MRI System Block Diagram

1
MRI System Block Diagram
X amp
Y amp
Z amp
spectrometer
r.f.coil
gradient coil
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Principle of Gradient Coil
?Bz
?Bz
?x
?z
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Common NMR Active Nuclei
Isotope Spin age ?
I abundance MHz/T 1H 1/2 99.985 42.575 2H
1 0.015 6.53 13C 1/2 1.108 10.71 14N
1 99.63 3.078 15N 1/2 0.37 4.32 17O
5/2 0.037 5.77 19F 1/2 100 40.08 23Na
3/2 100 11.27 31P 1/2 100 17.25
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Alignment of Spins in a Magnetic Field
M
M0
B0 field
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Energy in a Magnetic Field(Zeeman Splitting,
Spin ½)
E1/2 ???B0/2
E-1/2 ??B0/2
mI ½
mI ?½
P1/2 0. 5000049
P-1/2 0.4999951
1.5T, T310K, P(E)?exp(?E/kT)
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Larmor Frequency
mI ?½
mI ½
E1/2 ???B0/2
E-1/2 ??B0/2
Allowed transitions ?E ??B0
??0
?0 ?B0
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Quantum Mechanical Description(Spin ½ Case)
mI ?½
I½, 2I1 Zeeman splittings
mI ½
??gt a?½??½gt a½?½gt
Mz lt??Iz??gt ? a½?2 ?? a?½?2
Mxy lt??Ix iIy??gt
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Coupling with a B1 Field
A
B1
time
Birdcage coil
B0
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Spin Excitation
M
M
M
rotating frame
laboratory frame
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Free Induction Decay
FT
M
time
frequency
FT
time
frequency
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Free Induction Decay
M
90?
small positive shim mis-set
M
90?
medium positive shim mis-set
M
90?
large positive shim mis-set
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Free Induction Decay
M
90?
small negative shim mis-set
M
90?
medium negative shim mis-set
M
90?
large negative shim mis-set
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Product Operators
r.f.
?x
?y
Mx ? Mx
Mx ? Mycos? ? Mzsin?
?x
?y
My ? Mycos? Mzsin?
My ? My
?x
?y
Mz ? Mzcos? ? Mysin?
Mz ? Mzcos? Mxsin?
? t
Mx ? Mxcos?t Mysin ?t
z
y
? t
free precession
My ? Mycos?t ? Mxsin ?t
x
? t
Mz ? Mz
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Bloch Equations
Mz
Mz
Mz
Mxy
Mxy
Mxy
dMxy(t) ? Mxy(t)
dt
T2
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T1 Relaxation
Mz(t) M0 Mz(0) ? M0exp(-t/T1)
saturationrecovery
inversionrecovery
M0
M0
Mz
Mz
t
t
Mz(0) ?M0
Mz(0) 0
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Spin Echo
M
90?
180?
small positive shim mis-set
90?
180?
medium positive shim mis-set
M
90?
180?
large positive shim mis-set
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Spin Echo
M
90?
180?
small negative shim mis-set
M
90?
180?
medium negative shim mis-set
M
90?
180?
large negative shim mis-set
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T2 Relaxation
dMxy(t) ? Mxy(t)
dt
T2
Mxy(t) Mxy(0) exp(?t/T2)
Mxy
t
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Slice Selection
FT
time
frequency
FT
time
frequency
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Slice Selection
time
frequency
G
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