MRI Physics 1: Image Acquisition
 Chris Rorden & Paul Morgan
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Magnetic Resonance
Radio frequency absorption
Relaxation: Radio frequency emission
Gradients
Increases signal/noise: antenna selection, field
strength.
 Excellent references:
– www.cis.rit.edu/htbooks/mri/
– www.easymeasure.co.uk/principlesmri.aspx
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Units of magnetic strength
Tesla and Gauss are measures of magnetic
field strength
– Earth’s magnetic field ~0.5 Gauss.
– 1Tesla = 10,000 Gauss.
– Our fMRI system is 3T.
~x60,000 earth’s 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.
 Protons determine the element, e.g. hydrogen has one
proton, helium has two.
 Neutrons determines the isotope.
– Helium:
 Usually, two neutrons: 4He.
 Rarely, only have one neutron: 3He.
– Hydrogen
 Usually, no neutrons: 1H.
 Rarely, Deuterium (2H) is found in ‘heavy’ water
 Tritium (3H) is radioactive (spontaneous decay).
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?
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Resonance Frequency (MHz)
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
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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 absorption, net
magnetization is orthogonal to
magnetic field
– 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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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:
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1H
= 42.58 Mhz/T
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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– 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).
Non-Ionizing Radiation
Heating
 MRI signals are in the same range as
FM radio and TV (30-300MHz).
 MRI frequency is non-ionizing
radiation, unlike X-rays.
 Absorbed RF will cause heating.
 Specific absorption rate (SAR):
measure of the energy absorbed by
tissue.
Ionizing Radiation
Breaks Bonds
Electromagnetic Spectrum
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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128 Mhz
127 Mhz
127 Mhz
RF pulse
Field Strength
 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.
126 Mhz
Slice Selection Gradient
Larmor
Freq
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 scanner’s 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 brief muscle twitches.
Z Position
Z Position
Field Strength
Field Strength
Field Strength
Field Strength
 Position of gradient determines which 2D slice is selected.
Z Position
Z Position
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Phase encoding gradient
Y Position
 Orthogonal gradient applied between RF pulse and
readout
 This adjusts the phase along this dimension.
 Analogy: Phase encoding is like timezones. Clocks in
different zones will have different phases.
Field Strength
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Frequency encoding gradient
X Position
 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’.
Field Strength
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Raw MRI image: K-Space
Raw MRI is 2D Frequency Map.
Apply Fourier Transform to reconstruct image.
Source: Traveler’s Guide to K-space (C.A. Mistretta)
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Reconstruction
 Medical scanners automatically reconstruct your
data.
 You can manually reconstruct data using Tokarczuk’s
free Intel Reconstruction Tool:
www.mricro.com/import.html
 Fourier Transforms are slow: 1021-sample data
requires >2 million multiplications (2*N2)
 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.
Mansfield
EPI
Multi-shot
EPI does have a cost:
– Image warping due to slow
encoding.
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www.fmrib.ox.ac.uk/~karla/
MRI terminology
 Orientation: typically coronal,
sagittal or axial, can be inbetween these (oblique)
 Matrix Size:
Axial Orientation
64x64 Matrix
192x192mm FOV
3x3mm Resolution
– Voxels in each dimension
 Field of view:
– Spatial extent of each
dimension.
 Resolution:
– FOV/Matrix size.
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
3mm
2mm Thick
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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
…
…
Time
Time
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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
Signal = 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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www.fmrib.ox.ac.uk/~karla/
Signal to Noise: Antennas
 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.
Head coil
Surface coil
Volume coil
Surface coil 28
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 kspace.
8-channel array
– SENSE R=2 collects half of the lines.
– SENSE R=3 collects one third
– Reduces spatial distortion and increases speed
of acquisition. Some loss in signal.
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Parallel Imaging (SENSE, iPat)
Effects of SENSE factor (R) on EPI
 Increasing SENSE reduction factor decreases
acquisition time and spatial distortion, but high values
lead to reduced signal.
R=1
R=2
R=3
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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
 Maximum for NbTi MRI ~11.7T
 World record for superconductive MRI ~22T (Nb3Sn)
 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, Money, SAR,
wavelength effects, auditory noise
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Magnetic attraction
 Force in magnetic field (1.8T, unit dynes)
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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
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