软骨之黏弹特性

12.1IntroductionBoneworksinsmallstrainrange,biologysensitivetostrain(stress)Anisotropic,stress-strain&strain-displacementarelinearCartilagerelatedtobone(calcifiedcartilage);smallfrictioncoefficient,Lubrication&shockabsorption,multi-phasicstructure(fluids,ions,solids)triphasictheory12.1.1AnatomyofalongboneShaft(diaphysis),expansion(metaphysis),forimmature,metaphysissurmountedbyepiphysisunitedtometaphysisviagrowthplate(epiphysealplate)Coefficientoffrictionbetweenarticulatecartilage~0.0026!Growthplate-placewherecalcificationofcartilageoccur.Formatured,epiphysesfusedwithmetaphyses

Diaphysis:hollowtube,walldensecortex(compactum)Medullaormedullarycavity:centralspace,containsbonemarrowPeriosteum:coveringexternalsurfaceoflongbone,exceptarticulationInnerlayer,activecellsenlargement&remodeling;osteogeniclayerOuterlayer,fibrouscomprisedalmostentireperiosteumOvermostofdiaphysis,periosteumistenuous&looselyattached&bloodvesselsarecapiliary;Atexpandedends,ligamentsareattchedfirmly&canconveylargesizebloodvessels;Sameatridgesalongdiaphysis.Note:mechanicalpropertiesdependonwhichpartofboneisconsidered.Table12.1:1NotescorticalregionofdiaphysisSpecimenstakenfromcompactumMicroscopicobservationCompositematerialBasicunit:Haversiansystem(osteon)ArteryorveinatcenterBloodvesselsconnectedbyVolkmann’scanals(transverse)Weight%2/3inorganicmaterial,mainlyhydroxyapatite,3Ca3(PO4)2.Ca(OH)2&smallquantityofotherionsTinycrystals200Along,area2500A2,Collagen,HAcrystalsarrangedalonglengthofcollagenfibrils.ArrangementinfibersWoven-fiberboneLamallaeinosteons:concentricLamallaeinsurface:paralleltosurface12.1.2BoneasaCompositeMaterialCollagen&hydroxyapatiteYoung’smodulusoffluorapatite~165GPaSteel200GPa,6061Aluminumalloy70GPaCollagentangentmodulus~1.24GPaYoung’smodulusofhumanfemur18GPaBone’sstrengthishigherthaneitherHAorcollagen:softercomponentpreventstiffonefrombrittlecracking,stiffcomponentpreventthesoftfromyieldingMechanicalpropertiesdependon:compositionstructureofbonegeometricshapeofcomponentsbondbetweenfibers&matrixbondsatpointsofcontactoffibersStrengthofbonecorrelateswithmassdensityofbonelooselyCorrelationcoefficientbetweenstrength&density0.40-0.42Density&strengtharenon-unifromlydistributedinfemur;density2.20-2.94;strength1.35x12.2BoneasaLivingOrganBoneisliving–bloodcirculation;transportmaterialstoandfrombone&bonecanchange,grow,removedbyresorption,(stress-dependent)Under-stressedorover-stressedbonebecomesweakened,properrangeofstressisrequired;Localstressconcentrationimposedbyimpropertighteningofscrews,nuts&boltsinbonesurgerymaycauseresorptionandresultedinloosening!Evolutionprocesshasresultedinoptimumdesignofbone:GeneralshapingtominimizestressDistributionofmaterialtoachieveminimum-weightTheoriesUniformstrengthunderaspecifiedsetofloadingconditionsTrajectoryarchitecture,putmaterialonlyinthepathsoftransmissionofforcesandleavevoidselsewhere.ExamplesofoptimumstructuredesignThin-walledsubmarinecontainertoencloseavolumeVandtoresistanexternalpressurepwhilemaintaininginternalpressureatatmospheric;Sphericalshell~lightest&mosteconomical;cylindricalshelltwiceasheavy;egg-shapeliesinbetweenMinimum-weightDesignofabeamtosupportaloadPoveraspanBendingmomentM(x),maximumbendingstresss=M(x)c/IAbeamofvariablecrosssectionwithc/IvaryingwithxinsamemannerasM(x)OptimuminsenseofeconomyofmaterialComparedifferentshapesofbeamcrosssectionLoadtrajectorydesign,upperflangecompression,lowerflangetension,compression&tensileforcesaretransmittedalongthesetrajectories.PrincipleoffunctionaladaptationPrincipleofmaximum-minimumdesignMaximumstrengthisachievedwithaminimumofconstructionalmaterialThroughhypertrophy&atrophymechanismboneadaptstolivingconditiontoachievemax-mindesignSpongybonerepresentsatrajectorystructure(Roux1895)Theoreticalconstructionof3Dtrajectorysysteminfemurmodel(Kummer1972)12.3BloodCirculationinBoneImportanceofbloodcirculationonstress-dependentchangesinbone.Bymethodsofinjection,vasculatureinbonewerestudied.VascularpatternsinbonecortexPrincipalarteryentersbonethroughdistinctforamenWithinmedullabranchesintoascending&descendingmedullaryarteries;DividedintoarteriolesthatpenetrateendostealsurfacetosupplydiaphysealcortexCartilageEpiphysealarteriesGrowthcartilageEndochondralboneEndostealbonePeriostealboneOrientationofvesselsaredifferentHemodynamicsofboneisdifficulttostudyduetosmallnessofbloodvessels&inaccessibilityfordirectobservationIndirectestimatesofbloodflowratehavebeenmadeunderassumptionthatheattransferisproportionaltobloodflow.Directmeasurementsofflow&pressureareneeded!!12.4ElasticityandStrengthofBoneBoneishard&stress-straincurvesimilartomanyengineeringmaterials.Stress-strainrelationshipofahumanfenursubjecttouniaxialtension(Fig.12.4.1)Note:dryboneisbrittle&failurestrain0.4%;wetboneiselastic&higherfailurestrain1.2%.Mechanicalpropertiesofwetcompactbonesofanimalandman(p.511)Notes:Ultimatestrength&strainincompression>valuesintensionEintensionislargerthanthatincompressioniscausedbynon-homogeneousanisotropiccompositestructureofbone.humanfemur:bendingstrength160MPa,shearstrengthintorsion54.1MPa,Modulusofelasticityintorsion3.2GPa.Strengthofbonedependsonage&sexofanimalStrengthandmodulusofelasticityofspongybonearemuchsmallerthanthoseofcompactbone.12.4.1AnisotropyofBoneAnisotropicmechanicalpropertiesofmetaphysealbone:transverseisotropicmodel物理特性非等向性(anisotropy)非等向非均質沿骨幹方向剛性最大，沿徑向剛性最小正向性材料(orthotropic)，即材料特性對稱於三個平面，其材料係數共有九個ABCFLABC正向性材料構成方程式

