mri system block diagram
TRANSCRIPT
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MRI System Block Diagram
RFamp
spectrometer
r.f.coil gradient coil
Xamp
Yamp
Zamp
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Principle of Gradient Coil
Bz
xBz
z
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Isotope Spin %age I abundance MHz/T
1H 1/2 99.985 42.5752H 1 0.015 6.5313C 1/2 1.108 10.7114N 1 99.63 3.07815N 1/2 0.37 4.3217O 5/2 0.037 5.7719F 1/2 100 40.0823Na 3/2 100 11.2731P 1/2 100 17.25
Common NMR Active Nuclei
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Alignment of Spins in a Magnetic Field
spin
magnetic moment
B0 field
M
M=0
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Energy in a Magnetic Field(Zeeman Splitting, Spin ½)
E+1/2= B0/2 E-1/2= +B0/2P+1/2= 0. 5000049 P-1/2= 0.4999951
1.5T, T=310K, P(E)exp(E/kT)
mI = +½ mI = ½
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Larmor Frequency
E+1/2= B0/2 E-1/2= +B0/2
Allowed transitions E = B0
= 0
mI = ½
mI = +½
0 = B0
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Quantum Mechanical Description(Spin ½ Case)
> = a½½> + a+½+½>
I=½, 2I+1 Zeeman splittingsmI = ½
mI = +½
Mz = <Iz> = a+½2 a½2
Mxy = <Ix+ iIy>
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Coupling with a B1 Field
B0
B1
Birdcage coil
A
time
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Spin ExcitationM M
M
rotating frame
laboratory frame
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Free Induction Decay
FT
FT
frequency
frequency
time
time
M
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Free Induction DecayM
M
M
90
90
90
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set
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Free Induction DecayM
M
M
90
90
90
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set
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Product Operators
Mx Mx
My Mycos + Mzsin
Mz Mzcos Mysin
x
x
x
Mx Mycos Mzsin
My My
Mz Mzcos + Mxsin
y
y
y
Mx Mxcost + Mysin t t
My Mycost Mxsin t t
Mz Mz
t
r.f.
freeprecession x
yz
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Bloch Equations
dMz(t) = [Mz(t) M0]dt T1
dMxy(t) = Mxy(t)dt T2
Mz
Mxy
Mz Mz
Mxy Mxy
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T1 Relaxation
Mz(t) = M0 + {Mz(0) M0}exp(-t/T1)
Mz Mz
t t
saturation–recovery
inversion–recovery
dMz(t) = [Mz(t) M0]dt T1
M0 M0
Mz(0) = 0 Mz(0) = M0
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Spin EchoM
M
M180
180
18090
90
90
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set
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Spin EchoM
M
M180
180
18090
90
90
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set
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T2 Relaxation
Mxy(t) = Mxy(0) exp(t/T2)
Mxy
t
dMxy(t) = Mxy(t)dt T2
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Slice Selection
0
0time
time
frequency
frequency
FT
FT
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Slice Selection
0time frequency
G
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