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Original Article

Biomechanical assessment of orbital fractures using patient-specific models and clinical matching

A. Darwich

a,b

, A. Attieh

c

, A. Khalil

d

, S. Sza´vai

e

, H. Nazha

e,

*

aFacultyofBiomedicalEngineering,Al-AndalusUniversityforMedicalSciences,Tartous,Syria

bFacultyofTechnicalEngineering,UniversityofTartous,Tartous,Syria

cFacultyofDentistry,Al-AndalusUniversityforMedicalSciences,Tartous,Syria

dFacultyofDentistry,TishreenUniversity,Lattakia,Syria

eFacultyofMechanicalEngineeringandInformatics,UniversityofMiskolc,Miskolc,Hungary

1. Introduction

Orbitalfracturesarecommonfacialfracturesinmaxillofacial surgery,andtheyhaveaestheticandfunctionalconsiderationssoit is important to understand their mechanisms for effective prevention and treatment [1,2]. Orbital walls fracture happens eitherisolatedwhichconstitute4–16%offacialfractures,oraspart ofotherfractureslikezygomatico-maxillarycomplexfracturesor naso-orbital-ethmoidfractures. Theincidenceofthesefractures approaches30–55%[3].

Isolatedorbitalfracturesoftendescribedbytheirlocationand sizeofthedefect.Threepatternsofisolatedorbitalfractureshave beendescribed:linear,blow-out,and complex[4]. Zygomatico- maxillary complex fractures are the most common fractures involving orbital fractures.Naso-orbital-ethmoid fracturesmost often occur blunt trauma to the midface, and usually involve orbitalwallsfractures[3].

Theorbitisshapedlikepyramidwithitsbaseisformedbythe orbitalrimsanteriorly.Thebonyorbitisconsistedofsevenbones:

frontal, zygomatic, lacrimal, maxillary, ethmoid, sphenoid, and palatal.Ithasfourwallsvaryin thicknessandstrength.Medial wall,whichisthethinnest,iscomposedofsphenoid,lacrimal,and palatalbones.Lateralwallwhichiscomposedofzygomaticand sphenoid.Orbitalroofiscomposedoffrontalboneandsphenoid bone and it separates the orbit from anterior cranial fossa. In addition,orbitalflooriscomposedofmaxillary,zygomaticoand palatalboneanditformsthemaxillarysinusroof[3].Orbitalfloor fractureseithersolely(blow-outfracture)oraspartofzygomatico- maxillarycomplex(ZMC)fractures.

Severalstudieshavebeenconductedtoillustratethemecha- nismsoforbitalfloorfractures[4,5].Orbitalfractureshappenwhen increasedpressurewithinthecomponentsoftheorbitcausesthe fragilewallsoftheorbittofracture[6].InthecaseofZMCfractures, infraorbitalrim and orbitalfloorare bend.Medial orbitalwall fractureshappeneitherwithblow-outfractures,oraspartofnaso- orbitoethmoid complex fractures [7]. This complex consists of manyanatomicalstructuresanditisadjacenttotheanteriorskull base where fractures extended to this area might have severe ARTICLE INFO

Articlehistory:

Received14November2020 Accepted28December2020

Keywords:

Orbitalfractures Hydraulicmechanism Bucklingmechanism Finiteelementanalysis

ABSTRACT

Introduction:Orbitalwall fracturesconsideroneofthemostcommonfracturesinthemaxillofacial trauma.Thesefracturescausedbytwomechanisms,thebucklingmechanismandhydraulicmechanism.

Thisstudyaimstocomparebetweenthetwomechanismsintermsofintensityandextensionusingthe finiteelementsmethod.

Materialandmethods:Three-dimensionalmodeloftheskullwasgeneratedusingcomputedtomography dataofyoungmalepatient.Virtualloadswereappliedontheeyeballandtheinfra-orbitalrimseparately.

VonMisesstresseswereexaminedineachsimulation.

Results:Thesimulationpredictedfracturesontheinfra-orbitalrimandorbitalfloorwhensimulatingthe hydraulic mechanism, and on the orbital floor and mesial wall when simulating the buckling mechanism.

Conclusion: Biomechanical studies are essential part in understanding maxillofacial fractures mechanisms.Theresultsconfirmedandascertainedwhatisseenclinically,andexplainedclearlythe twomechanismsoforbitalfractures.

C 2020PublishedbyElsevierMassonSAS.

