MR Physics in 230 Minutes

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MR Physics in 230 Minutes
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• A Talk from Hell
• One reason why this is a talk from hell there
  is a lot to say in just 20 30 minutes.
• The second reason is on slide 6.

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• Changing electric fields make magnetic fields,
  changing magnetic fields make electric fields.
• Hydrogen nuclei (protons) are slightly magnetic
  due to their spin. In water they are relatively
  naked of electrons so their nuclear magnetic
  resonance is less obscured. Water is abundant in
  the body.
• In the MRI scanner a very large coil cooled with
  liquid helium has a very strong electric current
  flowing continuously. This makes the strong (3
  Tesla) unchanging magnetic field called B0.
  Protons in this strong field become (a) more
  magnetic and (b) lined up with B0, rather than
  lining up in random fluctuating directions.

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• There is also a radio-frequency (RF) antenna
  (head coil it looks like a bird cage) that
  both transmits and receives RF energy.
• If we transmit a pulse at exactly the right
  frequency (127.68 MHz at 3T) we can spiral the
  hydrogen nuclei out of alignment with B0 over to
  flip angle. More RF pulse energy is needed for
  larger flip angles (larger amplitude or longer
  duration more energy).
• The head coil will receive this RF back as
  hydrogen nuclei spiral back up toward B0. T1 is
  the time constant for getting back this
  longitudinal (Mz, spin-lattice) magnetization.T2
  is the time constant for losing transverse (Mxy)
  magnetization due to spin-spin interactions and,
  when combined with faster losses due to magnetic
  field variation (e.g., from blood oxygenation
  changes), yields T2.

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• Three other coils in the scanner have flowing
  electric currents from time to time. These make
  weaker magnetic fields, called gradients, that
  vary over time as well as over space (field of
  view). One gradient varies up-down, another
  varies left-right, the third varies fore-aft.
• One of those gradients is turned on at the same
  time as the head coil transmits RF energy at
  127.68 MHz. This gradient makes the magnetic
  field too strong near one end (3.0001 T) and too
  weak near the other end (2.9999 T) for 127.68 MHz
  to be exactly the right frequency. Only those
  hydrogen nuclei where magnetic field strength is
  exactly 3T get bumped out of alignment with B0
  by this RF. The is called slice selection
  because only a thin sheet out of the whole volume
  fits the criteria. Slice thickness is determined
  by RF pulse bandwidth (thinner slices longer
  pulses) and by gradient slope (thinner slices
  more Gauss/cm). The slice-select gradient could
  be up-down (axial slices, like here), left-right
  (sagittal slices), fore-aft (coronal slices) or
  any combination (oblique slices).

Slice selection

Magnetic vectors in the selected slice , seen
from above. They spin around at 127.68 MHz and
point in the same direction.
Not selected, field too strong
Selected slice, field just right
Not selected, field too weak
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Phase Encode Frequency Encode (Readout)
Gradients
Magnetic vectors in selected slice while phase
encode gradient is on (one of 64 possible
gradient magnitudes illustrated). Speed changes
left to right.
Magnetic vectors in selected slice while
frequency encode (readout) gradient is on. Speed
changes top to bottom and pointing direction
changes left to right.
Magnetic vectors in selected slice after the
phase encode gradient turns off. Speed no longer
differs but pointing direction changes left to
right.
Fast Medium Slow
Slow Medium Fast
Behind Ahead
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Why This Is a Talk from Hell

• While working on this talk I recalled a joke
  about a man who died and found himself in Hell.
• He was standing waist-deep in feces. He looks
  over to the next condemned soul and remarks,
  This sure stinks but somehow I thought Hell
  would be worse.
• Then the Devil gave the order, Everyone stand on
  their head!

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Dephasing Rephasing Protons Stand on Their
Heads
Stand on your head at inversion time (TI)
Echo time (TE) 2 TI
This is where the protons are made to stand on
their head, rotating 180 degrees out of the
plane of the drawing at time (TI). What forces
them to do this is a strong RF inversion pulse
for spin echo images..
Rephasing
Dephasing
Some protons move faster because they are in a
place having a stronger magnetic field. The
recorded signal grows weaker with more dephasing
(the vectors are not pointing in the same
direction).
The vectors points are lined up again after a
predictable length of time, the echo time (or
TE). The recorded signal gets stronger with
rephasing.
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Spin Echo sequence
Stand on your head, protons
The inversion pulse is not very sensitive to t2
inhomogeneity
Repeat after time TR with a different magnitude
of phase encode gradient