參數:九個

12.4.2FailureCriteriaofBoneCorticalbone:vonMises’syieldcriterionTrabecularbone:Mises&Hoffman’syieldcriterions1,s2,s3:principalstresses;St,Sc:ultimatestrengthsintension&compression;IfSt=Sc

thenitreducedtovonMisescriterion;Overestimateunderhydrostaticcompression12.5ViscoelasticPropertiesofBonePhysicalprocessescontributedtoviscoelasticityofbone(Lake,Katz&Sternstein1979)Thermo-elasticcouplingPiezoelectriccouplingMotionoffluidincanalsInhomogeneousdeformationinosteonsCementlines,lamellae,interstitium&fibersMolecularmodesincollagenTrianglespectrumforwetcorticalboneNotes:therelaxationwasnotnormalizedHissumofseveraltermsproportionaltologtNonlinearityinviscoelasticityofboneUsingtheQLVmodelinsec.7.6,elasticstressisnonlinearfunctionofstrainbutmemory(relaxationfunction)islinearMulti-integralmethodofGreen&RivlinMulti-integralmethodofPipkin&Rogers骨生長模型s(massrate)(stress)bcaa:Stableequilibriumpointb,c:unstableAtadm/dt=0Ds>0dm/dt>0(增骨)Ds<0dm/dt<0(減骨)骨生長模型(續)[Y.C.Fung]Notes(1)Stresshasdifferenteffects:growthinhealingprocess,modelinginoverload,remodelinginunderload.(2)growthofboneisalsoinfluencedbyheredity(3)typeofloadinginfluencebonemodeling/remodeling12.6FunctionalAdaptationofBoneX-raymeasurementofopacityofbone~mineralcontentofboneWavetransmissionvelocity&vibrationmodestodeterminedensityofboneChangesofboneduetoactionofbonecellsOsteoclasts–resorptionOsteoblast-appositionLivingboneschangeaccordingtostress&strainactinginthemExternalorsurfaceremodeling(shape)Internalremodeling(porosity,mineralcontents,opacity,density)Stress-controlledbonedevelopmentCompressivestressstimulatesformationofnewboneandimportantfactorinfracturehealingDuringimmobilization,netlossofbonecalcium&phosphorous;afterresumeofnormalactivityminerallossphenomenareversed!Astronautssubjectedtoweightlessnesshassameresults:subnormalstressescauseslossofbonestrength,radiographicopacity&size.Intermittentstressisamorphogeneticstimulustofunctionaladaptationofbone&effectofcompressivestressissameastensilestress!Distributionofmaterial&strengthisrelatedtoseverityofstressinnormalactivity.Rigidplatefixationindogyieldsthinningoffemoraldiaphysiscortexratherthanosteoporosisincortex!骨破損後在修補過程有把骨整直的傾向，凸出部的骨會被吸收，凹部的骨會增生Frost(1964)提出骨質增生與切面方向應變及受負荷後骨表面曲率有關。若表面凸度增加→減骨作用。若表面凸度減少→生骨作用