* Correspondingauthor.

E-mailaddress:hasan.nazha@uni-miskolc.hu(H.Nazha).

Availableonlineat

ScienceDirect

www.sciencedirect.com

https://doi.org/10.1016/j.jormas.2020.12.008 2468-7855/C 2020PublishedbyElsevierMassonSAS.

Pleasecitethisarticleas:A.Darwich,A.Attieh,A.Khaliletal.,Biomechanicalassessmentoforbitalfracturesusingpatient-specific modelsandclinicalmatching,JStomatolOralMaxillofacSurg,https://doi.org/10.1016/j.jormas.2020.12.008

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consequences[8].Lateralorbitalwalltraumaisusuallyaccompa- niedwithZMCfracturesaslargepartoflateralorbitalrimisfrontal processofzygoma.

TheZygomatico-MaxillaryComplex(ZMC)isafacialbonewith aquadrupedshape.Itarticulateswiththefrontalbone,temporal bone,maxilla,andsphenoidbone,andservesasthemainbridge betweenthesebones[9].Itisanaestheticandfunctionalunitofthe facialskeleton.Afterthenasalbone,theyconsiderthesecondmost commonlyfracturedsites[10].

Finite element models showeda high degree of success in predictingthebiomechanicalbehaviorofskeletalbonessuchas longbonesandiliac[11,12].Thistechniquereliesonreplacement ofcomplicateddifferentialequationsofirregularshapeswithan extensive system ofalgebraic equations,which representsmall geometricentitiesthatcanbesolvedbyacomputer[13].Inthis method, the studied structure is modeled into a mesh of tetrahedral elements that are connected together with nodes.

Thephysicalpropertiesoftheseelementsareassigned,anumber oftheseelementsareconstrainedandknownforcesareapplied andthestressesandstrainsarecalculatedateachnodeandineach element[14].

Simulationoffacialfracturesusingfiniteelementsmethodcan help tounderstand their biomechanical behavior and improves currentsurgicaltreatmentprotocols.Theaimofthis studyisto investigate the biomechanical behavior of orbital walls when sustainingasingleloadusingthefiniteelementsmethod.

2. Materialsandmethods

Finite element analysis was used to investigate fracture patternsoforbitalwalls.The0.6mmthicknessDICOMfileswere obtainedfromCT scanner(Siemens SOMATOM)of35 yearsold malepatient,wherethemalesfromthisagerangearethemostof thoseexposedtofacialtrauma[15].Thedatawasobtainedfrom RadiologyDepartmentat TishreenUniversity Hospital,Lattakia, Syria.PatientapprovalwastakentousehisCTdatainthisstudy.

DICOMfileswereimportedintoMIMICSsoftware(Materialise,inc, Belgium)toIsolatetheboneusingTresholdingalgorithm,builda 3DmodeloftheskullasshowninFig.1,andEmitthemandible fromtheskullbecauseourstudyfocusesontheorbitonly.

3-MATIC software (Materialse, inc, Belgium) was used in exportingthe3Dmodeltodesignaspherethattouchestheinner wallsoftheorbit,thussimulatingtheeye,meshthesurface,where itwasdividedintotriangularelementsconnectedtoeachotherby nodes(Fig.2A),Createvolumemeshbasedonthesurfacemesh (dividingthebodyintotetrahedralelementsthatareconnected withnodes)which comprised560,000elements,andconvert4- nodedtetrahedralelementsinto10-nodedtetrahedralelements whicharebetterforanalysisresultsaccuracy.

3-MATICfile(.cdb)wasexportedtoANSYSsoftware18.1(Ansys inc,USA)forfiniteelementanalysisasfollows:Theareaswherethe loadswill beappliedweremarked(ontheinfra-orbital, supra- orbital,medial-orbital,lateral-orbitalrimsandthecenterofthe

Fig.2.(A)Skullsurfaceandvirtualeyeballandsurroundingfatin3-maticsoftware,(B)markedsitesinAnsyswhereloadswasapplied.

Fig.1.MIMICSsoftware,usedin3Dmodelconstruction.

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virtualeyeball)asshownin(Fig.2B).Markareastobeconstrained (thetwooccipitalcondylesoftheskull).

