Transcript Introduction to Magnetic Resonance Imaging
Introduction to Magnetic Resonance Imaging
Benjamin M Ellingson, MS Marquette University 21 February 2007
Quantum Theory of Magnetic Resonance
Quantum Theory of Magnetic Resonance Angular Momentum Magnetic Moment, M 0 Low Energy = Parallel High Energy = Antiparallel
Quantum Theory of Magnetic Resonance
Quantum Theory of Magnetic Resonance So, B 0 (static magnetic field) causes some particles to align antiparallel, but most align parallel
Classical View
: Vector sum of all magnetization is parallel to B 0 M 0 B 0 Classical View is easier to conceptualize…however some quantum restraints…
Theory of Magnetic Resonance
Because of the
Uncertainty Principle
, spins cannot completely align with B 0 because the momentum of the particle cannot be defined completely, instead they precess or wobble around B 0 at the Larmor Frequency.
Magnetic Field Larmor Frequency Gyromagnetic Ratio
(specific to atom; 1 H 42.6 MHz/T
Theory of Magnetic Resonance
Laboratory Frame of Reference
: See m rotating about
B 0
in z-direction,
M z
. The time average value of M xy is 0. with net magnetization
M z
m
M xy
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 M 0 . So, placing many 1 H atoms in a static magnetic field M 0 = M z .
Perturb Magnetic Equilibrium
By applying a horizontal oscillating field at Larmor frequency (
B 1
) produces a torque on the magnetization vector, M 0 .
Since |B 1 | << |B 0 | the net field is still in z-dir Causes M 0 to “tip” into xy-plane.
RF Excitation
Laboratory Frame of Reference: Rotating Frame of Reference:
RF Excitation: Effect of Frequency
Static B 1
:
B 1 (t) = B 1 cos (0.5
w
t) B 1 (t) = B 1 cos (
w
t) B 1 (t) = B 1 cos (1.5
w
t) B 1 (t) = B 1 cos (2
w
t)
Relaxation
After excitation, if B 1 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 M xy
Longitudinal Relaxation = T1-relaxation = Lattice Relaxation
Causes increase in M z after excitation
MR Signal
If we have
a lot
of 1 H 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
As T2 relaxation occurs (M xy decreasing), sinusoidal signal at antenna decays with T2 envelope
Free Induction Decay (FID)
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 1 H are precessing at same frequency):
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.
Localization via Magnetic Field Gradients
Localization via Magnetic Field Gradients
FREQUENCY ENCODE
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
Localization via Magnetic Field Gradients
Same frequency but different phase!
2-D Spatial Frequency Domain: k-space
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.
Slice Selection
The previous RF excitation was applied to all 1 H-spins in the body because they were all at the Larmor Frequency ( w 0 = g B 0 ).
If we apply a gradient, G ss , 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
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
Clinical Applications
Too Numerous to list them all Angiography Diffusion fMRI (BOLD & ASL) Cardiac
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
Additional Info & References
Additional Information http://www.ellingsonbiomedical.com/MRI/Lectures/Intro_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