骨之增骨或減骨的要因

(1)應變模式(strainmode)(2)應變方向(straindirection)(3)應變率(strainrate)(4)應變變動頻率(strainfrequency)(5)應變分佈(straindistribution)(6)應變能(strainenergy)壓應變主導增骨作用(osteoblastic)，骨細胞會依主應力方向排列(principaldirection)增骨主要由於間斷性負荷所致，固定的靜負荷再加上動態負荷促使骨生長，應變變動頻率影響生長。

Wolff’sLaw外減骨或面減骨(surfaceremodeling)：即骨外形之改變

內減骨(internalremodeling)：即骨內多孔度(porosity)，密度的改變

活骨會隨其承受之應力及應變而改變又分:內減骨模型

假設骨由骨細胞，胞外液體及骨基質(bonematrix)即胞外固體構成ξ:基質之體積比率(volumefraction):為基質之密度，εij為應變張量σij為應力張量Atconstanttemperature

外減骨模型

hx1x3x2設x3沿著法線方向，x1、x2與骨面平行ε11，ε12，ε22為沿x1-x2平面之應變

U為沿x3方向骨厚度變化率12.6.1TensorialWolff’slawCowinetal.suggestedthattemporalchangesinarchitectureofbonemustbenonlineartensorequationstoaccountforthefeedbackbetweenstressandgrowth.SeeEqs.(5)-(8)p.517.12.6.2MechanismforcontrolofremodelingPiezoelectricityMechanismforbonetosensestress&causeremodelingCollagenElectricalfieldiscapableofactivatingprotein-synthesizingorganellesinosteogeniccells(frog).Electricalfieldcausetropocollagenalignment.BiochemicalactivityofcalciumStrainingboneincreasescalciumconcentrationininterstitialfluidChangeinsolubilityofHAcrystalsinresponsetostressEndocrineSTH(somatotropicorgrowthhormone):increasescelldivision&allsubsidiaryprocesses(totalproteinsynthesis,netproteinsynthesis,totalturnover,tissuegrowth)ACH(adrenal-corticalhormone):decreasescelldivision&subsidiaryprocesses.T4(thyroxine):affectsalltissues.Estrogens:selectivelydecreasecelldivision&subsidiaryprocesses;affectcartilage&lamellarbone.VitaminsA,C&D&calcitoninImportanceofmechanicalaspectsIfweknowthemechanicalaspectwell,thenonecancontrolboneremodelingthroughmechanicalstressthatappliedthroughexerciseeithervoluntarilyorwiththehelpofmechanicaldevices.(orthopedics)12.6.3OsseointegrationinskeletalreconstructionBranemark1977titaniumfixturestosupportfixeddentalprostheses;long-termsuccessrateofstableusefulprostheses95%25yr!Titaniumscrewfixturesappliedtohead,neck,eyeandear,hearingaids,hand,knee;boneintegratedwithtitaniumwell.12.7CartilageCompositionCells(chondrocyte)IntercellularmatrixSystemoffibersEarlyfetallife:greaterpartofskeletoniscartilaginousAdultlife:articulatingsurfaceofsynovialjoints,wallsofthoraxmlarynx,trachea,brobchi,nose,ears,smallmassesinskullbase.TypesofcartilagesHyalinecartilageCostal,nasal,tracheo-bronchialandalltemporarycartilages,mostarticularcartilageSplit-linefeature,patternofsplit-linefollowspredominantdirectionofcollagenbundles;proportionofcollageninmatrixincreaseswithageWhitefibrocartilageIntervertebraldisks,articulardisks,liningofbonygroovesthatlodgetendonsYellowelasticfibrocartilageExternalears,larynx,epiglottis,apicesofarytenoidsFunctionsInter-vertebraldiskElastic&makespineflexibleCartilageatendsofribsDesiredmobilityofribcageArticularcartilageatendsoflongbonesLubricationforsurfaceofjoints,shockabsorberBrochiolesofmananddivinganimalsCartilageisbiologicallyactive,rheologicallyunique12.8ViscoelasticPropertiesofArticularCartilageCartilageisporous&interstitiumfilledwithfluid;understressfluidmovesinandoutoftissue&mechanicalpropertieschangewithfluidmovement.InsituIndentationtestInstantaneousrecoveryfollowedbyatime-dependentrecovery;notcompleteinairbutcompleteinabathbyfluidresorptionduringunloadingTestingofarticularcartilageBovinehumeralhead;largejointsurface1.25cmdiameterplug,diecutting,slice250-325um;specimendimension1x4.25x0.25-0.325mmStrainratedependentandcyclictests(compression)FaststressrelaxationwasobservedStressresponseofbovinefemuralarticularcartilageSalinesolution,37degCl=1.07~1.1010UniaxialtensilestressrelaxationQLVmodel(Woo)RelaxationfunctionKt1=0.006,t2=8.38,C=2.02Experimentalreducedrelaxationfunction(Woo,1979)AssumeSetobeapowerseriesinEn=2,a1=30,a2=56Comparisonofexperimentaldataonstressresponsetofirst3cyclesCompressiontestofcartilageplug(Mow1977)RapidstressrelaxationEaseofextrusionoffluidintissueRamp-stepstrainDynamicstraindistributionFluidmovement3-2關節軟骨(ArticularCartilage)

