Introduction to Magnetic Resonance Imaging

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Introduction to Magnetic Resonance Imaging

• Benjamin M Ellingson, MS
• Marquette University
• 21 February 2007

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Quantum Theory of Magnetic Resonance
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Quantum Theory of Magnetic Resonance
Angular Momentum
Magnetic Moment, M0
Low Energy Parallel
High Energy Antiparallel
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Quantum Theory of Magnetic Resonance
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Quantum Theory of Magnetic Resonance

• So, B0 (static magnetic field) causes some
  particles to align antiparallel, but most align
  parallel
• Classical View Vector sum of all magnetization
  is parallel to B0

M0
B0
Classical View is easier to conceptualizehowever
some quantum restraints
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Theory of Magnetic Resonance

• Because of the Uncertainty Principle, spins
  cannot completely align with B0 because the
  momentum of the particle cannot be defined
  completely, instead they precess or wobble around
  B0 at the Larmor Frequency.

Magnetic Field
Larmor Frequency
Gyromagnetic Ratio (specific to atom 1H ? 42.6
MHz/T
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Theory of Magnetic Resonance
Laboratory Frame of Reference See m rotating
about B0 with net magnetization in z-direction,
Mz. The time average value of Mxy is 0.
Mz
m
Mxy
Rotating Frame of Reference Observer is rotating
at the precession frequency, such that m is not
moving. All we see all the components of m. In
rotating frame of reference we will call this M0.
So, placing many 1H atoms in a static magnetic
field ? M0 Mz.
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Perturb Magnetic Equilibrium

• By applying a horizontal oscillating field at
  Larmor frequency (B1) produces a torque on the
  magnetization vector, M0.
• Since B1 ltlt B0 the net field is still in
  z-dir
• Causes M0 to tip into xy-plane.

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RF Excitation
Laboratory Frame of Reference
Rotating Frame of Reference
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RF Excitation Effect of Frequency
B1(t) B1 cos (0.5wt)
Static B1
B1(t) B1 cos (wt)
B1(t) B1 cos (1.5wt)
B1(t) B1 cos (2wt)
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Relaxation

• After excitation, if B1 field is turned off the
  spins undergo relaxation in both transverse and
  longitudinal directions at different rates.
• Transverse Relaxation T2-relaxation Spin-Spin
  Relaxation
• Corresponds to dephasing of neighboring spins
• Causes decrease in Mxy
• Longitudinal Relaxation T1-relaxation Lattice
  Relaxation
• Causes increase in Mz after excitation

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MR Signal

• If we have a lot of 1H excited such that they are
  spinning in phase in the xy-plane (i.e. changing
  magnetic field) we can detect this with an
  antenna due to Faradays Law of Induction

Antenna
Total Magnetization
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MR Signal Free Induction Decay

• As T2 relaxation occurs (Mxy decreasing),
  sinusoidal signal at antenna decays with T2
  envelope ? Free Induction Decay (FID)

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Localization via Magnetic Field Gradients

• In a static magnetic field, we have no way of
  knowing where MR signal is coming from (i.e. all
  1H are precessing at same frequency)

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Localization via Magnetic Field Gradients

• To solve this problem we introduce a GRADIENT
  FIELD
• Gradient magnetic fields add to or subtract from
  the main magnetic field in a controlled and
  predictable pattern so the field is no longer
  homogeneous.

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Localization via Magnetic Field Gradients
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Localization via Magnetic Field Gradients
FREQUENCY ENCODE
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Localization via Magnetic Field Gradients

• Frequency Encoding causes 1-D localization but
  what about other dimensions?
• Use field gradients to Phase Encode signal
• By pulsing a gradient in another direction we can
  speed up or slow down spins

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Localization via Magnetic Field Gradients
Gradient Turned On
Gradient Turned Off
Spins in Static Magnetic Field
Same frequency but different phase!
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2-D Spatial Frequency Domain k-space
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The FID Echo

• We get maximum signal when all spins are in phase
  and no signal when spins are dephased.
• Just as we used a pulsed gradient to phase
  encode, we can use pulsed gradients to rephase
  after dephasing has occurred.
• The process of rephasing spins causes a symmetric
  FID with maximum at time when spins are
  completely rephased.

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Slice Selection

• The previous RF excitation was applied to all
  1H-spins in the body because they were all at the
  Larmor Frequency (w0 gB0).
• If we apply a gradient, Gss, while applying RF
  excitation at a very specific frequency we can
  excite an infinitely thin layer of spins.
• Practically, we want to excite a slab of spins
  so we have high signal, therefore we envelope the
  RF excitation in a sinc function.

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The MRI Pulse SequenceIdeal Gradient Recalled
Echo (GRE)
K-space
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MRI Pros Cons

• Pros
• Non-ionizing radiation
• Limitless Contrast Possibilities (based on Pulse
  Sequence Design)
• Can image in any plane (vs. Axial only for CT)
• Exquisite Resolution Soft Tissue Contrast
• Cons
• Relatively Slow (changing due to better hardware
  and sequence design such as EPI)
• No metal (although most implants are now MR
  compatible)
• Claustrophobia Loud

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Clinical Applications

• Too Numerous to list them all
• Angiography
• Diffusion
• fMRI (BOLD ASL)
• Cardiac

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Medical Imaging Computing

• Making information accessible
• CAD, 3D Visualization, Modality Registration
• Reconstruction Processing Algorithms
• Novel Pulse Sequence Image Reconstruction
• Real-time Image Reconstruction
• Code optimization for fast imaging sequences
• Archival Storage
• DICOM, PACs, Image Compression

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Additional Info References

• Additional Information
• http//www.ellingsonbiomedical.com/MRI/Lectures/In
  tro_to_MRI.htm
• Medical College of Wisconsin Biophysics
• http//www.mcw.edu
• NIH Image Processing Interest Group
• http//image.nih.gov
• Johns Hopkins Biophysics Group
• http//biophysics.jhu.edu
• Stanford Magnetic Resonance Laboratory
• http//smrl.stanford.edu