MRI Physics 1: Image Acquisition

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MRI Physics 1 Image Acquisition

• Chris Rorden
• Magnetic Resonance
• Radio frequency absorption
• Relaxation Radio frequency emission
• Gradients
• Increases signal/noise antenna selection, field
  strength.
• Excellent source Hornaks The Basics of MRI
• www.cis.rit.edu/htbooks/mri/
• Another nice source
• www.easymeasure.co.uk/principlesmri.aspx

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Units of magnetic strength

• Tesla and Gauss are measures of magnetic field
  strength
• Earths magnetic field 0.5 Gauss.
• 1Tesla 10,000 Gauss.
• Our fMRI system is 3T.
• x60,000 earths field strength

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Anatomy of an atom

• Atoms are the building blocks of our world.
• Composed of 3 components
• Electrons tiny negatively charged particles.
• Protons heavy positively charged particles.
• Neutrons heavy particles without charge.
• Electrons are often thought of like planets tiny
  objects distantly orbiting a massive core.
• Neutrons and protons form the dense nucleus of an
  atom.

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Atomic Nuclei

• Atomic nuclei are composed of protons and
  neutrons.
• The number of protons determines the element,
  e.g. hydrogen has one proton, helium has two.
• The number of neutrons determines the isotope.
• Most helium has two neutrons 4He.
• Some helium atoms only have one neutron 3He.
• Most hydrogen has no neutrons 1H.
• Deuterium (2H) is found in heavy water, Tritium
  (3H) is radioactive (spontaneous decay) and is
  used to enhance nuclear bombs.

4He
3He
1H
2H
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Nuclear Magnetic Resonance

• Felix Block and Edward Purcell
• 1946 the nuclei of some elements absorb and
  re-emit radio frequency energy when in magnetic
  field
• 1952 Nobel prize in physics
• Atoms with odd number of protons/neutrons spin in
  a magnetic field
• Nuclear properties of nuclei of atoms
• Magnetic magnetic field required
• Resonance interaction between magnetic field and
  radio frequency

Bloch
Purcell
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How fast do hydrogen atoms spin?
180
The rate of rotation is determined by the
strength of the magnetic field. Larmor
equation f ?B0 For Hydrogen, ? 42.58
MHz/T At 1.5T, f 63.76 MHz At 3T, f 127.7
MHz
Resonance Frequency (MHz)
40
1.0
4.0
Field Strength (Tesla)
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Radiofrequency Pulses

• A radiofrequency (RF) pulse at the Larmor
  frequency will be absorbed.
• This higher energy state tips the spin, so it is
  no longer aligned to the field.
• An RF pulse at any other frequency will not
  influence the nuclei.
• This is resonance.

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Source of MR signal

• At rest, atoms align parallel to magnetic field.
• Lowest energy state.
• After RF transmission, magnetization is
  orthogonal to magnetic field
• Generates RF emission at larmor frequency
• RF emission decays with time

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Absorption and Relaxation

• Our RF transmission is absorbed by atoms at
  Larmor frequency.
• After the RF pulse, atoms will begin to realign
  with the magnetic field relaxation
• During this period, an RF signal is emitted.
• This signal will be at the Larmor frequency.
• An antenna can measure this signal.

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MRI compass analogy
N

• Compass needle points North
• Briefly tap magnet needle no longer points North
• Wait, needle returns to North (lower energy
  state)

N
N
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Hydrogen is the mainstay for MRI

• We will focus on Hydrogen
• Hydrogen abundant in body (63 of atoms).
• Elements with even numbers of neutrons and
  protons have no spin, so we can not image them
  (4He, 12C).
• 23Na and 31P are relatively abundant, so can be
  imaged.
• Larmor frequency varies for elements
• 13C 10.7 Mhz/T
• 19F 40.1 Mhz/T
• 31P 17.7 Mhz/T
• Therefore, by sending in a RF pulse at a specific
  frequency we can selectively energize hydrogen.

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Electromagnetic Spectrum

• MRI signal s are in the same range as FM radio
  and TV (30-300MHz).
• MRI frequency is non-ionizing radiation, unlike
  X-rays.
• Absorbed RF signal will cause heating.
• Specific absorption rate (SAR) measure of the
  energy absorbed by tissue.
• Increases with square of field strength.
• Higher SAR more energy more signal more
  heating
• FDA limits SAR, and is a limiting factor for some
  protocols (3 W/kg averaged over 10 minutes).

