Chapter 2v4.docx
- 文档编号:5453487
- 上传时间:2022-12-16
- 格式:DOCX
- 页数:9
- 大小:325.72KB
Chapter 2v4.docx
《Chapter 2v4.docx》由会员分享,可在线阅读,更多相关《Chapter 2v4.docx(9页珍藏版)》请在冰豆网上搜索。
Chapter2v4
IntroductoryRemarks
Thecoilisthephysicalinterfacebetweenpatientandtheelectronics.TheRFcoilisatransducer.Inthetransmitmode,itconvertsRFpowerintoanRFfieldB1thatexcitesthespins.Duringthereceivemode,itconvertstheprecessingmagnetizationintoanelectronicsignalthatisprocessedbytherestofthesystem.
Asaconduitforalltheinformationtransferredtoandfromthepatient,theRFcoilisthefundamentaldeterminantofimagequality.Theimagequalityisdegradedbyanythermallyactivatednoiseaddedtothedesiredsignal.Thisisreferredtoasthesignal-to-noiseratio(SNR).TheimagecanalsobedegradedbyincorrectexcitationofthespinsduetodistortionoftheB1fieldduringthetransmitmodeormisplacedsignalduringthereceivemode.Theseeffectsarereferredtoasartifactsorstructurednoise.Thecoildesigner’sjobistomaximizeimagequalitybyminimizingthesetypesofnoise.
TheRFcoilassemblyprovidestwofunctions:
excitationofthespinsandreceptionoftheresultingsignal.Asinglecoilcanperformbothfunctionsbutmoreoftenseparatecoilsareusedforthetransmitandreceivefunctions.
Theprimaryrequirementsofatransmitcoilare:
1.ItshouldproduceauniformB1fieldintheregionofinterest(ROI).
2.Itshoulddepositaminimumofenergy(heat)inthepatient.
TheforemostrequirementofthereceivecoilisthatitmaximizetheSNRintheROI.Theuniformityofthesignalsensitivityisnolongersoimportantbecausemodernscannerscancorrectsignalintensityvariationsduetonon-uniformityofthereceivecoil’ssensitivity.
Therearethreeadditionalpropertiesthatareabsolutelynecessaryforasuccessfulreceivecoildesign.
First,becausetheRFcoilisofteninclosecontactwiththepatient,itpackagingmustbedesignedtomaximizepatientcomfortandcompliance.Whenanuncomfortablepatientmovesduringascan,artifactscangreatlydiminishimagequality.
Second,thecoilmustbeoperator/userfriendly.MRItechnologistsareunderextremepressuretomaximizethenumberofpatientsscannedperday.Ifacoilisdifficulttopositionoradjustonthepatient,theunhappytechnologistwilladviseothersnottobuyit.
Thirdly,theRFcoilassemblymustbehighlyreliable.Ifacoilfailsinaclinicalsetting,itcancausedelaysinthedailyschedulethatcosthundredsorthousandsofdollars.Likewise,ifaresearchcoilfails,itmaywastethelimitedaccesstoascannerandtheexpenseofpreparingthespecimenorcausealossofirretrievabledata.
Inexperiencedcoilbuildersoftenoverlooktheseissuesbecausetheydonotinvolvethehigh-techfeaturesofRFcircuitdesign.
RFCoilFundamentals
Notanantenna:
Althoughitisinvolvedwiththetransmissionorreceptionofasignal,theMRIRFcoilshouldnotbethoughtofasanantenna.Traditionally,anantennaisdesignedtoproduceradiatedfieldsatdistancesmuchgreaterthanawavelength,whichisreferredtothefarfieldlimit.WhereasanMRIRFcoiloperatesinthenearfieldlimitandshouldnotinvolveradiation.Ideally,anMRIcoilshouldproduceorrespondtoonlyalocalmagneticfieldandnotanelectricfield.Therefore,designprinciplesforanantennadonotapplytoanMRIcoil.
LCRresonator:
AllMRIRFcoilsareoperatedasresonatorsbytuningthemtotheLarmorfrequency.ThesimplestmodelisanLCRcircuit:
Fig.1
TheRFvoltagesourceV0couldrepresenteitherthepoweramplifierusedtogeneratealargeB1fieldduringthetransmitpulseorthesmallvoltageinducedbytheprecessingnuclearspinsduringthereceivemode.Themaximumcurrentflowswhenthereactanceoftheinductorequalsthe(negative)reactanceofthecapacitor.Theresonantfrequencyis(approximatelyforsmallR)
Eqn1
IfoneknowsthevalueofCandtheresonantfrequency,onecancalculateLfromEqn1.
Magneticenergystorage:
Theoscillatingcurrentalternatelystoresenergyinthemagneticfieldcreatedbytheinductororintheelectricfieldcreatedinthecapacitor.Thecurrentthroughtheresistordissipatesaportionofthestoredenergyeachcycle.
CoilQ:
ThequalityofaresonatorischaracterizedbyitsQfactor,whichisdefinedastheratioofthemaximumstoredenergydividedbytheaverageenergydissipatedperradian.AlternativeexpressionsforQare
Eqn2
where∆ωisthefullwidthat3dBbelowthepeak.BoththecapacitorandtheinductorcanindividuallybeassignedaQvalueusingEqn2.Generally,oneshoulduseonlyhighqualityporcelainmicrowavechipcapacitors,whoseQismuchhigherthanthetypicalcoilinductance.
DirectmeasurementsofasmallRFresistancesuchasRabovearedifficultorinaccurate.CalculatingQfromameasureofbandwidthandresonantfrequency,onecandeduceRfromEqn2.
