralhead by means

(5)

Fig.6–Testmachineused.

Table1–LoadvaluesinNwith5mmofdisplacement,

maximumloadvaluesandrotationaldisplacement,in

thetestgroup.

Sample Loadwith5mm

ofdisplacement (N)

Maximum load(N)

Rotation (degrees)

1 1512 2064 4.9

2 1439 1895 3.27

3 1205 1682 2.62

4 1251 1713 0.66

5 1273 1354 0.66

Mean 1336 1742 2.42

Standarddeviation 132 265 1.81

offitting it to the surface of the piston of the equipment (Fig.6).

Statisticalanalysis

Thestatisticalmethodforcomparingthemaximumforce(N)

betweenthegroupswastheMann–Whitneytest.A

nonpara-metricmethodwasusedbecausethemaximumforcedidnot

presentnormaldistribution(Gaussiandistribution),duetothe smallnumberofsamplesanalyzedineachgroup.

Thecriterion usedfordeterminingsignificance wasthe

levelof5%.Thestatisticalanalysiswasprocessedusingthe SAS6.11software(SASInstitute,Inc.,Cary,North Carolina, USA).

Results

Testgroup

TheloadvaluesinNewtons(N)thatwereapplieduntil dis-placementofthefractureby5mmwere:1512,1439,1205,1251 and1273,respectively,forsamples1–5.Themeanvaluewas 1336N,withastandarddeviationof132N(Table1,Fig.7).

Extension (mm)

0

1

2

3

4

5

6

7

8

9 10 11 0

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Load (N)

1 2 3 4 5

Fig.7–Forcevs.displacementcurveforthetestgroup.

Table2–MaximumloadvaluesinNinthecontrolgroup.

Sample Maximumload(N)

1 1544

2 1110

3 1359

4 1194

5 1437

Mean 1329

Standarddeviation 177

ThemaximumloadvaluesinNewtonsthatwereapplied untildisplacementofthefractureby10mmwere:2064,1895, 1682,1713and1354,respectively,forsamples1–5.Themean valuewas1742N,withastandarddeviationof265N(Table1,

Fig.7).

Therotationaldisplacementvaluesforthefivesamplesin degrees,afterphase1,were:4.90◦,3.27,2.62,0.66and0.66,

respectively.Themeanwas2.42◦andthestandarddeviation

was1.81◦(Table1).

Controlgroup

ThemaximumloadvaluesinNewtonsinthefivesamplesof

thecontrolgroupwere,respectively,1544,1110,1359,1194and 1437.Themeanvaluewas1329Nandthestandarddeviation was177N(Table2,Fig.8).

AccordingtotheMann–Whitneytest,itwasobservedthat

thetestgrouppresentedamaximumforceat10mmof

dis-placement that was significantly greater than that of the

controlgroup(p=0.047),asshowninFig.9.

Discussion

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1600 1400 1200 1000 800 600 400 200 0

0

1

2

3

4

5

6

7

8

9 10 11 12 13

Extension (mm)

[1]

2

3

4

5 Load (N)

Fig.8–Forcevs.displacementcurveforthecontrolgroup.

A

B

Maximum force (N)

Median p=0.047 2200 2000 1800 1600 1400 1200 1000 800 600 400

Fig.9–Comparisonbetweenthetestgroup(A)andthe controlgroup(B).

healingprocess,soastoallowrapidandsecurerecoveryfor thepatientandareturntoactivitiesofdailyliving.Secure fix-ationalsoreducesthehighratesofcomplicationsrelatingto treatmentsforthistypeoffracture.7

Duringdailyactivities,theloadonthefemoralhead alter-natesanteriorlyandposteriorlyand causesvarusforces.In thepresenceoffracturesthis loadcausesverticalshearing.

Theforceappliedtotheheadofthefemoralneckdepends

onthepatient’sweightandontheactivitycarriedout.These parametersarefundamentalforevaluatingtheresistanceof theimplantincasesoffemoralneckfracture.Inourstudy,we usedanaxialforceof1400Nastheforceappliedtothehip ofanindividualweighing70kgwhoisstandingononeleg.8

ThevaluesobtainedinthesetestsusingtheDHSand antiro-tationalscrews,with5mmofdisplacement,reachedamean loadof1336Nandameanrotationaldisplacementof2.42◦.

However,this osteosynthesis withstood a mean maximum

load of1742N beforefailure, with10mmof displacement. Thisvaluewas significantlyhigher(p=0.047)than theload

withstoodbyanintactsyntheticfemur(controlgroup),which withstoodameanof1329N.

