Chapter 5v5.docx

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