• Spin echo

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Gradient Echo sequence
No RF pulse
DO NOT stand on your head, protons
De-phasing Race backwards fast
Re-phasing Race forwards slow
Both races are very sensitive to t2 inhomogeneity

• Gradient echo

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Echo-Planar Imaging
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64
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k - space
Zoomed in view of
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1 2 3 4 5 6
Click here repeatedly if no image
1 2 3 4 5 6 ...
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Adjusting Parameters to Change Image Contrast
MRA Very short TR
CSF, gray matter and white matter (also water,
fat, protein, etc.) all have different values for
T1, T2, and T2. As a consequence there are
multiple ways to reveal contrasts among tissues
(T1-, T2-, proton density contrasts shown). For
MRA (angiogram), the TR is so short that protons
stuck in the selected tissue have their vectors
stuck at the flip angle ... while protons in
flowing blood escape the selected slice, relax
toward B0 and emit RF. The MRA thus makes blood
vessels stand out from other tissues.
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Two more imaging types

• Arterial Spin Labeling (ASL) The common or
  internal carotid artery is selected either by a
  slice made well below the brain, or by placing a
  supplemental surface coil on the neck. Protons
  in the common/internal carotid blood are inverted
  (FA 180) with an RF pulse. Those protons will
  alter magnetic signal recorded from slices in the
  brain into which this labeled blood has perfused,
  as it dilutes signals from blood previously in
  the brain that did not get inverted protons.
• High Angular Resolution Diffusion Weighted
  Imaging (HARD) Diffusion weighting of MR images
  is achieved with two extra gradient pulses per
  TR, one strongly dephasing, the other strongly
  rephasing unless the protons have moved during
  the time between the pulses. Diffusion is
  movement at the molecular level driven by heat.
  The more diffusion, the less successful is the
  rephasing pulse, and the smaller the recovered
  signal. In brain tissue diffusion is directional,
  being channeled by the cell membrane to move more
  readily along than across each axon. A voxel of
  white matter is sampled from many directions (the
  more directions the higher the angular
  resolution) to determine the predominant
  diffusion directions, from which the travel
  directions of axons passing through that voxel
  can be inferred.

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Terms

• B0 unchanging strong (3T) magnetic field,
  always on
• RF radio frequency, approximately 127.68 MHz at
  3T, Larmor frequency of H in H2O
• flip angle tilt of proton magnetization vector
  away from axis of longitudinal magnetization,
  initially related to transmitted RF pulse energy
• T1 time constant for recovery of longitudinal
  magnetization, a relatively large length of time
• T2 time constant for the loss of transverse
  magnetization, for two main reasons
• 1/T2 1/T2spin-spin interactions, a medium
  length of time 1/T2magnetic field
  inhomogeneities, such as varying blood oxgenation
  levels, a short length of time
• gradient magnetic field that varies over space
  (field of view) and/or over time
• slice selection gradient makes a thin slice of
  tissue have the proper magnetic field for a
  coincident transmitted RF pulse, so as to tilt
  protons only within the slice to the flip angle
• slice thickness determined by bandwidth of
  transmitted RF and gradient rate of change
• phase encoding gradient temporarily speeds up
  or slows down precession on one slice axis,
  turned off while receiving RF
• frequency encoding (readout) gradient speeds up
  or slows down precession on the orthogonal slice
  axis, turned on while receiving RF
• dephasing mismatched pointing directions of
  vectors that precessed at different rates
• TI inversion time, when vectors are rotated 180
  degrees out of plane by an RF pulse
• rephasing rematched pointing directions of
  vectors at 2TI or at the echo time (TE)
• TE echo time(s). More than one
  dephasing-rephasing can be used per tilting
  pulse.
• TR repetition time, how long to wait before
  tilting the protons again, perhaps using a new
  phase encoding gradient or perhaps selecting a
  new slice
• Echo-planar imaging (EPI) one method of spatial
  encoding, another popular method is spiral
• T1-, T2-, T2-, proton density-,
  diffusion-weighted, MRA, BOLD (fMRI), ASL
  types of image contrast

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Cartoon of How RF signals are captured into
k-space (via 2-D FFT )
Selected slice before phase or frequency encoding
Readout after zero slope phase encoding, complex
plane stays flat
Readout after large slope phase encoding, complex
plane wrinkled up/down
real
real
imag
imag
real
real
imag
imag
real
imag
x,y
x,y
psd (complex 2-D vector)
psd (complex 2-D vector)
psd (complex 2-D vector)



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Link to k-space tutorial

• http//www.revisemri.com/tutorials/intro_kspace1.h
  tm