Stiasnyet al.conductedastudythat comparedthe

sur-gicalresultsfrom112patientswhoweretreatedusingMCS, DHSorDHSplusantirotationalscrews.Theyconcludedthat

comparableresultscouldbeobtainedthroughusingMCSor

DHSforsurgicaltreatmentofstablefracturesofthefemoral neck(Gardentypes1and2).Incasesofunstablefracturesof thefemoralneck(Gardentypes3and4),goodresultsfrom thetreatmentdependongoodreductionandstabilizationof thefracture,whichcanbeachievedthroughusingtheDHS. Inthesepatients,withfracturesofGardentypes3and4,the likelihood ofobtaininggood resultsthroughusingtheDHS

wasthreetimesgreater thaninthosewhounderwent

fixa-tionusingMCS.Intheevaluationontheuseofantirotational screws,itwasconcludedthattheiruseinadditiontotheDHS prolongedthedurationofthesurgery,increasedthebloodloss

and didnotimprovethe biomechanicsofthe femoralneck

fixation.9

Inastudyoncadaverbones,Blairetal.comparedthe resis-tanceofbasicervicalfracturefixationusingMCS,DHSorDHS plusantirotationalscrewsandreachedmeanvaluesfor resis-tance toaxial loadingof1736±494NforMCS, 2880±679N forDHSand2903±598NforDHSplusantirotationalscrews.

TheyconcludedthattheDHSwasbiomechanicallysuperior

to MCS for treating femoral neck fractures at the base of

the neck. Moreover, theyobserved that althougha spongy

screw located superiorly would beable to control rotation duringtheinsertionoftheslidingscrewofthehip,itwould notprovideadditionalfixationafterplacementofthissliding screw.10

Biomechanical tests on implants perform a vital role

in evaluating any new implant technology.11 It is difficult

and may be extremely expensive to obtain fresh

cadav-ericbone thatisfreefrom diseases,foruse inmechanical

tests on orthopedic implants.12 Another problem is that

cadaver samples are not uniform, which results in

inclu-sionofsampleswithbonequalityandstrengththatisvery variable.13,14 Differencesin age and degree ofosteoporosis

amongspecimensfromcadaversmayalsopartiallyinfluence thevariabilityofthemechanicalproperties.15,16This

variabil-ityingeometricandmaterialpropertiesofcadaverspecimens frequentlyrequiresprohibitivelylargesamplesizes,inorder to detect statistically significant differences in implant performance.17

Werecognizethelimitationsofourstudy.Useofsynthetic bonesinsteadofbonesfromcadaversdoesnotcorrectly trans-latetheanatomyofthefemoraltrabeculaeandtheforcesthat theycanwithstand.Wedidnotsimulateallthephysiological componentsoftheforce(cyclical,torsionalandaxial)towhich thehipissubjectedduringtheprocessesofwalkingormuscle contractionalone.Directionalforcevectorsmayhaveresulted inchangestotheloadvaluesandconsequentlychangestothe stabilizationoftheimplant.Anaxialloadinasingledirection

does notsimulatethecomplex loadsystemthatisapplied

(7)

Syntheticboneswerechosentoensurecomparable biome-chanicalpropertiesbetweenthegroupsandeliminatecertain variables.13Thus,weremovedpossiblevariationsinherentto

humanbonesthatwould cause difficulty inevaluatingthe

methodologyoffixationbecauseoftheirnon-uniform char-acteristics(bonedensity,diameterandlength).

Webelievethattheprincipleofosteosynthesisfor treat-ingfemoralneckfracturesrequiresmethodologythatprovides

absolutestability and that it is improved whenperformed

in a minimally invasive manner. Although the DHS does

notincludetheprincipleofabsolutestability,withor with-out antirotationalscrews, it presentssurprisingly favorable results.9,10 This may contribute towards a less pessimistic

prognosisintreatingunstablefracturesofthefemoralneck.

Wesuggestthatnewstudiesshouldbeconducted.These

couldmakeuseofthepresentresultstodevelopnewimplants thatwouldrespecttheneedforabsolutestabilityandcouldbe

implementedinaminimallyinvasivemanner.

Conclusion

Theanalysisshowedthatthe mechanicalresistanceofthe

testgroupwassignificantlygreater thanthatofthecontrol groupandestablishedthepossibilitythattheDHSand antiro-tationalscrewscanbeusedforosteosynthesisoffemoralneck fractures,especiallythoseofPauwelstypeIII.