Materialpropertieswereassignedforboththeskullboneand the eyeball (density, Young‘s modulus and Poisson ratio) as follows:Youngmoduluswascalculatedbasedondensityvalues according to Morgan approach [16]. Each element of the volumetricmeshwasassignedwithindividualvaluesforphysical properties,includingbothdensityvaluesandYoungmoduluswith the help of APDL Script in ANSYS software. Poisson ratio was assignedto0.3accordingtoHuskes[17].Thevirtualeyeballwas assignedtoYoungmodulusofWaterat2000MPaduetoitshigh watercontent,anddensityofwaterisknowntobe997kg/m3[17].

Poisson ratio of the entire eyeball was obtained from medical literature at 0.47 [18]. The contact surface between skull and virtual eyeballwasmodeledusingcoulomb frictionmodel.The coefficientoffrictionforthis contactwasdefinedwith0.3[19].

Fivestudydesignswerechosentosimulatewhatisseenclinically:

Applyloadtothevirtualeyeball,applyloadtotheinfra-orbitalrim, applyloadtothemedial-orbitalrim,applyloadtothesupra-orbital rim,andapplyloadtothelateral-orbitalrim.

Orbitalfatwastakenintoaccountastheroleofthefatiscrucial to explain the hydraulic mechanism of orbital fractures as indicated in Folettiet al.[20]. Virtual staticloads wereapplied ineach studydesign alongY-axiswhichisperpendiculartothe surface onwhich theloadwasapplied.Theloadwasgradually increasedby100Natatime untilwereachedvonMisesstress valueof153MPaorabove.Whenresultantstressesexceededthe valueof153MPa,thecausalloadwasrecordedandsimulationwas stopped ineach design. We assumedthat thevon Misesstress above153MPawasthecriteriaoffailureforskullbonesaccording toNagasaoetal.study[21],wherethisstressvalueiswhenthe bonechangefromtheelasticphasetotheplasticphaseandthen begins to fail (fracture). The skull was fixed at the occipital condylesinalldegreesoffreedom.

3. Results

VonMisesstresswasevaluated,whichcanbeusedtopredict material failure successfully. Results were plotted as color spectrumrangedfrombluetored,whereredindicatesthehighest valueofcalculatedstress,andinthisstudyredcolorindicatethat stresshasreachedtheyieldstrength(153MPa)atwhichthebone begantofail(fracture).

3.1. Loadonvirtualeyeball

It has been found a maximum von Mises stress value of 155MPawhenapplyingaforceof7200Nontheeyeballalongthe Y-axisonthemarkedareaasshowninFig.3.Theanalysisresults revealed concentration of stresses in the orbital floor and the medialwalloftheorbit(Fig.3),withthehighestattheorbitalfloor indicating that the stresses are approaching or exceeding the 153MPathreshold,whichmeanswecanpredictafractureinthis area.Moreover,thepresenceoforbitalfatseemedtoincreasethe forcevalueuntilthefracturethresholdisreached(9000N).This pointouttoasignificantprotectiverole,whichtheorbitalfatmay play.Highstresseswereconcentratedatorbitalmedialwalland floor;theyalsospreadtoskullbasewithoutreachinghighvaluesas showninFig.3.

3.2. Loadontheinfra-orbitalrim

It has been found a maximum von Mises stress value of 156MPawhenapplyingloadof8600Nattheinfra-orbitalrim alongtheY-axisonthemarkedareaasshowninFig.4.

Simulation revealed concentration of stresses in the infra- orbitalrimandfrontsectionoftheorbitalfloor,whereredspots indicate that the stresses are approaching the threshold of 153MPa,which meanswe can predicta fracture in thesetwo

Fig.4.Thedistributionofstresseswhentheforcewasappliedontheinfra-orbitalrimwithout(left)andwith(right)thepresenceoforbitalfat.

Fig.3.Concentrationsofstressesatorbitalfloorandorbitalmesialwallwithout(left)andwith(right)thepresenceoforbitalfat.

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regionsasshown inFig.4.Thepresenceoforbitalfatseemsto cause a stress concentration in in the orbital floor and tothe maxillarysinuswallsandskullbasewithoutreachingthe153MPa thresholdasshownintherightshapeofFig.4.

3.3. Loadonmedialorbitalrim

Whensimulatingablowonthemedialorbitalwall,ithasbeen foundthatvonMisesstressvalueof154MPawhenapplyingstatic loadof5400N.Thesestresseswereconcentratedatsiteofloadand spread to frontal, ethmoidal, and nasal bones. This simulation result issimilartowhatis foundinNOEfracturesasshown in Fig.5.Minimalroleoforbitalfathasbeennoticedinthistypeof loadingassimilarpatternshasappearedwithapproximativestress values.

