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Charged particle. Moving charge = current. Associated magnetic field - B. Macroscopic picture (typical dimensions (1mm) 3 ). Consider nucleus of hydrogen in H 2 O molecules: proton magnetization randomly aligned. Macroscopic picture (typical dimensions (1mm) 3 ). - PowerPoint PPT Presentation
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Charged particle
Moving charge = current
Associated magnetic field - B
Macroscopic picture (typical dimensions (1mm)3 )
Consider nucleus of hydrogen in H2O molecules:proton magnetization randomly aligned
Macroscopic picture (typical dimensions (1mm)3 )
Bo
M
Apply static magnetic field:proton magnetization either aligns with or against magnetic field
Macroscopic picture (typical dimensions (1mm)3 )
Can perturb equilibrium by exciting at Larmor frequency
= ( /2 ) Bo
Bo
Mxy
Can perturb equilibrium by exciting at Larmor frequency
= ( /2 ) Bo
With correct strength and duration rf excitation can flip magnetization
e.g. into the transverse plane
Spatial localization - reduce 3D to 2D
BoB
z
y
x
z
Spatial localization - reduce 3D to 2D
z
BoB
rf
Spatial localization - reduce 3D to 2D
B
z
y
x
z
Spatial localization - reduce 3D to 2D
z
BoB
Spatial localization - reduce 3D to 2D
B
z
y
x
z
Spatial localization - reduce 3D to 2D
z
Bo+
Gz.zB
Spatial localization - reduce 3D to 2D
B
z
y
x
z
Spatial localization - reduce 3D to 2D
z
Bo+
Gz.zB
Spatial localization - reduce 3D to 2D
B
z
rf
resonance condition
y
x
z
Spatial localization - reduce 3D to 2D
z
Bo+
Gz.zB
Spatial localization - reduce 3D to 2D
B
zy
x
y
x
z
MR pulse sequence
Bo+
Gz.zB
z
Gz
Gx
Gy
rf
time
Spatial localization - e.g., in 1d what is (x) ?
Once magnetization is in the transverse planeit precesses at the Larmor frequency = 2 B(x)
M(x,t) = Mo (x) exp(-i.. (x,t))
If we apply a linear gradient, Gx ,of magnetic field along x the accumulated phase at x after time t will be:
(x,t) = ∫o
t x Gx(t') dt'
(ignoring carrier term)
Spatial localization - What is (x) ?
x
Bo
B
no spatial information
object
x
S(t)
Spatial localization - What is (x) ?
x
Bo+Gxx
B
x
object
Spatial localization - What is (x) ?
x
Bo+Gxx
B
x
objectS(t)
Spatial localization - What is (x) ?
x
Bo+Gxx
B
x Fouriertransform
object
image
x
(x)
S(t)
For an antenna sensitive to all the precessing magnetization, the measured signal is:
S(t) = ∫ M(x,t) dx
= Mo ∫ (x) exp (-i.(. Gx) x.t) dx
therefore:
(x) = ∫ M(x,t) dx
= Mo ∫ S(t) exp (i. c. x.t) dt
MR pulse sequence
Gz
Gx
Gy
rf
time
For NMR in a magnet with imperfect homogeneity, spin coherence is lost because of spatially varying precession
Hahn (UC Berkeley)showed that this could be reversed by flipping the spins through 180° - the spin echo
In MRI, spatially varying fields are appliedto provide spatial localization - these spatially varying magnetic fields must also becompensated - the gradient echo
MR pulse sequence(centered echo)
Gz
Gx
Gy
rf
time
ADC
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
Gx
spins alignedfollowing excitation
Gx
dephasing
Gx
dephasing
ADC
Gx
rephasing
ADC
Gx
rephased
echoADC
GxADC
GxADC
ADC
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++
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ADC
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ADC
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ADC
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ADC
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ADC
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ADC
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ADC
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ADC
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FOV
ADC
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FOVN
= resolution
FOV
FOV smaller than object
FOV
FOV
FOV smaller than object:- wrap-around artifact
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
phase encoding 128
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
phase encoding 64
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
phase encoding 0
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
phase encoding -64
MR pulse sequence for 2D
Gz
Gx
Gy
rf
time
ADC
phase encoding -127
k-space
Fourier
Fourier Fourier transform(ed)
inner k-space Fourier transform
overall contrast information
outer k-space Fourier transform
edge information
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