Nuclear Magnetic Resonance (NMR) Magnetic Resonance Imaging (MRI)
Magnetic Resonance Imaging - Wisewire · 2018. 1. 13. · Magnetic Resonance Imaging Equations and...
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Magnetic Resonance Imaging Equations and Relations: Energy between spin states: Electromagnetic radiation equation: Characteristic hydrogen factor, Hγ: 2.79 Speed of light: c = 3.0 x 10⁸ m/s Nuclear magneton: = 5.05 x 10⁻²⁷ J/T Energy of a photon: Planck’s constant: h = 6.626 x 10⁻³⁴ J*S Magnetic resonance imaging, MRI, has become an essential diagnostic tool worldwide due to its ability to non-invasively depict and distinguish soft tissues within the body. At the most basic level, it utilizes an induced magnetic field and a pulsed radio frequency wave to create detailed images of a patient. Several key discoveries paved the way for its creation including the theories of electromagnetism, nuclear physics, and quantum mechanics, which led to the discovery of characteristic particle spin. History: Over the course of the 19 th century Michael Faraday, James Clerk Maxwell, and others laid the foundational theories of electromagnetism. There was found to be an inherent duality in nature between magnetic and electric energy fields, which could be manipulated and quantified in concert with one another. A classical MRI device contains a solenoid that carries high currents to generate a magnetic field of a few Tesla. The figure above shows a cross section of solenoid where the crosses represent a current into the paper and the dots a current out of the paper. From the right hand rule you can find the direction of the resulting magnetic field depicted in the figure.
Transcript of Magnetic Resonance Imaging - Wisewire · 2018. 1. 13. · Magnetic Resonance Imaging Equations and...
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.
