外文资料--Numerical Simulation Method of Acoustic Field Positive Problem based on Magnetoacoustic Tomography with Magnetic Induction.PDF外文资料--Numerical Simulation Method of Acoustic Field Positive Problem based on Magnetoacoustic Tomography with Magnetic Induction.PDF

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NumericalSimulationMethodofAcousticFieldPositiveProblembasedonMagnetoacousticTomographywithMagneticInductionHuiXia1,GuoqiangLiu1,YanhongLi1,YangZhang1,ShiqiangLi1andLaifuZhang21.InstituteofElectricalEngineering,ChineseAcademyofSciencesBeijing,China2.ShanxiElectricPowerResearchInstituteShanxi,Chinaxiahuimail.iee.ac.cnAbstractMagnetoacousticimpedancetomographywithmagneticinductionMAT-MIisanewimagingmethod.Itsimagesreflectconductivitydistribution.Inthispaper,wefirstlyproposedthenumericalsimulationmethodofmulti-physicsfieldscouplingtoobtainthedistributionofacousticfieldinMAT-MIwithoutthestaticmagneticfield.Simpleacousticdetectionexperimentsareconductedtovalidatethealgorithm.Theresultsdemonstrateditsfeasibility,andmayprovidesometheoreticalfoundationforthefurtherresearchonthereal-timedetectionofacousticsignalsandthereconstructionmethodoftheMAT-MI.Keywords-magnetoacoustictomographywithmagneticinductionMAT-MI,Multi-physicsfieldscoupling,two-dimensionalaxisymmetricmodel,numericalsimulationofacousticfieldI.INTRODUCTIONAsakindoffunctionalimaging,ElectricalimpedancetomographyEIThasmanypredominancecomparedwithconventionalimagingmeans,suchasnon-invasivediagnose,highimagingqualityandsoon.ButEIThasnotbeenusedinclinicalapplicationbecauseofit’slowresolutionnow[1-3].Inordertoresolvetheproblem,MagnetoacoustictomographywithmagneticinductionMAT-MIisproposedbyBinHeetal[4],whichisshowninFig.1.InMAT-MI,imagingtargetisplacedinastaticmagneticfieldwithpulsedmagneticstimulationimposedonit,thepulsedcurrentinduceseddycurrentinthesample,andtheinducededdycurrentinstaticmagneticfieldgeneratesLorentzforce.TheLorentzforcecausesacousticvibration,andthegeneratedacousticwavecanbemeasuredaroundthesampletoreconstructtheconductivitydistributionofthesample.Figure1.TheillustrationofMAT-MIquotedfrom[4]OnthebasisoftheprincipleMentionedabove,weproposeanewnon-static-magnetMAT-MImethod.Inthispaper,weanalyzetheprinciplesofmulti-physicsfieldscoupling,includingthetwo-dimensionalaxisymmetrictransientelectromagneticfield,displacementfield,soundfield,andputforwardthemethodofmulti-physicscalculations.Onthebasicofaboveall,theformulaforcalculatingthevariousfieldsarederivedindetail,andconductthesimpleacousticdetectionexperimentstovalidatethemethod.II.THENUMERICALSIMULATIONMETHODOFMULTI-PHYSICSFIELDSCOUPLINGThemethodadoptsimpulsingpowersourceasthedrivingsource,excitingcoilgeneratesalternatingelectromagneticfieldwhichexcitesLorentzforceinthesample.TheLorentzforcecausesvibrationofsampleboundary,thenacousticwavesisexcitedintheair.Wecaninversethesampleresistivitybydetectingacousticwavesignal.Thesoundfielddistributionofthesamplecanbesimulatedthroughsolvingthemulti-physicalequationwhichincludeselectromagneticequation,wienerequationofelasticsolidsandsoundfieldequationintheair.A.TheequationofaxisymmetricelectromagneticfieldsTheexcitingcoilishollowcylindricalcoil,androundcoppersheetisselectedasthesample,thesimulationmodelhasaxialsymmetry,sothevectormagneticpotentialAKonlyhascircumferentialcomponent,labeledasA,thecorrespondingaxisymmetricelectromagneticequationis22s2A1AAAAJrrrrzt∂∂∂∂−−σ−∂∂∂∂1Whereismagneticpermeability,σiselectricalconductivity,andsJiscurrentdensityoftheexcitingcoil.Althoughthecurrentdensityoftheexcitingcoilgeneratesonlycircumferentialcomponent,magneticfluxdensityincludesradialandaxialcomponent,wecangetAJt∂−σ∂978-1-4244-4713-8/10/25.002010IEEErABz∂−∂zAABrr∂∂2Inordertoavoidthesingularityattheboundarywhichrequalstozero,sosupposeuistheratioofAandr,thentheEq.2becomes222suuuuur3rrrJrrztt∂∂∂∂∂−σ−ε−∂∂∂∂∂3OnbothsidesoftheEq.3aremultipliedby2r,wecanget222323332suuuuur3rrrrJrrrztt∂∂∂∂∂−σ−ε−∂∂∂∂∂4Ifnotetherandzforxandyrespectively,weget233332s2uuuuxxxxJxxxyytt⎛⎞∂∂∂∂∂∂⎛⎞−σ−ε−⎜⎟⎜⎟∂∂∂∂∂∂⎝⎠⎝⎠5FromtheEq.5,wecansee⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂⎟⎠⎞⎜⎝⎛∂∂∂∂yuxyxuxx33isthe3ux∇⋅∇underrectangularcoordinatesystem,wecanget23332s2uuxuxxJxtt∂∂∇∇−σ−ε−∂∂6AccordingtothesolvingrangeoftheFig2a,wecanseethatΩ1istheairrange,Ω2isthesampleposition,Ω3istheexcitingcoilposition.IntheΩ1area,conductivityequalszero,andthereisnoexcitingsource.IntheΩ2area,thereisalsonoexcitingsource.IntheΩ3area,thecurrentinthecoilisthesourcecurrent.Thenequationofthethreesolvingareascanbewroterespectively3xu0∇−∇7−133uxux0t∂∇−∇σ∂7−232sxuJx∇−∇7−3Atthesymmetryaxisandinfinityboundary,theboundaryconditionisthatuequalszero.So,afterobtainingtheu,substitutingrAU/intoEq.1,wecangetelectricfieldintensityandmagneticfluxdensityAuErtt∂∂−−∂∂,ruBrz∂−∂,zuBr2ur∂∂81Ω2Ω3Ω2Γ3Γ2Ω3Ω2Γ3Γ1Γ1Ω2Ω3Ω2Γ3ΓFigure2.Solvingmodels(aElectromagneticfieldsolvingmodel(bdisplacementfieldsolvingmodel(cSoundfieldsolvingmodelBasedonEq.8,wecanget.sFJBKKK9B.AxisymmetricNavierequationsofelasticsolidsAcordingtothetheoryofcontinuummechanics,thewienerequationofelasticsolidcanbederivedthroughusingmomentumconservationprinciple,lawofconservationofmassandconstitutiveequationofmechanicalpropertiesinaninertialreferenceframe.Thevectorformofthewienerequationcanbewroteas222uGGuuFt12v∂ρ∇∇∇⋅∂−KKKK10Whereuurzt,,Kisdisplacementfield,FKisunitvolumeforce,ρisdensityofcoppersheet,Gisshearmodulus,andvisPoisson’sratio.Underthecylindricalcoordinates,Eq.10canbewrote22rrrr22uuGGuF12rrt∂∂θ⎛⎞∇−ρ⎜⎟−ν∂∂⎝⎠10−122zzz2uGGuF12zt∂∂θ∇ρ−ν∂∂10−2rrzuuuurrz∂∂θ∇10−3Where2ru∇、2zu∇、r∂θ∂andz∂θ∂canbewrote222rrrr22uuu1urzrr∂∂∂∇∂∂∂11−1222zzzz22uuu1urzrr∂∂∂∇∂∂∂11−2rzrr2uuuu1rrrzrrr∂∂∂∂θ∂⎛⎞−⎜⎟∂∂∂∂∂⎝⎠11−3rzruuu1zzrzrz∂∂∂∂θ∂⎛⎞⎜⎟∂∂∂∂∂⎝⎠11−4Inordertovoidthesingularityattheboundary,supposeorruur,andsubstitutingroruuintoEq.10-1,andOnbothsidesoftheequationmultipliedbythe2r,wecanget22323ororor22223orzr22G1uuur3rGr12rrzuuGrFr12rzt−ν⎛⎞∂∂∂⎜⎟−ν∂∂∂⎝⎠∂∂ρ−ν∂∂∂12Thesolvingrangeisshowninfigure2b,theboundaryconditionscanbewroteatthe2Γand3ΓsFnp−KK13WheresnKisunitnormalvectorwhichpointingtheoutsideofthesampleorcoil.C.AxisymmetricacousticwaveequationIntheexperiment,becausethereisnoLorentzforceintheair,theacousticwaveequationinthesolvingrangeofFig2ccanbewroteas222210ppct∂∇−∂14Inthecylindricalcoordinate,wecanget2222222110∂∂∂∂−−−∂∂∂∂ppppctrrrz15Wheretheboundaryconditionisr0attheaxisofsymmetry,andp0attheinfinitepoint.Onthe2Γand3Γ,theboundaryconditionareasfollows,22unpnt∂⋅∇⋅∂KK16AccordingtotheEq.10Eq.16,wecansolvethesoundwavedistributioninthesoundfieldofthesample.III.EXPERIMENTSA.SimulationexperimentInthesimulationprocess,thewaveformofexcitingcurrentcanbeshownasfollow0sin−tVItetLαωω17wheredischargevoltage0V1000V,inductionL7.7μH,resistanceR8.06e-3Ω,capacityC200μF,αR/2L,21/LCωα−.Inthecourseofpracticalapplication,thecurrentwaveformisinterceptedbyathyristor,andonlyreservesthefirstpositivespike.Theimpulsewidthisabout120μS,numericalsimulationresultofsoundfielddistributionat60μSisshownbelowinFig.3.Figure3a.Atthetimeof60μs,soundfielddistributionoftheexcitingcoilitselfFigure3b.Atthetimeof60μs,soundfielddistributionofthesampleFromtheFig.3a,wefindthatthesoundfielddistributionofexcitingcoilcanbeapproximatelyconsideredasacircularringwhosecenteristhecoil’stheinsideandoutsideboundaries,andatthesymmetryaxis,thesoundfieldisthestrongest.Atthesametime,wefind,inthedisplacementy0,theacousticsignalstrengthgeneratedbycoilitselfisweak,itcanbeshieldedbymeansofsomemeasuresthatcaneffectivelyeliminatetheinfluenceofacousticsignalgeneratedbythecoilitself.0.000000.000030.000060.000090.00012-250000-200000-150000-100000-50000050000100000150000Signalintensity/a.uTime/s0.00050.0010.0020.0050.0080.01Figure4a.Atx0,thesimulationacousticsignal0.000000.000030.000060.000090.00012-200000-1000000100000Signalintensity/a.uTime/s00.00050.0020.0050.010.15Figure4b.Aty0.0005,thesimulationacousticsignalInFig.3b,wecanseethatsoundfielddistributionconcentratearoundtheaxisofsymmetry.Inordertofurtherunderstandthecharacteristicsofacousticsignals,weselectthedifferentcoordinatepointstosimulatetheacousticsignal,andthetime-stepsetto10μS.Afterachievingtheacousticsignalofthevariouspoint,thecontinuous120μSdataweresegmentedinto0.1μSepochsforFFTtransformandobtainthesignalfrequency.Intheaxisofx0,weobtainthesimulationacousticsignalshowninFig.4a,andintheaxisofy0.0005m,weobtainthesimulationacousticsignalshowninFig.4b.Afteranalysisandcalculation,wefindthatthefrequencyofacousticwavesignalmainlyconcentrateintherangeof3-5KHzinthesphericalsoundfieldrangewhosecenteristhesample’scenterandradiusisapproximately0.005m.B.AcousticdetectionexperimentWeadopttheexperimentalsystemtodetectthesoundfieldofthecoppersheetsample.Withregardtoadetaileddescriptionoftheexperimentcanrefertoliterature[5].Inthesphericalsoundfieldrangewhosecenteristhesample’scenterandtheradiusisapproximately0.005m,theacousticsignalunderexcitationisdetected.ThenweprocessthedetectedsoundsignalbyFFT,andobtainsignalspectrum.TheacousticsignalofmeasurementpointtisshowninFig.5.Figure5.Detectedacousticwavesignalandit’sspectrumAftermulti-pointmeasurementandanalysis,wefindthatthefrequencyofdetectedsoundwavesignalmainlyconcentrateinthespectrumrangeof3-5KHz,itisconsistentwiththesimulationresults.Itprovesthatthesimulationmethodofmulti-physicalfieldcouplingiscorrect,themethodofMAT-MIisfeasible.IV.CONCLUSIONMedicalimagingisaresearchdomainwithbroaddevelopmentprospect,itisessentialtotheadvancementofmedicineandimprovementofpeople’slife.Inthispaper,ourmethodshowsthatitispossibletocompletetwo-dimensionalaxisymmetricacousticwavepositionproblemofMAT-MIwithoutthestaticmagneticfield.ItcanbeseenasthetheoreticalreferenceforthefuturestudyonMAT-MI.ACKNOWLEDGEMENTSTheauthorsthanktheNationalNaturalScienceCouncilofChinaforfinancialsupportGrantNo.60802086,50977084,FoundationofChinaPostdoctorGrantNo.20090450570,BeijingNovaProgramGrantNo.2009B48andtheNationalHighTechnologyResearchandDevelopmentCouncilofChinaGrantNo.2007AA06Z212.REFERENCES[1]V.Cherepeninetal.A3DelectricalimpedancetomographyEITsystemforbreastcancerdetection[J],Physiol.Meas.,2001.221,918.[2]J.P.MorucciandB.Rigaud.BioelectricalimpedancetechniquesinmedicinepartIIIImpedanceimagingthirdsectionMedicalapplications[J].Crit.Rev.Biomed.Eng,1996.244-6655677[3]A.D.Seagar,D.C.Barber,B.H.Brown.TheoreticalLimitstoSensitivityandResolutioninImpedanceImaging[J].Clin.Phys.Physiol.Meas.,1987.81331.[4]X.Yuan,B.He.MagnetoacousticTomographywithMagneticInductionMAT-MI[J].Phys.Med.Biol.,2005.5051755187.[5]H.Xia,G.Liu.etal.ImagingMethodofNewMagneto-acousticImpedanceTomographywithMagneticInductionProcedingsofsecondinternationalconferenceonSportsScienceandSportsEngineeringSSSE2009,99-103
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