Terry M. Button, Ph.D.

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Introduction to NMR Physics

• Terry M. Button, Ph.D.

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Tiny Magnets

• Nucleons behave as small current carrying loops.
• Such current carrying loops give rise to a small
  magnetic field.

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Tiny Magnets

• Like nucleons pair such their net magnetic fields
  cancel.
• Only nuclei with unpaired nucleons have magnetic
  properties.

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Nuclear Spin Quantum Number

• I is quantized in half units of h
• 0, ½, 1, etc
• Nuclear magnetic moment is proportional to I
• ? ?Ih

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Which nuclei are useful?

• Not useful for MRI (even-even, I 0)
• 4 He
• 12C
• 16O
• Useful for MRI (one unpaired)
• 1H
• 13C
• 31P
• 129Xe

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Magnetic Moment
N
S
A current carrying loop (l by w) will experience
a torque ? 2 (w/2) I dl x B ? IA x B ?
? x B, where ? is the magnetic moment
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Effect of Applied Field - Classical

• An external magnetic field (Bo) causes the proton
  to precess about it.
• Larmor (precessional) frequency fL gBo/2?.
• For protons fL is approximately 42 MHz/Tesla.

B0
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Magnetization

• A sample of protons will precess about an applied
  field. The sample will have
• a net magnetization along the applied field
  (longitudinal magnetization).
• no magnetization transverse to the applied field
  (transverse magnetization).

B0
M
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Classical Picture of Excitation

• A second field (B1) at the fL and at right angles
  to Bo will cause a tipping of the longitudinal
  magnetization.
• The result is a net transverse component this is
  what is detected in MRI.
• B1 is radiofrequency at fL.

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RF Excitation for Transverse Magnetization
B0
B0
90o RF at fL
M
M
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(No Transcript)
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Signal from the Free Induction Decay
S
exp(-t/T2)
M
t
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Longitudinal Relaxation

• Relaxation of the longitudinal component to its
  original length is characterized by time constant
  T1
• Spin lattice relaxation time
• Tumbling neighbor molecules produce magnetic
  field components at the Larmor frequency
  resulting in relaxation.
• following a 90o tip, T1 provides recovery to
  1-1/e or 63 of initial value.

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T1
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Transverse Relaxation

• Relaxation of the transverse magnetization to
  zero is characterized by time constant T2
• Spin-spin relaxation time.
• following a 90o tip, reduction to 1/e or 37 of
  initial value.
• T2 combined dephasing due to T2 and field
  inhomogeneity.

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T2
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In vivo Relaxation

• T1 T2 T2
• T1 increases with Bo
• T2 is not strongly effected.

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Relaxation
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Application of FFT to S vs. t

• FT
• FFT provides real (a) and imaginary (bi)
  components at frequencies dictated by Nyquist
  sampling
• Magnitude a2 b21/2
• Phase arctan (b/a)
• The magnitude
• Has center frequency at the Larmor frequency
• The decay is contained within an exp (-t/T2)
  envelope
• T2 determines the line width

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Spectra
long T2
I
short T2
f
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Effect of Applied Field - Quantum Mechanical

• Protons can be in one of two state
• aligned with the field (low energy)
• aligned against the field (high energy)
• The energy separation is E h fL.

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Quantum Mechanical
?E hfL

• Protons moving from low to high energy state
  require radiofrequency.
• Protons moving from high to low energy release
  radiofrequency.

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State Population Distribution

• Boltzmann statistics provides population
  distribution these two states
• N-/N e-E/kT where
• E is the energy difference between the spin
  states
• k is Boltzmann's constant (1.3805x10-23
  J/Kelvin)
• T is the temperature in Kelvin.
• At physiologic temperature approximately only 1
  in 106 excess protons are in the low energy state.

-.
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Chemical Shift

• Electrons in the molecule shield the nucleus
  under study
• Bobserved Bapplied - ?B Bapplied (1 - ?)
• The chemical shift is measured in frequency
  relative to some reference
• ? (fsample freference )/freference x106
  ppm
• Usually freference is tetramethylsilane (TMS)
  for in vitro.
• In the body fat and water 3.5 ppm shift.

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In Body
Fat and water have 3.5 ppm shift at 1.5 T this
amounts to 220 Hz.
water
I
lipid
220Hz
f
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Recovery of Rapid T2 Signal Loss Using Spin-Echo
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Spin Echo
echo
90o
180o
TE/2
TE/2
Bo ?
Bo - ?
Bo
t 0
t TE/2
Echo!
t TE
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Multi Echo Decay T2
exp(-t/T2)
exp(-t/T2)
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Introduction to Image Formation
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Simple NMR Experiment
Bo
S
I
FFT
t
f
fL
f
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Modify with a Gradient
Bo
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Linear Gradient - Simple Projection
Bo
S
I
FFT
t
f
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Rotating Gradient Provides Projection Data
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2D Filtered Backprojection

• Rotating gradient
• Difficult to collect projections exactly though
  the origin.
• Artifacts.
• Most often 2D FT used in present MR.