Magnetic Resonance Imaging: Physical Principles

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Magnetic Resonance ImagingPhysical Principles

• Richard Watts, D.Phil.
• Weill Medical College of Cornell University,
• New York, USA

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Physics of MRI, Lecture 1

• Nuclear Magnetic Resonance
• Nuclear spins
• Spin precession and the Larmor equation
• Static B0
• RF excitation
• RF detection
• Spatial Encoding
• Slice selective excitation
• Frequency encoding
• Phase encoding
• Image reconstruction

• Fourier Transforms
• Continuous Fourier Transform
• Discrete Fourier Transform
• Fourier properties
• k-space representation in MRI

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Physics of MRI, Lecture 2

• 2D Pulse Sequences
• Spin echo
• Gradient echo
• Echo-Planar Imaging

• Medical Applications
• Contrast in MRI
• Bloch equation
• Tissue properties
• T1 weighted imaging
• T2 weighted imaging
• Spin density imaging
• Examples

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Physics of MRI, Lecture 3

• 3D Imaging
• Magnetization Preparation
• Chemical Shift and FatSat
• Water/Fat Separation
• Inversion Recovery and T1 Measurement
• Double Inversion Recovery

• Imaging blood flow
• Time-of-Flight
• Phase Contrast
• Fast Imaging
• Spoiling
• Spin Saturation
• Ernst angle, signal and contrast levels

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Summary So Far

• Spatial encoding
• Its all done with gradient fields
• Spatially varying Larmor precession frequency
• Slice select
• Frequency encode
• Phase encode

• Tissue contrast
• Different magnetic properties of tissues
• Different relaxation times
• T1 Longitidunal relaxation constant
• T2 Transverse relaxation constant
• Scan Parameters
• TE Echo time
• TR Repetition time

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Spatial Encoding Slice Selection
RF
Gz
Resonant Frequency
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2D Spatial Encoding Frequency and Phase Encoding
Gx
Phase Shift
Frequency ? X-Position Phase ? Y-Position
Phase encoding
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3D Imaging

• Instead of exciting a thin slice, excite a thick
  slab and phase encode along both ky and kz
• Greater signal because more spins contribute to
  each acquisition
• Easier to excite a uniform, thick slab than very
  thin slices
• No gaps between slices
• Motion during acquisition can be a problem

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2D Sequence (Gradient Echo)
ky
acq
Gx
Gy
kx
Gz
b1
TE
Scan time NyTR
TR
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3D Sequence (Gradient Echo)
acq
kz
Gx
Gy
Gz
ky
kx
b1
Scan time NyNzTR
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3D Imaging - example

• Contrast-enhanced MRA of the carotid arteries.
  Acquisition time 25s.
• 160x128x32 acquisition (kxkykz).
• 3D volume may be reformatted in
  post-processing. Volume-of-interest rendering
  allows a feature to be isolated.
• More on contrast-enhanced MRA later

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Chemical Shift - Spectroscopy

• Precession frequency depends on the chemical
  environment e.g. Hydrogen in water and hydrogen
  in fat have a ?f fwater ffat 220 Hz
• Single voxel spectroscopy excites a small (cm3)
  volume and measures signal as f(t). Different
  frequencies (chemicals) can be separated using
  Fourier transform
• Concentrations of chemicals other than water and
  fat tend to be very low, so signal strength is a
  problem
• Creatine, lactate and NAA are useful indicators
  of tumor types

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Spectroscopy - Example
Intensity (Concentration)
Frequency
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Chemical Shift - FatSat

• Use a small bandwidth (long, 20ms) 90º pulse to
  excite only protons within fat
• Destroy the transverse magnetization by dephasing
  (spoiling)
• Not spatially selective no gradients
• Useful for reducing the fat signal in abdominal
  and breast imaging
• Cost extra acquisition time

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Chemically Selective Saturation
Resolution Phantom (water)
Bottle of Oil (fat)
No saturation
Fat saturation
No saturation
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Water/Fat Separation
Proton spin in fat precesses at a frequency lower
than in water (-220Hz at 1.5T). fwater ffat
2p.Df.TE _at_ TE1 1/Df 4.55 msec, I1
Iwater Ifat _at_ TE2 3/(2Df) 6.82
msec, I2 Iwater ? Ifat Then, Iwater
(I1I2)/2, Ifat (I1 ? I2)/2
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Inversion Recovery (IR)