ForapracticalwaytomeasureQinthelaboratory,seeNote2.1.
Impedancematching:
ThevoltagesourceinFig.1isnotapracticalwaytopoweratransmitcoil.RFpoweramplifiersdelivertheirmaximumoutputtoaloadequaltothesourceimpedanceofthepoweramplifier.Typicalpoweramplifiershaveanoutputimpedanceof50ohms,whichmaybemuchlargerthantheRinFig.1.Fiftyohmsisusedbecausetypicalcoaxialcableshaveacharacteristicimpedanceof50ohms.Atresonance,thevoltageacrossthecapacitorCorinductorLwillbeQtimeslargerthanthevoltageacrossR.Thisinductivestep-upinvoltagecanbeusedtotransformtherelativesmallvalueofRto50ohms.
OnepossiblematchingschemeisformacapacitivevoltagedividerbyreplacingthesinglecapacitorCbytwocapacitorsC1andC2inseries.
Fig.2
Thenetcapacitanceforthetwocapacitorsisgivenby
Eqn3
TheimpedanceZinobservedacrossC2attheresonantfrequencyis
Fig.3
where
Eqn4
Togetarealimpedance,oneaddsaseriesinductorL2thatresonateswithC2andcancelsoutthecapacitivereactance.Thatis,
Fig.4
with
Eqn5
NotethattostepuptheseriesresistorRtoanewvalueR’,onechoosesacapacitorC2,whosereactanceisequaltothegeometricmeanRandR’.
Eqn6
TogetmaximumpoweroutofanRFpoweramplifier,onematchestheimpedanceofthecoiltotheamplifierbysettingR’equaltotheoutputimpedanceoftheamplifier,whichistypically50ohms.
CoilTransducerorSensitivityFactorB1xy/I:
Theperformanceofatransmitcoilcanbecharacterizedbythex,ycomponentoftheRFfieldB1xy(r)producedperunitofcoilcurrentIorbytheratiooftheB1xy(r)/I.NotethatthevectorB1(r)referstothestrengthofthefieldbutdoesnotincludethetimedependencegivenbycos(ωt)orejωt.Thevariationofthestrengthanddirectionofthefieldwiththelocationrisdeterminedbythegeometryofthecurrentcarryingconductors:
Eqn7
Fig.5
wherei,j,andkarethethreeorthogonalunitvectors.(Vectorswillbeindicatedbyuseofboldfacetypeinthetext.)ThetransmitcoilservesasatransducerthatconvertscurrentintoRFmagneticfieldinthexyplane.SotheratioB1xy/Icanbethoughtofasatransducerfactor.
Thissamefactor,B1xy(r)/I,alsodetermineshowwellthecoilworksasareceivecoil.ThevoltageE(r)inducedinacoilbyatimedependentmagneticmomentm(r)locatedatpositionrisgivenbythereciprocitytheorem:
Eqn8
Forthemagneticresonanceofnuclearspins,onlythecomponentofthemagnetizationm(r)thatisperpendiculartothestaticmagneticfieldB0istimedependent:
Eqn9
SoonlythexycomponentoftheRFfieldisusefulinboththetransmitandthereceivefunctionofanRFcoil.Notethat,becauseofthescalarproductinEqn8,thephaseofthetimedependentsignalisdeterminedbythedirectionoftheB1magneticfieldrelativetothedirectionofthemagnetizationattimeequalszero:
Eqn10
Biot-SavantLaw:
OnecangetanestimateofthefieldstrengthduetoadistributionofcurrentbyapplyingtheBiot-SavantLaw:
Eqn11
wheredBistheincrementalfieldduetheincrementalcurrentelementdllocatedatadistancer.Thisformulaappliestostaticfieldsandisonlyaccurateatlowfrequencies,whereallthedimensionsaresmallcomparedtothewavelength.
Weconsiderseveralsimplecurrentdistributionsthatwillbeusefulinourlaterdiscussions.TheinfinitelylongstraightwirewithcurrentIhasatangentialfieldgivenby
Fig6
Eqn12
whereristheradialdistancefromthewireandthedirectionofthefieldisgivenbytherighthandrule.(Aconstantisusedinthisandotherequationstoemphasisthedependenceonthephysicalparametersandnottheirnumericalvalueswhichdependonthechoiceofunits.)
Itisrelativelyeasytocalculatethefieldstrengthalongtheaxisofasimplecircularloop.Forasinglecircularturnofwirewithradiusainthey-zplaneandacurrentI,thefieldalongitsaxisgivenby
Fig.7
Eqn13
wherexisthedistancefromthecenterofthecoil.
HomogeneousFieldProduction:
Thesimplestway,inprinciplebutnotinpractice,tocreateahomogeneousmagneticfieldiswithasheetofcurrent.Consideraninfinitesheetonthey=0planewithauniformcurrentdensityσdirectedinthenegativezdirection.Theresulting
magneticfieldforallpositiveyvaluesisaconstantequaltoμ0σ/2anddirectedinthepositivexdirection.Fornegativeyvalues,thefieldisdirectedinthenegativexdirection.
Fig.7
Fortwosuchsheetsspacedaty=d/2and–d/2withcurrentdensitiesσintheoppositedirections,thetwofieldscombineconstructivelybetweenthesheetstoproducefieldofstrengthμ0σandcombinedestructivelytoproduceazerofieldoutsidethesheets.
Fig.8
TimeDependentFields:
Thefieldfromasinglesheetistotally
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Chapter 2v4 v4