Introduction to
Magnetic Resonance Imaging
Benjamin M Ellingson, MS
Marquette University
21 February 2007
Quantum Theory of Magnetic Resonance
Quantum Theory of Magnetic Resonance
Magnetic Moment, M0
Angular Momentum
Low Energy = Parallel
High Energy = Antiparallel
Quantum Theory of Magnetic Resonance
Quantum Theory of Magnetic Resonance
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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 conceptualize…however some quantum restraints…
Theory of Magnetic Resonance
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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
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.
Perturb Magnetic Equilibrium
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By applying a horizontal oscillating field at
Larmor frequency (B1) produces a torque on
the magnetization vector, M0.
Since |B1| << |B0| the net field is still in z-dir
Causes M0 to “tip” into xy-plane.
RF Excitation
Laboratory Frame of Reference:
Rotating Frame of Reference:
RF Excitation: Effect of Frequency
Static B1:
B1(t) = B1 cos (0.5wt)
B1(t) = B1 cos (1.5wt)
B1(t) = B1 cos (wt)
B1(t) = B1 cos (2wt)
Relaxation
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After excitation, if B1 field is turned off the spins undergo relaxation
in both transverse and longitudinal directions at different rates.
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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
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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 Faraday’s Law of Induction:
Antenna
Total Magnetization
MR Signal: Free Induction Decay
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As T2 relaxation occurs (Mxy decreasing),
sinusoidal signal at antenna decays with T2
envelope  Free Induction Decay (FID)
Localization via Magnetic Field Gradients
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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):
Localization via Magnetic Field Gradients
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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.
Localization via Magnetic Field Gradients
Localization via Magnetic Field Gradients
FREQUENCY ENCODE
Localization via Magnetic Field Gradients
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Frequency Encoding causes 1-D localization
but what about other dimensions?
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Use field gradients to Phase Encode signal
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By pulsing a gradient in another direction we can
speed up or slow down spins
Localization via Magnetic Field Gradients
Gradient
TurnedMagnetic
Off:
On:
Spins in Static
Field:
Same frequency but different phase!
2-D Spatial Frequency Domain: k-space
The FID Echo
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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.
Slice Selection
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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.
The MRI Pulse Sequence
Ideal Gradient Recalled Echo (GRE)
Slice Selection
Phase Encode
Frequency Encode
K-space
FID Echo
FID
MRI Pros & Cons
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Pros
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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
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Relatively Slow (changing due to better hardware and
sequence design such as EPI)
No metal (although most implants are now MR compatible)
Claustrophobia & Loud
Clinical Applications
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Too Numerous to list them all
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Angiography
Diffusion
fMRI (BOLD & ASL)
Cardiac
Medical Imaging & Computing
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Making information accessible
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Reconstruction & Processing Algorithms
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CAD, 3D Visualization, Modality Registration
Novel Pulse Sequence Image Reconstruction
Real-time Image Reconstruction
Code optimization for fast imaging sequences
Archival & Storage
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DICOM, PACs, Image Compression
Additional Info & References
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Additional Information
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Medical College of Wisconsin Biophysics
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http://image.nih.gov
Johns Hopkins Biophysics Group
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http://www.mcw.edu
NIH Image Processing Interest Group
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http://www.ellingsonbiomedical.com/MRI/Lectures/Intro_to_
MRI.htm
http://biophysics.jhu.edu
Stanford Magnetic Resonance Laboratory
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http://smrl.stanford.edu