Chapter 5v5.docx
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Chapter 5v5.docx
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Chapter5v5
ReceiveCoils
Asstatedearlier,RFcoilsservetwofunctionsinMRI.TheymustprovideanRFmagneticfieldB1duringthetransmitmodewhenthenuclearspinsareexcitedand/ormanipulated.Theymustalsopickupthesmallsignaloriginatingfromtheprecessingnucleiduringthereceivemodefollowingtheexcitation.Inearlyscanners,thesetwofunctionswereperformedbythesamecoil.AsaproducerofB1field,thecoil’stransmitfunctioncouldbecharacterizedbyitstransducerfactorB1xy(r)/I,whichspecifiesthestrengthofthex-ycomponentoftheB1fieldproducedatpositionrbyaunitofcoilcurrentI.Thecoil’sabilitytopickupasignalfromaunitofprecessingmagnetizationwasgovernedbythissamefactor.ThereciprocitytheoremstatesthatthevoltageinducedincoilbyaunitofmagnetizationlocatedatapositionrisproportionaltoB1xy(r)/I.
Duringthetransmitmodeinmostimagingapplications,thespinsaremanipulatedtorevealpropertiesofthetissueincludingpathologicalconditions.Therefore,itisdesirabletoapplythesameB1toallofthenuclei.ThefactorB1xy(r)/IspecifiesthedegreeofhomogeneityofthetransmitB1.Initially,itwasthoughtthatallthenucleishouldbeobservedwithuniformsensitivitytoavoidinterpretinganyinhomogeneityinthesignalsensitivityasduetopathology.Therefore,usingthesamecoilforreceivingwithauniformB1xy(r)/Iseemedreasonable.However,theintroductionofhighlysensitivesurfacecoilsasreceivecoilsdemonstratedthatradiologistswerewillingtoacceptverynon-uniformsensitivitytogaingreatlyincreasedsignalsensitivity.Sincethen,themajorityofnewcoilshavebeenreceive-onlysurfacecoilsorcoilarraystargetingspecificregionsofthebody.
TheT/RSwitch
OnemustnotetheextremedifferenceinthemagnitudeoftheRFpulsestransmittedbytheRFpoweramplifierandtheresultingMRIsignalprocessedbythereceivechannel.Whethertheinputofthereceiverisconnectedtothetransmitcoildirectlyorislocatedincloseproximitytoit,thereceivermustwithstandalargeRFpulsewithoutdamageandamplifyasmallsignalafterward.Thereceivermustbeprotectedduringthetransmitpulses.Thetransmittermustbedisconnectedfromthetransmitcoilduringthereceivemodetopreventitfromgeneratingnoiseinthereceiver.Thesetwofunctionsareperformedbywhatiscalledthetransmit/receiveorT/Rswitch.Atypicalcircuitis
Fig.5.1
ThetwopindiodesareturnedonduringtheRFpowerpulsebyapplyingavoltagebywayoftheinductor(calledachokewhenusedinthemanner)locatedatpointB.Apindiodeexhibitsaverysmallresistancewhenarelativelysmalldirectcurrentflowsthroughit.Itappearstobeasmallcapacitorwhennocurrentflowsthroughit.Whenthepindiode#1isturnedon,itconnectsthepoweramplifier’soutputtothecoil.Thequarterwavelengthcoaxiallineappearstobeahighimpedanceatitsendnearthecoilduringthetransmitpulsebecauseitisterminatedbyashortcircuitcreatedbypindiode#2.Thepindiode#2hasalowresistancebecauseitisturnedonbythesamecurrentthatpassesthroughpindiode#1.Itpreventsalargevoltagefrombeingappliedtothepreamplifierduringthetransmitpulse.Duringthereceivemode,bothpindiodesappeartobehighimpedances.Thetransmitpoweramplifierisdisconnectedfromthecoilandthesmallsignalfromthecoilcanreachthepreampunimpeded
ReceiveCoilPerformance
Thereceivecoilprovidestheinterfacebetweenpatientandcomputerinthescanner.Inperformingthistask,thereceivecoildeterminestheintrinsicqualityofthedatathatisusedtoformtheimage.Thereceivecoilpicksupthesignalgeneratedbytheprecessingnucleiandthenoisethatmustaccompanythesignal.Therefore,theprimarygoalofthecoildesigneristomaximizethesignal-to-noiseratio(SNR)oftheresultingimage.Ourtreatmentwillcoverthetwofactors,signalandnoise,separately.Wewillconsideronlysurfacecoilsasopposedtothevolumecoilsconsideredinthepreviouschapters.Thetermsurfacecoiloriginallyreferredtoasinglecoilloopthatwasplacedontheoutersurfaceofthesampletoobtainasignalfromalocal,superficialregion.Morerecently,arraysofsurfacecoilelementsareusedtoimagelargesuperficialregionsorthewholevolumeofthesample.
