Introduction to MRI: NMR

1
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)

2
Electromagnetic spectrum
http//www.nps.gov
3
Electromagnetic spectrum
c ?? ? 3 x 108 m/s /?
www.yorku.ca/eye/spectru.htm
4
RF Antennae vs. RF coils
Antennae disperse energy
Coils focus energy
www.yorku.ca/eye/spectru.htm
5
Nuclei and subatomic particles
6
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/Har
rison/SternGerlach/SternGerlach.html
7
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
• For a nucleus, the number of protons and neutrons
  determines I
• L and ? are related by ?, the gyromagnetic ratio

8
Periodic table some nuclei are magnetic
9
Water
www.lsbu.ac.uk/water/
10
Magnets
Dipole in a static field
Units of magnetic field 1 Tesla 104 Gauss
0.5 G earths magnetic field 50 G
refrigerator magnet
Lowest energy
Highest energy
B
N S
N S
11
Magnets
Proton in a static magnetic field
Dipole in a static field
Lowest energy
Highest energy
? magnetic dipole
B
N S
N S
12
Single spin-1/2 particle in an external magnetic
field
Nucleus in magnetic field
Nucleus in free space
Spin-up and spin-down are different energy
levels difference depends linearly on static
magnetic field
All orientations possess the same potential energy
13
Resonant frequency
Transition emits energy
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

14
Electromagnetic spectrum
c ?? ? 3 x 108 m/s /?
www.yorku.ca/eye/spectru.htm
15
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/abso
rption.html
16
Precession and resonant frequency
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.
17
Gyromagnetic (magnetogyric) ratio
18
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
M
Equilibrium 1 ppm excess in spin-up (low
energy) state creates a net magnetization
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
20
Proton NMR spectrum ethanol
/grupper/KS-grp/microarray/slides/drablos/Structur
e_determination