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IntroductionIntroductiontoto
Magnetic Resonance ImagingMagnetic Resonance Imaging
© 2002, J.P. Hornak
-- Spin Physics Spin Physics --
© 2002, J.P. Hornak
SpinSpinA fundamental property of nature like electrical charge or mass.A fundamental property of nature like electrical charge or mass.Comes in multiples of 1/2 and can be + or Comes in multiples of 1/2 and can be + or --. . Protons, electrons, and neutrons possess spin. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesIndividual unpaired electrons, protons, and neutrons each possesses a spin of 1/2.ses a spin of 1/2.
Deuterium Atom ( Deuterium Atom ( 22H )H )
ElectronElectronProtonProtonNeutronNeutron
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SpinSpinTwo or more particles with spins having opposite signs can pair Two or more particles with spins having opposite signs can pair up to eliminateup to eliminatethe observable manifestations of spin. the observable manifestations of spin.
Helium Atom ( Helium Atom ( 44He ) He ) -- No SpinNo Spin
ElectronElectronProtonProtonNeutronNeutron
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SpinSpin
When placed in a magnetic field, particles with a net spin absorWhen placed in a magnetic field, particles with a net spin absorb photons.b photons.
νννννννν = = γγγγγγγγ BBoo
BBoo = magnetic field strength= magnetic field strengthνννννννν = frequency of the absorbed photon= frequency of the absorbed photonγγγγγγγγ = = gyromagneticgyromagnetic ratio (for hydrogen, ratio (for hydrogen, γγγγγγγγ = 42.58 MHz/Tesla)= 42.58 MHz/Tesla)
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© 2002, J.P. Hornak
Nuclei with SpinNuclei with Spin
Many elements have an isotope with a non zero nuclear spin. Many elements have an isotope with a non zero nuclear spin.
© 2002, J.P. Hornak
Nuclei with SpinNuclei with Spin
NMR can only be performed on isotopes whose natural abundance isNMR can only be performed on isotopes whose natural abundance is high high enough to be detected.enough to be detected.
NucleiNuclei UnpairedUnpaired Unpaired Unpaired Net Net γγγγγγγγ NaturalNatural BiologicalBiologicalProtonsProtons Neutrons Neutrons Spin Spin (MHz/T)(MHz/T) AbundanceAbundance AbundanceAbundance
of Isotopeof Isotope of all Atomsof all Atoms
11HH 11 00 1/21/2 42.5842.58 99.98599.985 0.630.633131PP 00 11 1/21/2 17.25 17.25 100100 0.00240.00242323NaNa 22 11 3/23/2 11.27 11.27 100100 0.000410.000411414NN 11 11 11 3.08 3.08 99.6399.63 0.0150.0151313CC 00 11 1/21/2 10.71 10.71 1.111.11 0.0940.094
Most clinical MRI is done with Most clinical MRI is done with 11HH..
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© 2002, J.P. Hornak
Energy LevelsEnergy Levels
Low EnergyLow Energy High EnergyHigh Energy
Configurations for Spins in a Magnetic Field.Configurations for Spins in a Magnetic Field.
© 2002, J.P. Hornak
Transitions Between Energy Levels Transitions Between Energy Levels
h = Planck’s Constant (6.626x10h = Planck’s Constant (6.626x10--3434 J s).J s).
ENER
GY
ENER
GY
MAGNETIC FIELD, BMAGNETIC FIELD, Boo
N
S
∆∆∆∆∆∆∆∆ E = hE = hν = ν = ν = ν = ν = ν = ν = ν = hhγ γ γ γ γ γ γ γ BBoo
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© 2002, J.P. Hornak
CW NMR CW NMR
© 2002, J.P. Hornak
BoltzmannBoltzmann StatisticsStatistics
How many spins areHow many spins arealigned with the field and aligned with the field and how many are opposed?how many are opposed?
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© 2002, J.P. Hornak
BoltzmannBoltzmann StatisticsStatistics
How many spins areHow many spins arealigned with the field and aligned with the field and how many are opposed?how many are opposed?