CoilSensitivity
Wewillbeginbyconsideringthesignalsensitivityofasinglesurfacecoilelement.Thereciprocitytheoremstatesthatthecoilpickupsupthesignalfromaregionlocatedatthepositionrproportionaltothex-ycomponentofthefieldB1xy(r)thatwouldhavebeenproducedbyaunitcurrentinthecoil.Hence,ourdiscussionofcoilsensitivityfocusesoncomputingtheB1xy(r)createdbythecoileventhroughasareceive-onlycoil,wewillnotuseittogenerateaB1field.Inprinciple,onecangetaprettygoodestimateofB1xy(r)byusingBiot-Savant’slaw.Thiswillrequireanumericallycalculationonacomputer.Instead,wewillconsidersomeverysimplecoilgeometriestodemonstratetheirrelevantfeaturesofB1xy(r).Wewillassumethatthesamplevolumeconsistsofthesemi-infinitespacehavingpositivex-values.Ourcoilelementswillbeplacedonthex=0plane.Inotherwords,wewouldobservetheperformanceofoursurfacecoilbyplacingitonalargeflatwaterfilledphantom.
CoilsMadefromLongWires
Westartbyconsideringaverysimple,butimpractical,coilgeometry,namelyasinglelongwirelocatedonthez-axiswithcurrentinthepositivez-direction:
Fig.5.2
Thefieldatrhasastrengthinverselyproportionaltorandisdirectedtangentialtothecirclewithradiusr.Currentsdirectedinthez-directionproducefieldsonlyinthex-ydirection.ThiscurrentdistributionishighlyefficientforMRIbecausethereisnowastedfielddirectedalongthez-direction.Wedefinethecoil’sfield-of-view(FOV)asthatregionwherethesignalisgreaterthanacertaincutoffvalueequivalenttofieldstrengthB1xy(r)greaterthanBc.Forthecaseofthelongwire,wewillconsiderthatithasanadequatesignalsensitivityintheregionfallingwithinthecircleofradiusr1.Therefore,wewouldsaythatthiscoil’sFOVis2r1wideandr1deep.
Sinceallrealcoilsmusthaveareturnpathfortheircurrenttoformaclosedloop,weconsidertwolongwiresrunninginthez-direction.Onewirewithapositivecurrentislocatedaty=aandtheotheronewithanegativecurrentislocatedaty=-a.
Fig.5.3
TheB1xy(r)fieldisthevectorsumofthetwoindividualfields.Intheregionbetweenthewires,thefieldsaddconstructively.Forlocationsonthex=0planeoutsideofthecoil,thefieldsadddestructively.Forpositionsalongthex-axis,thefieldstrengthdecreasesmorerapidlythanthe1/rdependenceoftheindividualwires.Theredlinesinthefigureindicatecontoursofconstantfieldstrength.Thenumericalestimateofthecoil’sFOVwillbeleftasanexerciseforthereader.Butqualitatively,onecanestimatethatthelateralFOVissignificantlywiderthanthewidthofthecoild.
Nowconsiderasinglelongwirerunningalongthey-axis.Inthiscase,thefieldgeneratedhascomponentsdirectedinthex-and/orz-directions.
Fig.5.4
Again,thefieldstrengthdecreasesas1/r.However,theusefulfieldcomponentforpickinguptheMRIsignalonlyoccursaboveandbelowthewire.Onthex-axis,thefieldhasonlyaz-componentandsothesignalsensitivityiszero.Theredlinesrepresentthecontoursofconstantsignalsensitivity.
Finally,weconsidertwowiresorientedinthey-direction.
Fig.5.5
Thefieldsaddconstructivelyintheregionbetweenthewires.Theregionswherethereisonlyaz-componentarenowdisplacedawayfromcenterline.Ifaimagewereacquiredinthey=0planewiththisconfiguration,itwouldlooksomethinglikethefigurebelow:
Fig.5.6
ThetwodarkbandsofpoorsignalstrengthlimittheusefulFOVinthez-directiontobeonlythecoilheightd.Theredlinedelineatestheregionofhighsignal.
Oneothercurrentdistributionthatissometimesusedcanbemodeledwiththreelongwireswithcurrentinthez-directionandlocatedaty=d,y=0,andy=-d.Thecenterwirehasoneunitofcurrentinthepositivedirectionandthetwootherwireshaveonehalfunitofcurrentinthenegativedirection.Thefielddistributionis
Fig.5.7
Thenotablefeatureofthiscurrentdistributionisthatthefieldatlocationsalongthex-axisisdirectedinthey-direction.Thatis,inthecentralregionofthiscoil,thefieldisparalleltothesurfaceofthephantom.ThisisincontrastwiththecoilinFig.5.2,wherethefieldisprimarilyperpendiculartothesurfaceofthephantom.InourdiscussionofthereciprocitytheoreminChapter2,Eqn10indicatedthatthephaseofasignalinducedinacoilisdeterminedbythedirectionofitsB1field.Therefore,thesignalspickedupbycoilsinFigures5.6and5.2willhaveaphasedifferenceof900.Likewise,ifthetwocoilswereplacedonthephantomtogether,theycouldbedrivenasaquadraturetransmitcoiltoproduceacircularlypolarizedB1fieldintheircentralregion.
Practicalcoilsmustbemadeinfinitesizesandformclosedloops.Thetracearoundagivencoilmustincludeportionsthatareparalleltothez-axis,perpendiculartothez-axis,orsomecombinationofbothorientations.Thepurposeofdiscussingthesimplerexamplesgivenabovewastoemphasisthatdifferentpartsofthecoilmakedifferentcontributionstoitssignalsensitivity.Forexample,acircularcoilwithdiameterdandplacedonthesurfaceofaphantom(orpatient)willhaveanellipticalshapedFOV.
Fig.5.8
TheFOVwou
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