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MRI System Block Diagram
RF
amp
spectrometer
r.f.coil
gradient coil
X
amp
Y
amp
Z
amp
Principle of Gradient Coil
โˆ‚Bz
โˆ‚x
โˆ‚Bz
โˆ‚z
Isotope Spin %age ฮณ
I abundance MHz/T
1
H 1/2 99.985 42.575
2
H 1 0.015 6.53
13
C 1/2 1.108 10.71
14
N 1 99.63 3.078
15
N 1/2 0.37 4.32
17
O 5/2 0.037 5.77
19
F 1/2 100 40.08
23
Na 3/2 100 11.27
31
P 1/2 100 17.25
Common NMR Active Nuclei
Alignment of Spins in a
Magnetic Field
spin
magnetic moment
B0 field
M
M=0
Energy in a Magnetic Field
(Zeeman Splitting, Spin ยฝ)
E+1/2= โˆ’ฮณ๏จB0/2 E-1/2= +ฮณ๏จB0/2
P+1/2= 0. 5000049 P-1/2= 0.4999951
1.5T, T=310K, P(E)โˆexp(โˆ’E/kT)
mI = +ยฝ mI = โˆ’ยฝ
Larmor Frequency
E+1/2= โˆ’ฮณ๏จB0/2 E-1/2= +ฮณ๏จB0/2
Allowed transitions โˆ†E = ฮณ๏จB0
= ๏จฯ‰0
mI = โˆ’ยฝ
mI = +ยฝ
ฯ‰0 = ฮณB0
Quantum Mechanical Description
(Spin ยฝ Case)
๏ฃฆฯˆ> = aโˆ’ยฝ๏ฃฆโˆ’ยฝ> + a+ยฝ๏ฃฆ+ยฝ>
I=ยฝ, 2I+1 Zeeman splittings
mI = โˆ’ยฝ
mI = +ยฝ
Mz = <ฯˆ๏ฃฆIz๏ฃฆฯˆ> =๏ฃฆ a+ยฝ๏ฃฆ2
โˆ’๏ฃฆ aโˆ’ยฝ๏ฃฆ2
Mxy = <ฯˆ๏ฃฆIx+ iIy๏ฃฆฯˆ>
Coupling with a B1 Field
B0
B1
Birdcage coil
A
time
Spin Excitation
M M
M
rotating frame
laboratory frame
Free Induction Decay
FT
FT
frequency
frequency
time
time
M
Free Induction Decay
M
M
M
90ยฐ
90ยฐ
90ยฐ
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set
Free Induction Decay
M
M
M
90ยฐ
90ยฐ
90ยฐ
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set
Product Operators
Mx โ†’ Mx
My โ†’ Mycosฮธ + Mzsinฮธ
Mz โ†’ Mzcosฮธ โˆ’ Mysinฮธ
ฮธx
ฮธx
ฮธx
Mx โ†’ Mycosฮธ โˆ’ Mzsinฮธ
My โ†’ My
Mz โ†’ Mzcosฮธ + Mxsinฮธ
ฮธy
ฮธy
ฮธy
Mx โ†’ Mxcosฯ‰t + Mysin ฯ‰t
ฯ‰ t
My โ†’ Mycosฯ‰t โˆ’ Mxsin ฯ‰t
ฯ‰ t
Mz โ†’ Mz
ฯ‰ t
r.f.
free
precession x
y
z
Bloch Equations
dMz(t) = โˆ’ [Mz(t) โˆ’ M0]
dt T1
dMxy(t) = โˆ’ Mxy(t)
dt T2
Mz
Mxy
Mz Mz
Mxy
Mxy
T1 Relaxation
Mz(t) = M0 + {Mz(0) โˆ’ M0}exp(-t/T1)
Mz Mz
t t
saturationโ€“
recovery
inversionโ€“recovery
dMz(t) = โˆ’ [Mz(t) โˆ’ M0]
dt T1
M0 M0
Mz(0) = 0 Mz(0) = โˆ’M0
Spin Echo
M
M
M
180ยฐ
180ยฐ
180ยฐ90ยฐ
90ยฐ
90ยฐ
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set
Spin Echo
M
M
M
180ยฐ
180ยฐ
180ยฐ90ยฐ
90ยฐ
90ยฐ
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set
T2 Relaxation
Mxy(t) = Mxy(0) exp(โˆ’t/T2)
Mxy
t
dMxy(t) = โˆ’ Mxy(t)
dt T2
Slice Selection
ฯ‰0
ฯ‰0
time
time
frequency
frequency
FT
FT
Slice Selection
ฯ‰0
time frequency
G
260 mri system block diagram

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