Conflicts

of

interest

Theauthorsdeclarenoconflictsofinterest.

Acknowledgement

ToProf.AnaPatríciaPaula, supervisorofthe master’s pro-gramoftheFoundationforTeachingandResearchinHealth Sciences(FEPECS),forherunconditionalassistance.

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1. KeatingJ.Fracturesoftheneckoffemur.In:BucholzRW, HeckmanJD,Court-BrownCM,editors.RockwoodandGreen’s fracturesinadults.7thed.Philadelphia:LippincottWilliams &Wilkins;2010.p.1561–87.

2. CooperC,CampionG,MeltonLJ3rd.Hipfracturesinthe elderly:aworld-wideprojection.OsteoporosInt. 1992;2(6):285–9.

3.SingerBR,McLauchlanGJ,RobinsonCM,ChristieJ. Epidemiologyoffracturesin15,000adults:theinfluenceof ageandgender.JBoneJointSurgBr.1998;80(2):243–8.

4.CummingsSR,NevittMC,BrownerWS,StoneK,FoxKM, EnsrudKE,etal.Riskfactorsforhipfractureinwhitewomen. StudyofOsteoporoticFracturesResearchGroup.NEnglJMed. 1995;332(12):767–73.

5.Yih-ShiunnL,Chien-RaeH,Wen-YunL.Surgicaltreatmentof undisplacedfemoralneckfracturesintheelderly.IntOrthop. 2007;31(5):677–82.

6.SendtnerE,RenkawitzT,KramnyP,WenzlM,GrifkaJ. Fracturedneckoffemur–internalfixationversus arthroplasty.DtschArzteblInt.2010;107(23):401–7.

7.KaplanT,AkesenB,Demira ˘gB,BilgenS,DurakK. Comparativeresultsofpercutaneouscannulatedscrews, dynamiccompressiontypeplateandscrewforthetreatment offemoralneckfractures.UlusTravmaAcilCerrahiDerg. 2012;18(1):65–70.

8.DenhamRA.Hipmechanics.JBoneJointSurgBr. 1959;41B:550–7.

9.StiasnyJ,DraganS,KulejM,MartynkiewiczJ,PłochowskiJ, DraganSŁ.Comparisonanalysisoftheoperativetreatment resultsofthefemoralneckfracturesusingside-plateand compressionscrewandcannulatedAOscrews.Ortop TraumatolRehabil.2008;10(4):350–61.

10.BlairB,KovalKJ,KummerF,ZuckermanJD.Basicervical fracturesoftheproximalfemur.Abiomechanicalstudyof3 internalfixationtechniques.ClinOrthopRelatRes. 1994;(306):256–63.

11.ChouekaJ,KovalKJ,KummerFJ,CrawfordG,ZuckermanJD. Biomechanicalcomparisonoftheslidinghipscrewandthe domeplungereffectsofmaterialandfixationdesign.JBone JointSurgBr.1995;77(2):277–83.

12.SzivekJA.Syntheticmaterialsandstructuresusedasmodels forbone.In:AnYH,DraughnRA,editors.Mechanicaltesting ofboneandthebone-implantinterface.BocaRaton:CRC Press;1999.p.159–75.

13.CristofoliniL,VicecontiM,CappelloA,ToniA.Mechanical validationofwholebonecompositefemurmodels.JBiomech. 1996;29(4):525–35.

14.MartiA,FankhauserC,FrenkA,CordeyJ,GasserB. Biomechanicalevaluationofthelessinvasivestabilization systemfortheinternalfixationofdistalfemurfractures.J OrthopTrauma.2001;15(7):482–7.

15.HeinerAD,BrownTD.Structuralpropertiesofanewdesignof compositereplicatefemursandtibias.JBiomech.

2001;34(6):773–81.

16.BolligerNetoR,RossiJD,LeivasTP.Experimental

determinationofbonecortexholdingpoweroforthopedic screw.RevHospClinFacMedSaoPaulo.1999;54(6): 181–6.

Imagem

Fig. 2 – Radiograph on synthetic bone fixed with DHS before the test.
Fig. 5 – (A) DHS before the test, without rotational displacement. (B) DHS after the test, with rotational deviation.
Table 1 – Load values in N with 5 mm of displacement, maximum load values and rotational displacement, in the test group.
Fig. 8 – Force vs. displacement curve for the control group.

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