各向异性松质骨压缩模量和强度的数值预测

29320106ChineseJournalofBiomedicalEngineeringVol.29No.3June2010doi10.3969/j.issn.0258-8021.2010.03.0242009-04-302010-02-241057201310932001XK100060522*。[e-mail]*100191NumericalPredictionforCompressiveModulusandStrengthofAnisotropicCancellousBoneLUZi-Xing*PEIHeSchoolofAeronauticScienceandEngineeringBeihangUniversityBeijing100191ChinaKeywordsanisotropiccancellousbonemechanicalpropertiescompressivemoduluscompressivestrengthfiniteelement。。O346.1TB330.1D0258-8021201003-0468-06、、1。2－4。。15。Guo145Diamant6－7。14。11。Gefen7Tb.ThTb.3SpL。rz=±2Τb.Τh－β1+α×cos2zLcos－1123－α－β1+α2Τb.Τh－()()()β－()321LzrzzTb.Thα=1.3736β=40.9μm6。114。abFig.1Thetetrakaidecahedralunitcellmodelforsimulatingthemicrostructureofcancellousbone.athree-dimensionalsketchbtwo-dimensionalsketchTb.Th、bl。14HDλ=H/Dl/b。8E012GPa0.3107MPa。SOLID45。9。22.1149。。2.214。10。。2VonMises。yy。Mises“”2“”。Mises-σult。11－12。Hou12σult=0.0101Eaprt+0.0852964292。aMisesb“”c“”dMisese“”f“”Fig.2ThestressnephogramandgriddingmapofmodebytheFEMunderdifferentloadingsteps.aMisesstressunderoneloadingstepbkillingelementscreactivatingelementsdMisesstressunderanotherloadingstepekillingelementsagainfreactivatingelementsagainCrawford13σy=0.833σult3σult3。33.13BV/TVTb.Th。BV/TVTb.ThTb.ThBV/TVl/bBV/TVTb.Thl/bBV/TVl/bλ。3.24Eyy/E0BV/TV。BV/TV14Tb.ThbBV/TV3BV/TVTb.Thb=1.2mmFig.3TherelationsbetweenBV/TVandTb.ThCarterHayes1。。。GrantαEασ140743αE=Et/Emασ=σyt/σym4EtEmσytσym。αETb.ThBV/TVTb.Spl+b/2αEασ。4。4Eyy/E0BV/TVFig.4ThevariationofEyy/E0withBV/TV3.3-5-Fig.5Thecurvesofcompressivestressandstrain5b=0.9mm、l/b=1.5、BV/TV=10.3%--。1.9MPa。。l/b1.01.251.501.75BV/TV-l/b=1.506。BV/TV。6BV/TV-l/b=1.50Fig.6ThecurvesofcompressivestressandstrainunderthedifferentvaluesofBV/TVl/b=1.503.4l/b=1.01.251.501.75BV/TV-。σultσultBV/TV12157。BV/TVBV/TV0.15l/bσultBV/TVσultl/bBV/TV。BV/TVl/bBV/TV。l/b1BV/TVσultBV/TVσultσult。174297σultBV/TVFig.7TherelationsbetweenσultandBV/TVandthecomparisonwiththeexperimentalvalues3.5Houσult12。l/bEyy28。σultl/bl/bl/bσult。8σultFig.8ThecomparisonbetweentheFEresultsofσultandtheempiricalformula411423。1CarterDRHayesWC.Thecompressivebehaviorofboneasatwo-phaseporousstructureJ.BoneJointSurg1977592954－962.2PassiNGefenA.TrabecularbonecontributestostrengthoftheproximalfemurundermediolateralimpactintheavianJ.BiomechEng20051271198－203.3GibsonLJ.ThemechanicalbehaviorofcancellousboneJ.Biomech1985185317－328.4TeoJCSi-HoeKMKehJEetal.RelationshipbetweenCTintensitymicro-architectureandmechanicalpropertiesofporcinevertebralcancellousboneJ.ClinBiomech2006213235－244.5GuoXEKimCH.Mechanicalconsequenceoftrabecularbonelossanditstreatmentathree-dimensionalmodelsimulationJ.Bone2002302404－411.6DiamantIShaharRMasharawiYetal.Amethodforpatient-specificevaluationofvertebralcancellousbonestrengthInvitrovalidationJ.ClinicalBiomechanics.2007223282－291.7GefenAPortnoySDiamantI.Inhomogeneityoftissue-levelstraindistributionsinindividualtrabeculaeMathematicalmodelstudiesofnormalandosteoporosiscasesJ.MedicalEngineering＆Physics2008305624－630.8DucheminLBoussonVRaossanalyCetal.PredictionofmechanicalpropertiesofcorticalbonebyquantitativecomputedtomographyJ.MedicalEngineering＆Physics2008303321－328.9LiShuguang.BoundaryconditionsforunitcellsfromperiodicalmicrostructuresandtheirimplicationsJ.ComposSciTech20086891962－1974.10ZihuiXiaChuweiZhouQiaolingYongetal.Onselectionofrepeatedunitcellmodelandapplicationofunifiedperiodicboundaryconditionsinmicro-mechanicalanalysisofcompositesJ.InternationalJournalofSolidsandStructures.2006432266－27811GouletRWGoldsteinSACiarelliMJetal.Therelationship48027429。3。80%。4。1ZipesDPCammAJBorggrefeMetal.ACC/AHA/ESC2006guidelinesformanagementofpatientswithventriculararrhythmiasandthepreventionofsuddencardiacdeath-executivesummaryJ.JournaloftheAmericanCollegeofCardiology20064851064－1108.2..J2007112110－114.3GoldbergerJJCainMEHohnloserSHetal.AmericanHeartAssociation/AmericanCollegeofCardiologyFoundation/HeartRhythmSocietyscientificstatementonnoninvasiveriskstratificationtechniquesforidentifyingpatientsatriskforsuddencardiacdeathJ.JournaloftheAmericanCollegeofCardiology200852141179－1199.4.J.200544236－238206.5.J.200728495496.6ThomasKEJosephsonME.TheroleofelectrophysiologystudyinriskstratificationofsuddencardiacdeathJ.ProgressinCardiovascularDiseases200851297－105.7HaghjooMAryaASadr-AmeliMA.MicrovoltT-wavealternansareviewoftechniquesinterpretationutilityclinicalstudiesandfutureperspectiveJ.InternationalJournalofCardiology2006109293－306.8DaccarettMSerafimovskiNMachadoC.EpidemiologicalimpactofmicrovoltT-wavealternansinsuddencardiacdeathprimarypreventionJ.InternationalJournalofCardiology2007119127－128.9SantangeliPInfusinoFSguegliaGA.VentricularlatepotentialsacriticaloverviewandcurrentapplicationsJ.JournalofElectrocardiology200841318－324.10MoritaHWuJiashinZipesDP.TheQTsyndromeslongandshortJ.Lancet2008372750－763.11.J.2006205461－463.12.J.2006295272－276.13.2006-ACC/AHA/ESCJ.2007421817－1822.14.J.200730294－97.15.J.2007165352－355.16.J.2007263182－185192.17.J.2007264244－249.18.J.2008302218－223.19.J.2008134307－310.20.TJ.200595344－347.21.J.2008