3-2-1基本名詞：

軟骨細胞(chondrocyte)蛋白澱粉(proteoglycans)膠原(collagen)3-2-2研究史

1898Hultkrantz

股骨髁面軟骨，發現表面細縫，沿著關節面方向相對運動1925Benninghoff

提出arcadetheory說明軟骨深層結構1960microscope,SEM(scanningelectronmicroscope)

關節面膠原纖維潮記軟骨下骨arcade3-2-3形態學與組織學

形態與功能：

軟骨為薄的纖維結締組織，通常在滑液關節之關節面上。由軟骨細胞及胞間基質所組成，其中軟骨細胞佔5％，胞間基質佔95％，其中65～80％為水軟骨之機械性質為黏彈性。其特點為低摩擦，係數約0.0025金屬與金屬之乾摩擦係數約0.15～0.25，濕摩擦約0.1，鋼與冰之摩擦係數約0.03，濕摩擦約0.015。

主要功能

(1)傳遞力量(2)分佈力量(3)使關節以最低磨擦運動軟骨基質胞間基質(intercellularmatrix)，基質(matrix)為組織中細胞間的物質，結構由基質發展而成三種基質：細胞周質(pericellular)，胞區質(territorial)及胞區間質(interterritorial)等三種。

細胞周質完全包住軟骨細胞，含有少量的膠質(collagen)，及蛋白澱粉。(proteoglycan

胞區質(territorial)包圍細胞周質，含有纖細狀膠質並黏附於其上，形成巢狀組織以保護軟骨細胞。

胞區間質(interterritorial)在胞區質的外面，由分布較開，厚的平行膠質纖維所組成

軟骨結構

異質(heterogeneous)依深度可分

(1)表層區(superficialzone)厚度10~20%，由細的膠質纖維排列，且排列面與關節面平行(2)轉變區(transitionzone)厚度40~60%，纖維間空間變大，纖維方向任意排列。(3)深區(deepzone)厚度30%，纖維之方向與潮記垂直

(4)鈣化區(calcifiedzone)

表層區

表層區佔厚度10~20%，由細的膠質纖維排列，且排列面與關節面平行。轉變區，約佔厚度40~60%，纖維間空間變大，纖維方向任意排列。深區(厚度30%)，纖維之方向與潮記垂直。

3-2-4組織學

固體基質(solidmatrix)約佔重量20~40%，由60%的膠原纖維(collagenfiberII)，纖維間的蛋白澱粉膠(proteoglycangel)

組成，蛋白澱粉具高親水，其他部分是水(60~80%)軟骨之生物力學行為由其成分之分佈以及成分間的相互作用決定。

膠原(collagen)

膠原是蛋白質的一種，具高度結構組織，基本單位是轉膠原(tropocollagen)分子，先排列成微纖維(filament)直徑4n