主动脉英文paper

–ApplicationtoresiduallystressedarteriesTobiasWaffenschmidta,n,AndreasMenzela,baInstituteofMechanics,DepartmentofMechanicalEngineering,TUDortmund,Leonhard-Euler-Str.5,D-44227Dortmund,GermanybDivisionofSolidMechanics,LundUniversity,P.O.Box118,SE-22100Lund,SwedenarticleinfoArticlehistory:Received11March2013Receivedinrevisedform11May2013Accepted16May2013Availableonline31May2013Keywords:AnisotropicbiologicaltissuesArteriesResidualstressesThick-walledtubeInflationEnergy-minimisationabstractVariousbiologicaltissuesaredesignedtooptimallysupportexternalloadsforcomplexgeometriesandmechanobiologicalstructures.Thisresultsincomplexmicrostructuresofsuchmaterials.Thedesignof,forinstance,(healthy)arteries,whichareinthefocusofthiswork,ischaracterisedbyaresiduallystressedfibre-reinforcedmulti-layeredcompositewithhighlynon-linearelasticresponse.Thecomplexinteractionofmaterialpropertieswiththegeometryandresidualstresseffectsenablestheoptimalsupportunderdifferentbloodpressures,respectivelybloodflow,withinthevessel.Thefibresreinforcingthearterialwall,aswellasresidualstressespresentinthevessel,stronglyinfluenceitsoverallbehaviourandperformance.Turn-overandremodellingprocessesofthecollagenousfibresoccurringintherespectivelayers–eitherresultingfromnaturalgrowthphenomenaorfromartificiallyinducedchangesinloadingconditionsuchasstentdeployment–supporttheoptimisationofthemulti-layeredcompositestructureofarteriesfortheparticularloadingconditionspresentintheartery.Withinthiscontribution,theoverallenergeticpropertiesofanarteryarediscussedbymeansoftheinflation,bendingandextensionofadouble-layeredcylindricaltube.Differentstatesofresidualstressesanddifferentfibreorientationsareconsideredsothat,forinstance,representativefibreanglesthatresultinextremalstatesofthetotalpotentialenergycanbeidentified.Inviewofturn-overandremodellingprocesses,theseorientationsareconsideredtoconstitutepreferreddirectionsoffibrealignment.Insummary,themaingoalofthisworkistocalculateoptimalmaterial,structuralandloadingparametersbyconceptsofenergy-minimisation.Severalnumericalstudiesshowthattheobtainedvalues–suchasthefibreorientations,theresidualaxialstretchandtheopeningangle–areingoodagreementwithrespectivephysiologicalparametersreportedintheliterature.&2013ElsevierLtd.Allrightsreserved.1.IntroductionTheinvestigationofthemechanicalbehaviourofsoftbiologicaltissues,suchasarteries,hasgainedmuchattentionduringthelastdecades;seee.g.Humphrey(2002)forageneraloverview.Variousbiologicaltissuesandstructuresaredesignedtoopti-mallysupportexternalloading,whichoftenresultsincomplexmicrostructuresofthesematerials.Thedesignof,forinstance,healthyarteriesischaracterisedbyaresiduallystressedfibre-reinforcedlayer-wiseorthotropiccompositewithhighly1751-6161/$-seefrontmatter&2013ElsevierLtd.Allrightsreserved.:[phone];fax:[phone].E-mailaddresses:[e-mail](T.Waffenschmidt),[e-mail],[e-mail](A.Menzel).journalofthemechanicalbehaviorofbiomedicalmaterials29(2014)635–654nonlinearelasticresponse.Asaresultoftheinteractionbetweenresidualstressesandnonlinearanisotropicmaterialproperties,arteriesmayoptimallysustaindifferentbloodpres-sures,respectivelybloodflow,withinthevessel.Inadditiontoreducingorratherhomogenisingthedistributionsoftherespectivestresscomponents,theoptimaldesignofthearterye.g.reducesthechangeinitsaxialdirectionundertheactionofbloodflowtoaminimum.Fig.1showstworepresentativemicrographsofathoracicaorta,namelythemedia(a)andtheadventitia(b);thefiguresaretakenfromtheworkbySchriefletal.(2012).Severaladvancedconstitutivemodelsforthesimulationofthemechanicalresponseofarterieshavebeenproposedintheliteratureandhavesuccessfullybeenappliedtorealisticpatient-specificcasestudies;see,forinstance,theworksbyRisslandetal.(2009),HolzapfelandOgden(2010),Balzanietal.(2012)andCreaneetal.(2012).Inordertotestbasiccapabilitiesoftherespectivecon-stitutivemodelswithapplicationtothesimulationofarteries,itiscommontoanalyseanidealisedtestcase,namelytheinflationofathick-walledcylindricaltube.Asanadvantage,theunderlyingboundaryvalueproblemcanbesolved(almost)analyticallywithouttheneedforextensivenumericalmethodssuchasthefiniteelementmethod.Nevertheless,allrepresentativecharacteristicsoftheloadingconditionsandthegeometrycanbecaptured;seeHolzapfelandOgden(2003,2009)andreferencescitedtherein.Forthepresentcaseofapplicationofaresiduallystressedarterysubjectedtodifferentbloodpressures,commonlycombinedloadingcasesincludinginflation,bending,andaxialexten-sionofthethick-walledtubeareconsidered,therebyoftenneglectingthetorsionmode;seethearticlebyHolzapfeletal.(2000)foraparticulartreatmentonarterialwallmechanics.Thebendingandextensionmodesaretypicallyrelatedtoresidualstressstateswithinthearterialwall–whichmaychangeintimedueto,forinstance,ageingeffectsasdis-cussedinCardamoneetal.(2009)–whereastheinflat