Nuclear Magnetic Resonance
1952
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1991
2003
?
Instrumental - principles
Prøveholder
Radiosender/
mottager
Datamaskin
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Magnet
Applications of MR
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Objective
To Derive and to Discuss the Bloch Equation
Free precession
Diffusion
Relaxation
gradient

 

  
M
u  v  M  M0 
2
 MxBeff  i 
j
k  D M   (r  g )k
t
T2
T2
T1


 
M  ui  vj  M z k



Beff  B1i  0 j  (  0 ) /   g 0 z k
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Characteristics of a nucleus
Magnetic dipole moment (m) and angular momentum (P)
µ
m = P
Exercise 1.1: Derive the above equation (qualitatively)
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Magnetic moment in a magnetic field
motional characteristics
dμ
 μ  B
dt
Exercise 1.2: Derive the above equation and discuss its solution
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Solution
Larmor Equation - the basic NMR equation
 = -B
m
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Conclusion
•THE LARMOR EQUATION ( = B) IS DERIVED FROM A CLASSICAL
MECHANICAL APPROACH
THE SPIN MOTION IS WITHIN THE MHz-RANGE (Radio-frequencies)
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SPIN QUANTUM NUMBER I FOR SOME NUCLEI
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MOTION OF m IN A ROTATING FRAME OF REFERENCE
MY
m
V
U
t
MX
y
x
d 
d 

 dt 
 dt   x
fixed
rot
; rotation frequency of the reference frame relative to the static frame
dμ
dt
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 μ  B eff ;
B eff  B 0  ω / 

Exersize 1.4. Find the solution of the above equation
in the rotating frame, (Note 0= -B0)
U  cos(-0)t
V  sin(0)t
0; rotational frequency of M in the static frame
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How can we observe an MR-signal?
z
y
y
x
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x
Mxy = 0 !!!!!
LINEAR POLARIZED FIELD (B1)
Rf-irradiation
e it  eit
2
 2 cos(t )
2
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Application of an rf-pulse along the u-direction
(Why and what effect ?)
dM
Beff
dt
Bo - /
M
B1
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 M  Beff


Beff  B1i  (  0 ) / k
Excersize 1.5: What effect will B1have on the magnetization
when on resonance ? Discuss
dU
 (0   )V
dt
dV
 (0   )U  B1M z
dt
dM z
 B1V
dt
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