Ionizing Radiation Breaks Bonds
Non-Ionizing Radiation Heating
Excites Electrons
Excites Nuclei
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Making a spatial image

• To create spatial images, we need a way to cause
  different locations in the scanner to generate
  different signals.
• To do this, we apply gradients.
• Gradients make the magnetic field slightly
  stronger at one location compared to another.
• Lauterbur first MRI 2003 Nobel Prize.

Lauterbur
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Slice Selection Gradient
128 Mhz 127 Mhz 126 Mhz

• Gradients make field stronger at one location
  compared to another.
• Larmor frequency different along this dimension.
• RF pulse only energizes slice where field
  strength matches Larmor frequency.

Field Strength
Z Position
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Slice Selection Gradient

• Gradual slice selection gradients will select
  thick slices, while steep gradients select
  thinner slices.
• The strength of your scanners gradients can
  limit minimum slice thickness.
• FDA limits speed of gradient shift (dB/dt) and
  some of our protocols can elicit slight tingling
  sensation or a brief muscle twitches.
• Position of gradient determines which 2D slice is
  selected.

Field Strength
Field Strength
Field Strength
Field Strength
Z Position
Z Position
Z Position
Z Position
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Phase encoding gradient

• Between RF pulse and readout, we apply an
  orthogonal gradient.
• This adjusts the phase along this dimension.
• Analogy Phase encoding is like making timezones.
  Clocks in different zones will have different
  phases.

Y Position
Field Strength
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Frequency encoding gradient

• Apply final orthogonal gradient when we wish to
  acquire image.
• Slice will emit signal at Lamour frequency, e.g.
  lines at higher fields will have higher frequency
  signals.
• Aka Readout gradient.

X Position
Field Strength
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Raw MRI image K-Space
Raw image is 2D Frequency Map. Apply Fourier
Transform to reconstruct image.
Source Travelers Guide to K-space (C.A.
Mistretta)
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Reconstruction

• Medical scanners automatically reconstruct your
  data.
• You can manually reconstruct data using
  Tokarczuks free Intel Reconstruction Tool
  www.mricro.com/import.html
• Fourier Transforms are slow 1021-sample data
  requires gt2 million multiplications (2N2)
• Fast Fourier Transform 1024-sample data requires
  20,000 multiplications. (2(N log N))
• Optimal when data is power of two (64,128,256,
  512), reverts to traditional Fourier for prime
  numbers
• This is why most image matrices are a power of 2.

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MRI scanner anatomy

• A helium-cooled superconducting magnet generates
  the static field.
• Always on only quench field in emergency.
• niobium titanium wire.
• Coils allow us to
• Make static field homogenous (shims solenoid
  coils)
• Briefly adjust magnetic field (gradients
  solenoid coils)
• Transmit, record RF signal (RF coils antennas)

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MRI scanner anatomy
Antennas
Magnet
Gradient
RF Transmit
RF Receive
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EPI

• In conventional MRI, we collect one line of our
  matrix with each RF pulse.
• So a 64x64 matrix with a TR of 2sec will be
  generated in 128 seconds.
• Problem this is unacceptable if the object
  changes rapidly
• Images of the heart shape changes quickly,
  conventional image would be blurred.
• Imaging brain activity could not see changes
  that occur within a few seconds.
• Echo Planar Imaging By rapidly applying the
  frequency gradient, we can collect a 2D slab with
  a single RF pulse.

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Echo Planar Imaging

• EPI was devised in 1977 by Sir Mansfield.
• 2003 Nobel Prize.
• EPI remains the principle technique for fMRI
  acquisition.
• Alternative is spiral imaging.
• EPI does have a cost
• Image warping due to slow encoding.

Mansfield
Multi-shot
EPI
www.fmrib.ox.ac.uk/karla/
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MRI terminology

• Orientation typically coronal, sagittal or
  axial, can be in-between these (oblique)
• Matrix Size
• Voxels in each dimension
• Field of view
• Spatial extent of each dimension.
• Resolution
• FOV/Matrix size.