3.4. Loadonthesupra-orbitalrim

Gradually increasing loads were (100N at time) on supra- orbitalrimtoinvestigateorbitalrooffractures.Themaximumvon Misesstressvalueof153MPawasfoundwhenapplyingloadof 9000Natthesupra-orbitalrimalongtheY-axisonthepre-defined areaFig.6.Stressesspreadtofrontalboneandorbitalroofwith

relativelyhighvalueswherethehigheststresswasatthesiteof load (orbital roof). Stress also spread to temporal bone. The presenceoforbitalfatcausedaslightelevationinstressvaluesand causedinamoreexpandedfracturepatternattheupperrimas seeninFig.6.

3.5. Loadonlateralorbitalrim

The maximum stress value of 154MPa was found when applyingloadof9300Natthelateral-orbitalrimalongtheY-axis onthemarkedareaasshowninFig.7.Stressesspreadtolargeareas ofthezygomatico-maxillarycomplex.Minimalroleoforbitalfat hasappearedinthisfracturepatternastheshapesandthevalues weresimilar.

Simulationshowsstressconcentrationinthelateralorbitalwall andrim.Thefracturescanbepredictedfracturesintheseareasand inthezygomatico-maxillarycomplex,asthesimulationshowsin Fig.7stressspreadtolargeareasofthiscomplex.

Fig. 8 shows a 19-years old patient withblow-out fracture caused by personal violence, CT scan revealed an orbital floor fracture which is corresponded to ourresults as shown in the sagittalcrosssection.Fig.9showstheclinicalvalidationoffracture stresseswhentheforcewasappliedonthelateral-orbitalrim.

Fig.5.Thedistributionofstresseswhentheforcewasappliedonmedialorbitalwallwithout(left)andwith(right)thepresenceoforbitalfat.

Fig.6.Thedistributionofstresseswhentheforcewasappliedonthesupra-orbitalrimwithout(left)andwith(right)thepresenceoforbitalfat.

Fig.7.Thedistributionofstresseswhentheforcewasappliedonthelateral-orbitalrimwithout(left)andwith(right)thepresenceoforbitalfat.

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4. Discussion

Orbitalwallsfracturesoccurwhenthetraumaticforceaffects theorbitareaintheeventoftrafficaccidents,personalviolence, andwarinjuries[22,23].Mostexistingstudiesonorbitalfractures usedexperimentalmethodslike,hittingskullswithpre-measured objects [4–6,24–27]. However, it is difficult to maintain the continuityoftheexperimentconditionsbecausetheseconditions areeasilyaffectedbydifferencesin:impactpoints,angleofthe skull orskull stabilization.To solvethis problem,theskullwas simulated andperformed a finiteelementanalysison it, which allowsustoarrangeexactexperimentalconditionsincludingthe directionandintensityofimpactandtheregionstobestrucksowe usedfiniteelementanalysisforthisstudy.Thesimulationwasable toberepeatedmanytimesineachdesignuntilreachingthestress threshold describedbyNagasao etal.[21], which isdifficultto achieveusingexperimentalmethods.

Adetailedmodelof(theskullofyoungmale)wasabletobe generated with a dense volume mesh of about 560,000 finite elements.Usingsuchdensemodel,thedetailsofmideface,orbit, surrounding fat wererepresented in this study. Finite element models showed a high degree of success in predicting the biomechanical behavior of skeletal bones such as long bones andiliacbone[11,12].

Severalstudiesusedfiniteelementmethodtoillustrateorbital fractures.Nagasaoetal.[21]placed1085pointsonthesurfaceofa dry skull, then the coordinates of the marking points were measuredusinga3Dscanner,andthentheybuilta3Dmodelbased onthedatafromthescanner.Themodelusedinthisstudywas based on data froma computedtomography of a 35-years-old male, producing a model that represents the skull well and simulatesrealanatomy,includingthevariablebonethickness.

Thedetailedfiniteelementmodelusedforsimulation(560k elements),therelativelygoodresolutionofbonystructures,and materialassignmentofeachregionensuregoodrepresentationof the skull both anatomically and biomechanically. This good representationensuresgoodandreliableresults.

ThefirsttointroducethebucklingmechanismwasLeFort[28].

