magnetic resonance imaging - wisewire...magnetic resonance imaging equations and relations: energy...

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.

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

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.

b)Usingtheequationsfromthefrontpage,createasingleequationthatrelatestheenergydifferenceandtheassociatedfrequency.

c)CalculatethetheoreticalLarmorfrequencyforamagneticfieldof1T.Howclosewasyourvaluetothepredictedvalueabovefromtheapplet?

5)CalculatetheLarmorfrequencyfor2T.Checkyouranswersusingthejavaprogram.Thistime,setthepowerto100%andchangeyourfrequencytotheresultyoucalculatedanddragyourmagneticfieldaccordinglyuntilyoureachthemaxoutput.Werethevaluesclose?

Dealinginsingleplanes:Aswithseveralotherdiagnosticimagingdevices,mostofMRIimagesaretakeninasingleplane.Infact,CTscansrequirehundredsofindividualslicestocomprisetheirthree-dimensionalimages.Asaresult,itisimportantforphysicianstobecomecomfortabledealingwithviewingimagesfromdifferentorientationsthroughoutthebody.6)OntheMRIimagesbelow,givethenameofthespecificplanethateachimagewastakenfromandsuggestwhichregionofthebodyisshown.

a) b)c)

InordertogenerateaslicetheMRIneedstoexcitehydrogennucleiinoneplane.Thisisdonebyaddingagradientmagneticfield.

7)Adjusttheslideroftheverticalfieldfirstto0.04Tandthento0.08T.Whatdoyouobserve?

8)PressAddtumorandtrytoselectivelytargetthehydrogennucleiatthelocationofthetumor.Youcanachievethisbychangingthefrequencyoftheradiowaveorbychangingthestrengthofthemainmagneticfield.Note:inanactualMRIneitherisdoneandthegradientmagneticfieldischanged.Explainwhychangingthestrengthofthegradientfieldallowstheselectivestimulationofthehydrogennucleiinoneslice.