Axial Orientation 64x64 Matrix 192x192mm
FOV 3x3mm Resolution
Sagittal Orientation 256x256 Matrix 256x256mm
FOV 1x1mm Resolution
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Volumes

• 3D volumes are composed of stacks of 2D slices,
  like a loaf of bread.
• Each slice has a thickness.
• Thicker slices have more hydrogen, so more signal
• Volume of 1x1x1mm voxel is 1mm3
• Volume of 1x1x2mm voxel is 2mm3
• Thinner slices provide higher resolution.
• Optional gap between slices.
• Reduces RF interference
• Allows fewer slices to cover whole brain.

1mm Gap 2mm Thick
3mm
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Creating 3D volumes from 2D EPI

• Slices can be either collected sequentially (e.g.
  ascending axial slices) or in interleaved order
  (e.g. collect all odd slices, then all even
  slices).

Sequential
Interleaved


TR
TR
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Sequential vs Interleaved Volumes

• Interleaving reduces interference between slices.
  Useful if thin gap between slices.
• Unfortunately, any head movements will cause
  worse spin history effects for interleaved
  slices than sequential. (TR will be shorter for
  regions that were previously in another slice).
• You must know slice order if you want to slice
  time correct data (temporal processing lecture).

Slice 4
Slice 4
Slice 3
Slice 3
Slice 2
Slice 2
Slice 1
Slice 1
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Signal to Noise

• Signal To noise is given by the formula
• V?N
• Where V is the volume and N is the number of
  samples averaged (referred to as Nex, as in
  number of excitations).
• For example, to get the same SNR as a single
  3x3x3mm scan (27mm3) we would need to collect 12
  2x2x2mm (8mm3) scans or 768 1x1x1mm (1mm3) scans.

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Signal to Noise Antennas
www.fmrib.ox.ac.uk/karla/

• The MRI antenna is called a coil.
• We use different coils for different body parts.
• For brains, the most common antenna is the head
  coil, which is a volume coil it shows the whole
  brain.
• We can also use a surface coil it gives great
  signal for a small field of view.

Volume coil
Surface coil
Head coil
Surface coil
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Parallel Imaging (SENSE, iPat)

• Parallel imaging uses multiple surface coils to
  generate a volume image.
• Dramatically reduces spatial distortion and
  increases signal.
• Optionally, you can acquire images more rapidly
  by only collecting a portion of k-space.
• SENSE R2 collects half of the lines.
• SENSE R3 collects one third
• Reduces spatial distortion and increases speed of
  acquisition. Some loss in signal.

8-channel array
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Parallel Imaging (SENSE, iPat)

• Increasing SENSE reduction factor decreases
  acquisition time and spatial distortion, but high
  values lead to reduced signal.

Effects of SENSE factor (R) on EPI
R1
R2
R3
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Signal and Field Strength

• Outside magnetic field
• Spins randomly oriented

• In magnetic field
• Spins tend to align parallel or anti-parallel to
  magnetic field.
• At room temperature, 4 parts per million more
  protons per Tesla align with versus against
  field.
• As field strength increases, there is a bigger
  energy difference between parallel and
  anti-parallel alignment (faster rotation more
  energy).
• A larger proportion will align parallel to field.
• More energy will be released as nuclei align.
• Therefore, MR signal increases with square of
  field strength.

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Signal and Field Strength

• Most clinical MRI 1.5T
• Our fMRI systems 3.0T
• Our small bore animal system 7.0T
• Field strength influences
• Faster Larmor frequency
• Bigger energy difference between parallel and
  anti-parallel alignment
• Larger ratio of nuclei aligned more signal
• More signal as nuclei realign.
• Reduced TR and TE less time to take images (next
  week).

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Signal and Field Strength

• In theory
• Signal increases with square of field strength
• Noise increases linearly with field strength
• A 3T scanner should have twice SNR of 1.5T
  scanner 7T should have 4.7 times SNR of 1.5T.
• Unfortunately, physiological artifacts also
  increase, so advantage is less in practice.
• Benefits speed, resolution
• Costs Artifacts, RF heating, wavelength effects,
  auditory noise,

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Magnetic attraction

• Force in magnetic field (1.8T, unit dynes)
• Water -22
• Copper -2.6
• Copper Chloride 280
• Iron 400,000
• Diamagnetic material repelled (e.g. H2O).
• Paramagnetic material attracted (e.g. CuCl, Gd).
• Ferromagnetic material strongly attracted (Fe).
• Even without magnetic field, magnetic moments
  aligned
• Dangerous near MRI scanner