Introduction to Nuclear Magnetic Resonance

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Introduction to Nuclear Magnetic Resonance

• Topics
• Nuclear spin and magnetism
• Resonance behavior and the Larmor Frequency
• Larmor frequency
• flip angle
• Energy Absorption and Emission
• NMR spectroscopy
• Energy absorption in tissue (safety issues)
• Relaxometry
• T1,T2,T2 relaxation

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Nuclear Magnetism

• Nucleons (protons, neutrons) have a quantum
  property known as spin.
• Nucleons have been shown to obey Fermi
  statistics, and thus have a maximum spin
  magnitude of 1/2 Bohr magneton. (spin1/2)
• In the absence of a magnetic field, nuclear spin
  is not an observable
• In the presence of a homogeneous magnetic field,
  the energy of the nucleus depends on the relative
  orientation of the magnetic field and the nuclear
  spin vector

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• M net magnetization from collection of nuclei
• At thermal equilibrium, a sample of N protons in
  a static field B0 will have magnetisation
• at room temperature is very
  small.
• Electron paramagnetism dominates nuclear
  paramagnetism

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net magnetization
Individual nuclear spins
single voxel
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Nuclear Magnetic Resonance

• It is very difficult to observe static nuclear
  magnetism at room temperatures
• Resonance techniques can dramatically amplify
  effects
• Note uncertainty principle Nf1 in
  radiofrequency regime of NMR, N is very large,
  s.t. a classical description is valid

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• At thermal equilibrium, M is aligned with static
  field
• application of a perturbative field nuclei
  experience a torque t
• if applied field is rotating about Bo at angular
  frequency w, (recall that torque is the angular
  analogue of force Fma t )

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• Rotating Bapp B1 B1(t)
• Bloch Equation
• switching to rotating frame of M (
  )

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• When , M is at rest in rotating
  frame
• there are two conditions (i.e. solutions)
• M parallel to Be (only when Be B0)
• w-gBewo Larmor frequency
• wo is the frequency at which M rotates about Be
  ( B0)

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Resonance

• Application of perturbative field at t0 causes
  precession of M about Be (net field)
• Resonance occurs when w1wo, since B1 will appear
  to be stationary in the frame of M

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• After a time t, the angle of M with respect to B0
  is
• aw1tgB1t flip angle

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Nuclear Magnetic ResonanceProperties in Matter

• Energy Absorption
• In matter, resonance frequency depends on
  magnetic field at the nucleus
• in complex molecules, electron moments will alter
  the field seen by the nucleus (chemical shift)
• Absorption spectrum is a reflection of the
  chemical composition

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Nuclear Magnetic ResonanceProperties in Matter

• Relaxation
• After we have delivered energy to the nuclei in
  our sample at the Larmor frequency, there are two
  possible ways for the sample to lose this energy
  (back to lowest energy state)
• spontaneous emission
• induced emission

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• Spontaneous emission
• negligible effect at RF frequencies (dominant at
  visible frequencies)
• Induced emission
• Energy emission requires interaction of the
  nucleus with its external environment
• The nature of energy emission depends strongly
  on the environment of the excited nucleus
  (Relaxation)

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• NMR Spectroscopy is the study of the chemistry of
  matter using the NMR absorption spectrum
• Relaxometry is the study of the chemistry of
  matter using the NMR relaxation properties.
• MRI generates tissue contrast based (mostly)
  on NMR relaxation differences.

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NMR in tissue

• Protons in water molecules are the dominant
  nuclear species in the human body
• At 1.5T, 10-6 more protons are aligned with the
  static field than anti-aligned at room
  temperature very small magnetic moment.
• Proton Resonance frequencies g4257 Hz/gauss
• 0.5T 21.28 MHz
• 1.0T 42.57 MHz
• 1.5T 63.86 MHz (Channel 3!)

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NMR Absorption in Tissue

• RF energy at the Larmor frequency will be
  absorbed by water protons in tissue
• MRI scanner 16 Kilowatt RF transmitter
• Dosage Specific Absorption Rate (SAR)
• mass normalized rate of RF energy coupling to
  biologic tissue (watts/kg)

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Specific Absorption Rate

• Depends on
• frequency
• pulse sequence (shape of RF pulse,repetition
  time, pulse width)
• RF coil
• Volume of tissue in coil (i.e. exposed)
• resistivity of tissue
• geometry (spherical vs. cylindrical volume)

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Specific Absorption Rate

• Regulated by the FDA
• 0.4 W/kg averaged over the whole body, or 8.0
  W/kg peak SAR in any 1g of tissue, and 3.2 W/kg
  averaged over the head
• RF energy insufficient to produce a 1o C rise in
  core temp. and localized heating less than 38o C
  in the head, 39o C in the trunk, and 40o C in the
  extremities (except pts. with impaired
  circulation)

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Specific Absorption Rate
r tissue density
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Specific Absorption Rate

• RF Heating occurs mostly at the surface

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NMR Relaxation

• Energy emission occurs through interaction with
  environment
• time evolution
• Free Induction Decay solution

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• Longitudinal relaxation
• Transverse relaxation

1
1
1



T

T
T
2
2
2
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NMR Relaxation

• T1 relaxation
• time constant of recovery of longitudinal
  component of magnetization
• physics
• reflection of spin thermal interactions with the
  environment (i.e. the lattice)
• induced emission molecules moving near the
  Larmor frequency will induce relaxation
• pure water molecular motion too fast
  long T1
• solids molecular motion too slow
  long T1
• tissue molecular motion near Larmor freq
  short T1
• Field strength fraction of protons moving near
  Larmor frequency decreases with Ho T1 increases
  with Ho

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NMR Relaxation

• T2 Relaxation
• Time constant of disappearance of transverse
  magnetization
• Geometry dictates that T1 is a part of T2 (as
  longitudinal component grows, transverse
  component decays)
• T2 is always greater or equal to T1

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NMR Relaxation

• T2 Relaxation (contd)
• physics
• Induced emission from interactions with immediate
  surroundings (spin-spin interactions)
• Each nucleus experiences slight, temporary
  changes in local field due to slow interactions
  with other nuclei. This causes temporary changes
  in Larmor frequency leading to permanent phase
  dispersion
• Field strength change in Larmor frequency
  doesnt affect much
• T1 versus T2 in tissue
• T1 and T2 roughly correlate (e.g. low T1 implies
  low T2)
• T1 5 T2

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Bo
Spin Dephasing after excitation
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NMR Relaxation

• Relaxation times (msec)
• 0.5T 1.0T 1.5T
• T1 T2 T1
  T2 T1 T2
• Gray Matter 650 100 800 100
  900 100
• Muscle 550 50 700 50
  880 50
• Fat 200 80
  250 80 270 80

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NMR Relaxation

• T2 versus T2
• True T2 decay of transverse magnetization due to
  natural processes at the molecular level
• T2 the observed or effective decay of
  transverse magnetization due to magnetic field
  inhomogeneity and susceptibility effects

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• Longitudinal relaxation
• Transverse relaxation

1
1
1



T

T
T
2
2
2
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• T1 contrast
• Inversion-recovery
• T2 contrast
• Spin Echo
• T2 contrast
• Gradient echo