Thismechanismwasdefinedasthetransferofforceacrossthe bonefromtheinfra-orbitalrimtotheorbitalfloor.Thistheorywas widelyacceptedaswellasthehydraulicmechanismasacauseof orbital wall fractures [29]. Several experimental studies in literature support the buckling mechanism [4–6,24–27] they simulatedthefracturesoftheorbitbydroppingapre-measured weightorhittingthebonyorbitusinghammer.

Fujino et al. [24] conducted experiments using skulls without the eyes and the contents ofthe orbit, they hitthe skullsontheinfra-orbitalrim,thuseliminatingtheinfluenceof thehydraulicmechanism,focusingonthebucklingmechanism [25].Waterhouseet al.[5]alsodevelopeda newdevicethat allowsapoint-basedimpacttoaspecificareaoftheorbit.Using thisdevice,andstrikingtheeyeballortheinfra-orbitalrimon skulls individually, theyillustrated the fracture patterns for bothmechanisms.

Several studies simulated orbital wall fractures based on differentnumericalenvironmentsandunderdifferentbothstatic and dynamic scenarios. Takizawa et al. tried to explain orbital fractures,especiallythedynamiccharacteristicsoftheorbitatthe timeofthefracture.Theyanalyzedthedegreeandconcentrationof stresswithintheorbitdependingontheappliedloads,andthey found that direct force appliedagainst theinferior orbital rim resultedinincreasedstresswithinthelowerwalloftheorbit,and thatstresstendstoconcentrateinthethinnasalsideoftheorbital grooveaspressurewithintheorbitmounts[30].

Fig.8.(A)CTscanrevealedanorbitalfloorfracture,(B)19-yearsoldpatientwithblow-outfracturecausedbypersonalviolence,(C)theresultsinthesagittalcrosssection.

Fig.9.Theclinicalvalidationoffracturestresseswhentheforcewasappliedonthelateral-orbitalrim.

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Themechanicalresponseofourskullmodelwascomparedwith theresultsofsimilarliteraturestudies.Thecurrentstudydiffers fromthestudy ofNagasaoet al.in whichtheskull modelwas dividedintoseveraltriangularpartsofdifferentthicknesses,while the model in the current study was based on CT images. This allowed to accurately detect the borders and to produce the thicknessofdifferentareasoftheskull[21].

Ontheotherhand,andincontrasttothestudyofNagasaoetal.

inwhichthenumberoffiniteelementswithintheskullmodelwas 248,000,thenumberoftheseelementsinthemodelstudiedinthis paperwasequalto560,000elements,whichwouldproducestress valueswithahigherspatialaccuracy[21].

Thisnumberofelementswasdeterminedbasedontheresults ofTaddeigroupresearchwhichcarriedoutanumericalapproach to analyze the influence of the number of finite elements on numerical results. From another side, high resolution results shouldbediscussedmorespecifically,asimagesaccuracyof1mm thicknessnecessitatesmodifyingtheimagesegmentationmanu- ally in order to preserve the continuity shape of the bone, especiallyintheregionsoforbitalandethmoidbones,inwhichthe thicknessoforbitalwallisapproximatelyequalto2.27mm[31].

Ourhitorientedtotheinfra-orbitalrimrevealedafracturein theinfra-orbitalrimandtheorbitalfloor,whichcorrespondstothe experimental model developed by Waterhouse et al. [5]. Our fracturepatterncorrespondsalsowiththeresultsofNagasaoand Miyamotostudy[21],wheretheyfoundthatfractureoccursinthe weakestpartsoforbit(orbitalfloor).

Schaller et al. modeled three different fracture mechanisms based on finite element analysis. A finer skeletal model and a transientdynamic simulation wereusedtotestpure hydraulic, purebucklingandamixedforcetransmission,andtheyfoundthat theroleofthosemechanismsinexplainingthevarietyofclinical fracturesituations[32].Inthisconcern,ourresultsofeye-ballhit seemstobesimilar.Wefoundconcentrationof stressesonthe wallsoforbitwiththegreatestattheorbitalfloor,whichsimulates ablow-outfractureinboththemesialwallandorbitalfloor,which isoftenseenclinicallyinpatientswiththistypeoftrauma(Fig.8).

Kosowski et al. presented initial results of finite element analysis of a blow-out type traumaof orbital wall.This study simulatedthetestsachievedinlaboratories.Inthefiniteelement analysistheneighborhoodoforbitalwallismodelledbytriangle thinshellfiniteelements,andtheresultsofnonlinearstaticand transientdynamicanalysiswerecompared[33].

