Magnetic Resonance Imaging: Physical Principles

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Magnetic Resonance ImagingPhysical Principles
Lewis Center for NeuroImaging

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Physics of MRI, An Overview

• 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

• Echo formation
• Vector summation
• Phase dispersion
• Phase refocus
• 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
• 3D Imaging
• Spectroscopy

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Many spins in a voxel vector summation
spins not in step
spins in step
Rotating frame Lamor precession
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Phase dispersion due to perturbing B fields
Spin Phase f ? gBt B B0 dB0 dBcs dBpp
sampling
sometime after RF excitation
Immediately after RF excitation
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Refocus spin phase echo formation
time
Echo Time (TE)

• Invert perturbing field dB -dB
• Invert spin state f -f

Phase 0 dBt f-dB(t-TE/2) 0
(gradient echo, k-space sampling)
Phase 0 dBt -fdB(t-TE/2)
0
(spin echo)
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Spin Echo

• Spins dephase with time
• Rephase spins with a 180 pulse
• Echo time, TE
• Repeat time, TR
• (Running analogy)

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Frequency encoding - 1D imaging
Spatial-varying resonance frequency during RF
detection
B B0 Gxx

• S(t) eigBt
• S(t) ?m(x)eigGxxtdx

m(x)
kx gGxt
x
S(t) ?m(x)eikxxdx S(kx), m(x) FTS(kx)
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Slice selection
Spatial-varying resonance frequency during RF
excitation
w w0 gGzz
w
B1 freq band
z
Excited location
Slice profile
m mximy g ?b1(t)e-igGzztdt B1(gGzz)
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Gradient Echo FT imaging
ky
Readout
kx
Repeat with different phase-encoding amplitudes
to fill k-space
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Pulse sequence design
prewinder spoiler
rephasor
rewinder spoiler
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EPI (echo planar imaging)
X
ky
Y
Z
kx
RF
time
Quick, but very susceptible to artifacts,
particularly B0 field inhomogeneity. Can acquire
a whole image with one RF pulse single shot EPI
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Spin Echo FT imaging
ky
Readout
kx
Repeat with different phase-encoding amplitudes
to fill k-space
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Spin Relaxation

• Spins do not continue to precess forever
• Longitudinal magnetization returns to equilibrium
  due to spin-lattice interactions T1 decay
• Transverse magnetization is reduced due to both
  spin-lattice energy loss and local, random, spin
  dephasing T2 decay
• Additional dephasing is introduced by magnetic
  field inhomogeneities within a voxel T2' decay.
  This can be reversible, unlike T2 decay

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Bloch Equation

• The equation of MR physics
• Summarizes the interaction of a nuclear spin with
  the external magnetic field B and its local
  environment (relaxation effects)

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Contrast - T1 Decay

• Longitudinal relaxation due to spin-lattice
  interaction
• Mz grows back towards its equilibrium value, M0
• For short TR, equilibrium moment is reduced

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Contrast - T2 Decay

• Transverse relaxation due to spin dephasing
• T2 irreversible dephasing
• T2/ reversible dephasing
• Combined effect

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Free Induction Decay Gradient echo (GRE)

• Excite spins, then measure decay
• Problems
• Rapid signal decay
• Acquisition must be disabled during RF
• Dont get central echo data

MR signal
e-t/T2
time
0
90 RF
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Spin echo (SE)
e-t/T2
MR signal
e-t/T2
time
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MR Parameters TE and TR

• Echo time, TE is the time from the RF excitation
  to the center of the echo being received.
  Shorter echo times allow less T2 signal decay
• Repetition time, TR is the time between one
  acquisition and the next. Short TR values do not
  allow the spins to recover their longitudinal
  magnetization, so the net magnetization available
  is reduced, depending on the value of T1
• Short TE and long TR give strong signals

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Contrast, Imaging Parameters
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Properties of Body Tissues
MRI has high contrast for different tissue types!
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MRI of the Brain - Sagittal
T1 Contrast TE 14 ms TR 400 ms
T2 Contrast TE 100 ms TR 1500 ms
Proton Density TE 14 ms TR 1500 ms
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MRI of the Brain - Axial
T1 Contrast TE 14 ms TR 400 ms
T2 Contrast TE 100 ms TR 1500 ms
Proton Density TE 14 ms TR 1500 ms
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Brain - Sagittal Multislice T1
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Brain - Axial Multislice T1
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Brain Tumor
T1
T2
Post-Gd T1
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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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Spectroscopy

• Precession frequency depends on the chemical
  environment (dBcs) 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 transforms
• 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
Frequency
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Future lectures

• Magnetization preparation (phase and magnitude,
  pelc)
• Fast imaging (fast sequences, epi, spiral)
• Motion (artifacts, compensation, correction,
  navigator)
• MR angiography (TOF, PC, CE)

• Perfusion and diffusion
• Functional imaging (fMRI)
• Cardiac imaging (coronary MRA)

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3rd dimension phase encoding
Before frequency encoding and after slice
selection, apply y-gradient pulse that makes spin
phase varying linearly in y. Repeat RF
excitation and detection with different gradient
area.
S(ky, t) ? ? (? m(x,y,z)dz)eikyyeigGxxtdxdy