• After 180 inversion pulse the longitudinal
  relaxation Mz grows back towards its equilibrium
  value, M0
• Mz 0 when e-t/T1 ½
• T T1.ln2
• Select the inversion time, TI to null out the
  required signal

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Inversion Recovery (IR)
1800 RF
Rest of Sequence
TI (inversion time)
T1260
Mz
T11000
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Inversion Recovery - Example
No Inversion Recovery
Inversion Recovery, TI 150ms
Oil (fat)
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Measurement of T1

• Image using different inversion times (TI) until
  the signal is minimized
• Signal ? Mz(TI)

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Measurement of T2

• Measure signal as a function of echo time, TE
• Spin echo sequence gives T2 (irreversible)
• Gradient echo sequence gives T2 (reversible and
  irreversible)

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Double Inversion Recovery

• With two inversion pulses at appropriate times,
  two tissue types can be nulled out
• e.g. CSF and fat in the brain

1800
1800
Mz
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Blood Flow Time of Flight Effect

• Fast imaging TRltT1, T2
• Spins do not fully recover after each repetition
• Magnetization producing MR signal decreases with
  the number of pulses until equilibrium reached
• Spins flowing into the slice have not seen
  previous excitations, so have greater signal

a
RF
Mz
fresh inflow spin
inplane stationary spin
More on spin saturation later
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Time of Flight - Example
Renal arteries
Aorta
Inflow from vein
Inversion recovery (TI 300 ms) FatSat
Inversion recovery (TI 300 ms) FatSat IR Volume
extends more inferior so that vein signal is also
saturated
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Time of Flight Brain MRA
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Blood Flow Phase Contrast

• With a given gradient field, stationary spins
  precess at a constant rate
• Moving spins experience a change in precession
  frequency, depending on their velocity v, and the
  gradient strength, G.
• This causes a velocity-dependent phase shift, ?f

• For constant flow velocity,
• With an x-Gradient Gx, the field strength is
• The phase shift is linear with velocity

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Blood Flow Phase Contrast

• Add bipolar gradient in the flow direction after
  RF excitation
• Stationary spins are not dephased
• Repeat acquisition with reversed gradients
• Complex subtraction of images gives flow image

Acquisition 1 Gx
Acquisition 2 Gx
Gz
RF
Gx1 fflow gvM1, fstationary 0 Gx2 fflow
-gvM1, fstationary 0 I1-I2 rflowsin gvM1
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Phase Contrast - Example
Kidney Transplant
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Fast Imaging

• Fast imaging TRltT1,T2
• Spins do not have time to relax between one RF
  pulse and the next
• Transverse magnetization Spin memory produces
  artifacts in images. Many RF pulses contribute
  to each acquisition

• Longitudinal magnetization Spins get beaten
  down so that after each pulse there is less
  magnetization available.
• Equilibrium between pulses and relaxation
• Optimum angle to maximize steady-state signal
  Ernst angle

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Spoiling

• Destroy transverse magnetization so it doesnt
  contribute to later echoes
• Dephase the spins with large spoiling gradients
  after each acquisition
• Assume perfect spoiling

Readout
Phase encoding
Slice encoding
Spoiler
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Spin Saturation

• At equilibrium full magnetization is available
• Each pulse and spoiling reduces the magnetization
• Some signal regrowth due to T1 decay

1. Equilibrium MM0
3. Spoiling MM0cos ?
5. RF Excitation Flip Angle ?
2. RF Excitation Flip Angle ?
4. T1 Regrowth
6. Spoiling
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Ernst Angle
Maximize the equilibrium transverse magnetization
available ? signal Calculate the optimum flip
angle for a required TR
Immediately after nth TR
After RF Flip of ? and spoiling
After T1 recovery
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Ernst Angle
In equilibrium, Mz(n1)Mz(n)Mz
Equilibrium Transverse Magnetization, M?Mzsin?
Show that Maximum Transverse Magnetization
(signal) when
?E Ernst Angle
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Tissue Contrast
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Ernst Angle