(((( ))))KTE
o
j eNN ∆∆∆∆−−−−
∝∝∝∝
NNjj = Spins in high energy configuration= Spins in high energy configurationNNoo = Spins in low energy configuration= Spins in low energy configuration∆∆∆∆∆∆∆∆E = Energy difference between E = Energy difference between
configurationsconfigurationsK = K = BoltzmannBoltzmann Constant Constant
(1.3805x10(1.3805x10--23 J/Kelvin)23 J/Kelvin)T = Temperature (T = Temperature (KelvenKelven))
© 2002, J.P. Hornak
Spin PacketsSpin Packets
Groups of spins experiencing exactly the sameGroups of spins experiencing exactly the sameBBoo magnetic field.magnetic field.
It is convenient to talk of the It is convenient to talk of the magnetization in a spin packet magnetization in a spin packet and represent it as a vector. and represent it as a vector.
At equilibrium, this vector is At equilibrium, this vector is pointing in the direction of Bpointing in the direction of Boo..
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© 2002, J.P. Hornak
Net MagnetizationNet Magnetization
The sum of all the spin magnetization vectors from allThe sum of all the spin magnetization vectors from allthe spin packets in a sample region.the spin packets in a sample region.
At equilibrium, this vector is At equilibrium, this vector is pointing in the direction of Bpointing in the direction of Boo..
© 2002, J.P. Hornak
MR Coordinate SystemMR Coordinate System
BBoo Net MagnetizationNet Magnetization
At equilibrium:At equilibrium: Longitudinal Magnetization (Longitudinal Magnetization (MMzz) = net magnetization ) = net magnetization Transverse Magnetization (Transverse Magnetization (MMxx , M, Myy) = 0) = 0
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XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Lattice RelaxationLattice Relaxation
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
BBoo
NetNet MagnetizationMagnetization
XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Lattice RelaxationLattice Relaxation
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
BBoo
NetNet MagnetizationMagnetization
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XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Lattice RelaxationLattice Relaxation
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
BBoo
NetNet MagnetizationMagnetization
XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Lattice RelaxationLattice Relaxation
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
BBoo
NetNet MagnetizationMagnetization
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XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Lattice RelaxationLattice Relaxation
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
BBoo
NetNet MagnetizationMagnetization
© 2002, J.P. Hornak
SpinSpin--Lattice Relaxation Time (TLattice Relaxation Time (T11))
The time constant that describes how MThe time constant that describes how MZZ returns to returns to its equilibrium value Mits equilibrium value Moo..
The time (t) required to change the Z component ofThe time (t) required to change the Z component ofmagnetization by a factor of e.magnetization by a factor of e.
−−−−====
−−−−11 T
t
oZ eMMMMZZ
tt
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© 2002, J.P. Hornak
PrecessionPrecession
Net magnetization placed in the XY plane will rotate about the Net magnetization placed in the XY plane will rotate about the Z axis at the frequency of the photon that causes a transition Z axis at the frequency of the photon that causes a transition between the two energy levels of the spin. between the two energy levels of the spin.
This frequency is called the This frequency is called the LarmorLarmor frequency.frequency.
© 2002, J.P. Hornak
SpinSpin--Spin RelaxationSpin Relaxation
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
TransverseTransverseMagnetizationMagnetization
BBoo
XX
ZZ
YY
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© 2002, J.P. Hornak
SpinSpin--Spin RelaxationSpin Relaxation
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
BBoo
XX
ZZ
YY
© 2002, J.P. Hornak
SpinSpin--Spin RelaxationSpin Relaxation
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
SpinSpin--Spin RelaxationSpin Relaxation
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
XX
ZZ
YY
BBoo
© 2002, J.P. Hornak
SpinSpin--Spin RelaxationSpin Relaxation
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
MMXYXY=0=0XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
SpinSpin--Spin Relaxation Time (TSpin Relaxation Time (T22))
The time constant that describes how MThe time constant that describes how MXYXY returns to returns to its equilibrium value Mits equilibrium value MXYXY=0.=0.
The time (t) required to reduce the XY component ofThe time (t) required to reduce the XY component ofmagnetization by a factor of e.magnetization by a factor of e.
2)0()( Tt
XYXY etMtM−−−−
========MMXYXY
tt
© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
BBoo
XX
ZZ
YY
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© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
BBoo
XX
ZZ
YY
© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
XX
ZZ
YY
BBoo
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© 2002, J.P. Hornak
TT2 2 << TT11
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
BBoo
XX
ZZ
YY
© 2002, J.P. Hornak
Rotating Frame of ReferenceRotating Frame of Reference
It is convenient to define a rotating frame of reference It is convenient to define a rotating frame of reference that rotates about the Z axis at the that rotates about the Z axis at the LarmorLarmor frequency. frequency.
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© 2002, J.P. Hornak
Rotating Frame of ReferenceRotating Frame of Reference
Vector precession compared to the rotating frame.Vector precession compared to the rotating frame.faster than faster than equal toequal to slower thanslower than
X’ X’ X’Y’ Y’Y’
© 2002, J.P. Hornak
Rotating Frame of ReferenceRotating Frame of Reference
Longitudinal relaxation is looks the same in theLongitudinal relaxation is looks the same in therotating frame and laboratory frame of reference.rotating frame and laboratory frame of reference.
X’X’
ZZ
Y’Y’
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© 2002, J.P. Hornak
Rotating Frame of ReferenceRotating Frame of Reference
DephasingDephasing of a net magnetization vector.of a net magnetization vector.
X’X’
ZZ
Y’Y’
© 2002, J.P. Hornak
Pulsed Magnetic FieldsPulsed Magnetic Fields
Current:Current: DCDC ACAC ACACFrame:Frame: LabLab LabLab RotatingRotating
X’X’
ZZ
Y’Y’BB11XX
ZZ
YYBB11XX
ZZ
YYBB11
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© 2002, J.P. Hornak
Pulsed Magnetic FieldsPulsed Magnetic FieldsSpins react to BSpins react to B11 by rotating clockwise about Bby rotating clockwise about B11..
θθθθθθθθ = 2 = 2 π γπ γπ γπ γπ γπ γπ γπ γBB11 ττττττττwhere:where: θθθθθθθθ = rotation angle in radians= rotation angle in radians
γγγγγγγγ = = gyromagneticgyromagnetic ratioratioττττττττ = pulse length (time B= pulse length (time B11 is on)is on)
XX
ZZ
YYBB11X’X’
ZZ
Y’Y’BB11
Lab FrameLab Frame Rotating FrameRotating Frame
© 2002, J.P. Hornak
Spin RelaxationSpin RelaxationSpin relaxation is caused by time varying magnetic fields.Spin relaxation is caused by time varying magnetic fields.Source:Source: Translational motion of moleculesTranslational motion of molecules
Rotational motion of moleculesRotational motion of moleculesParamagnetic atoms or moleculesParamagnetic atoms or molecules
Paramagnetic atoms have unpaired electrons and hence a net Paramagnetic atoms have unpaired electrons and hence a net electron spin (magnetic field). Gadolinium is an example of a electron spin (magnetic field). Gadolinium is an example of a paramagnetic atom, and oxygen is an example of a paramagnetic paramagnetic atom, and oxygen is an example of a paramagnetic molecule.molecule.
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© 2002, J.P. Hornak
Spin RelaxationSpin Relaxation
SpinSpin--Lattice Relaxation {TLattice Relaxation {T11} requires time varying magnetic fields at } requires time varying magnetic fields at the the LarmorLarmor frequency.frequency.
SpinSpin--Spin Relaxation {TSpin Relaxation {T22} requires time varying magnetic fields with } requires time varying magnetic fields with frequencies frequencies << to the to the LarmorLarmor frequency.frequency.
Num
ber o
f Mot
ions
Num
ber o
f Mot
ions
Frequency (Frequency (νννννννν))
SolidSolid
Viscous LiquidViscous Liquid
LiquidLiquid