Introduction to MRI: NMR
• Physics reminders
– Nuclei and atoms
– Electromagnetic spectrum and
Radio Frequency
– Magnets
– Vectors
• NMR phenomena
– nuclei, atoms and electron clouds
(molecular environment)
– excitation and energy states,
Zeeman diagram
– precession and resonance
quantum vs. classical pictures of
proton(s)
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Electromagnetic spectrum
http://www.nps.gov
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Electromagnetic spectrum
c = 
 = 3 x 108 m/s /
www.yorku.ca/eye/spectru.htm
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RF Antennae vs. RF coils
Antennae disperse energy
Coils focus energy
www.yorku.ca/eye/spectru.htm
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Nuclei and subatomic particles
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Stern-Gerlach experiment: discovery of spin
• Discovery of magnetic moment
on particles with spins
• Electron beam has (roughly) even
mix of spin-up and spin-down
electrons
– Beam should be bent to the side
because a force is exerted on
moving charge in a magnetic field
– Beam was also split vertically,
because electrons posses inherent
magnetic moment
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html
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Spin and magnetic moment
• Sub-atomic particles have intrinsic
angular momentum (spin), L
• Aligned with L is , a magnetic
moment
• The quantum number I determines
how many spin states a particle
might be found in
Lz  m
z  Lz
– For a nucleus, the number of
protons and neutrons determines I

• L and  are related by , the
gyromagnetic ratio
L  I(I  1)
  L

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Periodic table: some nuclei are magnetic
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Water
www.lsbu.ac.uk/water/
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Magnets
Dipole in a static field
Lowest
energy
Highest
energy
B
N
Units of magnetic field:
1 Tesla = 104 Gauss
0.5 G = earth’s magnetic field
~50 G = refrigerator magnet
S
E   B
   B
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Magnets
Dipole in a static field
Lowest
energy
Proton in a static magnetic field
Highest
energy
: magnetic
dipole
B
N
S
E   B
   B
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Single spin-1/2 particle in an external magnetic field
Nucleus in free space
Nucleus in magnetic field
Lz  m
Lz  
z  Lz
2
z  Lz

L  I(I  1)
  L


Spin-up and spin-down are different
energy levels; difference depends
linearly on static magnetic field
All orientations possess the
same potential energy
m
E

B
m
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2
1
2
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Resonant frequency
m
E

1
2
Transition emits energy
B
m
1
2
Excitation promotes transition

• Resonant frequency is determined by gyromagnetic
ratio, a property of the nucleus
• At 3T, protons resonate at ~128 MHz
• At 7T, protons resonate at ~300 MHz
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Electromagnetic spectrum
c = 
 = 3 x 108 m/s /
www.yorku.ca/eye/spectru.htm
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Hydrogen spectrum: electron transitions
1 electron volt = 1.6 × 10-19 J
Fixed energy transitions
result in discrete absorption
lines
http://csep10.phys.utk.edu/astr162/lect/light/absorption.html
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Precession and resonant frequency
Lz  
2
z  Lz

Spin-up and spin-down are different
energy levels; difference depends
linearly on static magnetic field
Torque exerted by magnetic force
on dipole creates precession.

 dL  
 
 B
dt
Lz  B sin(  )

B sin(  )
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Lz

m
E
1
2
E   
2 B  

L

B
B
1
m
2
Introduction to MRI


L
B
16
Gyromagnetic (magnetogyric) ratio


B
L  I(I  1)
  L

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
L
B
  B


B
 

L

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From spin-1/2 particles to bulk magnetization
B
M: net (bulk) magnetization
isochromat
Excitation affects phase and distribution between
spin-up and spin-down, rotating bulk magnetization
M||
Equilibrium: ~ 1 ppm excess in
spin-up (low energy) state creates a
net magnetization
M
M
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Information in proton NMR signal
• Resonant frequency depends on
• Static magnetic field
• Molecule
• Relaxation rate depends on physical environment
• Microscopic field perturbations
– Tissue interfaces
– Deoxygenated blood
• Molecular environment
– Gray matter
– White matter
– CSF
Excitation
Relaxation
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Proton NMR spectrum: ethanol
/grupper/KS-grp/microarray/slides/drablos/Structure_determination
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