magnetic resonance imaging - wisewire · 2018. 1. 13. · magnetic resonance imaging equations and...
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MagneticResonanceImaging
EquationsandRelations:
Energybetweenspinstates: Electromagneticradiationequation:
Characteristichydrogenfactor,Hγ:2.79 Speedoflight:c=3.0x10⁸m/sNuclearmagneton: =5.05x10⁻²⁷J/T Energyofaphoton:
Planck’sconstant:h =6.626x10⁻³⁴J*S
Magneticresonanceimaging,MRI,hasbecomeanessentialdiagnostictoolworldwideduetoitsabilitytonon-invasivelydepictanddistinguishsofttissueswithinthebody.Atthemostbasiclevel,itutilizesaninducedmagneticfieldandapulsedradiofrequencywavetocreatedetailedimagesofapatient.Severalkeydiscoveriespavedthewayforitscreationincludingthetheoriesofelectromagnetism,nuclearphysics,andquantummechanics,whichledtothediscoveryofcharacteristicparticlespin.
History:Overthecourseofthe19thcenturyMichaelFaraday,JamesClerkMaxwell,andotherslaidthefoundationaltheoriesofelectromagnetism.Therewasfoundtobeaninherentdualityinnaturebetweenmagneticandelectricenergyfields,whichcouldbemanipulatedandquantifiedinconcertwithoneanother.
AclassicalMRIdevicecontainsasolenoidthatcarrieshighcurrentstogenerateamagneticfieldofafewTesla.Thefigureaboveshowsacrosssectionofsolenoidwherethecrossesrepresentacurrentintothepaperandthedotsacurrentoutofthepaper.Fromtherighthandruleyoucanfindthedirectionoftheresultingmagneticfielddepictedinthefigure.
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1)Ontheimageofthescanner,predictanddrawthedirectionofpropagationoftheinducedmagneticfield.Thearrowsdenotethedirectionofcurrentthroughthesolenoid
Thediscoveryofnuclearspinstateshashadagreatimpactonhowweunderstandthequantumnatureofparticles.Imagingtechnologiessuchasnuclearmagneticresonance(NMR)spectroscopyandMRIaretheresultofourgrowingknowledgeinthisfield.Ithasbeenshownthatanucleuswilloccupyeitheroneoftwoorientations.ThisintrinsicphysicalpropertyiswhatismanipulatedbyanMRImachine.
AspectsofMagneticResonanceImaging:Thehumanbodyiscomposedprimarilyofhydrogenatoms(63%)andmostofourtissuescontainroughly75%water.MRImachinesthatarecurrentlyusedforclinicaldiagnosticpurposesmakeuseofthisfactthroughwhatisknownasthechemicalshift.Thechemicalshiftisdefinedasthedifferenceinresonantfrequencybetweenisolatedhydrogenanditsvaluewhenboundtoaspecificsitewithinamolecule.Differenttissueswillcontaindiversechemicalcompositions/environments,andthereforedifferentchemicalshifts,allowingfordiscernablecontrastbetweenthem.
2)Bothprotonsandneutronshaveamagneticmoment.Unlessthenucleuscontainsanevennumberofprotonsandanevennumberofneutrons,theatomicnucleushasanetmagneticmoment.Anucleusmusthaveanetmagnetizationforittobediscernableusingmagneticresonancespectroscopy.Fromthelistbelowcirclepossiblecandidatesformagneticresonancespectroscopy(youmayneedtolookataperiodictable,unlessspecifiedotherwisechoosethemostabundantisotopforeachelement):Carbon¹³ Helium Carbon¹² Calcium
Oxygen Hydrogen Phosphorous Sulfur
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AnMRIscanneriscomprisedofseveralcomponents.Averylargesolenoid,whichcreatesthemagneticfield(Bfield)withinthecentralcanalwherethepatientlays.Thatmagneticfieldalignsthenucleiofthepatient’sbodyparalleltoitsBfield.Aradiopulseexcitesthenucleiofthebodytissuestotransientlyflipspinstates.Asthenucleiflipandrealign,theyproducedetectableamountsofphotons.Thesegradientcoilscaneitherbebuiltintothelargeheadunitorcustomizedforindividualbodyparts.Duringtheimaging,thecurrentfromthesecoilsareturnedonandoffinintervalsandareusedtopreciselyshapetheimagethatiscollected.Itistheforcesgeneratedonthesegradientcoilsbythemainstaticmagneticfieldthatgeneratestheloud“knocking”noisesthatareassociatedwiththescan.Thevideolinkbelowprovidesagooddemonstrationoftheoverallcomponentsofascannerandthegeneralprocessthattakesplacewhenusingone.http://www.analogic.com/collateral/documents/english-us/mr-qt.htmlCalculatingtheLarmorFrequencyandusingaMRIcomputersimulation:First,opentheMRIjavasimulation(foundat:http://phet.colorado.edu/en/simulation/mri)andclickonthesimplifiedMRItab.
Trybothwaveandphotonviewandchoosetheoneyouprefer
MakesurethattheHead,atomicnucleiandthemagneticfieldboxesareselected.
Beginwiththemainmagneticfieldat1.00Teslaandturnthepowerupto100%
3)Nowadjustthefrequencybartodifferentlevelsanddescribewhatyounotice.Findthefrequenciesthatstimulatethenuclei.Arethereawiderangeoffrequenciesthatpromotearesultantphoton?Whathappensaswedecreasethepower?
ThevaluethatyoujustrecordedforyourresonancefrequencyisknownastheLarmorfrequency.ThisisthefrequencyatwhichtheHydrogenatomswillflipbetweenspinstatesandemitresultantphotons.InordertocalculatetheLarmorfrequencywemustfirstfindthedifferenceinenergystatesforthehydrogennucleus.
4)a)CalculatetheΔEvalueforhydrogenat1Tesla.
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b)Usingtheequationsfromthefrontpage,createasingleequationthatrelatestheenergydifferenceandtheassociatedfrequency.
c)CalculatethetheoreticalLarmorfrequencyforamagneticfieldof1T.Howclosewasyourvaluetothepredictedvalueabovefromtheapplet?
5)CalculatetheLarmorfrequencyfor2T.Checkyouranswersusingthejavaprogram.Thistime,setthepowerto100%andchangeyourfrequencytotheresultyoucalculatedanddragyourmagneticfieldaccordinglyuntilyoureachthemaxoutput.Werethevaluesclose?
Dealinginsingleplanes:Aswithseveralotherdiagnosticimagingdevices,mostofMRIimagesaretakeninasingleplane.Infact,CTscansrequirehundredsofindividualslicestocomprisetheirthree-dimensionalimages.Asaresult,itisimportantforphysicianstobecomecomfortabledealingwithviewingimagesfromdifferentorientationsthroughoutthebody.6)OntheMRIimagesbelow,givethenameofthespecificplanethateachimagewastakenfromandsuggestwhichregionofthebodyisshown.
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a) b)c)
InordertogenerateaslicetheMRIneedstoexcitehydrogennucleiinoneplane.Thisisdonebyaddingagradientmagneticfield.
7)Adjusttheslideroftheverticalfieldfirstto0.04Tandthento0.08T.Whatdoyouobserve?
8)PressAddtumorandtrytoselectivelytargetthehydrogennucleiatthelocationofthetumor.Youcanachievethisbychangingthefrequencyoftheradiowaveorbychangingthestrengthofthemainmagneticfield.Note:inanactualMRIneitherisdoneandthegradientmagneticfieldischanged.Explainwhychangingthestrengthofthegradientfieldallowstheselectivestimulationofthehydrogennucleiinoneslice.