Folettietal.developedaclinicallyprovenfiniteelementmodel (FEM)ofthehumanorbitinordertostudystressbehaviorunder differentblunttraumas.Meshproduction,and modelproperties wereusedtoperformblunttraumasimulationsbasedona3DFEM comprisingof640000elements.Fracturepatternswereexplained basedonbucklingandhydraulictheoriesoforbitalfloorfractures.

Thisstudypointedouttothegreatestroleofthesurroundingfatin varying facture patterns,which may changeour knowledge in decidingabouttherealfactorscausingthefractures[20].

Our resultsappearedtobesimilartoHuempfner-Hierlstudy investigatingNaso-orbito-ethmoidfracturesusingfiniteelement method [10], where he foundsimilar results when hittingthe medialthirdoftheinfra-orbitalrimwithimpactor.Thisresultalso correspondstowhatisseenclinicallyasshowninFig.8.

Trzebiatowskietal.used2differentthree-dimensionalfinite elementmethod(FEM)modelsofthehumanorbitalregionto simulatethepure‘‘buckling’’mechanismoforbitalwallfracture in twovariants: the model of orbitalbone elementsand the modeloforbitalbone,orbitandintraorbitaltissueelements.A nonlinear transient analysisof the contact problem between bodiesthatdiffersubstantiallyintermsoftheYoung’smodulus wascarriedouttoinvestigatetheinteractionofdifferentbodies within an instantinjury. Potential damageareas were found

withinthelowerorbitalwallandthesewerevalidatedagainst realinjuries[34].

Fracture patterns corresponded with zygomatico-maxillary fractures,anditissimilartowhatisseenclinicallyasshownin Fig.9.Theresultsofthestudycanbeusedtopredicttheriskof blow-outfracturesduringclinicaltrials.Modelingorbitalcontents (muscles and fat) and the soft tissue covering the bone will increasetheaccuracyoftheresults,Thisconsiderationshouldbe takenintoaccountinthefuturewhenbettercomputercapabilities andmoreadvancedcomputedtomographyisavailable,allowing themodelingoftheorbitalcontentsseparately.

ComparedtothenumericalresultsofNagasaoetal.,thefracture pattern resulting from this study is identical to the numerical fracturemodeldistributedthroughtheorbitalfloorinresponseto theloadappliedonthesuborbitalrimevenatlowweightsofthe impactpart[21].

Inthesecondmodelincludingtheeffectofthehydraulictheory highlightedbyadirecthitontheeyeball,itcanbeconsideredthat fracturepattern andstresslines arecorrectbasedon thelatest theoretical and clinical studies [20,31,32]. The fracture model obtained in the current study can be compared to the results obtainedbyFolettietal.althoughtheforcevaluesisgreaterthan theforcecitedinthisstudy[20].

Transferringthisknowledgetotheclinicalpracticemayhelpin understanding the relationship between the direction of the appliedforceandtheresultingfracture,suchasbottom-directed loadscanresultseveralperiorbitaltraumaswithfewerimpactson theposteriorsideoftheorbitalfloor.

5. Conclusion

Biomechanical testing has proven to be appropriate in answeringquestionsregardingfracturemechanisms.Ourresults confirmedwhatisseenclinicallyandexplainedthemechanismsof orbital walls fractures. The results also can help to optimize fracturetherapiesandimprovetheiroutcomes.Thesesimulations help in investigating trauma scenarios and mechanism, which couldbeusefulinforensicsciences.

Conflictofinterest

Allauthorswerefullyinvolvedinthestudyandpreparationofthemanuscriptand declarethatthereisnoconflictofinterest.

Acknowledgment

TheauthorsaregratefulforUniversityofMiskolc(Instituteof MachineandProductDesign)foritsunlimitedsupport.

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Ábra

Fig. 2. (A) Skull surface and virtual eyeball and surrounding fat in 3-matic software, (B) marked sites in Ansys where loads was applied.
Fig. 3. Concentrations of stresses at orbital floor and orbital mesial wall without (left) and with (right) the presence of orbital fat.
Fig. 5. The distribution of stresses when the force was applied on medial orbital wall without (left) and with (right) the presence of orbital fat.
Fig. 9. The clinical validation of fracture stresses when the force was applied on the lateral-orbital rim.

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